78255 v1 Uncertainty and Climate Variability in the Design and Operation of Water Resources Projects Examples and Case Studies Ignacio Rodríguez-Iturbe Juan B. Valdés Technical HEF Report Technical 2010 Report 2 – November 2011 HEF Hydrology Expert Facility An Expert Support Team (EST) of the Water Partnership THE WORLD BANK Program (WPP) © 2012 The World Bank 1818 H Street NW Washington dc 20433 Telephone: 202-473-1000 Internet: www.worldbank.org Acknowledgments This work was made possible by the financial contribution of the water partnership program (wpp) - http://water.Worldbank. Org/water/wpp. This report was put together by Luis E. García from documents prepared by the authors, Professors Ignacio Rodríguez-Iturbe from Princeton University and Juan B. Valdés from the University of Arizona, under the direction of Julia Bucknall and Abel Mejía, Manager and Former Manager of the Water Anchor, respectively. The authors thank Grant Milne, Rita Cestti and all the members of the Bank’s Water Resources Management Thematic Group and Watershed Management Community of Practice (later merged into the Water Resources and Watershed Management Thematic Group) for their initiative in suggesting the topics covered in the report, and collaboration co-organizing and promoting the working sessions to successively discuss partial results and progress reports. The comments, suggestions and guidance received from the participants in these workshops is gratefully acknowledged, as well as contributions by Gabrielle Puz, Maryanne Leblanc, Soo Jung Yoo, Joy Kazadi , Chonlada Sae-Hau, Parivash Mehrdadi, and the English editor Graciela Testa. Special thanks to Professor José Salas of Colorado State University and the Bank peer reviewers Rita Cestti, Rikard Liden, and Winston Yu, who provided valuable guidance and suggestions for this report. 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Any queries on rights and licenses, including subsidiary rights, should be addressed to the Office of the Publisher, The World Bank, 1818 H Street NW, Washington, DC 20433, USA; fax: 202-522-2422; e-mail: pubrights@worldbank.org. B Uncertainty and Climate Variability in the Design and Operation of Water Resources Projects Examples And Case Studies Ignacio Rodríguez-Iturbe* Juan B. Valdés** Washington, DC. November, 2011 * Department of Civil and Environmental Engineering, Princeton University, USA. ** Departments of Hydrology and Water Resources and of Civil Engineering and Engineering Mechanics, University of Arizona, USA. ii Table of Contents Executive Summary..............................................................................................................................................................1 Introduction....................................................................................................................................................................1 Framework......................................................................................................................................................................1 Design Floods in the Caroni River Basin................................................................................................................2 Monthly Flows in the Rio Verde Basin.....................................................................................................................3 Water Balance in Arid and Humid Ecosystems....................................................................................................4 1. Introduction....................................................................................................................................................................7 Background....................................................................................................................................................................7 Objectives......................................................................................................................................................................8 General....................................................................................................................................................................8 Specific....................................................................................................................................................................8 General Framework......................................................................................................................................................8 Audience and Description....................................................................................................................................... 10 References.................................................................................................................................................................. 11 2.  Design Floods............................................................................................................................................................. 13 Introduction................................................................................................................................................................. 13 Objective..................................................................................................................................................................... 15 Methodology............................................................................................................................................................... 15 Common Extreme Value Distributions........................................................................................................... 15 Parameter Estimation Techniques................................................................................................................... 15 Application to the Caroni River at San Pedro de las Bocas (Venezuela)..................................................... 16 Sampling Uncertainty........................................................................................................................................ 16 Reducing Sampling Uncertainty..................................................................................................................... 20 Analysis of Extreme Values under Climate Variability and Change......................................................... 21 Summary of Procedure............................................................................................................................................. 24 Sampling Uncertainty........................................................................................................................................ 25 Model and Parameter Uncertainty.................................................................................................................. 25 Climate Change Uncertainty............................................................................................................................ 25 Final Comment........................................................................................................................................................... 26 References.................................................................................................................................................................. 26 3.  Evaluation Of Monthly Flows................................................................................................................................... 29 Introduction................................................................................................................................................................. 29 Objective..................................................................................................................................................................... 30 Methodology............................................................................................................................................................... 30 The REA Approach............................................................................................................................................ 30 Downscaling........................................................................................................................................................ 32 Water Balance Models...................................................................................................................................... 34 Simulation of Climate Change Impact on the Hydroclimatology of the Verde River Basin...................... 35 Model Calibration............................................................................................................................................... 35 Model Simulation Results................................................................................................................................. 35 Comparison of Results from the abcd Model and a Physically Based Rainfall-Runoff Model..........37 Summary of Procedure............................................................................................................................................. 38 Selection of GCM Models............................................................................................................................... 38 Downscaling........................................................................................................................................................ 39 Impact of Climate Change in the Hydroclimatology of a Particular Basin............................................ 41 Final Comments......................................................................................................................................................... 42 References.................................................................................................................................................................. 43 4.  Water Balance In Arid And Humid Ecosystems................................................................................................. 45 Introduction................................................................................................................................................................. 45 Objective..................................................................................................................................................................... 45 iii Methodology............................................................................................................................................................... 45 Rainfall................................................................................................................................................................... 45 Stochastic Soil Water Balance Model........................................................................................................... 48 Application to a Dryland Ecosystem in Central Kenya...................................................................................... 50 Dryland Vegetation Patterns............................................................................................................................ 50 Model Calibration............................................................................................................................................... 51 Modeled Changes in Species Patterns Due to Changing Rainfall Mean and Variability................... 54 Summary of Procedure...................................................................................................................................... 56 Application to Humid Ecosystems (Everglades National Park, USA)........................................................... 56 Wetland Vegetation Patterns........................................................................................................................... 59 Modeling Vegetation Patterns in the Everglades National Park.............................................................. 60 Likelihood of Future Changes in the Vegetation Community of the Everglades National Park........ 63 Final Comments......................................................................................................................................................... 66 References.................................................................................................................................................................. 71 List of Tables Table 2-1. Comparison of Parameters of GEV distribution for Caroni Annual Maxima Flows..........17 Table 2-2. Estimates of the 100-yr and 500-yr Annual Peak Flows using the Three Parameter Estimation Methods for the Caroni River (m3/s)...................................................17 Table 3-1. Bias correction procedure........................................................................................................... 33 Table 3-2. Models Available at CMIP............................................................................................................. 43 Table 4-1. Percent Coverage of Dominating Vegetation Types (Only vegetation with at least 1% coverage was reported)...................................................................................................... 61 Table 4-2. Percent Coverage and Relative Percent Change of Dominant Vegetation Types Between Present and High Future Emissions Scenarios for Everglades National Park.....................................................................................................................................70 List of Figures Figure 2-1. Net basin inflows to Lake Victoria, Africa.................................................................................. 14 Figure 2-2. June-October Precipitation Anomalies in the Sahel................................................................ 14 Figure 2-3. Annual Maxima of Caroni River at San Pedro de las Bocas (Venezuela)......................... 16 Figure 2-4. Comparison of GEV CDF Parameter Estimation Methods....................................................17 Figure 2-5. 100-yr and 500-yr Histogram of Flood Estimates................................................................... 18 Figure 2-6. Average Estimates of the 100-yr Peak Flow under Different Sample Lengths................ 18 Figure 2-7. Average Estimates of the 500-yr Peak Flow under Different Sample Lengths................ 19 Figure 2-8. Sampling uncertainty of the peak values at the French Broad Basin (North Carolina, USA).................................................................................................................... 19 Figure 2-9. Depth-Duration-Frequency Curves for Tucson (Arizona) – 1 hour...................................... 20 Figure 2-10. Caroni River Annual Peaks............................................................................................................ 22 Figure 2-11. NOAA Paleoclimatology Website............................................................................................... 23 Figure 2-12. GEV Distributions for Caroni Peaks for the Periods 1950–1977 and 1978–2006....... 24 Figure 2-13. GEV PDF and CDF for Future Periods Using Caroni River Estimated Parameters........ 24 Figure 2-14. Percent Increase in 100-yr and 500-yr Flood Peaks.............................................................. 25 Figure 3-1. Changes in Precipitation Type...................................................................................................... 29 Figure 3-2. Verde River Basin............................................................................................................................ 30 Figure 3-3. REA performance for GCMs in Southwest United States.................................................... 31 Figure 3-4. Monthly Temperature in K° (left) and Precipitation Averages in mm/day (right) for GCMs.......................................................................................................................................... 32 Figure 3-5. Monthly Average Precipitation for GCM models for the Southwest United States........ 33 Figure 3-6. Example of SCE Calibration Results of abcd Model.............................................................. 36 Figure 3-7. Simulation Results of Verde Basin using the abcd Model (no snow)................................ 36 Figure 3-8. Simulation Results of Verde Basin using the abcd Model (with snow)..............................37 Figure 3-9. Precipitation and Evapotranspiration for Three Emission Scenarios in the Verde Basin....................................................................................................................................... 38 Figure 3-10. Ground and Surface Water for Three Emission Scenarios in the Verde Basin................ 39 Figure 3-11. SPI Computations for the Average Multi-model GCM........................................................... 39 Figure 3-12. Intensity and Duration of Droughts Using the Multi-model GCM results......................... 40 iv Figure 3-13. Intensity and Duration of Wet Periods Using the Multi-model GCM Results................... 40 Figure 3-14. Comparison of Average Monthly Streamflows for Three Emission Scenarios.................. 41 Figure 4-1. Monthly Rainfall Summary of Jacobson Farm Gage – Two Rainy Seasons During the Year................................................................................................................................ 46 Figure 4-2. Summary of Total Rainfall Change through Time at Jacobson Farm Gage........................47 Figure 4-3. Ensemble Mean of GCM Models for Changes in Precipitation........................................... 48 Figure 4-4. Summary of Water Balance Components for Stochastic Point Model.............................. 49 Figure 4-5. Examples of Probability Density Functions of Soil Moisture................................................. 49 Figure 4-6. Study Area Map of Central Kenyan Highlands......................................................................... 51 Figure 4-7. The Upper Ewaso Ng’iro River Basin, a Heterogeneous Landscape................................. 52 Figure 4-8. Basin Growing Season Climate.................................................................................................. 53 Figure 4-9. Herders in Upper Ewaso Ng’iro River Basin of Central Kenya............................................. 54 Figure 4-10. Basin Changes in Species Composition with Time................................................................ 55 Figure 4-11. Range of Shifts in Basin Species Composition....................................................................... 55 Figure 4-12. Range of Shifts in Fractional Species Abundance.................................................................. 56 Figure 4-13. Resource Use versus Resource Scarcity...................................................................................57 Figure 4-14. Existence of Sawgrass Depending on the Time a Site is Inundated................................... 58 Figure 4-15. Existence of Muhly Grass Depending on the Time a Site is Inundated.............................. 59 Figure 4-16. Changes in the Probability Density Function of Water Depth above the Ground........... 59 Figure 4-17. Wetland Water Balance Model.................................................................................................... 60 Figure 4-18. Location of Everglades National Park......................................................................................... 60 Figure 4-19. Summary of hydroperiods for Everglades National Park....................................................... 62 Figure 4-20. Hydroperiod Descriptions of Different Vegetation Communities......................................... 63 Figure 4-21. Joint Probability Surface of Percent Time Inundated and Mean Depth.............................. 64 Figure 4-22. Present and Future Mean Annual Rainfall in Everglades National Park.............................. 65 Figure 4-23. Present and Future Storm Arrival Rates in Everglades National Park................................. 66 Figure 4-24. Present and Future Modeled Mean Water Depths in Everglades National Park...............67 Figure 4-25. Present and Future Modeled Percent Time Inundated in Everglades National Park....... 68 Figure 4-26. Change in Hydroperiods for Everglades National Park.......................................................... 69 Figure 4-27. Joint Probability Surfaces of Percent Time Inundated and Mean Depth............................ 69 Annexes in CD Annex I Statistical Methods Annex IA  Most Commonly Used Statistical Distributions for Maxima Annex IB  Parameter Estimation Methods Annex IC  The Mann-Kendall Test Annex II Dendrochronology of Hydrologic Records Annex III Downscaling Approaches Annex IV Stochastic Soil Water Balance Model Annex V Probabilistic Modeling of Water Table Dynamics v Executive Summary Introduction Framework This technical report deals with the estimation of design There is wide agreement in the scientific literature and floods and monthly flows in a river basin, which is the science community that greenhouse gases (GHG) considered of particular importance for the practitioner. It is are having a significant impact in the Earth’s climate. also important to evaluate the impact of climate fluctuations This is confirmed by instrumental evidence and results on the structures of both dry and humid ecosystems. from mathematical models. There is also consensus The report’s overall objective is to create awareness of that climate change will “intensify the hydrologic cycleâ€?; the challenges that practitioners face in the preparatory that is, more variability is to be expected in most of the hydrologic studies for water resources projects, and provide hydroclimatic variables, resulting in more extreme floods illustrative examples of how they have been solved in and droughts. There is no consensus, however, on the specific cases. This report was prepared in collaboration appropriate mitigation and adaptation measures needed with the Bank’s combined Water Resources and Watershed to cope with climate change. The spatial resolution of the Management Thematic Group and the examples and case presently available Global Circulation Models (GCMs) studies were taken from previously done work. No additional is too coarse for most hydrologic applications and water research was undertaken. The existing work covered a resources management. Statistical or dynamic techniques more ample spectrum from which specific situations were to increase the resolution of the results (“downscalingâ€?) selected. Although the methods used in these examples require significant information on the ground to calibrate and case studies should be taken only as illustrations and the downscaling models (particularly in case of statistical do not constitute a recommendation or preference from the techniques). To decide if all or which of the GCM results authors, the reader can make his (her) own judgment as to should be used to give a true picture of the uncertainty may whether some of these methods could also be applied to also pose a challenge. Some of these approaches have other similar cases. This technical report is aimed mainly been the subject of many discussions. at Bank project team members, project managers, and specialists involved in operations dealing with the design Moreover, studies have indicated that the traditional and operation of water resources projects. It is also approach of assuming that the future will be statistically applicable to those working in hydropower, agriculture, undistinguishable from past observations may not be the disaster management, environmental impact assessment, most appropriate course of action. However, the question and protected areas projects. In addition, it is expected that remains, which adaptation and mitigation actions should be other non-Bank practitioners involved in the design and carried out under these uncertainties? Would it be better operation of water resources projects may also find it useful. to wait until more and better information from the models is available? Although by no means obvious, the answer Due to its nature, the theme covers many topics. Although is a qualified no. This is not a realistic and valid approach. this may appear inconvenient, it is believed that there is Some decisions need to be made now, and at times waiting an advantage in having these topics discussed in a single may not be an option because of the existence of significant reference. It is thus inevitable that some issues will require evidence that indicates a long-term impact. The question some familiarity with the literature on the subject and, in then becomes, which actions should be carried out that addition, may not be amenable to being tackled with general acknowledge these uncertainties? guidelines of universal application. Therefore, the guidelines apply to the specific examples and case studies that are The most appropriate course of action is to carry out presented. Due to the broad audience, it is believed that “no regretâ€? activities that would produce positive results readers can be selective since not all of the topics will be of regardless of the changes in the hydroclimatology of interest to a single reader. a region. For example, actions that make regions more 1 resilient to long dry periods is a no-regret option regardless In practice, estimation of the design flood is mainly carried of whether there is climate change or not. It has also been out by statistical methods in most of the countries in the advocated that there is a need to increase the resources world. The most commonly used statistical distributions for dedicated to developing better GCMs with a more detailed maxima are the Gumbel (G) Probability Density Function resolution. However, several issues are not yet well resolved (PDF), Log Pearson III (LP 3) PDF and the Generalized (such as, for example, the effect of clouds, or taking into Extreme Value (GEV) PDF. Several methods have been consideration the atmosphere land-surface boundary proposed to estimate the parameters of these distributions, interaction). Improved GCMs could provide better insights from the simplest method of moments (MoM) to more about the inputs to hydrological models even if they are complex methods like the maximum likelihood (ML) and the still not designed to provide hydrologists with the kind L-moments methods. of information they need, and despite the fact that their use may not necessarily give more precise and accurate Even when relatively long historic records are available, estimates of the hydrologic design parameters. there are significant uncertainties that need to be accounted for in the determination of flood peaks for gauged basins. The technical report is organized around examples and case This is true even in the absence of human induced climate studies that were selected on the basis of previous local change. But in addition to sampling uncertainty, climate knowledge and experience by the authors, and because variability and change should also be considered in they reflect different conditions in hydrologic regimes as decision-making and design. However, there are significant well as different controlling hydrologic variables. Analysis challenges in separating climate variability from climate methodologies are described in the text and those that are change and the result will always be an educated guess. already well known for hydrologic analyses are included in Thus, for planning and design purposes the question will annexes for easy reference. The application of methodologies always be: what is the relative importance and to what is illustrated by four examples and case studies (see box). extent should anthropogenic climate change be considered for short, medium or long-term purposes under the presence of these sampling uncertainties? Design Floods in the Caroni River Basin It is made evident, as illustrated by the Caroni River Not only the effects of climate variability and change can example, that the estimation of design floods is hampered cause uncertainty in the estimation of project design floods. by uncertainty caused by the choice of the flood analysis Examples and Case Studies Caroni River Basin (Venezuela). Illustrates ways to evaluate and take into account the uncertainty introduced by sampling and discusses ways to account for climate variability and change (and some of their shortcomings) in the estimation of extreme values of hydrologic variables for design and operation of this hydropower and flood control project. Verde Basin (Arizona, USA). Illustrates a procedure used to take into account the impact of climate variability and change in the components of the hydrologic cycle in hydrologic studies of this semi-arid region using a simple monthly water balance model. Ecosystem Changes in Central Kenya. Describes a methodology used to detect ongoing changes in the main characteristics of rainfall that impact the water balance in the ecosystem of the region as a result of climate variability and change, as well as the effect of these changes on the vegetation of this arid ecosystem. Wetlands of Florida (USA). Identifies key variables studied in this humid region to account for the changes to be expected through possible scenarios of climate change and the corresponding data requirements. 2 model and by sampling uncertainty. Moreover, this Monthly Flows in the Rio Verde Basin uncertainty may be compounded by the effects of climate variability and change. Thus, the practitioner should The increase in temperature, particularly at the higher acknowledge and account for all uncertainties that may altitudes, brings significant differences in the partitioning impact the results. These uncertainties should be evaluated of precipitation between rainfall and snow. This also brings and explicitly communicated to the designers, planners, and changes to sublimation, evapotranspiration, and runoff other stakeholders so they can make informed decisions. seasonality that may require changes in the operation Although it is not possible to provide guidelines of universal of water resources systems to avoid placing in jeopardy application to solve these problems, the Caroni River project operations such as hydropower and water supply example and the literature on the subject yield lessons that deliveries. raise awareness about sampling uncertainty, model and parameter uncertainty, and trends and climate uncertainty To estimate the impact of climate change on the water (see box). resources of the river basin at the monthly level, projections Uncertainties in Design Flood Estimation Sampling Uncertainty Trend analysis or regionalization approaches (e.g. regional regressions) could be attempted to reduce sampling uncertainty. Additional information from other sources and proxies, such as those provided in the internet world-wide NOAA paleo proxies database could also be used. Although paleo-based flood values have significant uncertainty, they still provide insight on the problem (although its use may not be practical in current design). For example, paleo-based estimators provide another (or extended) view that may be useful to gain insight not evident in a limited historic sample. Model and Parameter Uncertainty A sensitivity analysis should be carried out using alternative extreme value distributions and alternative estimation methods of the distribution parameters. There is software available that provides estimates of the flood for a given return period as well as its corresponding uncertainty intervals. A sensitivity analysis should be carried out to assess the impact of the flood estimates confidence intervals on the project. For some cases, such as the design of a dam spillway, there are alternatives to statistical methods like the PMP (Probable Maximum Precipitation) and the related PMF (Probable Maximum Flood). Trends and Climate Uncertainty The presence of trends and other non-stationary signals in the historic record (and in the reconstructed record, if it is available) should be evaluated. It is important to determine, to the best of the available knowledge, if these trends are natural or anthropogenic. And, in the latter case, whether they are due to climate change or to other anthropogenic actions like deforestation, for example. It is becoming a “standardâ€? procedure to couple the results of GCMs with hydrologic models if climate change effect is suspected in the study area. A “bias correctionâ€? technique needs to be applied to adequately represent the seasonality of a given parameter (such as rainfall, for example). The application of a disaggregation (downscaling) technique to increase the resolution of the GCM is also commonly found in the literature. Statistical downscaling may be easier to implement than dynamic downscaling in certain cases. While using the historical skills of GCMs as a base for future predictions may be debatable, what is presented is only a discussion of some of the ways to do this based on the authors’ experience and on the existing literature. Similarly, also presented are the corresponding shortcomings that could be faced when trying to account for climate variability and change in the estimation of extreme values of hydrologic variables for design and operation of this type of projects. The full application of these in the estimation of peak flows for the Caroni River is not presented because the results are based on previous work that was not available for this example. Also due to the uncertainties involved, this is still a work in progress. 3 of future climate conditions were made using Global successfully used by several researchers, and each of the Circulation Models (GCMs). It may or may not be practical model’s four parameters—a, b, c, and d—is presumed to have to use all the results from the more than 24 GCMs available. some degree of physical interpretation. In some cases it may be better to either select one or a small number of GCMs that the analyst considers will best In this technical report, the application of the abcd model represent the conditions prevailing in the region under to the Rio Verde Basin is described as an example. Before study, usually seasonal precipitation and temperature applying the abcd model, it was calibrated for the region. variability. There are, however, large uncertainties in the The results of running the calibrated abcd model for the results of the plethora of GCMs available in the report Verde Basin with three of the emission scenarios (A1, A1B, of the Intergovernmental Panel on Climate Change and B2) and all of the GCMs available provided an idea (IPCC), whether all of them are used or only a few. of the uncertainty in the estimates. There was significant These uncertainties are even larger at the regional level, variability in the precipitation, but no significant trend, either which is the level in which the water resources of a basin positive or negative, was evident. There was also an increase need to be evaluated for project design and operational in potential evapotranspiration, but the limited amount of purposes. Since the spatial resolution of the GCMs is still water available made the actual evapotranspiration remain very coarse for practical application of the rainfall-runoff constant with a slight positive increase. The lessons learned models, it is becoming practice to disaggregate their results from this example are summarized in the following box. (downscale) at resolutions suitable for analysis. It has been suggested that the results can then be transformed to surface runoff and other hydrologic variables such Water Balance in Arid and Humid as actual evapotranspiration and soil moisture storage. Ecosystems There are a plethora of basin-level water balance models to evaluate the temporal characteristics of streamflows, Although a change in mean annual rainfall may not be usually at the monthly level. Monthly water balance models detectable throughout the years, other changes in the are simple representations of the rainfall-runoff process of climatology may have important consequences for the a basin that allow understanding the hydrologic process ecosystem and the population that depends on it. A simple and its changes at the basin scale. These models have way to detect these changes is through the analyses of the been used with the downscaled climate change-affected frequency of rainy days and their corresponding average monthly series of precipitation and temperature or potential rainfall (e.g., average precipitation in a rainy day). evapotranspiration as input to produce estimates of surface runoff, actual evapotranspiration and soil moisture storage Even if it is not possible to detect a decreasing trend in to take into account the effects of climate change. annual precipitation throughout the historical period, a crucially important decreasing trend in the frequency of rainy An example of an approach followed in the southwestern days as well as an increasing trend in the depth of average United States is presented to illustrate how these problems rainfall per rainy day may lead to different soil moisture were addressed using selection criteria for the GCMs. The dynamics and conditions for the ecosystem’s vegetation. criteria that was used (as an example) to select the GCM Through simple analyses, which can be carried out locally models was that of the REA (Reliability Ensemble Average) and without sophisticated models, the study of the possible method in which the performance is based on large scale impacts of hydrologic changes induced by ongoing or future circulation that drives moisture fluxes into the region. climate change scenarios on the vegetation and ecosystem Then, an example is presented using three of the emission services of a region may be started. scenarios (A1, A1B, and B2) and all the GCMs available for the Rio Verde Basin in Arizona. The results were previously First, a specific case study from a dryland ecosystem downscaled using the statistical downscaling method. A in central Kenya is presented. Using a variety of rainfall simple water balance model, the abcd model, was then scenarios, the impact of the changes on the ecosystem’s used, as an example. Although not the only one available vegetation structure was evaluated by understanding the or the only one than can be applied, this model has been relative changes in the water balance and the average 4 Accounting for Climate Change Impact on the Hydroclimatology of the Rio Verde Basin The information provided by the GCMs had significant variability and uncertainty in both space and time and is still at a resolution that is not directly applicable to hydrologic models. Processing the results of these models and doing bias corrections and downscaling are not simple tasks. The downscaling of these results, either by statistical or dynamic methods, introduces additional uncertainties that need to be considered in hydrologic design. The use of monthly water balance models is widely reported in the literature to evaluate changes in the basin due to climate change. These models use the downscaled climate change affected monthly series of precipitation and temperature or potential evapotranspiration as input to produce estimates of surface runoff, actual evapotranspiration, and soil moisture storage. Selection of GCM Models An example was first described where the REA (Reliability Ensemble Average) method was used to select the GCMs as an illustration of how this can be done, although it is not the only way to do it. In this method the performance is based on climatological features that include large scale circulation that drive moisture fluxes into the region. The elements to be considered may vary in each application (annual and seasonal precipitation and temperature, climatic precursors like ENSO, etc.). Once the models were selected, a bias correction was carried out to reflect the seasonality of the precipitation and temperature values. Then, all the GCMs results were used for the Rio Verde Basin, rather than the REA results previously mentioned, also as an illustration. Downscaling Even though dynamic downscaling offers more assurance of an adequate representation of the climatology of a region, statistical downscaling procedures can also be applied. There are significant uncertainties and the amount of effort to carry out dynamic downscaling may be high. Use of Water Balance Models Although it is becoming a “standardâ€? practice to link the results of a climate change model for temperature and precipitation with a hydrologic model for runoff, there are many problems involved and many factors that are not being taken into account. Even when the variability of the precipitation is not significant, like in the case of the Verde River Basin, there may be significant variability in the other components of the water balance, like evapotranspiration, groundwater recharge, and runoff. As shown in the example, climate change impacts all the components of the hydrologic cycle. Also, significant errors may be made when using historical data for calibration if the same parameters are then used for a changed climate in the future. Although not the only one that can be used for this purpose, the relatively simple rainfall-runoff abcd model was, in this case, a practical way to illustrate this impact. stress conditions over the growing season. The interactions of rainfall in drylands by a stochastic process. While the of climate, soil, and vegetation influence how water is mechanics of this modeling framework are more complex partitioned in ecosystems. Dryland ecosystems are thought than a deterministic treatment of rainfall, the estimation to be organized based on a tradeoff of how much water is of the mean of the random variables that control the daily used for growth and reproduction (evapotranspiration) and rainfall process is simple. the cost of survival (water stress). The consequence of treating rainfall in a stochastic sense Even though the framework was constructed for the central requires an appropriate modeling framework, adding to Kenyan highlands, it is believed that its applicability could the complexity of the problem. While there are a multitude be tried in other drylands around the world where rainfall is of models to choose from, a simple model at the daily the main driving mechanism in vegetation response. The key timescale that adequately preserves the properties (i.e. to the success of this framework was the realistic treatment mean, variance) of rainfall is often selected. The simplistic 5 properties of the marked Poisson point process rainfall United States. Instead of plant stress from prolonged model allow the rainfall to be filtered through modeling drought conditions, the vegetation in the Everglades frameworks such as the daily soil water balance, which can experiences stress when water levels inundate their root be used for understanding changes in water use. Rainfall systems causing anoxic conditions and potential mortality. R(t) (mm day–1), is represented as a marked Poisson point While the specific mechanisms differ between the process of storm arrivals in time with rate λ (day–1) and ecosystems, the general principles of balancing resource storm depth h (mm), where h is treated as an exponentially use and managing stress are the same that govern the distributed random variable with mean α (mm). natural organization of ecosystems. With a daily record of rainfall, the parameters α (mean rainfall The main difference between wetlands and drylands is the depth in a rainy day) and λ (mean arrival rate of storm events, availability of water. This includes both more rainfall arriving i.e. number of days with rain over length of season divided by at the surface and the presence of a water table near or number of days in the season) can be easily determined. In above the ground surface. In comparison with the dryland addition, the simplistic marked Poisson point process model water balance model, the interactions with the water table allows for estimation of the mean and variance of the seasonal require a more complex modeling framework of the physical rainfall over which α and λ are defined. With estimates about mechanisms governing system dynamics. Here the annual future rainfall scenarios (such as those obtained from GCM movement up and down of the water table impacts the runs), new α and λ values can be estimated. The new α and λ growth, reproduction, and survival of vegetation species values can then be run through the modeling framework to find that are present at a given location. Like drylands, a tradeoff changes in the ecosystem structure. exists in the organization of wetland vegetation between accessing limiting resources while mitigating the costs of The report also looks at the impact of changing rainfall extended periods of stress. patterns in the wetland system of the Everglades in the General Framework of Analysis for Impact of Climate Fluctuations on Ecosystem Structure Principles The framework presented here is based on two fundamental principles. The first is that rainfall should be treated stochastically, as the random fluctuations in the rainfall process have large impacts on the seasonal distribution of plant available soil moisture in drylands, and annual water depth and percent time inundated in wetlands. By better characterizing these fundamental processes, different relationships that control the distribution and abundance of vegetation are presented. The relationships are built on the second principle that a tradeoff exists between resource use/availability while mitigating the costs of resource use. Monitoring The development of a more complete theory of the processes governing the organization of ecosystems would lead to better tools and more accurate information to provide to land managers in order to make decisions about future land use and policy. However, even with the best theory there is a critical need for long-term monitoring. Long-term monitoring will provide invaluable information about testing, revising, and proposing new hypotheses that govern the organization of ecosystems. Finally and most importantly, the ultimate success of any sustainable land management or restoration project is with the cooperation and understanding of the local populations. 6 1. INTRODUCTION Background 2010 to discuss advances in flood forecasting (“Advances in Flood Forecasting: Taking into Account the Floods of the Meetings were held in September 2009 between the Futureâ€?). Hydrology Expert Facility (HEF, which has merged into the Water Expert Team, WET) of the Water Anchor (ETWWA, Given that the purpose of Bank’s engagement in water now TWIWA), the Water Resources Management Thematic projects is to help client countries in their development Group (WRM TG), and the Watershed Management efforts, environmentally sustainable growth and poverty Community of Practice (WRSCP), which have merged into alleviation are common denominators of any project. a single Water Resources and Watershed Management However, the role that water plays will be different in Thematic Group). The purpose of the meetings was to different regions and countries. The problems are different promote the use of the HEF’s available capacity and and so are the solutions. One of the recommendations expertise to produce innovative analytical work on key resulting from the meetings was not to focus on specific thematic areas of common interest to water practitioners models but, instead, on what needs to be done to solve in the Bank. Two broad thematic areas were tentatively those problems. Sometimes the solution may include selected: (i) watershed and disaster management to reduce models, sometimes it may not. Thus, it was recommended vulnerability and impacts, and (ii) managing downstream that examples and case studies in different regions should impacts and externalities. Within these two general thematic be selected and that those cases should be analyzed to areas, two topics were considered of particular importance establish the nature of prevailing problems and how they to practitioners: the estimation of design floods and monthly were addressed. In addition, the analysis should provide a flows, and the effect of climate variability in ecosystem discussion of better alternatives to solving those problems. response of dry and humid areas. Two members of the HEF The analysis focused on the most relevant variables that Expert Panel were selected to carry out this assignment make the largest contributions to solving those types of (Prof. Juan B. Valdés of the University of Arizona and Prof. problems, including those that were considered and those Ignacio Rodríguez-Iturbe of Princeton University). that were not. An effort was made to identify the most important variables in each region. As a follow-up, two presentations/discussion sessions were held at World Bank headquarters (HQ). The first session Several progress reports were produced (outline, was held during the training days following the Bank’s 2010 methodology, first two examples and case studies, second Sustainable Development Network (SDN) Week (January pair of examples and case studies) and made available to 27, 2010) and entailed a discussion of ideas about how to the Thematic Group for comments. A working session with put the eco-hydrological approach into practice. The second Bank staff was held on August 20, 2010 on submission of session was a brown bag lunch (BBL) held on February 4, the methodology and a BBL was held on December 14 to 7 present a first draft of the integrated report for additional have been considered in examples and case studies comments and suggestions from a wider audience. Several for hydrologic design and management of water drafts were produced and a final working draft of the resources projects that are considered of general completed report was submitted to external and internal interest. peer reviewers for comments and recommendations. This is the final report. The important changes in the key hydrologic inputs to different water management schemes are likely to arise from three different sources: Objectives 1. Sample errors and imprecise measurements. General 2. Natural climatic variability, which is not covered by the monitored data. The overall objective of this technical report is to create 3. Non-stationary conditions due to climate change or land- awareness of the uncertainty challenges that practitioners use change. face during the preparatory studies for water resources projects, and provide examples of how they can be solved in It must be remembered, however, that the impacts of these specific situations. This overall objective is framed along the changes vary greatly from region to region. In addition, following project design and operational questions: they differ according to the ecosystem where they take place as well as with the objectives of the project under 1. What are the key questions to consider in water-related consideration. Therefore, these examples and case studies projects when facing the reality of sampling uncertainties should be taken only as illustrations of the application of the and changes and variability in climate? methodologies; they cannot and should not be viewed as 2. Which are the key hydrologic parameters that should rules of universal application. be considered to account for the above realities in the design and operation of water-related projects? On which information collection activities should further ef- General Framework forts and investments focus? 3. How can variability and changes in climate impact Resilient water resources management covers many the different types of ecosystems that characterize many stages, such as drafting policy and strategy, development regions of the developing world (like savannas and/or and management planning, and design and operation of wetlands)? structures. The time horizon goes from real-time for the operation of major structures such as reservoirs, to short- Although there are no clear and precise answers to many and long-term policies, strategies, and plans. The design of the questions that arose during the study, the technical of structures and service provision services (such as report tries to provide a general methodological way of hydropower, water supply, irrigation, rural and urban drainage, approaching these types of analyses. More than providing and flood control) require short and medium-term estimates precise guidelines (which in many cases are impossible of specific hydrologic parameters. These include rainfall to provide given the diversity of scenarios that condition intensity and duration, evaporation and evapotranspiration, the approach), the report attempts to provide a general minimum flows, seasonal flows, and extreme high flow framework for these types of studies identifying the key frequencies and volumes. Each of these stages face several variables and the necessary incorporation of the different sources of pressures, some are non-climate related (such as uncertainties involved in the analyses. those resulting from population growth, institutions, finance, governance, etc.), while some are related to climate variability Specific and some to climate change. Although the non-climate related pressures are easier to identify, there are significant The specific objective of the technical report is to challenges in separating those that are due to climate illustrate how uncertainties and climate variability variability and those that are due to climate change. 8 When considering the above questions it should be The seminal paper by Milly et al. (2008), “Stationarity is emphasized that there is, however, wide agreement in dead: Wither Water Resources Management,â€? shows that the scientific literature and the science community that the traditional approach of assuming that the future will be greenhouse gases (GHG) are having a significant impact statistically undistinguishable from the past is not correct. in the Earth’s climate. This is confirmed by instrumental Thus, using past observations to mimic the future may not evidence and results from mathematical models. There be the most appropriate course of action. is also consensus that climate change will “intensify the hydrologic cycleâ€?; that is, more variability is to be expected Under these uncertainties two questions remain, which in most of the hydroclimatic variables and there will be more adaptation and mitigation actions should be carried out extreme floods and droughts. under these uncertainties? Would it be better to wait until more and better information from the models is available? Although hydrologists, planners, and decision makers have The answer is a qualified no. This is not a realistic and long dealt with climate variability, at least in concept, there is valid approach. Although the answer is by no means no consensus on the appropriate mitigation and adaptation obvious, some decisions need to be made now. Moreover, measures to cope with climate change. The spatial sometimes it may not be possible to wait since there is resolution of present Global Circulation Models (GCMs) significant evidence that indicates the long-term impact and is too coarse for most hydrologic applications and water possibility of irreversible changes in a region. The question resources management. Statistical or dynamic techniques then becomes, which actions should be carried out that to increase the resolution of the results (downscaling) acknowledge these uncertainties? require significant information on the ground to calibrate the downscaling models (particularly in the case of statistical The most appropriate course of action is to carry out techniques). “no regretâ€? actions that would produce positive results regardless of changes in the hydroclimatology of a region. In addition, there are significant differences in the GCM For example, actions that make regions more resilient results at a regional and basin level, particularly in to long dry periods are a no-regret option regardless of precipitation. The challenge is to decide if all the model whether or not there is climate change. There should also results should be used to give a true picture of the be an increase on the resources spent on developing better uncertainty. Furthermore, the IPCC report shows and more detailed resolution GCMs. Several issues are not several emission scenarios, and partial evidence in the yet well resolved (such as that of the clouds for example, last few years may suggest that emissions may be above or taking into consideration the atmosphere land-surface those indicated by the most “extremeâ€? emission scenarios boundary interaction). Improved GCMs could provide better like A2. insights about the inputs to hydrological models, despite the facts that they still are not designed to provide hydrologists Techniques like the one suggested by Giorgi and Mearns with the kind of information they need and that their use may (2002) and modified by Dominguez et al. (2009) allow not necessarily yield more precise and accurate estimates us to identify which GCM models are best suited for a of the hydrologic design parameters. particular region based on how well a particular model represents the current climate and how well it approximates No regret options include the development of better and the average of the future projections of all the models. For more accurate forecasting models, early warning systems example in the southwestern United States, Dominguez et for droughts, improved and longer lead flood forecasting al. (2009) have shown that while the best models represent techniques, and crops that are more resilient to droughts. well the temperature seasonality, problems representing These options also include, whenever possible, the the seasonality of the precipitation (particularly the construction of hydraulic structures in modular form so monsoon) in the region remain, requiring a “bias correctionâ€? they can be enlarged if needed. In addition, support for technique. Applying the technique to a neighboring region, knowledge transfer, outreach, and capacity building, as northwestern Mexico, yielded much better results for both well as increasing the support of specialized regional precipitation and temperature. organizations are actions that can be accomplished without 9 waiting for more precise information on the magnitude of example region, as well as the effect of these changes climate change. on the vegetation. These changes have a profound impact on rain-fed agriculture and on the livelihood of a This report does not include a general approach because large population that depends on this ecosystem for their it is not possible to come up with general and simple pastoral and/or farming activities. guidelines for such complex problems. Thus, the report is 4. Wetlands of Florida (USA). Wetlands present their organized around examples and case studies that were own challenges in regard to the impact of changing selected on the basis of previous local knowledge and hydrologic conditions associated with ongoing and likely experience by the authors, and because they reflect different future alterations in their climatic regime. The objec- conditions in hydrologic regimes as well as different tive here is to provide an example illustrating the key controlling hydrologic variables. Methodologies of analysis variables that need to be studied in humid regions, and are described in the text and those that are already well the changes to be expected through possible climate known for hydrologic analyses are included in the annexes change scenarios. for easy reference. The application of methodologies is illustrated by the following four examples and case studies: The guidelines presented apply to the examples and case studies and are not universal. 1. Caroni River Basin (Venezuela). A large basin in the tropics with significant hydropower development that is severely affected by climatic precursors. This example Audience and Description illustrates ways to evaluate and take into account sam- pling uncertainty, and discusses some of the shortcom- This report is aimed mainly at Bank project team members, ings that could be faced when trying to account for cli- project managers, and specialists involved in operations mate variability and change in the estimation of extreme dealing with water resources projects, especially those values of hydrologic variables for design and operation involved in the estimation of design floods, monthly flow of this type of project. Recommendations to account for sequences, and the impacts on the water balance in dry and uncertainties caused by short sample lengths, climate humid ecosystems. It is also applicable to those working variability and change, and the so-called “death of sta- in agriculture, disaster management, environmental impact tionarityâ€? are presented. assessment, and protected area projects. It is also expected 2. Verde Basin (Arizona, USA). The Verde Basin, a that other non-Bank practitioners involved in the design and tributary of the Colorado River, is a catchment with operation of water resources projects will find it useful. runoff produced by snowmelt and monsoon precipita- tion. Increases in temperature, particularly in the higher Due to its nature, the theme covers many topics. Although altitudes, produce changes in the precipitation mecha- this may appear inconvenient, it is believed that there is nisms affecting the timing of the runoff hydrograph and an advantage in having these topics discussed in a single the partitioning of the precipitation values. Although not reference. It is thus inevitable that some issues will require the only one that can be used for this purpose, the rela- some familiarity with the literature on the subject and are not tively simple rainfall-runoff abcd model was used in this amenable to being tackled with general guidelines of universal case as a practical way to illustrate this impact. While it application. Therefore, the guidelines that are presented apply is becoming a “standardâ€? practice to link the results of a to the specific examples and case studies. Due to the broad climate change model for temperature and precipitation audience, it is believed that readers can be selective since not with a hydrologic model for runoff, there are many prob- all of the topics will be of interest to a single reader. lems involved and many factors that are not being taken into account and this should be kept in mind. The report is organized in four chapters and five annexes 3. Ecosystem Changes in Central Kenya. The goal of included in a CD. After the initial Introduction, the four this case study is to describe a methodology used to examples and case studies are described in three separate detect ongoing changes in the main characteristics of chapters. Each one of these contains an introduction rainfall affecting water balance in the ecosystem of the including a general description of the case study area, 10 a section about the methodology used in the analysis, a the importance of future ENSO projections. Climatic description of the application of the methodology to that Change, doi: 10.1007/s10584-009-9672-5. case, and the conclusions. The annexes included in the CD Giorgi, F. and L. Mearns. 2002. Calculation of average, refer to other well-known hydrological analysis methodologies uncertainty range, and reliability of regional climate that were used and are included for easy reference. from AOGCM simulations via the “Reliability Ensemble Averagingâ€? (REA) method. J Climate 15:1141–1158. Milly, P.C.D., et al. 2008 “Stationarity is Dead: Whither References Water Management.â€? Science, (319) February. Domínguez, F. and J. Cañón and J. Valdés. 2009. “IPCC- AR4 climate simulations for the Southwestern US: 11 2. DESIGN FLOODS Introduction the parameters of the PDFs are not constant. As will be discussed later, this is not an easy task and additional In most countries, the estimation of the design flood, research is needed. Therefore, only a general approach in practice, is mainly carried out by statistical methods, will be presented in this report. Despite the suggestions although sometimes the PMP/PMF (Probable Maximum and approaches presented here, several difficulties remain, Precipitation/Probable Maximum Flood) method is also including the presence of gaps in the historic record. used. This report only addresses the estimation of flood Many studies in the literature address the issue of data peaks using statistical methods. The PMP/PMF estimation gap filling, mainly for sequential time series. For the case technique is not covered since it exceeds the scope of of annual maxima, since persistence is not considered, this report. Interested readers are referred to the World the usual procedure is to ignore those missing values. The Meteorological Organization publication on this topic techniques proposed for data gap filling include multiple (WMO, 2009). The most commonly used statistical linear regression analysis (which is the most commonly distributions for maxima are the Gumbel (G) Probability used approach in practice), fuzzy methods, artificial neural Density Function (PDF), Log Pearson III (LP 3) PDF, and the networks, and time series analysis among many others. Generalized Extreme Value (GEV) PDF. Several methods This is an important issue but falls outside the scope of this have been proposed to estimate the parameters of these report. However, a list of references about these methods distributions, from the simplest method of moments (MoM) may be found in Khalil et al. (2001). to more complex ones like the maximum likelihood (ML) and the L-moments methods. Thus, variability and its uncertainty poses a problem in, for example, the estimation of the firm power of a hydropower The challenge of short records or the impact of human development as seen in figure 2-1, which shows the net intervention in records that require the “naturalizationâ€? of balance inflows to Lake Victoria (Africa). In this case it is the records to remove the effects of human intervention clearly shown that the utilization of the entire period of (such as diversions or dams) are severe hindrances in the record will produce a significant smaller firm power estimate estimation of the model parameters. An additional challenge than using only the last period of record. in the practical use of hydrologic records is the principle of stationarity. Statistical (and stochastic) hydrology has been This chapter will show that, even in the presence of relatively based on this principle, which states that the future has the long historic records, there are significant uncertainties same statistical characteristics as the past. This has been that need to be accounted for in the determination of flood disputed due to climate variability and change in the widely peaks for gauged basins. This is true even in the absence discussed paper by Milly et al. (2008). Thus, it is necessary of anthropogenic climate change. But, in addition to sample to consider possible non-stationarity in flood records since uncertainty such as that shown in figure 2.2, climate 13 Figure 2-1. Net basin inflows to Lake Victoria, Africa Victoria Lake – Net Basin Supply – 106-year Time Series 100,000 90,000 80,000 Net Basin Supply (mcm/year) 70,000 60,000 50,000 40,000 30,000 20,000 10,000 0 –10,000 –20,000 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 Years NBS M1900/60 = 20 884 M1961/64 = 72 572 M1965/2005 = 32 572 M1900/2005 = 27 338 Source: Power Planning and Associates, 2006. Color horizontal lines are average values. variability and change should also be considered in decision- the result will always be an educated guess. The Sahel, for making and design. However, there are significant challenges example, is characterized by long period of precipitation in separating climate variability from climate change and above and below the mean as shown in figure 2-2. Figure 2-2. June-October Precipitation Anomalies in the Sahel 5 4 3 2 1 cm/month 0 –1 –2 –3 –4 –5 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 Source: JISAO University of Washington, 2010 (www.jisao.washington.edu/data/sahel/). 14 Thus, the question for planning and design purposes Common Extreme Value Distributions will always be: what is the relative importance and to what extent should anthropogenic climate change Several probability distributions have been proposed in the be considered for short, medium or long-term literature for the representation of annual maxima of peak purposes under the presence of these sampling values. As previously indicated, the most commonly used uncertainties? probability distributions for maxima are the Gumbel (G) PDF, Log Pearson III (LP 3) PDF, and the Generalized Extreme The example presented in this chapter refers to the Caroni Value (GEV) PDF (see annex IA). No single probability River in Venezuela, where the seasonality of flows as well distribution has been adopted in all regions and countries. as the characteristics of the changing high and low flow For example, in the United States the standard practice regime are of fundamental importance. The Caroni River is the use of the Log Pearson III as recommended in the has a basin area of approximately 100,000 km2 and a mean Water Resources Council (WRC) Guidelines (WRC, 1982). annual flow of approximately 4,700 m3/s. The basin has However, there seems to be an increasing use of the GEV, several hydropower plants with a total capacity of 17,000 which is more flexible and encompasses a two-parameter MW, including the large Guri dam with an installed capacity version (Gumbel) as well as three-parameter distributions. of 10,000 MW. The reservoir also plays an important role in flood control. The following two types of problems may be addressed by using one of the above as an assumed PDF for a particular hydrologic engineering case: Objective • Estimating the design flood for a given return period: This example illustrates alternative procedures given T find xT (e.g. find the design flood xT for a return to evaluate and take into account the uncertainty period of T years), and introduced by sampling in the hydrologic • Estimating the return period of a given flood: given xT regime of a large dam that is vital for the find T (e.g. a flood of magnitude xT has been observed, hydroelectric and flood control needs of a what is the return period T of the flood?) country. The most commonly used probability distributions for representing annual extremes, In any case, it is a standard practice in statistics to describe and the corresponding methods to estimate their the shape of the distribution of a population by means parameters are reviewed and applied to this river of a finite set of quantities summarizing the location, basin. Ways to evaluate and take into account the dispersion, skewness, peakedness, and tail behavior of an uncertainty introduced by climate variability and unknown population density function. Classical measures change in the estimation of extreme values for of distributional shape have been defined by means of design and operation of this type of projects are algebraic moments of different orders, resulting in the mean discussed. A summary of possible ways to account to estimate location, the variance to measure the spread, for these uncertainties is presented. and the standardized measures of skewness and kurtosis. Parameter Estimation Techniques Methodology The two most common procedures to estimate the This section describes a methodology to estimate the population moments related to the parameters of a parameters of the most commonly used statistical particular probability distribution are the method of moments distributions for flood estimates. In addition, it presents (MoM) and the method of maximum likelihood (ML). Despite some general guidelines for modeling changes in extreme the popularity of algebraic moments both in data description values (maxima and minima) due to climate variability and and more formal statistical procedures, they are known to change. suffer from several drawbacks. First, sample moments tend 15 to be very sensitive to a few extreme observations (outliers). (Gumbel, LP 3, and GEV) discussed at the beginning. The Second, the asymptotic efficiency of sample moments is methods are applied to the peak flows of the Caroni River rather poor especially for distributions with fat tails. The (Venezuela). As a background illustration, figure 2-3 displays last property is an immediate consequence of the fact that the annual maxima for the flows of the Caroni River at San the asymptotic variances of these estimators are mainly Pedro de las Bocas: determined by higher order moments, which will tend to be rather large or even unbounded, for heavy tail distributions. Sampling Uncertainty As an alternative to the conventional moments method, The three parameter estimation methods were applied to Hosking (1990) suggested a method of parameter evaluate the sensitivity of the different parameter estimation estimation that is based on quantities called L-moments methods to records whose length would be considered (LM) based on the probability-weighted method (PWM). acceptable in most applications. The results are shown, as There is no single parameter estimation technique that has an example, in table 2-1 for the GEV distribution. Similar prevailed in all applications, but the application of L-moments results were obtained for the other probability distributions. methods is increasing in hydrologic studies. Still the other two methods, particularly the MoM, are also widely used in The results of the three distributions and the three- many countries and in some widely used software like that parameter estimation methods are different, particularly of the US Army Corp of Engineers Hydrologic Engineering with shorter samples. The user should be aware of these Center (USACE HEC). In Hosking’s study, L-moments differences. In the case of the Caroni River the length of the are statistics used to summarize the shape of a probability record (57 years, 1950–2006) is reasonably long for most distribution. They are similar to conventional moments in developing countries but, nevertheless, it has significant that they are used to calculate quantities analogous to the sampling uncertainty. For example, the shape parameter mean, standard deviation, skewness, and kurtosis of the (k) estimated using the maximum likelihood method is not data. In the L-moment field these terms are called L-mean, statistically significant from 0 using a t-test (Gilbert, 1987). L-scale, L-skewness, and L-kurtosis to distinguish them These results are specific to the example under study and from conventional moments. They differ from conventional different conclusions may be arrived at other sites. moments in that they are estimated by linear combinations of order statistics. L-moments have been shown to be very useful in parameter estimation as compared to other Figure 2-3. Annual Maxima of Caroni standards methods; namely, methods of moments, maximum River at San Pedro de las Bocas likelihood, and least-squares (Pandey et al., 2001). One of (Venezuela) the main advantages of L-moments is that they are far more 20000 meaningful when dealing with outliers in data because they are less sensitive to them. Another advantage L-moments 18000 have is that the bias of their small sample estimates remains fairly small. As a result, it is anticipated that L-moments Annual Peaks (m3/s) 16000 can provide reliable estimates of tail-index with a relatively small sample. A more detailed but brief description of the 14000 L-moments method can be found in annex IB. It follows closely the book by Hosking and Wallis (1997). 12000 10000 Application to the Caroni River at San 8000 Pedro de las Bocas (Venezuela) 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 This section presents estimates of the performance of the Years three methods of parameter estimation for the three PDFs Source: Developed by author Juan B. Valdés. 16 Table 2-1. Comparison of Parameters Table 2-2. Estimates of the 100-year of GEV distribution for Caroni Annual and 500-year Annual Peak Flows Maxima Flows Using the Three Parameter Estimation Methods for the Caroni River (m3/s) Method Scale (α) Shape (k) Location (ξ) MoM 1728.30 0.141611 13112.34 Method 100 yr 500 yr L-moments 1795.74 0.189537 12379.69 MoM 24,319 30,329 ML 1706.39 –0.14844 12359.63 ML 18,048 19,285 Source: Author Juan B. Valdés. A description of the param- L-Moments 25,563 33,368 eters of the GEV may be found in annex IA of this report. Source: Author Juan B. Valdés Using these results for the GEV distribution, the following For the estimates of the 100-year and 500-year annual PDFs and Cumulative Distribution Functions (CDFs) have peaks the results are also different, particularly for the ML, been obtained for the Caroni River (see figure 2-4). As the as shown in table 2-2. figure shows, the maximum likelihood (ML) distribution, which is plotted using the Weibull plotting position (i.e. The ML estimates of the 100- and 500-year flood peaks m/(n+1) where m is the rank of the particular flow and are not as reliable because one of the model parameters is n is the number of observations), follows the records not significantly different from 0. Although this can be seen closely (Chow et al., 1988), but the other two estimation on figure 2-4, the ML method was included because it may methods produce a “heavierâ€? tail in the right hand side (i.e. be the best one for other applications. In this case, the ML increasing the estimates of the larger floods for a given estimates of the peak flows should not be used and are return period). shown here only for illustration.1 Figure 2-4. Comparison of GEV CDF Parameter Estimation Methods PDF Comparison-Caroni River CDF Comparison-Caroni River 45 1.0 40 0.9 0.8 Cumulative Exceedance Probability 35 0.7 30 0.6 Frequency 25 0.5 20 0.4 15 0.3 10 0.2 5 0.1 0 0 0 5000 10000 15000 20000 25000 0 5000 10000 15000 20000 25000 Peak Flows (m /s) 3 Peak Flows (m /s) 3 Moments L-moments ML Weibull Moments L-moments ML Source: Developed by author Juan B. Valdés. Note: The actual data are plotted using the Weibull plotting position m/n+1. 1. MATLAB software was used to do the computations. Software like that of HEC also provides estimates for both return periods. 17 Figure 2-5. 100-year and 500-year Monte Carlo experiments were conducted for the Caroni Histogram of Flood Estimates flows in order to provide a better illustration of the sampling uncertainty resulting from a record that, as mentioned earlier, 100-yr Peak Values 80 is usually considered acceptable. The experiments relied on 1000 traces of the same record length generated using 60 random number generators for a GEV PDF. The sample 40 parameters of the GEV were estimated for each sample and, from those, the 100- and 500-year flood peaks were 20 evaluated. As seen in the histograms of the results shown in 0 figure 2-5, significant variability exists in the estimates. 0 5 10 15 Peak Flows (m3/s) x 104 To further illustrate the impact of sample length on the 500-yr Peak Values variability of the estimates of the 100-year and 500-year 100 peak values, a long series (1000 values) of annual peaks was randomly generated using Monte Carlo techniques following a GEV distribution with the parameters estimated 50 from the Caroni records. The long sample was divided into equal intervals of the following lengths: 20, 40, 60, 80, 0 100, and so on. The average estimate of the 100-year and 0 0.5 1 1.5 2 2.5 500-year peak flows was computed for each of the sets Peak Flows (m3/s) x 105 using the three parameter estimation methods. The results Number of cases in each interval is shown in the y-axis are plotted in figures 2-6 and 2-7, which show that the Source: Developed by author Juan B. Valdés. estimates slowly converge to the given “trueâ€? parameter Note: Number of cases in each interval is shown in the y-axis. Figure 2-6. Average Estimates of the 100-year Peak Flow under Different Sample Lengths Comparison of 100yr Events (GEV) x 104 2.00 1.95 1.90 1.85 100yr Event (m3/s) 1.80 1.75 1.70 1.65 1.60 1.55 1.50 0 20 40 60 80 100 120 140 160 180 200 Sample Length (yrs) Moment L-moment ML True Source: Developed by author Juan B. Valdés. 18 Figure 2-7. Average Estimates of the 500-year Peak Flow under Different Sample Lengths Comparison of 500yr Event (GEV) x 104 2.0 1.8 500yr Event 1.6 1.4 1.2 1.0 0 20 40 60 80 100 120 140 160 180 200 # of RVs Moment L-moment ML True Source: Developed by author Juan B. Valdés. values (i.e., those estimated using the entire generated for the 5 percent confidence interval discharge and 180 sample) of the 100-year and 500-year peak flows. years for the 95 percent confidence interval discharge. The corresponding return period for the 500-year flood As the example of the Caroni River shows, there is ranges from 200 to 1000 years. This means that sampling significant sampling uncertainty as a function of the uncertainty is significant even when frequency analysis is sample size. As noted, records of the length of the Caroni performed on relatively long records. (57 years) are rather long for many developing countries and this sampling uncertainty should be taken into account. There are no general guidelines for a minimum Figure 2-8. Sampling Uncertainty of the record length. When records are missing, regionalization Peak Values at the French Broad Basin techniques may be used to replace or extend the length of (North Carolina, USA) the historic records as discussed earlier. 2000 1000 yr To illustrate that this is not an isolated case, figure 2-8 1000 presents another example, that of the French Broad 500 5% confidence Basin in North Carolina (USA) where a record of 200 Bounds on Return Period (yr) 180 yr 200 yr similar length (54 years) also introduces significant 100 95% confidence sampling uncertainty in the estimates of the 100-year 50 50 yr and 500-year floods. In the figure, natural variability 20 is represented by the central red line (a 45° line) and 10 expresses the relationship between the magnitude of 5 the flood discharge and its return period. Sampling uncertainty is expressed by the spread of the confidence 2 limits around this estimated line. As more information becomes available, the confidence bands around the flood frequency curve will decrease. Thus, the 100-year 2 5 10 20 50 100 200 500 1000 2000 return period (shown in the x-axis and across to the Estimated Return Period (yr) vertical axis) yields an equivalent return period of 50 years Source: National Research Council (NRC) “Mapping the Zoneâ€?, 2009. 19 Reducing Sampling Uncertainty inherent in the use of finite samples, providing the needed information that may help decision makers and engineers to There are several methods that could be used to reduce make informed decisions and better designs. sampling uncertainty. Unfortunately, no data were available to apply to this specific example because it was based on Regionalization previous work and no additional research was undertaken. Nevertheless, three of the most commonly used methods— Another approach to reduce sample uncertainty is to use interval estimates, regionalization, and rainfall-runoff—are regionalized estimates of the peak value. Regionalization is discussed below. the simplest approach for ungauged basins when gauged data is available in nearby sites. A related technique, the Interval Estimates “index floodâ€? originally proposed by Dalrymple (1960), is more attractive when less gauged information is available One interesting trend increasingly noted in the work of because it only regionalizes the mean of the distribution. many meteorological and hydrologic agencies is to move In this method, the T-year peak discharge at an ungauged from point estimates to interval estimates (confidence site is the product of two factors: a scale factor (the index band) at 90 or 95 percent confidence levels. For example, flood) and a dimensionless regional term, the growth the intensity-duration-frequency curves (IDF) developed factor. For most applications the index flood is chosen to by the US National Weather Service (NWS) are shown in be the sample mean of the annual maximum flood peak figure 2-9. The study carried out by the National Oceanic flows. and Atmospheric Administration (NOAA) compared several probability distributions and obtained the confidence Regionalization techniques, in which the physiographic intervals by Monte Carlo simulations. and climatic characteristics of a region are related to the peak flows of several return periods in gauged basins, have A similar approach can be followed for peak values. The use been extensively used to provide additional information of interval estimates more clearly reflects the uncertainty and reduce sampling uncertainty. The United States Figure 2-9. Depth-Duration-Frequency Curves for Tucson (Arizona) – 1 hour Partial Duration Based 60m Point Precipitation Frequency Estimates – Version: 4 32.2297 N 110.9539 W 2404 ft 4.0 3.5 3.0 Precipitation Depth (in) 2.5 2.0 1.5 1.0 0.5 1 2 5 10 25 50 100 200 500 1000 Average Recurrence Interval (yrs) Precipitation Frequency Estimates: Mean Upper Bound of the 90% Confidence Interval Lower Bound of the 90% Confidence Interval Source: NOAA Atlas 14, 2008. Note: Existing Results were used for this example. No such confidence interval curves were available for the Caroni River Basin. 20 Geological Survey (USGS) National Flood Frequency Rainfall-Runoff Program (now the National Streamflow Statistics Program, NSS) has related peak flows to catchment physiographic The use of rainfall-runoff models requires more information characteristics for all basins in the United States. Most of and computational efforts. In the National Research the relationships are estimated by means of a non-linear Council study mentioned before (NRC, 2009) the results regression of the form: of regionalization and rainfall-runoff methods for South Carolina basins were very similar when compared to qT = αA β1Sβ2 ... (2-1) regionalization equations. Obviously, these results are valid only for the region studied in the NRC report. Results might where qT is the T-year peak flow, A is the catchment area, also vary if other rainfall-runoff models are used. S is the main slope, and α, b1 and b2 are the regression parameters. For most cases, the area is the dominant As previously mentioned, no additional research was carried factor in a climatological homogeneous region. The out in the case of the Caroni Basin because the amount of additional information provided by the regionalization information and computational effort needed to apply these is generally measured in “equivalent yearsâ€? (Hardison, three methods exceeded the resources available for the study. 1971; Moss and Karlinger, 1974) and is computed by the following equation: Analysis of Extreme Values under Climate Variability and Change 2  100 ∗ CV  EY =   SE  (2-2)  The previous sections have addressed the significant issue  P  of samples of streamflow records and their associated sampling uncertainty even if periods in the order of 50 years where EY is the equivalent years record length, SEp is the are available (long for the length of records commonly found standard error of prediction of the regression (in percent), in the developing world, but short in terms of reducing and Cv is the coefficient of variation of the annual peak flows uncertainty). An additional challenge is how to cope with the used in the regionalization equation (Hardison, 1971). presence of climate change and how to differentiate it from long-term climate variability. How this could be done in the When both streamflow records and regionalization present example will be discussed next.2 equations are available, a weighting procedure is recommended, which is contained in the Guidelines of the Analyzing the Presence of Trends United States Interagency Advisory Committee on Water Data (1982). Following this procedure, the estimate using The first step is to analyze the historic records for the gauged records is weighted by n, the number of years of presence of trends in the record. The simplest procedure is actual record, and the regression estimate is weighted by to apply the popular non-parametric Mann-Kendall (MK) test EY, the equivalent years of record of the regression analysis. (see annex IC). Figure 2-10 shows the results of applying The equation is as follows: the test to the Caroni annual peaks. As can be seen, there is significant variability in the data. ln (qTw ) = (n ∗ ln(q ) + EY ∗ ln(q )) (2-3) Tg Tr The Mann-Kendall test, however, rejected the null (n + EY ) hypothesis (no trend) at the 5 percent significance level. If a trend is found, an evaluation of the reasons for the where qTg is the estimate of the T-yr flood peak using the trend should be carried out and a value judgment made gauged records and qTr is the estimate of the T-yr flood peak regarding climate change compared with other possible from the regional regression equation. No information was causes. It must be kept in mind that flood risk may tend to available in the case of the Caroni to apply regionalization. increase over many areas owing to a range of climatic and 2. However, with the exception of the trend analysis, this was not applied to the Caroni River since this example was based on work previously done. 21 Figure 2-10. Caroni River Annual Peaks historic and paleoflood information for the case of the log Pearson III probability distribution. Dworak (2011) also 20,000 used paleoflood data to provide bounds to peak estimates. 18,000 The application of this approach was not tried in this case study due to resource limitations, which place it outside its scope. Moreover, there is some controversy about the Annual Peaks (m3/s) 16,000 use of paleodata for design flood estimation because of 14,000 its inherent uncertainty and its use is not advocated here for that purpose. The topic is presented because it does 12,000 provide another (or extended) view that may not be present in a limited historic sample and may be a useful aid for 10,000 some studies. 8,000 1950 1960 1970 1980 1990 2000 2010 Climate Change Scenarios Years Source: Developed by author Juan B. Valdés. This could be the obvious approach to take given the current Note: The examples and case studies used in this report were based on pre- existing work and already available results were used. No new research was trends found in the literature. Unfortunately, even if there is involved. The MK technique is described in annex IC. no scarcity of published work on the topic of how to include climate variability and change into flood frequency analysis and methods supporting flood frequency evaluation based non-climatic impacts whose relative importance is site- on current downscaled climate projections (e.g. Sveinsson et specific (Kundzewicz, 2006). In the particular case of the al., 2005; Griffis and Stedinger, 2007; Raff et al., 2009), the Caroni River, local professionals noted that deforestation level of resolution of the present GCMs and the uncertainties due to mining activities in the upper basin of one of the in the downscaling of their results to a spatial and temporal tributaries may have been the cause for the slight increasing resolution suitable for flood peaks estimation is still a work in trend of the annual peak flows. progress. In the Raff et al. (2009) study, monthly values from the GCMs and statistically downscaled data were used to Use of Paleodata simulate weather characteristics at larger time scales. In turn, these series were used to estimate the flood frequencies for To further evaluate climate variability and possible look-ahead periods. change under relatively short record samples, additional information from other sources and proxies could be The flood values obtained using climate projections from explored to increase the insight beyond the record length GCMs should be compared with those obtained using of the series of extremes (see annex II). Examples of alternate methods, such as those presented in the following this are paleoclimatic records. NOAA has a database of sections. The use of future climate change scenarios will be paleoproxies for the entire world. Figure 2-11 shows the illustrated in the Rio Verde case study chapter, which discusses website’s main screen where these can be found. the extraction of hydrologic series from GCM runs to compute monthly streamflows. This application to the estimation of There is significant literature in the use of paleoflood peak flows for the Caroni River is not presented because the information (e.g. botanical information, sediment results are based on previous work and the downscaled series depositions, etc.) in the estimation of floods. The reader were not available for this example. Again, because of existing is referred to Baker (1987) for a review of the methods. uncertainties, this is also a work in progress. Frances et al. (1994) estimated the value of paleoflood information by a generalized two-parameter extreme value An Alternative Solution distribution and O’Connell et al. (2002) used a Bayesian approach with a paleohydrologic bound. England et An alternative solution has been suggested in the literature al. (2003) compared moment estimators utilizing both (Coles, 2001; Kharin and Zweirs, 2005; Griffis and 22 Figure 2-11. NOAA Paleoclimatology Website Source: NOAA Website (http://www.ncdc.noaa.gov/paleo/paleo.html). Stedinger, 2007) in which the parameters of the extreme where ζ(t0), α(t0), and k(t0) are the estimates of the GEV value distribution (e.g. GEV) are modified as a function of model using the historic records. Figures 2-12 and 2-13 use time. Dworak (2011) uses this approach as one of several the L-Moments estimates for the GEV obtained in table 2-1 in evaluating the impact of non-stationarity in flood peaks in and apply them to the Caroni River. Again this is shown as three US basins. an example of the technique. The challenge in this approach is to estimate the rate of To illustrate the procedure, the Caroni record was divided change of the parameters under, usually, short record in two periods following recent studies that indicated a length. Obviously, this approach assumes that past change in the regime starting in the late 1970s. Figure 2-12 information on the parameter trends will continue in the shows the difference in the PDF using the first period future, which in itself is uncertain. (1950–1977) and the second period (1978–2006). As can be seen, the second PDF increases the right tail of the An example, and only as an illustration, is shown below distribution making the peak estimates larger. for the GEV PDF. The three parameters of the PDF: ξ (location), α (scale), and k (shape): are modified as follows: The results for the next 20, 40, 60, and 80 years are shown in figure 2-13. The moments of the different distributions ζ (t ) = ζ 0 + β ζt were estimated using equations 2-4. The PDF tends to α(t ) = α0 + β αt increase the right tail of the distribution resulting in higher (2-4) k (t ) = k 0 + β kt values of the flood peaks. 23 Figure 2-12. GEV Distributions for Caroni Using the information on the parameters evaluated in these Peaks for the Periods 1950–1977 and two samples, annual variations of the GEV parameters were 1978–2006 created using equations 2-4. Figure 2-14 shows the percent increase for the above time periods for the 100-year and x 10–4 500-year peaks. 2 This simple procedure illustrates an approach to represent Density the increasing variability induced by climate change with 1 parameters estimated from the historic records. It should be kept in mind, however, that the loss of degrees of freedom in estimating six parameters of the GEV would be significant 0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 for historic records of short length. Monte Carlo techniques x 104 Peak flow [m /s] 3 may be used to estimate uncertainty bounds for these period 1 period 2 values. Source: Developed by author Juan B. Valdés. Summary of Procedure The Caroni River example shows that the estimation Figure 2-13. GEV PDF and CDF for of design floods is hampered by uncertainty caused Future Periods Using Caroni River by the choice of the flood distribution model and by Estimated Parameters sampling uncertainty. Moreover, this uncertainty may (Initial and looking 20, 40, 60 and 80 be compounded by the effects of climate variability and Years Ahead) change. Thus, the practitioner should acknowledge and x 10–4 account for all uncertainties that may impact the results, such as: 2 • Sampling uncertainty (how accurate are the flood esti- Density mates using the historical streamflows available?). 1 • Model and parameter uncertainty (which extreme value distribution should be used in this case? Standard good- ness of fit methods like Chi-square and Kolmogorov- 0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Smirnov may be used to select a particular model. Even x 104 Peak flow [m /s] 3 if the model is known, parameters have sampling uncer- tainty; in addition there are several parameter estimation x 10–4 methods, e.g. MoM, ML and LM). • Climate change uncertainty (are there non-stationarity Cumulative probability 1 signals in the historic and/or reconstructed record?). 0.5 The uncertainties in the estimation of the flood design values should be evaluated and explicitly communicated to the designers, planners, and other stakeholders so they 0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 can make informed decisions. In the present case of the x 104 Peak flow [m /s] 3 Caroni River, for example, the procedures discussed below Initial +20 +40 +60 +80 could be useful in dealing with sampling uncertainty, model and parameter uncertainty, and uncertainty caused by Source: Developed by author Juan B. Valdés. climate change. 24 Figure 2-14. Percent Increase in 100-yr flood estimates confidence intervals on the project. and 500-yr Flood Peaks Software like the Hydrologic Engineering Center (HEC) Streamflow Statistical Package (SSP) provides flood estimates for a given return period as well as also its cor- 250 responding uncertainty intervals. The software allows the Percent increase 200 user to select the level of confidence, the default being 5 150 and 95 percent. 100 50 Climate Change Uncertainty 0 0 10 20 30 40 50 60 70 80 • Evaluate the presence of trends and other non-stationari- Time [yrs] ty signals in the historic record (and in the reconstructed 100-yr 500-yr record, if it is available). Source: Developed by author Juan B. Valdés. • Determine, to the best of the available knowledge, if these trends are natural or anthropogenic; that is, if they are due to climate change or other anthropogenic ac- Sampling Uncertainty tions like deforestation, for example. • There is significant evidence both in the instrumental • There are no clear guidelines for minimum length of record and in the scientific literature that climate change record. Gaining insight using regionalization approaches is already being observed in many regions of the world. (e.g. regional regressions, paleoclimatology) should If climate change effects are suspected in the study be attempted whenever possible. Additional informa- area, the results of the complete set of GCMs or just tion from other sources and proxies should be used to those from a subset have been used as reported in increase the record length of the series of extremes. the literature. In the latter case, one method (although NOAA has a database of paleoproxies for the entire not the only one) could involve developing criteria to world and it is available at http://www.ncdc.noaa.gov/ facilitate selection of the GCMs that are best suited for paleo/paleo.html. the region under consideration based, for example, on • In spite of their inherent uncertainty, paleo-based estima- how well it represents the current climate and how well tors could provide another (or extended) view that might it approximates the average of the future projections of not be present in a limited historic sample and could be all the models. Then, a bias correction technique needs useful in some studies. to be applied to adequately represent the seasonality of a given parameter (such as rainfall, for example). More Model and Parameter Uncertainty about this can be found in the Rio Verde example pre- sented in the next chapter. • A sensitivity analysis should be carried out using alterna- • There is, however, large variability in the results of the tive extreme value distributions and alternative estimation GCMs and they are in a much coarser scale than the methods of the distribution parameters. one needed for most hydrologic applications. Apply a • The level of uncertainty is very high for longer return pe- disaggregation (downscaling) technique to increase the riods (>1000 years) such as those used for the design resolution (see annex III). Statistical downscaling is eas- of dam spillways. An alternative to statistical methods is ier to implement than dynamic downscaling approaches to use deterministic-probabilistic methods like the PMP and may be the only practical option in most projects, (Probable Maximum Precipitation) and the related PMF due to model uncertainties and the amount of effort re- (Probable Maximum Flood). However, in several coun- quired. For example, a comparison of both statistical and tries the 10,000-year flood is the limiting value used (e.g. dynamic downscaled results applied to water resources Russia). can be found in the work of Wood et al. (2004) for the • A sensitivity analysis, such as the one illustrated in figure US Northwest. The authors were able to reproduce the 2-9, should be carried out to assess the impact of the main features of the observed hydrometeorology from 25 the retrospective climate simulation by using the BCSD Proceedings 21st Century Dam Design-Advances and (bias-corrected spatially disaggregated) model. Applications, San Diego, CA, 1619–1629, April. England, J.F., J. D. Salas, and R. D. Jarrett. 2003. Comparison of two moments-based estimators that Final Comment utilize historical and paleoflood data for the log Pearson III distribution. Water Resources Research, 39(9), doi: This chapter has shown that there are significant 10.1029/2002WR001791. uncertainties in the determination of flood peaks for Frances, F., J. D. Salas, and D. Boes. 1994. Flood gauged basins even when relatively long historical Frequency Analysis with systematic and historical and records are available. This is true even in the absence paleoflood data based on the two-parameter general of anthropogenic climate change. There are also extreme value models. Water Resources Research, difficulties in separating natural climatic variability 30(65), 1653–1664. from climate change and the result will always be Gilbert, R. O. 1987. Statistical Methods for Environmental an educated guess. This fact, however, should not Pollution Monitoring. New York: Van Nostrand be used as an excuse to ignore the changes already Reinhold. observed and those expected to occur in the future. Giorgi, F. and L. Mearns. 2002. Calculation of average, uncertainty range, and reliability of regional climate These conclusions are based on the authors’ experience from AOGCM simulations via the “Reliability Ensemble and from the literature. The full application of these in Averagingâ€? (REA) method. J Climate 15:1141–1158. the estimation of peak flows for the Caroni River is not González, J. and J.B. Valdés. 2004. The Mean Frequency presented because the results are based on work previously of Recurrence of In-Time-Multidimensional Events done and was not available for this example. Also due to the for Drought Analyses. Natural Hazards and Earth uncertainties involved, this is still a work in progress. Environmental Science, (4), 17–28. Griffis, V. W. and J.R. Stedinger. 2007. Incorporating Climate Change and Variability into Bulletin 17B LP3 Model, References World Environmental and Water Resources Congress 2007: Restoring Our Natural Habitat. American Society Baker, V. R. 1987. Paleoflood Hydrology and Extraordinary of Civil Engineers, 8 pp. flood events. Journal of Hydrology, v. 96, no. 1–4, Hardison, C.H. 1971. Prediction error of regression 79–99. estimates of streamflow characteristics at ungaged Chow, V. T., D. R. Maidment, and L. W. Mays. 1988. Applied sites. In Geological Survey Research, 1971: U.S. Hydrology. New York: McGraw Hill. Geological Survey Professional Paper 750-C, Coles, S. 2001. An introduction to statistical modeling of C228-C236. extreme values. London: Springer. Hosking J.R.M. 1990. L-moments analysis and estimation of Dalrymple, T. 1960. Flood Frequency Analysis, U.S. distributions using linear combination of order statistics. Geological Survey Water Supply Paper 1543-A. Journal Royal Statistical, 52 (1), 105–124. Domínguez, F., J. Cañón and J. Valdés. 2009. IPCC-AR4 Hosking, J.R.M. and J. Wallis. 1997. Regional Frequency climate simulations for the Southwestern US: the Analysis. Cambridge: Cambridge University Press. importance of future ENSO projections. Climatic Interagency Advisory Committee on Water Data. 1982. Change, doi: 10.1007/s10584-009-9672-5. Guidelines for determining flood-flow frequency. Dumedah, G. and P. Coulibaly. 2011. Evaluation of Bulletin 17B of the Hydrology Subcommittee, Office statistical methods for infilling missing values in high- of Water Data Coordination, U.S. Geological Survey, resolution soil moisture data. Journal of Hydrology, 400 Reston, Va., 183 p., http://water.usgs.gov/osw/ (1–2), 95–102. bulletin17b/bulletin_17B.html Dworak, F. 2011. Using multiple methods to improve Intergovernmental Panel on Climate Change. 2007. Fourth hydrologic hazard estimates for dam safety. Assessment Report (IPCC AR4). Geneva, Switzerland. 26 Khalil, M., U.S. Panu, and W.C. Lenox. 2001. Groups and paleohydrologic bound data. Water Resour. Res. 38 Neural Networks Based Streamflow Data Infilling (5), 16-1-16-14. Procedures. Journal of Hydrology, Vol 241, Issues 3–4, Pandey, M. D., P.H.A.J.M. Van Gelder, and J.K. Vrijlling. 31 January, 153–176. 2001. The estimation of extreme quantiles of wind Kharin V. and F. W. Zweirs. 2005. Estimating Extremes in velocity using L-moments in the peaks-over-threshold Transient Climate Change Simulations. J Climate, 18, approach. Structural Safety, 23 (2001), 179–192. 1156–1173. Power Planning and Associates. 2006. “Hydrology and Kundzewicz, Z. W. 2006. Climate Change and Floods. Energy Generation of Hydropower Plantsâ€? In Bujugali Bulletin, World Meteorological Organization, Geneva, II: Economic and Financial Study. Guildford: PPA Switzerland, July. Energy. Milly P. C. D., J. Betancourt, M. Falkenmark, R. M. Hirsch, Raff, D.A., T. Pruitt, and L. D. Brekke. 2009. A framework for Z. W. Kundzewicz, D. P. Lettenmaier, and R. J. assessing flood frequency based on climate projection Stouffer. 2008. Stationarity is Dead: Whither Water information. Hydrol. Earth Syst. Sci. Discuss., 6, Management. Science (319) February. 2005–2040. Moss, M. and M. Karlinger. 1974. Surface Water Network Sveinsson, Oli G. B., J. D. Salas, and D. C. Boes. 2005. Design by Regression Analysis Simulation. Water Prediction of Extreme Events in Hydrologic Processes Resources Research, 10(3), 427–433. that Exhibit Abrupt Shifting Patterns. Journal of National Oceanic and Atmospheric Administration, Heavy Hydrologic Engineering, July/August. Rainfall Frequencies for the US: NOAA Atlas 14, Water Resources Council Hydrology Sub-Committee. www.ncdc.noaa.gov/oa/documentlibrary/rainfall. 1982. Bulletin 17B: Guidelines for Determining Flood html#atlas14. Flow Frequency. National Research Council. 2009. Mapping the Zone: Wood, A. W., L. R. Leung, V. Sridhar, and D. P. Lettenmaier. Improving Flood Mapping Accuracy, Committee on 2004. Hydrologic implications of dynamical and FEMA Flood Maps. Board on Earth Sciences and statistical approaches to downscaling climate model Resources/Mapping Science Committee. Washington, outputs. Climatic Change, 62, 189–216. D.C.: National Academy Press. World Meteorological Association (WMO). 2009. Manual O’Connell, D.R.H., D.A. Ostenaa, D.R. Levish, and R.E. on Estimation of Probable Maximum Precipitation Klinger. 2002. Bayesian flood frequency analysis with (PMP). WMO Technical Report 1045, 293 pages. 27 3. EVALUATION OF MONTHL FLOWS Y Introduction million people. The Salt-Verde Basin is located in central Arizona and is part of the lower Colorado River Basin There is significant evidence that climate change is affecting (figure 3-2). The drainage area is approximately 35,100 water resources worldwide. The increase in temperature, km2 with an elevation ranging from 280 to 3850 meters particularly at the higher altitudes, results in significant above sea level (masl). In the Salt River Basin, streamflow differences in the partitioning of precipitation between is regulated downstream from the Roosevelt reservoir, rainfall and snow. This also brings changes to sublimation, which has a storage capacity 2,040 hm3. In addition, evapotranspiration, and runoff seasonality that may require changes in the operation of water resources systems and Figure 3-1. Changes in Precipitation put in jeopardy hydropower and water supply operations. Type This is already being observed in the Southwest United States (see figure 3-1). There are, however, large uncertainties surrounding the results of the many Global Circulation Models (GCMs) available in the IPCC report (IPCC, 2007). These uncertainties are even larger at the regional level, which is the level at which the water resources of a basin need to be evaluated for project design and operational purposes. As mentioned in the previous chapter, the spatial resolution of the GCMs is still very coarse for practical application of the rainfall-runoff models and their results need to be disaggregated (downscaled) at resolutions suitable for analysis. This chapter presents an example of a relatively simple approach to address these problems in a semi-arid region, the Verde River Basin in the southwestern United States. The methodology, however, may be applicable to similar cases in other regions of the world. The Verde River Basin is part of the Salt-Verde Basin, which is the main source of water to the metropolitan area of Phoenix, Arizona, with a population of approximately 4 Source: Knowles et al., US Geological Survey (USGS). 29 there are four smaller multipurpose reservoirs downstream Methodology on the Salt River, which include power generation, municipal and agricultural water supply, and groundwater To estimate the impact of climate variability and change recharge. In the Verde River Basin, streamflow is regulated on the water resources of a river basin at the monthly downstream of the Horseshoe dam, which has a storage level, a projection of future climate conditions needs to be capacity of 110,000 acre-feet (112 million cubic meters). made. The methodology commonly found in the literature There is only one more reservoir downstream on the Verde involves the use of GCMs, downscaling the results to River. For this reason this example focuses on the Verde a river basin scale resolution, and transforming them to River Basin. surface runoff and other hydrologic variables such as actual evapotranspiration and soil moisture storage. Several The Verde River flows through a corridor of rich riparian approaches on the use of the GCM results have been used. habitat. It starts as a group of springs fed by the Big Chino One such approach is to simulate different scenarios to see aquifer in central Arizona, from where it heads east and then if the project can survive them and identify positive actions south, flanking the communities of Clarkdale, Cottonwood, under those scenarios. Another approach is to select one Jerome, Sedona, and Camp Verde. It is one of Arizona’s or a few GCMs based on some performance criteria for few perennial rivers and includes the state’s only wild and the region under study. In this case, the REA (Reliability scenic river segment, which also provides a habitat essential Ensemble Average) method is applied to the US Southwest. to endangered species. Yet another approach is to use all of the available models acknowledging the uncertainty existing in their results to provide a wider uncertainty interval. This approach is used Objective later in this chapter to estimate the monthly streamflows of the Verde Basin. This case study focuses on the impact of climate variability and change on hydrologic variables at The REA Approach the monthly level. Its objective is to illustrate a methodology that could be applied in semi-arid For most applications, there are not enough resources, regions to take these changes into account in both of time and personnel, to use all the results from hydrologic studies. the more than 24 GCMs available. In those cases it may be convenient to either select one or a small number of GCMs that the analyst considers will best represent Figure 3-2. Verde River Basin the seasonal precipitation and temperature variability conditions prevailing in the region under study. For that purpose, selection criteria should be established or adopted. The criteria used first in this example is that of the REA (Reliability Ensemble Average) method originally proposed by Giorgi and Mearns (2002) and modified by Domínguez et al. (2009) who added performance based on large scale circulation that drive moisture fluxes into the region. In this example, the temperature, precipitation, and effects of the location of the jet stream reflected in the 250 mb geopotential height field (GPH) are used to evaluate the model’s performance. The REA method combines two criteria: (i) how well a particular GCM represents historic records (reliability criterion); and (ii) how closely Source: Developed by author Juan B. Valdés. it approximates the average predictions of the GCMs 30 (convergence criterion) since there are no future records weighted average of the projections of all the models, which (Giorgi and Mearns, 2002). is a function of Ri. In this method, the reliability factor (Ri) for model i is Because the REA-weighted average is a function of Ri, computed as follows: the procedure is iterative. After the solution converges, the models that have largest Ri values correspond to Ri = RPi × RTi (3-1) those with largest difference from observations, and worst performance. The score system is normalized so the largest where RPi and RTi are calculated for precipitation and scores represent the best models. R B,i values are normalized temperature respectively as as follows:3 RPi = RB ,P ,i × RD ,P ,i (3-2) max(RB ) − RB ,i RTi = RB ,T ,i × RD ,T ,i RB ,i = ï?? (3-3) max(RB ) R B,i represents the reliability of model i in simulating present- day climate, and R D,i accounts for the convergence of each A similar procedure is followed to normalize R D,i. model to the REA average in the climate projections for both precipitation (P) and temperature (T). R B,i is calculated In Domínguez et al. (2009) the three scores (monthly using the mean square error (MSE) between historical precipitation, temperature, and large scale circulation) were monthly model output and observations (consisting of used to compute the REA. The results are presented in regionally averaged temperature and precipitation from the figure 3-3, which shows that the models that best represent available dataset). R D,i is also calculated using MSE, but the the regional characteristics of the region being analyzed difference is now between each model’s projections and the are the UK Meteorological Office model (ukmo_hadcm3) Figure 3-3. REA Performance for GCMs in the Southwest United States Ri 4.0   3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 bcc_cm1 bccr_bcm2_0 cccma_cgcm3_1 cccma_cgcm3_1_t63 cnrm_cm3 csiro_mk3_0 gfdl_cm2_0 gfdl_cm2_1 giss_aom giss_model_e_h giss_model_e_r iap_fgoals1_0_g ingv_echam4 inmcm3_0 ipsl_cm4 miroc3_2_hires miroc3_2_medres mpi_echam5 mri_cgcm2_3_2a ncar_ccsm3_0 ncar_pcm1 ukmo_hadcm3 ukmo_hadgem1 Scenarios A1B A2 B1 JJA All Months Source: Domínguez et al., 2009. 3. The program is complex and was implemented in MATLAB. 31 and the Max Planck Institute model (mpi_echam5). It should method gives a perturbation value, which can then be added be mentioned, however, that since some models do not to the historically observed climatology. Even though only encompass all scenarios, their score might be artificially low. the two selected models were finally used in the example, Proponents of the REA method felt that past performance the bias correction procedure significantly reduced the alone was not sufficient to select a model. biases in monthly precipitation for all of the models (see figure 3-5). Domínguez et al. (2009) also found that these two models provided a satisfactory representation of the ENSO, which Downscaling is an important climatic precursor of winter precipitations in the region. As mentioned in the previous chapter, GCM results are in a much coarser scale than the one needed for most hydrologic These results needed to be verified by seasonal bias. applications, requiring the application of a disaggregation Domínguez et al. (2009) found that the temperature results (downscaling) technique to increase the resolution. There were satisfactory but there were significant biases in are basically two approaches to downscale coupled climate monthly precipitation (see figure 3-4). model projections: statistical and dynamic downscaling. An excellent review of these methods is given by Fowler et al. To ensure that they are not transferred to future projections, (2007) and a summary is presented in annex III. Domíguez et al. (2009) removed the precipitation biases using the procedure suggested by Wood et al. (2002, Statistical Downscaling 2007). A summary of the bias correction procedure is In statistical downscaling, the GCM results are shown in table 3.1 disaggregated in space using statistical procedures ranging from simply using the ratio of the local mean to the mean To facilitate the analysis, the results of the two selected of the GCM cell, to more sophisticated ones relating the models (mpi-echam5 and ukmo_hadc3m) were regridded local results to climatic precursors like ENSO using MSSA to a common 2o resolution grid using a two-dimensional (Multichannel Singular Spectrum Analysis) as done in cubic spline interpolation. The goal of the bias-correction Cañón et al. (2011). method is to use the probability of excedence of monthly climate model projections and match this probability to The statistical downscaling techniques have the following the historically observed climate value. The bias-correction advantages (Domínguez, personal communication, 2009): Figure 3-4. Monthly Temperature in K° (left) and Precipitation Averages in mm/day (right) for GCMs 305 4 Monthly Precipitation (mm/day) Temperature (K) 2 285 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 265 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Source: Domínguez et al., 2009. 32 Table 3-1. Bias Correction Procedure 1. Compute empirical probability of excedence Pobs(T) curve from observed Tobs values for a particular month 2. Compute empirical probability of excedence PGCM(t) curve for a particular GCM results, for same period and same month as historic values of step 1 3. Do bias correction approach, i = 1, number of observations a. Select a given value TGCM b. For this particular value TGCM compute its probability of excedence PGCM(TGCM) from the curve derived in step 2 c. Using the probability obtained in step 3b go to the probability of excedence curve Pobs(T) and assume PGCM(TGCM) = Pobs(TGCM) d. Using the probability Pobs(TGCM) compute Tobs e. Do this for all observations 6. Repeat steps 2–3 for all GCM model results Source: Wood et al., 2002 • They are inexpensive and computationally efficient. of the more complex dynamic downscaling techniques. • They can be used in many different scenarios and model In most applications for operational and project design runs. purposes, statistical downscaling may be an appropriate • They can be used to derive variables not available in technique. Regional Climate Models (RCMs). • They are easily transferable to other regions. Dynamic Downscaling Dynamic downscaling involves the use of regional climate However, they have the following limitations: models (RCMs) that use, as boundary conditions, those provided by the GCMs. The most commonly used dynamic • They require long and reliable observation data records. model is the WRF (Weather Research and Forecast) • The results depend on the choice of predictors. developed by the National Center for Atmospheric Research • They involve the assumption of stationarity of predictor- (NCAR) and other agencies. The model is in the public predictand relationship. domain and is available at http://wrf-model.org/index.php • They do not account for feedbacks. Dynamic downscaling has the following advantages Nevertheless, there is literature that suggests that the (Domínguez, personal communication, 2009): statistical downscaled results may be comparable to those • It produces responses based on physically consistent processes. Figure 3-5. Monthly Average Precipitation • It captures feedbacks. for GCM Models for the Southwest • It can model changes that have never been observed in United States the historical record. After Bias-Correction Procedure Was • It is useful where topographic controls are important. Applied 2.0 It has, however, the following limitations: 1.8 • It requires significant computational power. SW Precipitation B1 1.6 • The number of models / runs / timescales that can be 1.4 used is limited. 1.2 • It is dependent on GCM boundary forcing. 1 • It presents problems with drifting of large-scale climate. 0.8 Regional Climate Models provide additional information 0 2 4 6 8 10 12 about the changes in physical processes that arise due to a Source: Domínguez et al., 2009. changing climate, including: 33 • Changes in intensity and/or frequency of precipitation In this case, the abcd model was selected because of its events. simplicity and because it is in the public domain and easy • Water holding capacity of the atmosphere. to implement.4 The abcd model is based on a previous • Diurnal cycle of precipitation. conceptual model by Thornwaite (1948) and has been • Changes in land-atmosphere feedbacks that might affect widely mentioned in the literature. It has been successfully the strength of monsoons. used by several researchers, among them Alley (1984) and more recently Martínez and Gupta (2010). The latter Examples and case studies included in this report were applied the model to 764 catchments in the conterminous based on work previously done. In this example only United States selected for their comprehensive coverage statistically downscaled data were used since they were of hydrogeological conditions, and made a thorough available for the basin being studied and the aim was to discussion of its advantages and disadvantages. However, illustrate that statistical downscaling may, in some cases, they cautioned that methods for diagnostic model offer a simpler alternative to RCMs, which are more labor evaluation and improvement remain weak. There is a intensive. No new research was involved. need for well-conceived, systematic strategies to guide model selection, establish data requirements, estimate Water Balance Models parameters, and evaluate and track model performance. It should be pointed out that the use of the abcd model is There are a plethora of basin-level water balance models only as an example of the approach since there are other to evaluate the temporal characteristics of streamflows, monthly rainfall-runoff models available (e.g. the 1977 usually at the monthly level (Alley, 1984). Monthly water Temez model, which also has four parameters). It should be balance models are simple representations of the rainfall- pointed out that uncertainty also exists in the selection of runoff process of a basin that allow an understanding of the rainfall-runoff model. the hydrologic process and its changes at the basin scale. They are widely used to evaluate changes in the basin due Each of the model’s four parameters, a, b, c, and d, is to modifications in the land and soil use, climate change, presumed to have some degree of physical interpretation. and so on (e.g. Valdes and Seoane, 2000). These models Thomas et al. (1983) describe the four abcd model use monthly series of precipitation and temperature or parameters as follows: potential evapotranspiration as input to produce estimates of surface runoff, actual evapotranspiration, and soil • a: propensity of runoff to occur before the soil is fully moisture storage. However, a word of caution is warranted saturated, (0 < a ≤ 1) as it is not clear whether existing models can reproduce • b: upper limit on the sum of evapotranspiration and soil the catchment dynamics observed in nature, nor has moisture storage researcher’s ability to evaluate model results kept pace • c: fraction of streamflow that arises from groundwater with computational and data processing abilities (Martínez • d: its reciprocal is equal to the groundwater residence and Gupta, 2010). time One of these models is the abcd model, which was The original four-parameter model only considered originally proposed by Thomas (1981). Its name reflects rainfall. However, if both snow and rainfall are present, a the four parameters (a, b, c, and d) utilized in the model. fifth parameter is included to separate total precipitation The use of input-lumped parameter models like abcd in this between these two components. In addition to these example does not mean that more sophisticated models four (for only rainfall) or five (when snow is considered) should be precluded. Simple models such as this, however, parameters the model needs the initial conditions of soil are a good way to highlight problems that may need to moisture content and snowpack for the case of snow. be studied in more detail with more time and resources. 4. FORTRAN and MATLAB versions were available. 34 Simulation of Climate Change Impact to direct the search in a given direction. The points are on the Hydroclimatology of the Verde periodically reorganized (“shufflingâ€?) and these points are River Basin reassigned to different subspaces to ensure that there is transmission of information among the subspaces. The The methodology outlined in the previous section was search tends to converge toward the neighborhood of the applied to the Verde River Basin in Arizona (USA) with global optimum if the initial population is sufficiently large. three of the emission scenarios (A1, A1B, and B2). The SCE method is public domain and it is available at the These scenarios were chosen to represent uncertainty. SAHRA (Sustainability of Semi-Arid Hydrology and Riparian Instead of using the REA results described in the previous Areas) website (www.sahra.arizona.edu). section to illustrate the impact of model uncertainty on the hydroclimatology of a basin, this example (see Wood et al., The RMSE (root of mean square error) was used as a 2002) relies on the results of all the GCMs. criterion of performance in the calibration of the parameters for the Verde Basin example. However, other performance A word of caution is needed here. Although it is becoming criteria were also computed to provide additional information “standardâ€? practice to link the results of a climate change on the model calibration.5 An example of the calibration model for temperature and precipitation with a hydrologic results is shown in figure 3-6, which is included to provide model for runoff, there are many problems involved. For another idea about performance beyond the RMSE. example, many environmental changes due to climate change that affect processes such as evapotranspiration, snow melt, Model Simulation Results and vegetation growth are not being taken into account. Also, the calibration is sometimes based on simple curve fitting Figure 3-7 shows the results of a simulation of the abcd methods. This may result in serious errors when using historical model calibrated using the SCE approach at the basin data for calibration and then using the same parameters for level discussed in the previous section when no snow was future climate changes. These issues, however, are beyond considered. Figure 3-8 shows the results when precipitation the scope of this report and should be the subject of future is divided into snow and rainfall. discussion. With the above caveats in mind, the remainder of this section explores the application of the abcd model. The results of running the calibrated abcd model for the Verde Basin with three of the emission scenarios (A1, A1B and B2) Model Calibration and all the GCMs available provide an idea of the uncertainty in the estimates. This was done to illustrate a case when The abcd model was calibrated using initial estimates of the results of all the GCMs are used instead of selecting just a parameters and time series of precipitation, temperature, and few of them (as illustrated in the previous section). Figure 3-9 streamflows for the period 1970–1995. The SCE (“Shuffled shows that there is significant variability in the precipitation Complex Evolutionâ€?) automatic calibration procedure but without any significant trend, either positive or negative. developed by Duan et al. (1992) was used. This method There is also an increase in potential evapotranspiration and later modifications and expansions at the University of (calculated using the Hargreaves equation, Hargreaves et al., Arizona have been successfully used in the calibration of 1985; Hargreaves, 1994), but the limited amount of water rainfall-runoff models. The SCE method is based on the available causes the actual evapotranspiration to remain use of multiple complexes that start at random points in the constant with a slight positive increase. Other experiments space parameter of the model under calibration. The search carried out in Arizona and reported by Serrat-Capdevila et al. starts in the most promising points dividing the parameter (2010) tend to confirm these results. space into several subspaces, each one containing 2n+1 points where n is the dimension of the problem (number The situation of the surface runoff and groundwater of parameters). Each subspace (called a community in recharge, however, is different and indicates that the region the description of the method) uses the “simplexâ€? method will be under increased water stress, as seen in figure 3-10. 5. The other performance criteria include Nash-Sutcliffe, correlation between observed and simulated values, and others. 35 Figure 3-6. Example of SCE Calibration Results of abcd Model ID: 6019500 35 Area: –999 Par a: 0.9455 Par b: 235 30 Par c: 0.4066 Par d: 0.02033 Par e: 89.58 25 Par f: 210.4 QQm (mm/month) Par g: –0.625 Par h: –10 20 Par i: 0.3817 Par j: 11.46 15 MSE A: 7.435 MSE N: 0 MSE L: 0 10 NSE A: 0.792 Bias: 0.002734 Corr: 0.11 5 m: 0.7901 b: 1.728 icall: 2.062e+004 0 oplag: 0 0 5 10 15 20 25 30 35 M.PPS: –999 D.PPS: 35.44 QQd (mm/month) Source: Martínez, 2008 (personal communication). QQm represents the model outputs and QQd represents the historic flows in mm/month. Figure 3-7. Simulation Results of Verde Basin Using the abcd Model (no snow) Red line represents observed values in the two bottom figures Watershed 6019500 [PP/b] (1/month) 0 PP 0.2 0.4 20 Tmax Tmin 0 °C –20 [E/b] (1/month) PET 0.5 AET 0 [Q/b] (1/month) QQd 0.1 QQm 0 [Q/b] (1/month) 10–1 QQd QQm 10 20 30 40 50 60 70 80 90 100 110 120 Month Source: Martínez, 2008 (personal communication). The values of evaporation E, observed and simulated inflows, and streamflows are in mm (volume/basin area) divided by the parameter b to facilitate the comparison. 36 Figure 3-8. Simulation Results of Verde Basin Using the abcd Model (with snow) Red line in the two bottom figures represents observed values Watershed 6019500 0 Rain mm/month Snow 100 200 50 Tmax °C Tmin 0 Train –50 Tsnow 150 Snow Storage mm/month Snowmelt 100 50 0 30 QQd 1/month QQm 20 10 0 10 20 30 40 50 60 70 80 90 100 110 120 Month Source: Martínez, 2008 (personal communication). The values of evaporation E, observed and simulated inflows and streamflows are in mm (volume/basin area) divided by the parameter b to facilitate the comparison. The AET is used here, not the PET (the PET is only used as The growing intensity of the droughts as the 21st century an upper bound since it is a function of T and this increases). advances is seen in Figure 3-12 where the SPI was computed for the three aggregation levels and for three Figure 3-11 depicts the average SPI (Standardized 50-year periods (a historic period 1959–1999, 2000– Precipitation Index). The SPI proposed by McKee et al. 2049, and 2050–2099). The figure shows that both the (1993) is a drought index based only on precipitation and can intensity (number of severe droughts with an SPI below –2) be used to monitor conditions on a variety of time scales. This and duration of droughts increases significantly in the last temporal flexibility allows the SPI to be useful in both short- 50-year period of the 21st century. term agricultural and long-term hydrological applications. The SPI is the number of standard deviations that the observed The results, however, are not as clear for wet periods (see value would deviate from the long-term mean, for a normally Figure 3-13). distributed random variable. Since precipitation is not normally distributed, a transformation is first applied so that the Comparison of Results from the abcd transformed precipitation values follow a normal distribution. Model and a Physically Based Rainfall- Runoff Model The SPI was computed for three different aggregation levels (3, 12, and 24 months). Figure 3-11 shows that the intensity The results obtained from the abcd model for the Verde and duration of the droughts will increase in the Verde Basin Basin where compared with those of a very widely used this century. physically based model—the VIC (Variable Infiltration 37 Figure 3-9. Precipitation and Evapotranspiration for Three Emission Scenarios in the Verde Basin Precipitation A1B Precipitation A2 Precipitation B1 900 900 900 800 800 800 700 700 700 600 600 600 mm/year mm/year mm/year 500 500 500 400 400 400 300 300 300 200 200 200 100 100 100 0 0 0 1960 1980 2000 2020 2040 2060 2080 2100 1960 1980 2000 2020 2040 2060 2080 2100 1960 1980 2000 2020 2040 2060 2080 2100 Evapotranspiration A1B Evapotranspiration A2 Evapotranspiration B1 2000 2000 2000 1500 1500 1500 mm/year mm/year mm/year 1000 1000 1000 500 500 500 0 0 0 1960 1980 2000 2020 2040 2060 2080 2100 1960 1980 2000 2020 2040 2060 2080 2100 1960 1980 2000 2020 2040 2060 2080 2100 ETP Spread Average AET Spread Source: Serrat-Capdevila et al., 2010 (notice the different scales in the graphs). Notes: Precipitation (in blue); Potential ET (in green), and Actual ET (in blue). The solid black line is the average of all the GCMs for that particular year. Since it goes to 2100 only the average of the models was plotted. Capacity) model—developed by Lettenmaier and Summary of Procedure collaborators at the University of Washington (Liang et al. 1994). The VIC model runs at a time step of 6-hours to The Rio Verde Basin water balance example yields the one day and with a spatial resolution of 1/8o. The results following conclusions: from the VIC model shown in figure 3-14 were provided by Seshadri Rajgopal and Hoshin Gupta from the University of Selection of GCM Models Arizona (personal communication, 2010). • The variability of the GCM results for a particular emis- The abcd model appears to be slightly better from a visual sion scenario and the alternative emission scenarios inspection than the VIC model in this particular basin. introduce uncertainty. Obviously this comparison is preliminary and it does not • As an alternative to using the results of all the GCMs, indicate that the performance of the abcd model will always criteria for selecting a single or a couple of GCMs that be better than more detailed rainfall-runoff models. However, are better suited to the region under study may be because of its simplicity, the abcd model allows carrying out used. An example of the selection criteria is the one more simulation runs and facilitates the understanding of proposed by Giorgi and Mearns (2002) and modified uncertainty in the meteorological inputs. For the particular by Domínguez et al. (2009). The elements to be consid- case of the Verde River Basin the results indicate that it ered may vary in each application (annual and seasonal will be drier and with more intense and longer duration precipitation and temperature, climatic precursors like droughts. ENSO, etc.). 38 Figure 3-10. Ground and Surface Water for Three Emission Scenarios in the Verde Basin (Groundwater Recharge and Surface Runoff) GW Outflow A1B GW Outflow A2 GW Outflow B1 25 25 25 20 20 20 mm/year mm/year mm/year 15 15 15 10 10 10 5 5 5 0 0 0 1960 1980 2000 2020 2040 2060 2080 2100 1960 1980 2000 2020 2040 2060 2080 2100 1960 1980 2000 2020 2040 2060 2080 2100 Streamflow A1B Streamflow A2 Streamflow B1 250 250 250 200 200 200 mm/year mm/year mm/year 150 150 150 100 100 100 50 50 50 0 0 0 1960 1980 2000 2020 2040 2060 2080 2100 1960 1980 2000 2020 2040 2060 2080 2100 1960 1980 2000 2020 2040 2060 2080 2100 GCM Spread Average Observed Source: Serrat-Capdevila et al., 2010. Figure 3-11. SPI Computations for the Average Multi-model GCM Multi-Model Average SPI 3 Months Multi-Model Average SPI 12 Months Multi-Model Average SPI 24 Months 1.0 0.6 0.6 0.4 0.4 0.5 0.2 0.2 0 0 0 –0.2 –0.2 –0.5 –0.4 –0.4 –1 –0.6 –0.6 –1.5 –0.8 –0.8 1950 1979 2008 2037 2066 2095 1950 1979 2008 2037 2066 2095 1950 1979 2008 2037 2066 2095 Source: Serrat-Capdevila et al., 2010. • Once the models are selected it is necessary to carry Downscaling out a bias correction to reflect the seasonality of the precipitation and temperature values.6 • Even though dynamic downscaling offers more assur- ance of an adequate representation of the climatology 6. The example used downscaled values for the purpose of illustration. 39 Figure 3-12. Intensity and Duration of Droughts Using the Multi-model GCM results (1950–1999 in blue, 2000–2049 in green and 2050–2099 in red) The trend was visually adjusted and is shown only as an illustration. Droughts in SPI03 Droughts in SPI12 Droughts in SPI24 –2.0 –1.9 –1.9 Period 1950–99 –2.1 –2.0 Period 2000–49 –2.0 –2.2 –2.1 Period 2050–99 –2.1 Intensity (SPI) Intensity (SPI) Intensity (SPI) –2.3 –2.2 –2.2 –2.4 –2.3 –2.3 –2.5 –2.4 –2.4 –2.6 –2.5 –2.5 –2.7 –2.6 –2.6 –2.8 –2.7 –2.7 0 10 20 30 40 50 0 5 10 15 20 25 0 5 10 15 20 Number of Events Number of Events Number of Events Droughts in SPI03 Droughts in SPI12 Droughts in SPI24 2.6 12 16 2.4 10 14 2.2 12 8 2.0 10 Duration Duration Duration 1.8 6 8 1.6 4 6 1.4 4 2 1.2 2 1.00 10 20 30 40 50 0 00 5 10 0 5 10 15 20 25 15 20 Number of Events Number of Events Number of Events Source: Serrat-Capdevila et al., 2010. Figure 3-13. Intensity and Duration of Wet Periods Using the Multi-model GCM Results (1950–1999 in blue, 2000–2049 in green and 2050–2099 in Gray) Wet Spells in SPI03 Wet Spells in SPI12 Wet Spells in SPI24 2.8 2.8 3.0 2.7 2.7 2.8 2.6 2.6 Intensity (SPI) Intensity (SPI) Intensity (SPI) 2.5 2.5 2.6 2.4 2.4 2.3 2.3 2.4 2.2 2.2 2.2 2.1 2.1 2.0 2.0 2.0 0 5 10 15 20 25 30 0 5 10 15 20 25 0 5 10 15 20 Number of Events Number of Events Number of Events Wet Spells in SPI03 Wet Spells in SPI12 Wet Spells in SPI24 3 10 25 8 20 2.5 6 15 Duration Duration Duration 2 4 10 1.5 2 5 1 0 0 0 5 10 15 20 25 30 0 5 10 15 20 25 0 5 10 15 20 Number of Events Number of Events Number of Events Period 1950–99 Period 2000–49 Period 2050–99 Source: Serrat-Capdevila et al., 2010. 40 Figure 3-14. Comparison of Average Monthly Streamflows for Three Emission Scenarios (a) Using the abcd Model Mean Streamflow A1B Mean Streamflow A2 Mean Streamflow B1 8 8 8 7 7 7 6 6 6 5 5 5 mm/month mm/month mm/month 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 2 4 6 8 10 12 2 4 6 8 10 12 2 4 6 8 10 12 Month Month Month (b) Using the VIC Model Mean Streamflow A1B Mean Streamflow A2 Mean Streamflow B1 8 8 8 7 7 7 6 6 6 xxx units xxx xxx units xxx xxx units xxx 5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 2 4 6 8 10 12 2 4 6 8 10 12 2 4 6 8 10 12 Month Month Month Period 196–1999 Period 2000–2049 Period 2050–2098 Observed Source: Serrat-Capdevila et al., 2010; Seshadri Rajgopal and Hoshin Gupta, 2010 (personal communication). The period used in this example was 1961–1999. of a region, statistical downscaling procedures may be however, that significant errors may be made when using applied as an alternative. historical data for calibration and then using the same • There are significant uncertainties and the amount of parameters for a changed climate in the future. effort to carry out dynamic downscaling may be exces- • For semi-arid regions in which the difference between sive for some hydrologic design purposes. As shown in actual and potential evapotranspiration may be signifi- Wood et al. (2004), statistically downscaled products cant and when approximate ET equations are used, it may produce satisfactory results in the estimation of the is important to evaluate the impact on the behavior of hydrology of a basin. plants under water stress. Serrat-Capdevila et al. (2010) presented results that indicate that atmospheric demand Impact of Climate Change in the will be greater and lead to increased reference crop Hydroclimatology of a Particular Basin evaporation, but evapotranspiration rates will remain largely unchanged due to stomatal regulation. However, • To analyze the impact of climate change in the hydrocli- the length of the growing season will increase leading matology of a particular basin, rainfall-runoff models are to greater annual riparian water use as found by Serrat- useful to evaluate all the components of the hydrologic Capdevila et al. (2011). These findings of increased cycle not just precipitation and temperature. There may be riparian water use and atmospheric demand, likely affect- many changes in the environment due to climate change ing recharge processes, will lead to greater groundwater that affect processes that should be taken into account. deficits and decreased streamflow and have important Even simple water balance models at the monthly level implications for water management in semiarid regions. are useful tools in this endeavor. It should be kept in mind, In the case of data limitations, a simpler ET equation 41 Summary of Steps for Carrying Out an Evaluation of Climate Change Impact on the Water Resources of a River Basin as Applied to the Verde River Basin 1. Extract monthly data from all available IPCC models for the emission scenarios under analysis by selecting a region of interest (See table 3-2 for a complete list of the models and available emission scenarios). Using all the models may provide information about model uncertainty. All the IPCC models participating in the World Climate Research Programme’s (WCRP’s) Coupled Model Intercomparison Project phase 3 (CMIP3) multi-model dataset are listed in table 3-2 (the x indicates the availability of specific runs for each given model). To download the data the user must first download the required model databases from the WCRP CMIP3 multi-model database available at http://esg. llnl.gov:8080/index.jsp. The website requires the user to register in order to deliver the information. 2. Regrid the data extracted in step 1, to a common grid (2o by 2o). This will facilitate the computation in case the REA (Reliability Ensemble Average) is used. The Domínguez et al. (2009) study used a cubic spline to do the regridding. 3. Extract monthly observational data (New et al. 2000, 2002) and regrid the data for the same region of analysis as the IPCC models. The data may be obtained at http://www.cru.uea.ac.uk/cru/data/hrg/ 4. If a limited number of models rather than the entire set of models is going to be used, perform the REA analysis to select the models that perform best over the region. 5. Do the bias-correction of the monthly data using the methodology of Wood et al., (2002) summarized in table 3.1 of this report. 6. Calibrate the abcd rainfall-runoff model (or any other appropriate model) using a calibration procedure, e.g. the SCE model. could be used. The Hargreaves method (Hargreaves et A relatively simple rainfall-runoff model, the abcd model, al., 1985) was used in this example. was shown, as an example, to be a practical way to evaluate climate change impact. As shown in the example of the Verde River Basin, climate change impacts all the Final Comments components of the hydrologic cycle. Even in the case in which the variability of the precipitation is not significant Although it is becoming standard practice to link the results (as in the case of the Verde Basin), there is significant of a climate change model for temperature and precipitation variability in the other components of the water balance, with a hydrologic model for runoff, there are many problems like evapotranspiration, groundwater recharge, and involved. For example, many changes in the environment runoff. due to climate change that affect processes such as evapotranspiration, snow melt, and vegetation growth may The information provided by the GCMs has not be taken into account. significant variability in both space and time and its resolution is not directly applicable to hydrologic This chapter has shown that it is useful to carry out the models. GCM results still have significant variability evaluation of the impact of climate change in the water and uncertainty. Processing the results of these resources of a river basin by means of a rainfall-runoff models, doing bias corrections, and downscaling are model. Rather than using simple curve fitting methods, not simple tasks. The downscaling of these results, the use of automatic calibration techniques may, in some either by statistical or dynamic methods, introduces cases, provide an expedient approach to model calibration. additional uncertainties that need to be considered This, however, should not be in substitution of, but rather in hydrologic design. as a complement, to evaluation of model performance by hydrologists. Serious errors may be made when using historical data for calibration and then using the same parameters for a changed climate in the future. 42 Table 3-2. Models Available at CMIP Emission Scenario Availability Original Group Model ID B1 A1B A2 Beijing Climate Center bcc_cm1 x Bjerknes Centre for Climate Research bccr_bcm2_0 x x x Canadian Centre for Climate Modelling & Analysis cccma_cgcm3_1 x x x Canadian Centre for Climate Modelling & Analysis cccma_cgcm3_1_t63 x x Météo-France/Centre National de Recherches Météorologiques cnrm_cm3 x x CSIRO Atmospheric Research csiro_mk3_0 x x x US Dept. of Commerce/NOAA/Geophysical Fluid Dynamics Laboratory gfdl_cm2_0 x x x US Dept. of Commerce/NOAA/Geophysical Fluid Dynamics Laboratory gfdl_cm2_1 x x x NASA/Goddard Institute for Space Studies giss_aom x x NASA/Goddard Institute for Space Studies giss_model_e_h x NASA/Goddard Institute for Space Studies giss_model_e_r x x LASG/Institute of Atmospheric Physycs iap_fgoals1_0_g x x x Instituto Nazionale di Geofisica e Vulcanologia ingv_echam4 x Institute for Numerical Mathematics inmcm3_0 x x Institut Piérre Simon Laplace ispsl_cm4 x x x Center for Climate System Research (The University of Tokyo), National miroc3_2_hires x x Institute for Environmental Studies, and Frontier Research Center for Global Change [IAMSTEC] Center for Climate System Research (The University of Tokyo), National miroc3_2_medres x x x Institute for Environmental Studies, and Frontier Research Center for Global Change [IAMSTEC] Meteorological Institute of the University of Bonn, Meteorological miub_echo_g x x x Research Institute of KMA, and Model and Data group. Max Planck Institute for Meteoroly mpi_echam5 x x x Meteorological Research Institute mri_cgcm2_3_2a x x x National Center for Atmospheric Research ncar_ccsm3_0 x x x National Center for Atmospheric Research ncar_pcm_1 x x x Hadley Centre for Climate Prediction and Research/Met Office ukmo_hadcm3 x x x Hadley Centre for Climate Prediction and Research/Met Office ukmo_hadgem1 x x Source: Domínguez et al., 2009. References Associations with PDO and ENSO Signals. Journal of Hydrology, 333, 252–264. Alley, W.M. 1984. On the Treatment of Evapotranspiration, Domínguez, F., J. Cañón, and J. Valdés. 2009. IPCC-AR4 Soil Moisture Accounting, and Aquifer Recharge in climate simulations for the Southwestern US: the Monthly Water Balance Models. Water Resources importance of future ENSO projections. Climatic Research, 20(8), 1134–1147. Change, doi: 10.1007/s10584-009-9672-5. Cañón, J., F. Domínguez, and J. Valdés. 2011. Downscaling Duan, Q., S Sorooshian, and V. K. Gupta 1992. 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New, M., D. Lister, M. Hulme, and I. Makin. 2002. A high- Uncertainty in hydrologic impacts of climate change resolution data set of surface climate over global land in the Sierra Nevada, California, under two emissions areas. Climate Research 21. scenarios. Clim Change 82:309–325. Serrat-Capdevila, A., J.B. Valdesm, F. Domínguez, and S. Rajgopal. 2010. Climate Change Effects Propagation 44 4. WATER BALANCE IN ARID AND HUMID ECOSYSTEMS Introduction The second study looks at the impact of changing rainfall patterns in the wetland system of the Everglades in the Although a change in mean annual rainfall may not United States. Instead of plant stress from prolonged be detectable throughout the years, other changes in drought conditions, the vegetation of the Everglades climatology may have important consequences for the experiences stress when water levels inundate their root ecosystem and the population that depends on it. A simple systems causing anoxic conditions and potential mortality. way of detecting these changes is through the analysis of While the specific mechanisms differ between the the frequency of rainy days and their corresponding average ecosystems, the general principles of balancing resource rainfall (that is, average precipitation on a rainy day). use and managing stress are the same. Even if it is not possible to detect a decreasing trend in annual precipitation throughout the historical period, a Objective significantly decreasing trend in the frequency of rainy days as well as an increasing trend in the depth of average The objective is to describe a methodology used to rainfall per rainy day may lead to different soil moisture detect ongoing changes in the main characteristics dynamics and conditions for vegetation (see Rodríguez- of rainfall that have an impact on the water balance Iturbe and Porporato 2004). It has been posited that of a region’s ecosystems, as well as the effect of studies of the potential impacts of hydrologic changes on these changes on the vegetation of arid and humid the vegetation and ecosystem services of a region resulting ecosystems. from ongoing or future climate change scenarios may be carried out locally through simple analyses using relatively unsophisticated models. Methodology This chapter reports on two cases studies. The first is a Rainfall case study from a dryland ecosystem in central Kenya. The impact of the changes on the structure of the ecosystem’s Representation of Rainfall as a Stochastic Process vegetation was evaluated using several rainfall scenarios. This allowed an understanding of relative changes in the A fundamental principle governing rainfall patterns is the water balance and average stress conditions over the random character of its fluctuations in time and space. This growing season. makes it necessary to model rainfall patterns stochastically 45 Figure 4-1. Monthly Rainfall Summary instead of deterministically. Treating rainfall in a stochastic of Jacobson Farm Gage – Two Rainy manner requires an appropriate modeling framework, adding Seasons During the Year to the complexity of the problem. While there are many models to choose from, a simple one at the daily timescale Average Climate Data from Jacobson Farm, Kenya (1934–2008) that adequately preserves the properties of rainfall (mean, 20 variance) is often selected. The simplistic properties of % of Total Rainfall by Month 18 the marked Poisson point process rainfall model allow the 16 14 rainfall to be filtered through modeling frameworks such 12 as the daily soil water balance, which can be used for 10 8 understanding changes in water use. Moreover, for the 6 purposes of the impact of rainfall on ecosystems, there 4 is ample evidence that daily rainfall modeled though a 2 0 marked Poisson process provides satisfactory results. A full J F M A M J J A S O N D description of the marked Poisson process can be found in Month Rodríguez-Iturbe and Porporato (1994). Source: Franz et al. 2010. Rainfall R(t) (mm day–1) is represented as a marked Poisson point process of storm arrivals in time with rate Jacobson Farm reveals two rainy seasons, the “long rainsâ€? λ (day–1) and storm depth h (mm), where h is treated as from March to May and the “short rainsâ€? from October to an exponentially distributed random variable with mean December. Approximately 70 percent of the total annual α (mm). The parameters α and λ can be easily estimated rainfall falls in these two periods. Once the two homogenous from a daily record of rainfall for homogeneous periods periods have been identified, the next step is to ascertain during the year, such as the growing season. The average how α and λ have changed over the period of record. storm arrival rate, λ, is the number of rainy days over the Figure 4-2 illustrates that the total amount of rainfall has not total number of days in the season, Tseas (day), and α is the changed with time, but daily rainfall patterns are becoming average daily storm total when rainfall occurs. The mean more intense (increasing α) and less frequent (decreasing seasonal rainfall is µp = αλTseas (mm) and the variance λ) leading to higher variability in the system. Simple linear of seasonal rainfall is σ 2p = 2α 2λTseas (mm2). Interval regression can be used to identify the slopes (m) of each estimates will be difficult to provide. A way to calculate a trend in time and the significance level (p) of the slope. rough approximation of the goodness of estimation involves calculating the variance of the series of λs (and αs) and Estimation of Future Rainfall Patterns dividing by the number of years (e.g., growing seasons). The standard deviation of the estimates will thus provide a The historical trends of rainfall patterns are highly informative rough picture of the goodness of estimation of these two about the average conditions and the natural level of very important parameters. variability to expect in the system. However, extrapolation of data beyond the length of record is a rough guess and Historical Analysis of Rainfall Patterns should be used with great caution. As a better alternative, the output of global climate change models (GCMs) can A fundamental understanding of historical rainfall patterns provide estimates of changes in precipitation that use a is critical to grasping and interpreting future scenarios in more realistic and diverse range of scenarios. Given the rainfall patterns. Daily precipitation data from 1934–2008 computation constraints of the GCMs, the predictions are for Jacobson Farm, Kenya (Franz et al., 2010) was used to over much larger areas than the ones that can be made provide an example of how to analyze historical data. As a using individual measurements like those from the Jacobson first step, the daily data is aggregated into monthly totals Farm gage. and the percentage of the yearly rainfall totals by month is computed (figure 4-1). This allows identifying the different Returning to the Jacobson Farm example, simple estimates homogeneous periods throughout the year. The data from of future rainfall conditions can be made given the average 46 Figure 4-2. Summary of Total Rainfall Change through Time at Jacobson Farm Gage (Illustrates how total rainfall, α, and λ have changed through time indicating a change to more intense infrequent rain events with the same annual total) Short Rainy Season Long Rainy Season p = 0.08 m = 0.57 p = 0.95 m = –0.04 600 600 Total Rain (mm) 400 400 200 200 0 0 1940 1960 1980 2000 1940 1960 1980 2000 p < 0.05 m = 0.061 p < 0.05 m = 0.062 25 25 Rain per Storm, α, (mm) 20 20 15 15 10 10 5 5 0 0 1940 1960 1980 2000 1940 1960 1980 2000 p < 0.05 m = –0.0024 p < 0.05 m = –0.0026 0.80 0.80 Inter−Storm Arrival, λ, (Day–1) 0.60 0.60 0.40 0.40 0.20 0.20 0 0 1940 1960 1980 2000 1940 1960 1980 2000 Year Year Data Linear Trend Source: Franz et al. 2010. Note: The estimation of α and λ was performed using daily data throughout the growing season. Thus, for each year, α and λ are calculated using the daily rainfall data of the growing season of that year. changes predicted by the GCMs. The ensemble of GCMs all of East Africa (figure 4-3). In addition, the ensemble of (SRES A1B scenario) predicts an increase of 0.5–0.6 GCMs predicts a change of 1.25–1.5 times the standard mm day–1 by 2080–2099 compared to 1980–1999 for deviation of inter-annual rainfall variability by 2080–2099 47 Figure 4-3. Ensemble Mean of GCM With this scenario, α would change from 10 mm in 1990 Models for Changes in Precipitation to 15.9 mm in 2090 and λ from 0.30 day–1 in 1990 to 0.223 day–1 in 2090. These results are consistent with (Total Precipitation and Precipitation Variability for 2080–2099 Compared to Conditions in 1980–1999) extrapolating the observed linear trends from the historical a) Total Precipitation data in figure 4-2. It is important to clarify that the use of GCMs in this context was only for the purpose of illustrating the methodologies presented using climate scenarios that have been considered in the literature. Thus, there is no assignment of probability of occurrence to these scenarios. The use of the scenario SRES A1B was only for illustrative purposes. In addition to the prediction of changes in mean and variability in rainfall, the 2007 IPCC report (Meehl et al., (mm day–1) 2007) provides a wealth of different climate parameters –0.3 –0.2 –0.1 0 0.1 0.2 0.3 0.4 0.5 –0.5 –0.4 that are predicted to change in the future around the globe. b) Precipitation Variability The range of test scenarios varies from business as usual to the best and worst case scenarios that scientists in this field can imagine. A critical remaining question is how these different scenarios at this larger global scale will manifest into the scales of individual ecosystems. Stochastic Soil Water Balance Model The interactions of climate, soil, and vegetation influence how water is partitioned in ecosystems. Dryland ecosystems are thought to be organized based on a tradeoff between (std. dev) –0.5 –1.25 –1 –0.75 –0.25 0 0.25 0.5 0.75 1 1.25 how much water is used for growth and reproduction Source: Meehl et al. 2007. (evapotranspiration) and the cost of survival (water stress). Figure 4-4 shows a simple representation of these interactions, a soil water balance framework that represents compared to 1980–1999 values for East Africa (figure 4-3). a single point in space. With these estimates, the total growing season rainfall, µp, would increase from 270 mm in 1990 to approximately 320 The model is driven by water inputs from the stochastic mm in 2090 (=270+90*0.55), and growing season rainfall representation of rainfall presented at the beginning of 2 variance, σ p , would increase from 5400 mm2 in 1990 to section IV-3. Because of the simplified framework, an approximately 10200 mm2 (=[1.375*(5400)0.5]2). The new analytical solution exists that describes the state of soil values of the parameters describing the dynamics of daily moisture over the growing season in probabilistic terms rainfall can be obtained by rearranging the equations for the (details given in Rodríguez-Iturbe and Porporato, 2004). growing season mean and variance Changes in temperature are included because they impact σ2 evapotranspiration. Regardless of the methodology chosen α = 2µp (4-1) to calculate evapotranspiration, temperature will play a role p that will change according to the value used in the analysis. and 2µ2 −γ s +λ ' ∫ du λ= p p(s ) = Ï?C e Ï? (u ) s ≥ sh (4-3) 2 σ pTseas (4-2) (s ) 48 Figure 4-4. Summary of Water Balance Figure 4-5. Examples of Probability Components for Stochastic Point Model Density Functions of Soil Moisture for Different Type of Soil, Soil Depth and Mean Rainfall Rate Shallow Soil Deep Soil a) b) 10 10 8 8 Dry Climate 6 6 p(s) 4 4 2 2 0 0 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 c) d) 10 10 Intermediate Climate 8 8 6 6 p(s) 4 4 2 2 0 0 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 e) f) 10 10 8 8 Wet Climate 6 6 p(s) 4 4 2 2 0 0 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 Source: Laio et al. 2001. Saturation Saturation Source: Laio et al., 2001. Note: Continuous lines refer to loamy sand soil and dashed lines refer to loam where p(s) is probability density function of soil moisture, soil. s, over the growing season; C is an integration constant; Ï?(s ) = χ (s ) nZ r )+L ( s ) = E (snZ is the expression for the normalized The solution also gives the different partitioning of the water r losses where E(s) (cm) is the evapotranspiration, L(s) balance averaged over the growing season at a point. The (cm) is the leakage out of the effective root zone Zr solution of the growing season water balance at a point is nZ (cm), and n (dimensionless) is the soil porosity, γ = α r ; summarized by Rodríguez-Iturbe and Porporato (2004) (see −∆ λ ' = λe α is the censored rainfall process by canopy annex IV). interception with the depth of individual storm interception as ∆(mm), and sh is the soil hygroscopic point. Figure 4-5 Finally, the solution is able to describe the frequency and illustrates different probability density functions (PDF) of number of times the daily soil moisture values cross certain soil moisture by changing soil, vegetation, and climate points that affect how the vegetation is using water and how model parameters. much stress the vegetation is under. The solution is simple but powerful, as it describes the The dynamic stress is a simple way to evaluate the overall range of conditions the plant experiences over the growing stress a plant feels over the growing season. Changes in season. Plants whose soil moisture remains low for most the rainfall patterns may lead to conditions that lower or of the growing season will experience severe stress that raise the average stress felt by the plant. Depending on will affect their survival. Changes in mean rainfall as well as the magnitude and direction of the change in stress, the changes in the rainfall dynamics may have serious impacts changes may be significant enough to shift ecosystem on the soil moisture PDF, shifting its location and shape to patterns. Because the future is uncertain, the power of this more favorable or unfavorable conditions. model is its simplicity, allowing the analyst to explore the 49 changes in water balance properties and stress over a wide in ecosystem structure needs to be further constrained by range of scenarios and different ecosystems. making an assumption about how different vegetation types compete and use available resources and survive times of Different types of problems require different lengths of record resource scarcity. The optimality tradeoff hypothesis (Caylor (e.g. estimation of mean flows vs. estimation of extreme et al., 2009) is used, which states that dryland vegetation discharges) even if the analyses are being conducted with the patterns are constrained by maximization of water use same basic type of hydrologic model. A question frequently and simultaneous minimization of water stress. In addition, asked in the case of the marked Poisson model used to the relative importance of water use versus avoidance of represent the statistical structure of daily precipitation relates water stress is not known, so these weightings are left to the required length of record to perform an adequate as calibrated model parameters. Model calibration is a estimation of µ and l. As always, there is no general specific standard technique, as parameters are often dependent answer to that question in the geophysical sciences. Both on the specific study site and need to be estimated to parameters represent estimates of mean values. Thus, l is the match observed patterns. Typically, hydrologic models are mean occurrence of rainy days during the growing season calibrated to match observed streamflow. Because the and µ is the mean depth of rain in a rainy day of the growing interest here is primarily in ecosystem structure, a different season. The goodness of the estimation will depend on the calibration technique to match the observed spatial pattern variability of the rainfall pattern during the growing season of vegetation is proposed. (in arrivals and depth of events) for a particular site. As a rule of thumb, 20 or more years (and even a somewhat shorter The selection of the most “fitâ€? vegetation species at a given historical series) will allow, in most cases, an acceptable point is defined by: estimation of α and λ (although obviously a much larger series will be needed to detect temporal changes in these Opt = find species n which is the maximum of Fn ,(4-4) parameters). As previously stated, a rough assessment of the goodness of estimation can be obtained by calculating where Opt is the optimal species selected by the maximum the variance of the series of λs (and αs) and dividing them value of the magnitude of the fitness vector F , for each by the number of years (e.g., growing seasons) since both α species n. and λ represent mean values. The standard deviation of the ( ) nE i + sθ (1− θ ) θ j (4-5) 〈E 〉 n estimates will thus provide a rough picture of the goodness of F = SE 〈R 〉 estimation of these two very important parameters. where i and j denote the components of the fitness vector related to water use and water stress respectively, Application to a Dryland Ecosystem in sE ,nE ,sθ , nθ and are calibrated weighting coefficients 〈E 〉 Central Kenya all greater than zero, 〈R 〉 is the seasonal fraction of total evapotranspiration from available rainfall, and θ is the The previous section presented a relatively simple but average dynamic water stress over the growing season powerful framework for studying ecosystem changes in defined in the previous section. The weighting coefficients 〈E 〉 drylands. This section provides an example of the utility n sEs,E ,En,E and s, s , n, n θ θθ θ scale the magnitude of 〈R 〉 and θ . The weighting 〈E 〉 of this framework for the pastoralist system of the central coefficients sEs ,n ,s ,n , n , n control the nonlinearity in 〈R 〉 and ,s and E E E θ θθ θ 〈E 〉 Kenya highlands, where a direct coupling exists between θ . Caylor et al. (2009) explains how to estimate 〈 R〉 and θ the composition of vegetation and human populations. as functions of climate, soil, and vegetation characteristics. Note that both components of the fitness vector are values Dryland Vegetation Patterns between 0 and 1 and are defined in terms of the primary modeled state variable of soil moisture. In order to estimate The stochastic soil water balance presented in the previous the weighting coefficients, the site-specific distribution of section provides a simple and flexible way to quantify vegetation and a non-gradient search algorithm are used to seasonal water balance change at a point due to random maximize the agreement between observed vegetation and inputs of precipitation. However, the problem of changes modeled vegetation patterns. 50 Figure 4-6. Study Area Map of Central Model Calibration Kenyan Highlands In order to illustrate the utility of the methodology, the calibration is performed using the heterogeneous Upper Ewaso Ng’iro River Basin (15,200 km2) as a case study (Franz et al., 2010) (see figure 4-6). The Upper Ewaso Ng’iro River Basin spans gradients of elevation, temperature, and precipitation, and contains eight different soil texture classes (figure 4-7). The basin is a typical savanna ecosystem with woody vegetation (mostly Acacia) and grasses (figure 4-7c). In this analysis, the focus is on the 60 percent of the basin dominated by three Acacia species: A. drepanolobium “whistling thornâ€?, A. tortilis “umbrella thornâ€?, and A. xanthophloea “yellow-bark thorn.â€? These species were chosen because they represent a diversity of water use strategies and each occurs across a wide range of the basin. Moreover, these species are described in prior studies (for example, in Scholes and Walker, 1993) so their water use characteristics are well-known. Acacia drepanolobium is the dominant species on the black cotton clay soils and has been characterized as having a shallow wide spreading root system with a tap root. Acacia tortilis is a drought tolerant species and has a deep tap root, lifting water hydraulically from deep sources. The most geographically diverse species is A. xanthophloea, which occurs in riparian, upland clays, and a few select dry sandy areas. Source: Franz et al., 2010. Note: The figure illustrates the steep elevation gradient, Upper Ewaso Ng’iro The summary of soil, climate, and vegetation parameters River watershed boundary (15,200 km2) (red line), Laikipia District boundary are provided in figures 4-7 and 4-8 (more details are given (black line), and daily precipitation gauges organized by record length. in Franz et al., 2010). With this information it is possible to perform the basin-wide calculations describing the seasonal Figure 4-9 illustrates an example of the importance of A. tortilis water balance and average plant water stress presented in in these dryland pastoralist communities. The photograph was the previous section. The remaining areas (approximately 40 taken in July 2006 at Koija Group Ranch, Kenya, where no percent) of grass, shrubland, and woody vegetation are not rainfall had occurred over an 18-month period. The herder is included. shaking out the nutritious A. tortilis pods for his malnourished goats, given the lack of available ground forage. As for the More importantly, the composition of woody species other modeled species, Acacia xanthophloea provides an provides different nutritional value for livestock and wildlife, excellent source of pole timber and forage locations for bee which directly affects human populations (Fratkin et keeping operations (Dharani, 2006). Acacia drepanolobium al., 2004). Given the recent political history toward the provides edible fruit and the bark is used for sore throats and sedentarization of pastoralist societies, shifts in species as a diuretic for women after childbirth (Dharani, 2006). ranges can adversely affect human milk consumption, traditional medicine, and cultural activities. For example, As mentioned in the previous section, the rainfall patterns Acacia tortilis pods have been found to have high nutritional in this basin are changing in time toward more intense and value and the red bark is important for traditional initiation infrequent rain events. This observation is supported by the ceremonies (Dharani, 2006). historical rain gauge data and predictions by global climate 51 change models. Because each of the 60 individual gauges necessarily overlap, it was necessary to develop a method has a different length of record and all gauge data do not to describe average basin conditions and how they change over time. In order to maximize the amount of data used to Figure 4-7. The Upper Ewaso Ng’iro describe the average rainfall conditions in the basin, the River Basin, a Heterogeneous long-term averages α and λ were assumed to approximate Landscape the conditions in 1975 (midpoint of all precipitation data neglecting stations with record lengths less than 10 years). a) MAP (mm/yr) In addition, an estimate of the average basin change in time for α and λ can be made by taking the average values of the slopes from the individual rain gauges. Using stations with a minimum record length of 40 years (stations with shorter record lengths typically do not contain enough data to provide a robust statistical estimate and were neglected), the average linear slopes for α = 0.04 mm yr–1 and λ = –0.0018 day–1 yr–1 were found. Note that the trends for the Jacobson Farm gauge presented in the previous section are nearly double these values. Assuming the rainfall patterns of the entire basin are b) Soil Type similarly changing and the long-term average values of α and λ represent the conditions in 1975, an estimate of the average basin rainfall conditions throughout the period of record can be made using the linear slope estimates of α and λ. Due to the time lag for trees to reach maturity, the calibration of the fitness vector weighting coefficients was performed between the modeled species with 1950 rainfall parameters and the observed vegetation. The results of the calibration are presented in figure 4-10 (the comparison was visual and no attempt was made to do it otherwise due to resource and c) Observed Cover time limitations). After calibration, the performance of the model versus observed species cover provided a match of 78.7 percent of the total area covered by the three species.7 For the individual species the match was 89.4 percent for A. drepanolobium, 46 percent for A. tortilis, and 57.7 percent for A. xanthophloea. Figure 4-10 also provides the modeled species cover for different average rainfall conditions throughout the period of record, and one example with rainfall extrapolated into the future. The changes in rainfall patterns indicate that the more drought tolerant A. tortilis expands its territory while the territory of the most intense water user, A. xanthophloea, retreats. Source: Franz et al., 2010. a) Driven by the changes in elevation, there are steep gradients in mean an- nual precipitation (MAP) and contours of the coefficient of variation of annual For the Upper Ewaso Ng’iro River Basin, the calibrated rainfall (mean divided by standard deviation). b) The study area contains a wide range of soil texture classes from clay to nE sθ nθ fitness vector weighting coefficients resulted in sE =1, sandy soils. s nθ nE sθ =0.447, sE nE =0.451, sθ ns n s and θE E θ θ n =0.700. It was found that c) The ecosystem is a classical tree-grass savanna with a diversity of around E 10 acacia tree species, some dominant and others coexisting in areas. instead of being equal, the relative values of sEsEn n s s nn and EE θθθθ 7. Real land cover data was used. These data is required for the calibration and is generally available from satellite information. 52 Figure 4-8. Basin Growing Season Climate a) Temperature (Deg. C) b) Rnet (watts/m^2/day) c) Inter-Storm Arrival, λ (1/day) d) Rain per Storm, α (mm) Note: Climatic forcing is used to drive the water balance model presented in the previous section. Gage data for air temperature, Ta (°C) (a) and pan evaporation, Epan (mm day–1) were found to be linearly correlated with elevation. Net radiation, Rnet (W m–2 day–1) (b) was estimated from pan evaporation using the Penman- Combination equation and is used in determining maximum evapotranspiration, Emax (mm day–1). Average arrival rate of storm events, λ (day–1) (c), and average rain per storm, a (mm) (d), were estimated with ordinary kriging of the long-term averages of the gage data (n = 60) (data source NRM3 of Nanyuki, Kenya). Precipitation and temperature data were assembled using geostatistical techniques to interpolate the value at an unobserved location from observations of its value at nearby locations (kriging methodologies). A detailed description of data sources of different types is found in Franz et al. (2010). are such that fractional evapotranspiration from available factor in determining overall fitness when stress values are rainfall (equation 4-5 component i weighted by sE )nis s n E θ θ close to one because of its representation in equation 4-3 more important (that is, is weighted more heavily) than the as one minus dynamic water stress. dynamic water stress (equation 4-5 component j weighted sE n by s ) E θ θ nwhen determining species fitness. The magnitude The magnitude of the calibrated fitness vector illustrates the of these coefficients provides insight into the relative greater weighting due to fractional evapotranspiration from importance and degree of sensitivity that each fitness vector available rainfall than that corresponding to dynamic water component has on species distribution. Specifically, the stress. It is acknowledged that assigning global weighting relative importance of water use and stress occurrence coefficients downplays the possibility that individual species are given by the relative magnitude of sE sEn n s s n,nwhile the and EE θθθθ have their own specific fitness vector that allows them to degree of nonlinearity between each of these two terms and occupy specific niches. However, the fact that the used nEnE sEsE their effect on total fitness is described by s sn n . In the and θ θθ θ framework includes consideration of both water use and case s of n , s E E θ θ a n value less than one indicates that increasing water stress allows the use of a single representation of amounts of water use are less and less important for fitness to determine regional patterns of where species determining total fitness. In contrast, the sfact s n is less n that E E θ θ exist in the basin, even if the individual species have unique than one indicates that stress only becomes an important strategies of water use and stress avoidance. 53 Figure 4-9. Herders in Upper Ewaso Ng’iro River Basin of Central Kenya Following 18-months without rainfall, the Koija Group Ranch herder of central Kenya shakes out the nutritious A. tortilis pods to provide a much-needed meal for his goats. Photograph taken by T. Franz in July 2006. Modeled Changes in Species Patterns A. tortilis’s fractional cover slightly increases while A. Due to Changing Rainfall Mean and xanthophloea’s fractional cover decreases (figures 4-11a, Variability b, e, and f). The opposite patterns were found when moving away from the current rainfall toward either increasing µp The advantage of the relatively simple modeling framework or increasing σ2p (figures 4-11c, d, g, and h). Over most is that it allows testing a wide variety of scenarios to parts of the simulation range, A. drepanolobium remains understand the general behavior of ecosystem response the dominant species in the basin. The changing relative to perturbations in seasonal rainfall patterns. As a simple distribution of A. xanthophloea and A. tortilis is due to the and informative experiment, a look is taken at the changes separate effects of changing rainfall on evapotranspiration in ecosystem structure due to changes in mean rainfall, µp, and stress. while holding rainfall variability, σ2p, constant and vice versa. Figures 4-11 and 4-12 present the modeled changes and The model results suggest that the magnitude of shifts in specific test scenarios. species cover due to changing µp and σ2p are comparable. As either µp decreases (with σ2p held constant) or σ2p It was found that the response of species patterns and increases (with µp held constant), storms become more fractional cover are similar when changing the mean and intense and less frequent (figure 4-12). Initially, these variance of rainfall, but that these responses are opposite larger storm depths lead to deeper infiltration fronts, but in direction with respect to the frequency and intensity the reduction in storm frequency still causes average soil of rainfall. Moving away from the current rainfall toward moisture values over the growing season to be lower. either decreasing µp or decreasing σ2p, it was found that Overall, these changes lead to higher fractional water use 54 Figure 4-10. Basin Changes in Species Figure 4-11. Range of Shifts in Basin Composition with Time Species Composition a) Average Basin Rainfall from 1950 d) 2025 a) e) b) 1975 e) Observed Patterns b) f) c) 2000 c) g) A. drepanolobium A. tortilis A. xanthophloea Other (not modeled) d) h) Source: Franz et al., 2010. Note: Model results of woody species distribution patterns throughout the period of record and extrapolated into the future. The calibration results matching modeled “a)â€? and observed land cover “e)â€? are 78.7 percent for the total area, and by individual species: 89.4 percent for A. drepanolobium, 46 percent for A. tortilis, and 57.7 percent for A. xanthophloea. relative to total rainfall, but the reduction in soil moisture causes greater stress values. Because water use is weighted more heavily to total fitness, when either the A. drepanolobium average rainfall declines or the variance in growing season rainfall increases, species that are able to maximize water A. tortilis use will have higher fitness. This is demonstrated by the example of A. tortilis, using a location from the northern A. xanthophloea portion of the basin, where rainfall is low and A. tortilis is currently dominant because the stress values of A. Other (not modeled) xanthophloea and A. drepanolobium are high (figure 4-13). Although decreases in mean growing season rainfall lead to Source: Franz et al., 2010. Note: Model results of woody species distribution patterns using rainfall dramatic increases in A. tortilis’s water stress, overall it still parameters, α and λ: is able to maintain a lower stress value than the other two • Varying μpwhile holding σ2p constant (a-d) • Varying σ2p while holding μp constant (e-h) species, which exhibit chronic water stress across all values • Increases in either σ2p or μp lead to greater extent of A. xanthophloea (c, d, g, h of average rainfall (figure 4-13b). Therefore, the modest • Decreases in either σ2p or μp lead to greater extent of A. tortilis (a, b, e, f) Specific rainfall parameter estimates, α, λ, σ2p and μp, for each case can be increase in relative water use by A. tortilis (figure 4-13a) found in Figure 4-12 when rainfall is lowered is sufficient to allow it to remain 55 Figure 4-12. Range of Shifts in Fractional Species Abundance a b c d e f g h 1.0 1.0 0.15  0.9 0.9 0.10 incre 0.8 0.8 Fractional Species Cover Fractional Species Cover Basin change in λ (day–1) 0.7 0.7 . mea 0.05 0.6 0.6 n 0.5 0.5 inc 0 re. 0.4 0.4 va r. 0.3 0.3 –0.05  0.2 0.2 0.1 0.1 –0.1 0 0 400 450 500 550 600 80 90 100 110 120 –6 –4 –2 0 2 4 6 Basin μp (mm), Constant σp Basin σp (mm), Constant μp Basin change in α (mm) A. drepanolobium A. tortilis A. xanthophloea Basin Average Constant σp Constant μp Source: Franz et al., 2010. Note: Model sensitivity study of species fractional cover in the basin under changing σ2p or µp while holding the other parameter constant. The change in species fractional cover is comparable, but inversely related. Rainstorms become more intense and less frequent for the two cases of changing µp or σ2p while holding the other constant, but the direction of the changes is opposite. Specific species distribution patterns in the basin are illustrated in figure 4-11 and 4-10 (where the 1975 rainfall is defined as the long-term average of rainfall gage data). the dominant species under the lower mean total rainfall this modeling framework are more complex than a scenarios (figure 4-13c). However, when µp is increased deterministic treatment of rainfall, the estimation (with σ2p held constant), despite further reductions in water of the mean random variables that control the daily stress (figure 4-13b), lower relative water use (figure 4-13a) rainfall process is simple. causes A. tortilis to be replaced by species capable of using greater amounts of soil moisture (A. drepanilobium). With a daily record of rainfall, the parameters a (mean storm depth) and λ (mean arrival rate of storm events, i.e. There are still critical areas that need to be the subject number of days with rain over length of season) can be of extensive research in these analyses. One of the easily determined as presented in the previous section. most important findings is the relative relevance and In addition, the simplistic marked Poisson point process degree of sensitivity that each vector plays in the overall model allows for the estimation of the mean and variance of species determination. Sensitivity analysis is important to the seasonal rainfall over which a and λ are defined. With evaluate the relative importance of the parameters and the estimates about future rainfall scenarios (such as the GCM accompanying estimation uncertainties in the results. This predictions presented in the previous section), new a and λ is not a trivial matter given the complexity of the situations values can be estimated. The new a and λ values can then being researched. However, these fall outside of the scope be run through the modeling framework to find changes in of this report due to resource and time limitations. the ecosystem structure. The same approach can be used in the estimation of the different components of the water Summary of Procedure balance of a basin as described in Rodríguez-Iturbe and Porporato (2004). Even though the framework was constructed for the central Kenyan highlands, it is believed to be applicable to drylands around the world where Application to Humid Ecosystems rainfall is the main driving mechanism in vegetation (Everglades National Park, USA) response. The key to the success of this framework was the realistic treatment of rainfall in drylands The objective of this case study is to provide an by a stochastic process. While the mechanics of example illustrating the key variables that need to be 56 Figure 4-13. Resource Use versus Resource Scarcity a) d) 1.0 1.0 Fractional evapotranspiration from 0.8 0.8 available rainfall (a and d)  〈E 〉  0.6 0.6    〈R 〉  0.4 0.4 0.2 0.2 0 0 400 450 500 550 600 85 90 95 100 105 110 115 120 b) e) 1.0 1.0 Dynamic water stress (b and e) 0.8 0.8 0.6 0.6 θ 0.4 0.4 0.2 0.2 0 0 400 450 500 550 600 85 90 95 100 105 110 115 120 c) f) Magnitude of the ï¬?tness 1.00 1.00 vector (c and f) 0.98 0.98 F 0.96 0.96 0.94 0.94 0.92 0.92 0 0 400 450 500 550 600 85 90 95 100 105 110 115 120 μp σp Source: Franz et al., 2010. A. drepanolobium A. tortilis A. xanthophloea Basin Average Note: Model results for one point in the northern portion of the basin, which is currently dominated by the drought tolerant species A. tortilis. The sensitivity of the system is tested by varying µp, while holding σ2p constant, and by varying σ2p while holding constant µp. studied in humid regions, the changes to be expected variables that need to be described probabilistically. Such as a result of different climate change scenarios, and a characterization is quite challenging because in contrast the corresponding data requirements. to arid regions where the water table plays a negligible role, hydroperiods of wetlands are a result of water table Wetlands present their own challenges in regard to the fluctuations that frequently go above the ground level. The impact of changing hydrologic conditions associated with stochastic fluctuations of the water table are driven by the ongoing and likely alterations in their climatic regime. In random arrivals in time and quantity of the rainfall events many wetlands, especially those in tropical climates, a most interacting with the soil and vegetation characteristics of important characteristic driving the spatial distribution of the site in question. Thus vegetation is both a cause and vegetation and its diversity is that of the hydroperiods of the result of the water table fluctuations. Approximate models region. Hydroperiods are loosely defined as those intervals have been recently developed to obtain the probability where there is standing water in the ground. However, this distribution of water table fluctuations and thus that of the loose definition needs to be quantitatively framed around hydroperiods (Tamea et al., 2010). three key features of hydroperiods: their frequency of occurrence, their duration, and the depth of the standing The impact of hydroperiods on the vegetation of water. These three characteristics are themselves random wetlands can be seen in figure 4-14 from Todd et al. 57 (2010). As an example, figures 4-14 and 4-15 show average depth increases (keeping constant the mean two types of vegetation (sawgrass and muhly grass) seasonal rainfall over the region). In this example only according to their dependence of the percentage of the depth of water above ground has been plotted time that a site is inundated. The y-axis is the relative (hydroperiod). Thus, the percentage of time the site is abundance of the species being considered in those under water is just the integral of the functions shown in cells that are inundated a percentage of time, as given figure 4-16. in the x-axis of the figures. The green line represents the average coverage of the species over the entire The three graphs in Figure 4-16 show the changes in landscape. the probability distribution function (PDF) of water depth above the ground when the frequency and average depth It can be observed that sawgrass is indeed quite resilient to of the rainy days is changed but the total rainfall during the amount of time a site is inundated. The opposite is true the growing season is kept constant. Although the total for muhly grass, which is very sensitive to this hydroperiod rain is the same, the PDF displays a much more wet characteristic and is almost not present in sites of the character when the rate of arrivals of rainy days is greater, Everglades where inundation occurs for over 50 percent of and moves toward a much drier character when the rate the time. of arrivals is decreased and the average depth on a rainy day is increased. Total rainfall is not only important for the Scenarios of climate change and how they impact hydrologic dynamics of wetlands but it is also crucial to the hydrologic dynamics of wetlands can now be incorporate the temporal structure of arrivals of rainy events implemented specifying the new rate of arrival of rainy and their average depth. Moreover, the impact of changes days and the average depth of those rainy days. These in climate will be mainly felt through these two hydrologic two simple parameters interacting with the vegetation characteristics. and soil characteristics will yield a new probability distribution for water table fluctuations, and consequently, Once the changes in the statistical properties of for the stochastic structure of the hydroperiods of the hydroperiods is made, an attempt can be made to relate wetland. Figure 4-16 shows an example of how the these to the impact they will have on the occurrence of distribution of the depth of hydroperiods changes when different types of vegetation as seen earlier in figures 4-14 the rate of arrivals of rainy events decreases and their and 4-15. Figure 4-14. Existence of Sawgrass Depending on the Time a Site is Inundated PGc – Percent Wet 0.90 0.80 0.70 0.60 0.50 0.40 0.30 Legend 0.20 Sawgrass Percent Wet 0.10 High: 100 0 Low: 0 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 Kilometers 0 5 10 20 % Time Cell Inundated Source: Todd et al., 2010. 58 Figure 4-15. Existence of Muhly Grass Depending on the Time a Site is Inundated PGm – Percent Wet 0.25 0.20 0.15 0.10 Legend Muhly Grass 0.05 Percent Wet High: 100 Low: 0 0 Kilometers 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 0 5 10 20 % Time Cell Inundated Source: Todd et al., 2010. figure 4-4), the interactions with the water table require a more Wetland Vegetation Patterns complex modeling framework of the physical mechanisms governing system dynamics (Laio et al., 2009). Here, the The main difference between wetlands and drylands is the annual movement up and down of the water table impacts availability of water. This includes both more rainfall arriving the growth, reproduction, and survival of vegetation species at the surface and the presence of a water table near or that are present at a given location. As opposed to drylands, above the ground surface. Figure 4-17 illustrates the various the ubiquity of available plant water does not limit growth in processes influencing the plant’s available water in the soil root wetlands. To the contrary, extended periods of elevated water zone. In comparison with the dryland water balance model (see tables will lead to anoxic conditions and potential mortality. Figure 4-16. Changes in the Probability Density Function of Water Depth above the Ground 0.04 0.04 0.04 0.03 0.03 0.03 0.02 0.02 0.02 0.01 0.01 0.01 0 0 0 0 20 40 60 80 0 20 40 80 0 20 40 60 80 y, Water Level Above Ground (cm) y, Water Level Above Ground (cm) y, Water Level Above Ground (cm) Wet Dry Source: Todd et al., 2010. Note: When keeping the average total seasonal rainfall the same but decreasing the rate of arrival of rainy events and increasing their average depth. Parameters of soil and vegetation are similar to those in some sites of the Everglades. 59 Figure 4-17. Wetland Water Balance Model Source: Laio et al. 2009. However, the flow of water redistributes nutrients, which do are roughly half that size with a portion found within the limit vegetation growth and reproduction in these systems. Everglades National Park (figure 4-18). The 5,700 km2 Like drylands, a tradeoff exists in the organization of wetland park was established in 1947 and contains a mosaic of vegetation between accessing limiting resources while mitigating the costs of extended periods of stress. Figure 4-18 Location of Everglades Modeling Vegetation Patterns in the National Park Everglades National Park A stochastic modeling framework was developed for describing the probabilistic structure of the daily fluctuations of the water table in wetland ecosystems following the same line of thought as the dryland water balance model (Laio et al., 2009; Tamea et al., 2009). As described in the previous section, the water table fluctuations impact growth, reproduction, and survival by affecting access to the limiting resource of nutrients while avoiding extended periods of stress. This framework has been applied to the diverse and extensive vegetation community of the Everglades National Park (ENP) (Todd et al., 2010; Todd et al., 2011). The Everglades historically encompassed an area of over 10,000 km2 in South Florida. Today, the Everglades Source: Todd et al., 2011. 60 different vegetative communities. In total, the park has at forest, scrub, savanna, prairies and marshes, shrublands, least 830 different vegetation species. Prior to the 1900s, exotics, additional class headings, and special modifier. The the Everglades were a broad, slowly flowing (velocities less dominant vegetation community is identified at the spatial than 1 cm s−1) wetland originating at Lake Okeechobee resolution of 20×20 m resulting in over 5 million pixels for and flowing southward toward the Gulf of Mexico. Today, the ENP. The percent coverage of the dominant species is the Everglades are a hydrologically altered landscape due summarized in table 4-2. to human action and drainage. The flow of water in the Everglades is controlled by an extensive system of levees, By analyzing the extensive vegetation and hydroperiod pumps, and canals. datasets, Todd et al. (2010a) found that the hydroperiod descriptions of mean water depth and percent time A consensus exists that hydroperiods (e.g. time periods inundated provide an accurate and simple way to partition during which standing water is present) are a key factor the different vegetation communities. For example, the in determining the composition of vegetation and its relative abundance of three vegetation communities is spatial structure in wetlands. What has been lacking is a provided in figure 4-20. The figure illustrates that muhly quantitative description of the statistical characteristics grass prefers shallow water that is not inundated throughout necessary for adequately describing them. the year, whereas bay-hardwood scrub prefers deeper areas that are almost always inundated. These two metrics The Everglades Depth Estimation Network (EDEN) is an were combined into a joint probability surface of the relative extensive daily water level dataset (beginning in 2000) frequency of all vegetation pixels across the Everglades for the ENP (Conrads et al., 2007). Water surface level National Park (figure 4-21). The figure illustrates both data are generated into 400×400 m grid cells by using wide and narrow regions of these two metrics. The narrow monitoring well information and calibration functions. The regions indicate areas where the correlation between generation of such information was done using kriging these metrics and the vegetation community is strong and methodologies. Todd et al. (2011) used the EDEN dataset the wide range indicates the areas where the correlation to calculate four hydrologic measures at each 400×400 m is weak. In general, the joint probability surface provides pixel: number of hydroperiods per year, conditional mean depth (cm), mean duration of a hydroperiod, and percentage Table 4-1. Percent Coverage of of time inundated (figure 4-19). Dominating Vegetation Types (Only vegetation with at least 1% As defined by the analysis, a hydroperiod is an individual coverage was reported) inundation episode (that is, a single wetting-drying cycle). For a given pixel, those sections of the water level time series that Vegetation type % Coverage did not constitute a complete hydroperiod (that is, where depth Sawgrass 60.7 does not recross depth = 0 cm) were omitted. Conditional Mixed Graminoids 6.5 mean depth is the mean depth of all inundated days (depth Tall Sawgrass 5.8 > 0). Mean duration of a hydroperiod is the average length of Muhly Grass 4.1 time in days for a hydroperiod. Percentage of time inundated is Spike Rush 3.0 the number of days where there is standing water (depth > 0) Red Mangrove Scrub 2.2 divided by the total number of days. Bayhead 1.7 Because of the diverse vegetation communities that exist Pine Savanna 1.6 in the everglades, a detailed map was developed by the Willow Shrublands 1.5 Center for Remote Sensing and Mapping Science at Dwarf Cypress 1.5 the University of Georgia and the South Florida Natural Bay-Hardwood Scrub 1.4 Resources Center. Given the very large number of individual Brazilian Pepper 1.2 species, techniques were developed that reclassified the Cattail Marsh 1.1 species into 79 plant communities in 8 vegetation types: Source: Todd et al., 2010. 61 Figure 4-19. Summary of Hydroperiods for the Everglades National Park Spatial Distribution across the Everglades National Park of: a) Number of Hydroperiods per Year b) Mean Depth High: 52.1 High: 52.1 Low: 0 Low: 0 c) Mean Duration per Hydroperiod d) Percent Time Inundated High: 52.1 High: 52.1 Low: 0 Low: 0 Source: Todd et al., 2010a. a simple and strong relationship between the vegetation Figure 4-20 illustrates the relative abundance, mean depth, community and hydroperiod descriptive variables. This percent time inundated, and spatial distribution for three simple relationship was utilized to link future changes in vegetation communities in the Everglades National Park. climatology with changes in the vegetation community and The green line indicates the mean relative abundance of is described further in the next section. each species (see table 4-2) (Todd et al., 2010). 62 Figure 4-20. Hydroperiod Descriptions of Different Vegetation Communities a) Muhly Grass 0.35 0.25 0.30 Relative Abundance Relative Abundance 0.20 0.25 0.20 0.15 0.15 0.10 N 0.10 0 5 10 20 km 0.05 0.05 0 0 0 10 20 30 40 50 60 70 80 90 100 6 0 12 18 30 36 42 48 54 60 66 72 78 24 84 90 96 102 Mean Depth (cm) Percent Time Inundated b) Bay-Hardwood Scrub 0.25 0.08 0.07 Relative Abundance Relative Abundance 0.20 0.06 0.15 0.05 0.04 0.10 0.03 0 5 10 20 N 0.02 km 0.05 0.01 0 0 0 10 20 30 40 50 60 70 80 90 100 6 0 12 18 30 36 42 48 54 60 66 72 78 24 84 90 96 102 Mean Depth (cm) Percent Time Inundated c) Sawgrass 1.00 1.00 Relative Abundance Relative Abundance 0.80 0.80 0.60 0.60 0.40 0.40 0 5 10 20 N km 0.20 0.20 0 0 0 10 20 30 40 50 60 70 80 90 100 6 0 12 18 30 36 42 48 54 60 66 72 78 24 84 90 96 102 Mean Depth (cm) Percent Time Inundated Source: Todd et al., 2010. Likelihood of Future Changes in the arrival rate of storms (rainy days) and a is the mean depth Vegetation Community of the Everglades of storms (the amount of rain on a rainy day). Using 12 National Park stations and 15 years of data from the Everglades National Park (ENP), Todd et al. (2011) found the average annual Like the previous example in dryland ecosystems, rainfall a = 11.89 mm and λ = 0.33 day–1. In addition, a second is characterized by a Poisson process where λ is the gridded meteorological dataset was utilized to better 63 Figure 4-21. Joint Probability Surface from the remainder of the analysis. With the calibrated of Percent Time Inundated and Mean parameters, the model was rerun with the scenario of Depth future changes in future rainfall given in figures 4-22 and 4-23. The resulting changes in mean water depth and time 100 0.016 inundated are presented in figures 4-24 and 4-25. The 90 0.014 future decreases in MAP lead to lower mean water depths 80 and percent time inundated summarized in figure 4-26. 0.012 70 The corresponding present and future joint probability Mean Depth (cm) 60 0.01 surfaces of percent time inundated and mean depths are illustrated in figure 4-27. 50 0.008 40 0.006 As already depicted using the high-resolution vegetation 30 0.004 dataset, Todd et al. (2010) described the present 20 distribution and relative abundance of each vegetation 0.002 10 community for each hydrologic class composed of mean 0 0 depth and percent time inundated. Using this relationship, 0 10 20 30 40 50 60 70 80 90 100 Percent Time Inundated (%) future estimates of the vegetation community can be estimated by shifts in the joint probability surfaces given in Source: Todd et al., 2010. Note: The value of each pixel represents the relative frequency among all pix- figure 4-27. els across the Everglades National Park. The surface provides a way to easily connect hydroperiod descriptions with the associated vegetation community. With the assumptions described above, the changes in the vegetation community between the present and high characterize the historical spatial structure of rainfall emissions scenario are summarized in table 4-2, which events. By setting a to a constant value, the more sensitive shows that sawgrass is predicted to remain the most parameter λ was allowed to vary spatially across the ENP. abundant species, but that its territory will be reduced from Future estimates of mean annual precipitation (MAP) for 60.7 to 55.2 percent. 2049–2099 were characterized by the average estimates of 16 different modeling groups for high, middle, and low It is noted that these analyses are made without emissions scenarios (IPCC, 2007). The corresponding considering future changes in sea level or anthropogenic MAP and λ values for the present and different future rainfall changes in the vegetation-hydrologic interactions. In reality, scenarios are illustrated in figures 4-22 and 4-23 (under the change of vegetation at a particular location is likely the scenario that a remains constant). The figures illustrate dependent on habitat fragmentation, vegetation dispersal that rainfall total and arrival rates increase in a northeastern characteristics, soil and nutrient characteristics, and direction and decrease in MAP with different future emission competition dynamics. scenarios. While the changes in future vegetation types are less With the detailed description of rainfall, Todd et al. (2011) understood by this procedure, the impact to distinctive used a stochastic modeling framework to describe the landscape features are more likely to be identified. In movement of the water table across the ENP. A summary particular changes to the Taylor and Shark River Sloughs of the model is provided in annex V. Here, the two are pronounced with the different climate scenarios. The model parameters (LG and k) that control water loss river sloughs can be clearly seen in figure 4-25a in the due to evapotranspiration and lateral surface flow were southeast side of the image where each channel connects calibrated to match the annual changes in the water table. the northern and southern half of the Everglades. These Following calibration, the model was able to recreate corridors, which contain the unique tree islands of the the annual water table dynamics with an error of less ENP, are vitally important for exchanging nutrients and than 5 percent in 95 percent of all pixels in the ENP. The linking vegetation communities, and have been extensively areas with an error greater than 5 percent were omitted studied. The impact of future rainfall scenarios on the 64 Figure 4-22. Present and Future Mean Annual Rainfall in the Everglades National Park Illustrating a Decrease in MAP with Time a) Present Rainfall Conditions b) Estimates of Rainfall in 2049–2099 for Low Emissions Scenarios c) Estimates of Rainfall in 2049–2099 for Medium Emissions Scenarios d) Estimates of Rainfall in 2049–2099 for High Emissions Scenarios Low: 1150 High: 1570 mm Mean Annual Precipitation Source: Todd et al., 2011. percent time inundated shown in figures 4-25 b-d, clearly everglades will be affected by the shifts in the composition illustrates the potentially devastating effects on the of the vegetation. A great deal of effort and money has structure of the ecosystem of eliminating these corridors. been expended to return the Everglades to its historical Given the resulting changes to drier hydroperiods, hydrologic and vegetation conditions. The results of Todd vegetation conditions that are adapted to more xeric et al. (2010) suggest that future restoration efforts must conditions are likely to become more numerous. explicitly take into account the forecasted influences of Correspondingly, the unique and diverse wildlife of the climate change. 65 Figure 4-23. Present and Future Storm Arrival Rates in Everglades National Park a) Present Rainfall Conditions b) Estimates of Rainfall in 2049–2099 for Low Emissions Scenarios c) Estimates of Rainfall in 2049–2099 for Medium Emissions Scenarios d) Estimates of Rainfall in 2049–2099 for High Emissions Scenarios Low: 0.26 High: 0.36 day–1 Lambda (λ) Source: Todd et al., 2011. Final Comments The impact of changes in rainfall variability and changes in total rainfall on dryland woody vegetation patterns and This section presented a relatively simple framework to relative abundance are comparable, but inversely related. understand and predict ecosystem changes due to climate Along the gradient of increasing variance with a constant change in drylands and wetlands. mean growing season rainfall, the model predicts the expansion of the riparian species A. xanthophloea, which takes advantage of its higher transpiration rates. However, 66 Figure 4-24. Present and Future Modeled Mean Water Depths in Everglades National Park a) Present Water Depths b) Model Predictions with 2049–2099 Low Emissions Scenarios c) Model Predictions with 2049–2099 Medium Emissions Scenarios d) Model Predictions with 2049–2099 High Emissions Scenarios Low: 0 High: 102.1 cm Mean Depth Source: Todd et al., 2011. as the rainfall regime approaches the lower extremes of of the southwestern United States woody riverine species decreasing rainfall variability, the range of the most drought have been replaced by more drought tolerant species tolerant species A. tortilis expands. The expansion and such as Tamarix ramosissima (Cleverly et al., 1997). contraction of riparian and drought tolerant species is a These changes have occurred over a period during which major concern of many drylands around the world (Busch observations of rainfall have shown a shift toward more et al., 1995; Huxman et al., 2005). For example, in much frequent, less intense storms (Fu et al., 2006). The results, 67 Figure 4-25. Present and Future Modeled Percent Time Inundated in Everglades National Park a) Present Percent Time Inundated b) Model Predictions with 2049–2099 Low Emissions Scenarios c) Model Predictions with 2049–2099 Medium Emissions Scenarios d) Model Predictions with 2049–2099 High Emissions Scenarios Low: 0 High: 100% Percent Time Inundated Source: Todd et al., 2011. therefore, provide a theoretical context for prior studies both the expansion and the contraction of the drought that have linked the expansion of invasive drought-tolerant tolerant species, A. tortilis, in the basin studied depending species in the desert southwest of the United States to on the nature of changing rainfall scenarios. Changes in altered rainfall climatology (Zavaleta et al., 2002). As an the spatial distribution of keystone species like A. tortilis example, the model used in the Kenya case study predicts will have adverse consequences on human diets, traditional 68 Figure 4-26. Change in Hydroperiods for the Everglades National Park a) Changes in Mean Depth b) Changes in Percent Time Inundated 0.40 0.25 0.35 Relative Abundance Relative Abundance 0.20 0.30 0.25 0.15 0.20 0.15 0.10 0.10 0.05 0.05 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 Mean Depth (cm) Percent Time Inundated (%) Present Hign Future Emissions Scenario Source: Todd et al., 2011. Figure 4-27. Joint Probability Surfaces of Percent Time Inundated and Mean Depth Model Predictions with 2049–2099 Low b)  a) Present Emissions Scenarios 105 105 90 90 75 75 60 60 45 45 0.08 30 30 15 15 Mean Depth (cm) 0 0 0.06 0 20 40 60 80 100 0 20 40 60 80 100 Model Predictions with 2049–2099 Medium c)  Model Predictions with 2049–2099 High d)  Emissions Scenarios Emissions Scenarios 105 105 0.04 90 90 75 75 0.02 60 60 45 45 30 30 0 15 15 0 0 0 20 40 60 80 100 0 20 40 60 80 100 Percent Time Inundated (%) Source: Todd et al., 2011. medicine, and cultural activities if replaced by undesirable of pastoralist populations (Fratkin et al., 2004), the species that are more suited to the new climatic conditions. sustainability of this central Kenya pastoralist community Given the recent political trend toward the sedentarization may be in serious jeopardy. 69 Table 4-2. Percent Coverage and Relative Percent Change of Dominant Vegetation Types Between Present and High Future Emissions Scenarios for Everglades National Park Percent Cover Community Type Present High Relative Percent Change Sawgrass 60.68 55.21 –9.0 Mixed Graminoids 6.55 8.82 34.7 Tall Sawgrass 5.80 2.24 –61.4 Muhly Grass 4.07 10.25 152.0 Spike Rush 2.98 1.38 –53.5 Red Mangrove Scrub 2.16 0.92 –57.4 Bayhead 1.72 0.83 –51.7 Pine Savanna 1.59 5.17 224.3 Willow Shrublands 1.47 1.36 –7.9 Dwarf Cypress 1.45 0.69 –52.1 Bay-Hardwood Scrub 1.44 0.49 –66.1 Brazilian Pepper 1.22 2.50 104.4 Cattail Marsh Slash Pine with Hardwoods 0.88 2.96 237.2 Hardwood Scrub 0.71 1.57 121.9 Subtropical Hardwood Forest 0.75 1.43 91.1 Source: Todd et al., 2011. that accurately describe emergent vegetation patterns The framework presented here is based on two across myriad ecosystems, it gets closer to understanding fundamental principles. The first is that rainfall and testing a complete theory describing the organization of should be treated stochastically because random ecosystems. fluctuations in rainfall have large impacts on the seasonal distribution of soil moisture available to The development of a more complete theory of the plants in drylands, as well as annual water depth processes governing the organization of ecosystems and percent time inundated in wetlands. By better would lead to better tools and more accurate characterizing these fundamental processes, information to provide to land managers who need simple relationships that control the distribution to make decisions about future land use and policy. and abundance of vegetation are proposed. The However, even with the best theory, there is a critical relationships are built on the second principle; need for long-term monitoring. Long-term monitoring namely, that a tradeoff exists between resource will provide invaluable information about testing, use/availability and mitigating the costs of revising, and proposing new hypotheses that govern resource use. the organization of ecosystems. Finally and most importantly, the ultimate success of any sustainable While the framework has been more formally developed land management or restoration project depends for dryland ecosystems, the results presented for humid on the cooperation and understanding of the local ones are very encouraging and they provide a formal populations. description of vegetation interactions in wetlands. With the continued development of novel ecohydrological models The modeling implied in these examples and case studies is not simple and there is still much work to be done in many 70 aspects related to the application of these techniques. Assessment Report of the Intergovernmental Panel on Hopefully, that will be accomplished in the near future when Climate Change. Cambridge, UK: Cambridge University more and more experience is accumulated. Extensive use of Press: 542. the papers by Franz et al. (2010) and Todd et al. (2010) has Laio, F., A. Porporato, L. Ridolfi, and I. Rodríguez-Iturbe. been made in the description of these two last examples. 2001. Plants in water-controlled ecosystems: Active Those references provide a more in depth analysis of many role in hydrologic processes and response to water of the issues described here. stress – II. Probabilistic soil moisture dynamics. Advances in Water Resources 24:707–723. Laio, F., S. Tamea, L. Ridolfi, P. D’Odorico, and I. Rodriguez- References Iturbe. 2009. Ecohydrology of groundwater-dependent ecosystems: 1. Stochastic water table dynamics. Water Busch, D. E. and S. D. Smith. 1995. Mechanisms Resources Research, Vol. 45. 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Possible climate Huxman, T. E., et al. 2005. Ecohydrological implications of change impacts on the hydrological and vegetative woody plant encroachment. Ecology; 86(2): 308–319. character of Everglades National Park, Florida. IPCC. 2007. Climate Change 2007: The Physical Basis. Ecohydrology, Article first published online: 29 APR Contribution of Working Group I to the Fourth 541 2011,DOI: 10.1002/eco.223. 71 Zavaleta, E. S. and J. L. Royval. 2002. Climate Change and Responses to Climate Change: North American Case the Susceptibility of U.S. Ecosystems to Biological Studies Washington D.C.: Island Press, p. 277–341. Invasions: Two Cases of Expected Range Expansion. In S.H. Schneider and T. L. Root (eds). Wildlife 72 1818 H Street NW Washington dc 20433 202-473-1000 www.worldbank.org/water/wpp THE WORLD BANK