77780 Weather Data Grids for Agriculture Risk Management: The Case of Honduras and Guatemala FIDES A B Weather Data Grids for Agriculture Risk Management: The Case of Honduras and Guatemala Financed by: The Inter American Federation of Insurance Companies (FIDES), the Development Grant Facility (DGF) of the World Bank and the Trust Fund for Environmentally and Socially Sustainable Development FIDES i This volume is a product of the staff of the International Bank for Reconstruction and Development/The World Bank. The findings, interpretations, and conclusions expressed in this paper do not necessarily reflect the views of the Executive Directors of The World Bank or the governments they represent. The World Bank does not guarantee the accuracy of the data included in this work. The boundaries, colors, denominations, and other information shown on any map in this work do not imply any judgment on the part of The World Bank concerning the legal status of any territory or the endorsement or acceptance of such boundaries. ii TABLE OF CONTENTS List of Acronynms ................................................................................................................................... v Introduction ............................................................................................................................................. 1 I. Methodology for the Implementation of the Gridded Analysis............................................................. 3 1.1 Interpolation Method .................................................................................................................. 3 1.2 Gridded Analysis ........................................................................................................................ 4 II. Gridded Analysis of Meteorological Variables for Honduras and Guatemala ..................................... 7 2.1 Gridded Analysis for Honduras .................................................................................................. 7 2.2 Gridded Analysis for Guatemala .............................................................................................. 10 III. Applications for Weather Insurance.................................................................................................. 14 IV. Conclusions ...................................................................................................................................... 17 References ............................................................................................................................................ 19 Appendix I. Cressman Analysis Method ............................................................................................ 21 Appendix II. Characteristics of the Databases .................................................................................... 23 Appendix III. Implementation Methods ................................................................................................ 25 Appendix IV. Skill Scores for the Evaluation of the Gridded Datasets ................................................. 27 Appendix V. Skill Scores for Individual Stations .................................................................................. 29 iii iv List of Acronyms CI Conditional Interpolation CPC Climate Prediction Center CRE Compound Relative Error CRU Climate Research Unit CSI Critical Success Index ECMWF European Centre for Medium-Range Weather Forecasts ET Evapo-Transpiration IDW Inverse Distance Weighting INSIVUMEH Institute of Seismology, Volcanology, Meteorology and Hydrology (acronym in Spanish) MAE Mean Absolute Error MAGA Ministry of Agriculture of Guatemala (acronym in Spanish) NARR North American Regional Reanalysis NCEP National Center for Environmental Prediction NOAA National Oceanic and Atmospheric Administration NOAH (N) National Centers for Environmental Prediction; (O) Oregon State University; (A) Air Force (AFWA and AFRL); (H) Hydrological Research Lab-NWS (Office of Hydrologic Dev—OHD) PC Proportion Correctly Predicted R Correlation Coefficient RMSE Root Mean-Square Error SERNA Secretariat of Natural Resources and Environment (acronym in Spanish) SMN National Meteorological Service (acronym in Spanish) SR Solar Radiation v vi Introduction One of the major constraints for the improvement of agricultural risk management in Central America, and in particular to the development of weather index-based insurance, is the availability of complete meteorological data. Limitations with the data are related to restrictions in weather station coverage (density), and problems with the quality (errors and gaps in the information) and availability of historical records. This paper evaluates the reconstruction of historical meteorological records with gridded datasets for Honduras and Guatemala1 using the methodology in Uribe Alcantara et al. (2009). The reconstruction with synthetic series is implemented by replacing missing observations with estimations from regular grids (or gridded analyses2). The development of synthetic series proposed here will facilitate, among other potential uses, the implementation of risk analysis in insurance contracts where meteorological information is limited or incomplete. There are several additional applications of the gridded analysis that can be beneficial for the development of weather insurance. For example, gridded datasets can be used for the estimation of climatologies3 and hazard maps. They can also be combined with models such as crop productivity, atmospheric or hydraulic models and provide more specific products such as risk maps for drought, excess rain or flood risks. Furthermore, the availability of complete historical records together with more accurate risk assessments will not only facilitate the development of index-based insurance, but can also improve the risk assessments of traditional insurance contracts. There are some sources of error associated with the estimation of regular grids by the possible over or underestimation of weather station observations. This is because regular grids are estimated within a pixel and cover areas in the order of hundreds of square kilometers, while weather station observations represent point estimates covering a much smaller area. However, the degree of over or underestimation can be evaluated with specific statistical tests that can help to verify the applicability of regular grids for risk analysis and for the estimation of missing data. Furthermore, meteorological observations are incorporated along with gridded datasets to generate synthetic series so sub-estimation and overestimation associated with gridded analysis is prevented as much as possible. Most of the empirical studies of daily gridded datasets have been implemented among developed countries. More recently, regional studies are expanding coverage to more regions in developing 1 Based on “Gridded Analysis of Meteorological Variables for Guatemalaâ€? (2010); “Feasibility Analysis of Meteorological Regular Grids for Guatemalaâ€? (2010); “Feasibility Analysis of Meteorological Regular Grids for Hondurasâ€? (2010); “Gridded Analysis of Meteorological Variables for Hondurasâ€? (2010). 2 The Grid Analysis (and Display Systems) is an interactive tool that is currently in use worldwide for the analysis and display of earth science data. The grid analysis implements usually a 4D dimensional data model, where the dimensions are usually latitude, longitude, level, and time. Each data set is located within these dimensional spaces by use of a data description file. Both gridded and station data may be described. Gridded data may be non- linearly spaced. Since each data set is located within the 2 or 4D dimensional data space, intercomparison of disparate data sets is greatly facilitated. Operations may be performed between data on different grids, or between gridded and observational data. Data from different data sets may be graphically overlaid, with correct spatial and time registration. 3 Climatology is commonly known as the study of our climate, yet the term encompasses many other important definitions. Climatology is also defined as the long-term average of a given variable, often over time periods of 20-30 years. Climatologies are frequently employed in the atmospheric sciences, and may be computed for a variety of time ranges. A monthly climatology, for example, will produce a mean value for each month and a daily climatology will produce a mean value for each day, over a specified time range. Anomalies, or the deviation from the mean, are created by subtracting climatological values from observed data.(IRI/LDEO Columbia University). 1 countries and large economies4. In 2008, daily gridded analysis was also introduced by AGROASEMEX, S. A., in Mexico to facilitate the development of agricultural insurance in areas with limited or missing weather records. This paper is organized in four sections. Section one describes the conceptual approach and methods implemented for the evaluation of the data and the development of the gridded analysis. Section two describes the results of the implementation of the gridded analysis for Honduras and Guatemala. Section three provides a brief description of possible applications of the regular grids for the development of weather insurance contracts. Section four summarizes the main conclusions. 4 In South Africa and China (Hoffman et al., 2008). 2 I. Methodology for the Implementation of the Gridded Analysis This section provides a brief description of the methodology used for the implementation of the gridded analysis for Honduras and Guatemala. The conceptual approach for the evaluation of the data is summarized as well as a description of the methodology to develop the gridded analysis. The variables included in this study are maximum and minimum temperature, precipitation, evapo-transpiration (ET) and solar radiation (SR). 1.1 Interpolation Method Regular grids are derived from methods of interpolation. Traditional interpolation methods such as kriging, inverse distance weighting (IDW), conditional interpolation (CI), and regression analysis, directly interpolate the value under study from a direct source, i.e. weather stations. Other methods use a corrective iteration process, such as Cressman (1959), Barnes (1964), and Optimum Interpolation (Eliassen, 1954; Gandin, 1963), which in addition to observations use a second predictor (indirect method). The second predictor can be the result of atmospheric models, or other proxies such as satellite observations, radar or climatologies. The precision of the analysis depends on how the interpolation method chosen works better for particular weather variables, station densities, climate regimes, and to a lesser extent, differences in topography (Hofstra et al., 2008). The interpolation method selected for the estimation of regular grids in Honduras and Guatemala is the successive correction method based on Cressman (1959). Compared to other corrective methods, Cressman has been used extensively for its precision and feasibility in implementation (a brief description of the methodology is presented in Appendix I). Since developing countries usually have low coverage of weather stations, traditional methods might not be reliable as they directly interpolate data from observations. In contrast, the use of a second predictor, in addition to direct observations, makes successive corrective methods, such as Cressman, a more viable option for developing countries. A successive correction method performs recursive iterations in order to “correctâ€? a first-guess estimation coming from an indirect source. For example, the atmospheric model used as a second predictor is the North American Regional Reanalysis (NARR, see Appendix II for a summary of the characteristics of the dataset). The “correctionâ€? is performed by using more reliable information coming from direct observations from the stations. In meteorological terms, the resulting field is called “objective analysisâ€?. The advantages of using Cressman, a successive correction method, are: high reliability, the incorporation of a second predictor from indirect sources, and worldwide recognition, which can simplify negotiations relative to the reinsurance sector. Cressman has been applied extensively by different national weather services and scientists around the world, including the Climate Prediction Center (CPC) from the National Oceanic and Atmospheric Administration (NOAA), and the European Centre for Medium-Range Weather Forecasts (ECMWF). Also, gridded analyses based on Cressman (or other successive correction methods) have been developed for different countries and regions, i.e. for the US, Mexico (Uribe-Alcantara, 2009), Brazil (Silva, 2007), India (Sinha, 2006), and Europe (Drusch, 2004). 3 The pixel-length commonly used in previous studies had a relatively low resolution (28 km). However, the gridded analyses implemented for Honduras and Guatemala, as described in section two, were able to use higher resolutions (up to 9 km) based on the analysis of the countries’ optimal pixel size5. 1.2 Gridded Analysis The gridded analyses performed for Honduras and Guatemala is conducted in two stages. During the first stage, a feasibility analysis is performed to evaluate the reliability of the data. During the second stage, the gridded analysis is estimated and the results are evaluated based on statistical tests (skill scores). First Stage: Feasibility Analysis The homogenization and quality control of the data is performed in the first stage. A detailed analysis of the distribution and number of valid records is evaluated together with an assessment of the spatial distribution and density of weather stations. A visual inspection is conducted with the data in order to identify problems such as climate inconsistencies and outliers. Meteorological data has natural trends associated with the seasonal variability (e.g. lower temperatures during the winter). Therefore, whenever a trend is not consistent with either the season or with the data from previous years, the pattern is regarded as erroneous and removed from the dataset. Also, when some portions of the records do not comply with maximum temperatures being equal to or above minimum temperatures, they are also removed. The feasibility analysis also provides a detailed description of the characteristics of the weather stations such as, density, data coverage, frequency of the records (initial and final date), and percentage of valid records. All these characteristics are taken into account in the estimation of the pixel size for the development of the gridded analysis. The pixel-size is a valuable parameter to define the applicability of the gridded analysis. For example, if the pixel-size is too large, the grid will likely be missing small-scale events, which will probably result in a wrong risk assessment6. Regional regular grids around the world are traditionally close to 0.25° (around 28km) so pixel-lengths close or below this value are desirable. For example, index-based insurance schemes based on readings from weather stations cover crops within a pre-defined radius (e.g. in Mexico, this radius is around 25 km) so a pixel-length close or below this radius is also desirable. Second Stage: Implementation and Evaluation of the Gridded Analysis During the second stage daily gridded datasets are estimated for maximum and minimum temperature, precipitation, ET and SR. Then, final estimations are evaluated with statistical tests (skill scores) to assess the degree of over or under estimation of the station observations, i.e. the relative “skillâ€? at estimating point values. 5 The analysis of the optimal pixel length takes into account the characteristics of the weather stations. The characteristics considered are: spatial coverage and percentage of valid records per station for the period of interest. 6 There should be a balance between the number of pixels and the total number of weather stations for the implementation of the grid. There are two extreme cases that can make the gridded analysis irrelevant: 1) When the size of the pixel is bigger than 28 km or when there are limited number of pixels (based on the size of the country); and 2) When there is a convergence between the number of pixels and the number of weather stations, resulting in an overlap between the grid and the records from the stations. 4 Implementation - Gridded Datasets for Min-Max Temperature and Precipitation The generation of the gridded datasets is based on Cressman (1959) interpolation method for maximum and minimum temperature and precipitation (see Appendix I for a description of the Cressman analysis and methodology). The method performs successive corrections to a preliminary field with data from weather stations. The preliminary field is based on NARR (see Appendix II for a description of the databases). Cressman is iteratively applied to the initial preliminary field but with successively shorter scanning radii. Thus, the method ensures that the value finally assigned to the pixel converges to the observations at the nearest weather stations. If there are no stations nearby, the interpolation method assigns the value reported from the preliminary field (NARR), (see Appendix I and III for an explanation of the iteration process and for the implementation methods). - Gridded Datasets for Evapotranspiration and Solar Radiation Since observations of evapotranspiration and solar radiation are generally limited or not available, ET and SR are not estimated with the interpolation methodology described before. ET is estimated from the grid estimates for maximum and minimum temperature, and following the Hargreaves method7 (Hargreaves and Samani, 1982; Hargreaves and Samani, 1985. Daily Solar Radiation is estimated from three-hourly data for solar radiation reported by NARR, which is estimated with the ETA8 model using the NOAH9 land surface parameterization (Chen et al., 1996; Koren et al., 1999). For Guatemala, in addition to the NOAH’s land surface model, the Kumar method using topographic information is also estimated (see Appendix III describing the implementation methods). Evaluation with Test Scores In order to assess the applicability and validity of the gridded analysis several statistical tests based on “skill scoresâ€? are estimated. Gridded datasets can only be used to recover missing information as long as the differences between the observations from the stations and the estimations from the grids are negligible in terms of the application of interest. In fact, for insurance purposes, replicating the exact magnitude of the events is not as relevant as reproducing the frequency of specific catastrophic events. 7 Since Hargreaves also depends on radiation the radiation data is also estimated from NARR. 8 Eta stands for the greek letter η (eta) and represents an alternative vertical coordinate used instead of the actual height in order to simplify the solution of the atmosphere’s state equations. See: http://amsglossary.allenpress.com/glossary/search?id=eta-vertical-coordinate1 and http://etamodel.cptec.inpe.br/index.shtml (p – pt) (pref (zs) – pt) The vertical coordinate (Mesinger 1984), one of the model features, is defined as: η = * (ps – pt) (pref (0) – pt) Where p is the atmospheric pressure. The indices s and t refer to the surface and the top of the model atmosphere, respectively. The index ref refers to a prescribed reference atmosphere, and Zs is the surface height. The model orography is formed of steps. See: http://atmo.tamu.edu/class/metr452/models/2001/vertres.html 9 In 2000, given a) the advent of the “New Milleniumâ€?, b) a strong desire by the Environmental Modeling Center (EMC) to better recognize its Land-Surface Model (LSM) collaborators, and c) a new NCEP goal to more strongly pursue and offer “Community Modelsâ€?, EMC decided to coin the new name “NOAHâ€? for the LSM that had emerged at NCEP during the 1990s: N: National Centers for Environmental Prediction (NCEP) O: Oregon State University (Dept of Atmospheric Sciences) A: Air Force (both AFWA and AFRL - formerly AFGL, PL) H: Hydrologic Research Lab - NWS (now Office of Hydrologic Dev -- OHD) See: http://www.emc.ncep.noaa.gov/mmb/gcp/noahlsm/Noah_LSM_USERGUIDE_2.7.1.htm 5 A comparative risk assessment based on “skill scoresâ€? for temperature and precipitation are estimated for Honduras and Guatemala and compared with the results obtained for Europe10 by Hofstra et al. (2008). The skill scores evaluate the accuracy of the estimation by calculating (in levels and in percent) possible errors in the gridded analysis performed. The statistics used in this section and summarized in Appendix IV are: compound relative error (CRE), mean absolute error (MAE), root mean-square error (RMSE), correlation coefficient (R), Proportion correctly predicted (PC) and critical success index (CSI), (see Appendix IV for a summary of the methodology). Finally, in addition to specific test scores, representative climatologies can be estimated in order to evaluate the spatial consistency of the results. As included in the country reports11, representative climatologies for precipitations, maximum and minimum temperature, ET and SR from the regular grids are compared with climatologies reported by the National Weather Service and the Climate Research Unit (CRU) used as independent sources. 10 The skill scores calculated for Honduras and Guatemala are based on Hofstra et al. (2008) who documented the application of multiple skill scores for Europe. See Appendix IV with a description of the methodology. 11 See section “Discussions Based on Climatologiesâ€? in “Gridded Analysis of Meteorological Variables for Guatemalaâ€? (2010) and “Gridded Analysis of Meteorological Variables for Hondurasâ€?(2010). 6 II. Gridded Analysis of Meteorological Variables for Honduras and Guatemala This section summarizes the results of the gridded analyses estimated for Honduras and Guatemala. The gridded analysis generated a large dataset of 61.5 million daily data for Honduras and 54 million daily data for Guatemala12. The analysis includes five weather variables (maximum and minimum temperature, precipitation, ET, and SR) for a coverage period starting from January 1st, 1979 to December 31st, 2008. 2.1 Gridded Analysis for Honduras First Stage: Feasibility Analysis The meteorological dataset used for Honduras after the quality control performed during the first stage is summarized in Table 1. For precipitation, the average percent of valid records per station for the period of interest (1979-2008) is 77 percent, while maximum and minimum temperatures have around 95 and 84 percent of valid records respectively. Density of weather stations measuring precipitation is around 5.2 stations per average department size13 (6,188 km2) and for the stations measuring temperature is around 0.7 per average department size. Figure 1 provides an example of the distribution of weather stations measuring precipitation. The highest coverage per department corresponds to Islas de la Bahía, and the lowest (at least one) to Gracias a Dios. However, there are six departments with no temperature stations (Choluteca, Comayagua, El Paraíso, La Paz, Lémpira and Santa Bárbara) in such cases; the methodology used allows the incorporation of data from nearby stations and from the preliminary field (i.e. NARR)14. Table 1. Characteristics of the Database for Honduras Maximum Minimum Characteristic Precipitation Temperature Temperature Number of stations 94 13 13 Total valid records (%) 76.90 83.90 95.30 Initial date 01/01/1979 01/01/1979 01/01/1979 Final date 12/31/2008 12/31/2008 12/31/2008 Source: “Gridded Analysis of Meteorological Variables for Hondurasâ€?. 12 Daily data for Honduras comes from approximately 42.6x106 (10958 d × 81 pixels × 48 pixels) precipitation records. In addition, a total of 18.9 x106 records for the rest of the variables (10958 d × 27 pixels ×16 pixels × 4 variables). Daily data for Guatemala was generated from 10958d × 30 pixels × 33 pixels × 5 variables totaling approximately 54 x 106 records for all the 5 variables considered. 13 Average department size is calculated using the arithmetic mean. 14 Cressman is iteratively applied to the initial preliminary field but with successively shorter scanning radii. Thus, the method ensures that the value finally assigned converges to the observations at the nearest weather stations. In the case there is no data from a nearby meteorological station, the interpolation method assigns the value reported from the preliminary field (NARR), (see Appendix I and III). 7 Figure 1. Distribution of Weather Stations of Precipitation Used in the Gridded Analysis for Honduras Note: Labels indicate the station ID. Crosses indicate stations from SERNA and circles with squares in the center indicate a station from the SMN. Source: “Gridded Analysis of Meteorological Variables for Hondurasâ€?. Second Stage: Implementation and Evaluation of the Gridded Dataset Implementation Different pixel lengths are proposed based on the station densities for the implementation of the gridded datasets (Table 2). The pixel length of the gridded datasets for precipitation is 0.08° (near 9 km), while the pixel length for maximum and minimum temperature, ET and SR is 0.24° (near to 26 km). Both pixel lengths are less or equal to the length commonly used in regional empirical analysis (around 0.25°). Table 2. Characteristics of the Gridded Analysis for Honduras Features of the Grids of Element Features of the Precipitation Grid Temperatures, Evapotranspiration and Solar Radiation Pixel size dx=dy=0.08° (~9km) dx=dy=0.24° (~26km) Preliminary field NARR Frequency Daily No. of scans 5 Scanning radii 0.40°, 0.32°, 0.24°, 0.16°, 0.08° (~9km) 1.20°, 0.96°, 0.72°, 0.48°, 0.24° (~9km) Initial date 01/01/1979 Final date 12/31/2008 Geographic reference system Geographical Lower left corner (pixel center) Latitude: 12.96° Longitude: -89.42° Latitude: 12.96° Longitude: -89.42° Upper right corner (pixel center) Latitude: 16.48° Longitude: -83.10° Latitude: 16.48° Longitude: -83.10° Source: “Gridded Analysis of Meteorological Variables for Hondurasâ€?. 8 Test Scores Two analyses are performed for the evaluation of the gridded datasets, one for the complete series, and a second for individual stations. As summarized in Appendix IV, all test scores measure deviations from observed values. For test scores such as CRE, MAE and RMSE, best case scores are close to zero. Whereas, for R, PC, and CSI, best case scores are close to one (100% in the case of PC and CSI). The “skill scoresâ€? in Table 3 are calculated for the complete series and they are also compared with the test calculated for Europe in Hofstra et al. (2008). Test scores indicate lower errors for Honduras than the scores reported for Europe (in grey). For example, R, PC and CSI, are close to one and above the results obtained for Europe, suggesting that regular grids are in good agreement with observations from the stations. In particular, test scores for the complete series (Table 3) calculated for temperatures are very close to the ideal values (which is zero for CRE, MAE and RMSE) implying that estimates from the gridded analysis are close to the observations from the stations. In contrast, precipitation presents relatively lower skill scores; however, they are still better than similar scores in Europe. These results are consistent with the stronger temporal and spatial variability associated with precipitation. For example, error measurements for maximum and minimum temperature present compound relative and average errors (CREs) very close to zero. In contrast, these scores are between 3 and 1 mm for precipitation. The reason for near zero estimates for temperature is because it is a continuous variable with high inertia in terms of time and space. As a result of this pattern, there are fewer discrepancies between point estimates (from the stations) and area estimates (within a pixel). In contrast, rainfall patterns can register larger and more extreme events and may differ even over short distances. As a consequence, some discrepancies between point estimates and area estimates are possible. Table 3. Skill Scores for Precipitation and Temperatures (Max. and Min.) Number of Variable CRE MAE RMSE R PC CSI Observations Precipitation 797,411 0.0481 0.5432 2.8902 0.9757 95.91 88.10 Precipitation (Europe) N/A 0.3104 1.2883 2.9185 0.8349 88.41 79.64 Max. Temperature 128,699 0.0047 0.1358 0.2655 0.9979 – – Min. Temperature 125,707 0.0044 0.1492 0.2676 0.9979 – – (i.e. no missing records) 1,030,052 for Precipitation Ideal 0 0 0 1 100 100 142,454 for Max. Temp. 142,454 for Min. Temp. Note: Number of valid Observations (NO), Compound Relative Error (CRE), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Pearson Correlation (R), Percent Correct (PC), and Critical Success Index (CSI). Precipitation (Europe) in grey indicates the most favorable global measures registered for precipitation in Europe (Hofstra et al., 2008). Source: “Gridded Analysis of Meteorological Variables for Hondurasâ€?. A second analysis was performed for individual stations (Appendix V, Table 1). For the stations reporting temperature, RMSE remains below one degree Celsius. However, for precipitation, there are only ten 9 stations with RMSEs over 3mm, and one of them even exceeding 8mm. The stations with the largest errors seem to be grouped in clusters. This is because there are big discrepancies in the observations obtained from very close stations that are involved in the estimation of the same pixel. The differences can be due to instrumental errors, mistakes in the procedures used when the information was collected, or by natural causes (e.g. strong spatial variability associated with the topography). The author believes there is a combination of all factors. Arguably the most important feature of the probabilistic distribution of the errors estimated for Honduras is their symmetry. In terms of insurance contracts, if underestimations occur in the same proportion as overestimations (symmetrical distribution), it means that uncertainty is being fairly distributed between the insurer and the insured. 2.2 Gridded Analysis for Guatemala First Stage: Feasibility Analysis After quality control, data coverage for Guatemala is well above 90 percent of registered valid records (see Table 4 below). The number of weather stations measuring precipitation totals 48 (Figure 2), while the number of those measuring maximum and minimum temperature is 32 and 37 respectively. Table 4. Characteristics of the Database for Guatemala Maximum Minimum Characteristic Precipitation Temperature Temperature Number of stations 48 32 37 Total valid records (%) 93.85 95.10 92.95 Initial date 01/01/1979 01/01/1979 01/01/1979 Final date 12/31/2008 12/31/2008 12/31/2008 Source: “Gridded Analysis of Meteorological Variables for Guatemalaâ€?. 10 Figure 2. Distribution of Weather Stations of Precipitation Used in the Gridded Analysis in Guatemala Note: Labels indicate the station ID. Source: “Gridded Analysis of Meteorological Variables for Guatemalaâ€?. The average density of weather stations is around 5 stations per average department size (5,000 km2). The mountain region, known as Tierras Altas, presents a homogeneous and relatively high coverage of weather stations, while coverage tends to be sparse and poorly distributed in the plains (Planicies del Litoral and Planicies del Petén). For example, over 80 percent of the weather stations measuring precipitation are located in the mountains (Tierras Altas). The area with the maximum number of stations measuring temperature is located in Zacapa (5.54 stations per average department size) and Chimaltenango (5.36 stations per average department size). However, there are two departments with no weather stations reporting maximum temperature: Sololá and Sacatepéquez. Once again, the methodology provides estimates of the grid based on nearby stations and the second predictor (NARR). Second Stage: Implementation of the Gridded Dataset and Evaluation Implementation Based on the data characteristics and density of weather stations, the pixel length recommended for Guatemala is 0.15° (around 16 km) for the gridded analysis of both precipitation and maximum 11 and minimum temperature (Table 5). Both resolutions are distinctively higher than the size commonly obtained in other regional analysis (pixel-length=0.25°). Table 5. Characteristics of the Regular Grids for Guatemala Element Characteristic Pixel size dx=dy=0.15° (~16km) Background field NARR Temporal resolution Daily No. of scans 5 Scanning radii (pixels) 5, 4, 3, 2, 1 Scanning radii (degrees) 0.75°, 0.60°, 0.45°, 0.30°, 0.15° (~16km) Initial date 01/01/1979 Final date 12/31/2008 Geographic reference system Geographical Coordinates of the lower left corner (pixel center) Latitude: 13.50° Longitude: -92.40° Coordinates of the upper right corner (pixel center) Latitude: 18.30° Longitude: -88.05° Source: “Gridded Analysis of Meteorological Variables for Guatemalaâ€?. Test Scores Skill scores estimated for Guatemala are higher than similar scores reported for Europe (Table 6 in grey) and are close to the expected values (as defined in Appendix IV), suggesting that regular grid estimates are close to the observations from the stations. For example, for maximum and minimum temperature CRE is close to zero, and both MAE and RMSE are around 0.4°C and 0.6°C respectively. However, relatively higher errors are expected for precipitation, as explained for precipitation test scores registered in Honduras, and these results are consistent with the temporal and spatial discontinuities of this variable. Table 2 in Annex V presents the same results for individual stations. Again, RMSE remains below one degree Celsius for most stations reporting temperatures. For precipitation, only nine stations registered RMSE over 1.5 mm, implying that for those stations there is a discrepancy between the observations and the estimates from the grids. Overall, the frequency distribution of the errors for the complete series shows that extreme cases are minimal and that the distribution of errors is symmetrical, suggesting that uncertainty is fairly distributed between the insurer and the insured. 12 Table 6. Skill Scores for Precipitation and Temperatures (Max. and Min.) Number of Variable CRE MAE RMSE R PC CSI Observations Precipitation 439,650 0.0285 0.5743 1.7440 0.9857 94.63 85.75 Precipitation (Europe) N/A 0.3104 1.2883 2.9185 0.8349 88.41 79.64 Max. Temperature 333,480 0.0171 0.4423 0.6260 0.9915 – – Min. Temperature 376,865 0.0157 0.4501 0.6850 0.9927 – – 595,984 for Precipitation Ideal 360,656 for Max. Temp. 0 0 0 1 100 100 405,446 for Min. Temp. Note: Number of valid Observations (NO), Compound Relative Error (CRE), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Pearson Correlation (R), Percent Correct (PC), and Critical Success Index (CSI). Precipitation (Europe) in grey indicates the most favorable global measures registered for precipitation in Europe (Hofstra et al., 2008). Source: “Gridded Analysis of Meteorological Variables for Guatemalaâ€?. 13 III. Applications for Weather Insurance Gridded datasets are commonly used as an estimate when reproducing the exact values of daily records is not as relevant as the ability to reproduce the probability of the event .For example gridded dataset can provide estimates for the risk assessments of catastrophic events such as droughts, frosts, floods, etc. Regular grids have multiple applications within the context of risk analysis: • Risk Analysis with time series estimated directly from the grid or with synthetic series (SS); • Risk Analysis with Climatologies; • Hazard and Risk Map; and • Other applications: Input data for the local improvement of climate change scenarios, input data for the development of schemes of climatological seasonal forecasts, climate regionalizations (determination of climatologically homogenous regions). The applications that are more important for the development of weather insurance contracts are the ones that can facilitate a better risk assessment of the perils to be covered, i.e. risk analysis with climatologies, risk analysis with SS, and hazard and risk maps. Improved risk assessments will not only provide better information to develop index-based insurance contracts, but they can also facilitate the expansion in the coverage of parametric insurance contracts (See Box I for the implementation of regular grids in Mexico). Furthermore, traditional insurance contracts such as named perils can also benefits from an improvement in their risk assessments. Risk Analysis with Synthetic Series (SS) Risk analysis for insurance contracts using estimations from regular grids can use time series information generated in two ways: 1. Direct estimates from the gridded analysis: Using the time series generated from gridded datasets (estimated with interpolation methods, Figure 3) 2. A Combination of estimates from the gridded analysis with observations from weather stations (Synthetic Series): the reconstruction with synthetic series is implemented by replacing missing observations from weather stations with estimations from regular grids (gridded analyses). Direct estimates from regular grids are especially convenient for spatial analysis with limited weather station observations or limited historical records because the gridded datasets guarantee the generation of a complete dataset across the domain (space and time), even in places where no weather stations are available. The SS, on the other hand, consist of a combination of observations from weather stations with estimates from the gridded analysis. The SS is obtained by replacing missing records in the observed time series with records from the gridded dataset of the pixel that contains the station. The incorporation of meteorological observations to the grid estimates in the SS prevents the sub- estimation and overestimation associated with gridded analysis whenever possible. In case there is no weather station available in the pixel of interest, the time series will consist only of the time series from the gridded analysis. 14 Figure 3. Sample data of precipitation (cyan bars), maximum temperature (red line), minimum temperature (blue line), evapotranspiration (green line), and solar radiation (yellow line), for a given number of days after December 31st, 1978, at pixel -91.5° Longitude, 15° Latitude Source: “Gridded Analysis of Meteorological Variables for Guatemalaâ€?. Risk Analysis with Climatologies Climatology maps (climatologies) can help identify vulnerable regions when combined with the location of assets. For example, climatologies can be useful for a quick reference of what would be the expected values in the annual cycle for a given pixel in a specific location. The annual cycles can be helpful for the determination of coverage periods associated with parametric insurance since trends have a strong correlation with agricultural activities. Hazard and Risk Maps Risk maps are generated from the combination of hazard maps with vulnerability and exposure functions (i.e. from hydraulic or atmospheric models). Risk and hazard maps are a very valuable tool for the risk assessment in insurance contracts. For example, they can help identify extreme events of temperature and precipitation. In addition, these maps can be helpful for the identification of regions in risk of frost and floods. 15 Box 1. The Implementation of Regular Grids in Mexico: The Expansion of Parametric Drought Coverage with Gridded Datasets The application of the gridded datasets developed by AGROASEMEX, S.A. (2009) enabled to expand the coverage of parametric drought insurance for different crops. Parametric insurance schemes for drought are based on predefined thresholds of cumulative precipitation (“triggersâ€?) for different stages of the crop. In order to evaluate the applicability of the grids, a retrospective estimation of annual losses of maize caused by droughts for both stations and grids were estimated and compared. After the evaluation, the gridded datasets started to be applied in the portfolio in 2008 with forty-six additional weather stations. Given the lack of historical information necessary for risk analysis these stations had not been insured until then. A total of 585,316 acres (236,869 hectares) of maize and beans were additionally insured after the application of the gridded analysis. This area represented 9.21% of the portfolio only in the first stage of the project, and has increased in the following years given the potential to insure new or recently installed weather stations. It is expected that this program can be expanded and cover other perils related to extreme climatic events using temperature information. Source: “On the Use of Regular Grids for the Estimation of Synthetic Meteorological Records of Precipitation and their Application on the Assessment of Drought Riskâ€? (2009). 16 IV. Conclusions The implementation of the gridded analysis for the estimation of synthetic series in Honduras and Guatemala could be used to generate complete historical records of weather variables. The interpolation method proposed in this study to generate the gridded analysis for Honduras and Guatemala is based on Cressman (1959). The methodology involves the correction of weather records from indirect sources (i.e. atmospheric models) with direct observations from the stations. A total of 61.5 million of daily data figures were generated for the case of Honduras and 54 million for Guatemala for a period covering January 1st, 1979 to December 31st, 2008. The gridded analysis is conducted in two stages. A complete analysis of the data quality and the stations densities is evaluated during the first stage. In the second stage regular grids are estimated with an evaluation of the results. The total number of weather stations is between 13 and 37 for weather stations measuring temperature, and between 48 and 94 for weather stations measuring precipitation. Average percentage of valid records ranges between 77 percent (precipitation) and 95 percent (maximum and minimum temperature). All these characteristics are taken into account in the estimation of the pixel length. The final pixel length proposed for the implementation of regular grids has ranged so far between 0.08° and 0.24°. Both pixel lengths are less than or equal to the length commonly used in regional analysis (around 0.25°). Based on statistical test scores the gridded datasets estimated for Honduras and Guatemala are suitable for risk analysis. Visual inspection of climatologies and actual hazard events (droughts, hurricanes, frosts) confirms that the gridded datasets estimated for Honduras and Guatemala are able to reproduce extreme events closely and they also capture the impact associated with topography and the location of large water bodies on the spatial variability. Furthermore, the systematic error of the synthetic data is minimal and represents a small proportion of the data. The fact that the overall distribution of the errors estimated for all the variables is almost symmetrical implies that underestimations occur in the same proportion as overestimations. Consequently, in terms of insurance contracts uncertainty is being fairly distributed between the insurer and the insured. Synthetic gridded datasets generated through gridded analysis will be a fundamental input for the development of risk and hazard maps in Honduras and Guatemala. The possibility to combine regular grids with atmospheric, hydraulic and crop models, particularly, through the development of specific hazard and risk maps will be an important tool in the risk assessments of insurance contracts. The availability of improved and more accurate risk assessments to analyze risks for flood and drought risks will not only help to develop parametric contracts, but it will also help to introduce more accurate risk analysis in traditional insurance contracts such as named-perils. The use of regular grids can help to overcome limitations in the provision of insurance due to gaps in the historical records. However, the accuracy of the estimates, particularly in the provision of insurance at the micro and meso level, can be affected by current number of weather stations (density). Since gridded dataset cannot substitute weather stations information, caution should be taken especially for estimations in regions where there is a combination of micro-climates or sharp differences in the topography with an extremely limited number of weather stations. In those cases, the accuracy of the estimates will be limited, resulting in low correlations between the grid estimates and weather records. 17 18 References Barnes, S.L., 1964. A Technique for Maximizing Details in Numerical Weather Map Analysis. Journal of Applied Meteorology, 3(4): 396-409. Chen, F., et al., 1996. Modeling of land-surface evaporation by four schemes and comparison with FIFE observations. J. Geophys. Res., 101: 7251-7268. Cressman, G.P., 1959. An Operational Objective Analysis System. Monthly Weather Review, 87(10): 367-374. Drusch, M., D. Vasiljevic, et al. ,2004. ECMWF’s Global Snow Analysis: Assessment and Revision Based on Satellite Observations. Journal of Applied Meteorology, 43(9): 1282-1294. Eliassen, A., 1954. Provisional report on spatial covariance and autocorrelation of the pressure field. Gandin, L.S., 1963. Objective Analysis of Meteorological Fields. Hydromet Press: 242. Hargreaves, G.H. and Samani, Z.A., 1982. Estimating potential evapotranspiration. J. Irrig. and Drain Engr., ASCE, 108: 223-230. _____ .1985. Reference crop evapotranspiration from temperature. Transaction of ASAE, 1(2): 96-99. Hofstra, N., Haylock, M., New, M., Jones, P. and Frei, C., 2008. Comparison of six methods for the interpolation of daily, European climate data. J. Geophys. Res., 113. Koren, V., Schaake, J., Mitchell, K., Duan, Q.Y. and Chen, F., 1999. A parameterization of snowpack and frozen ground intended for NCEP weather and climate models. J. Geophys. Res., 104: 19569-19585. Kumar, L., Skidmore, A.K. and Knowles, E., 1997. Modeling topographic variation in solar radiation in a GIS environment. International Journal of Geographical Information Science, 11(5): 475 - 497. Magaña, V., Amador, J.A. and Medina, S., 1999. The Midsummer Drought over Mexico and Central America. Journal of Climate, 12(6): 1577-1588. Mesinger, F., et al., 2006. North American Regional Reanalysis. Submitted to the Bulletin of the American Meteorological Society. Silva, V. B. S., Kousky V. E, et al.,2007. An Improved Gridded Historical Daily Precipitation Analysis for Brazil. Journal of Hydrometeorology, 8(4): 847-861. Sinha, S. K., Narkhedkar, S. G., et al.,2006. Barnes objective analysis scheme of daily rainfall over Maharashtra (India) on a mesoscale grid. Atmosfera, 19: 109-126. Uribe Alcántara, E.M., Arroyo Quiroz, M.D.C., Escamilla Juárez, J. and Castellanos Hernández, L., 2009. On the Use of Regular Grids for the Estimation of Synthetic Meteorological Records of Precipitation and their Application on the Assessment of Drought Risk. Submitted to Atmosfera. 19 20 Appendix I. Cressman Analysis Method This study uses successive correction methods based on Cressman (1959) to generate the gridded analysis for Hondurans and Guatemala. The advantage offered by successive correction methods is the incorporation of a second predictor (indirect observation) in addition to meteorological records (direct observations). This predictor can be the result of atmospheric models, or other proxies such as satellite observations, radar or climatologies. Cressman Objective Analysis The Cressman method (1959) consists of the correction of a first-guess field, which is consecutively corrected by the weighted mean of the difference between the observed values in the preliminary field with observations from nearby stations. This process is repeated five times with successive shorter scanning radii. So the value of the variable at the pixel converges to the observations at the nearest weather station(s). On the other hand, if no weather stations are nearby, the pixel retains the value of the preliminary field. The procedure starts with a radius equal to five pixels and the preliminary field corresponds to the daily field reported by NARR. Cressman Algorithm The correction method is based on (1) and (2) below. The initial value in the preliminary field is corrected by the weighted mean of the errors based on a predefined scan radius (R): ∑ni =1 w(i,j) {y(i) - xb(i)} (1) xa(j) = xb(j)+ ∑n i =1 w(i,j) Where, R2 – di,,j 2 w(i,j) = max 0, n 2 2 2 variable in the pixel of interest; xa represents the value of the xb is the value of the ∑ + di,,j {y(i) R w(i,j) background i =1 (or-x (i)} preliminary) b field; x y is the (j) = valuex (j)+ of the variable n in the weather station; and a b ∑ i =1 w(i,j) w represents a weight factor given by the following equation: R2 – di,,j 2 (2) w(i,j) = max 0, R2 + d22 i,,j Where, R represents the current scanning radius for stations around the center of the pixel of the regular grid; di,j is the distance between station i, and the center of pixel j. The searching distances for five iterations are set at different scanning radius (R). The length of R is a multiple of the pixel length and the number of radii is equal to the number of iterations. For example, for Guatemala the radius values are 0.75°, 0.60°, 0.46°,0.30° and 0.15° (the initial pixel length was 0.15 and the radii number was five so the first radii value is 5*0.15=0.75, the second is 4*0.15=0.60°, and so on). Figure 1 exemplifies the procedure for a given pixel (orange). The procedure starts with a radius equal to five pixels (light blue). As the procedure progresses, the radius becomes smaller (darker blue). The final iteration corresponds to a radius of one pixel (darkest blue circle). After all five iterations, all the weather stations within the largest scanning radius are included in the analysis for the pixel of interest. 21 Figure 1. Cressman Methodology Exemplified for a Pixel (orange) Note: Blue circles indicate scanning zones for decreasingly smaller radii (the color blue becomes darker as the radius decreases); green pentagons with a black dot in the center indicate a weather station; grey lines indicate the division between pixels, while crosses indicate their center; the black dotted line indicates the distance from the center of the pixel to a station (d). The radius (R) is expressed in pixel’s units. Source: “Gridded Analysis of Meteorological Variables for Guatemalaâ€? (2010). 22 Appendix II. Characteristics of the Databases The method of Cressman can be defined in simple terms as the successive correction of a preliminary field (low reliability), based on observations (high reliability). The most important difference with traditional interpolation methods is precisely the use of a preliminary field, which works as a second predictor. This additional information is considered especially important for the determination of values in regions sparsely covered by weather stations, i.e. for developing countries. In the cases of Guatemala and Honduras, the North American Regional Reanalysis (NARR) is proposed as the preliminary field for the Cressman Analysis. The North American Regional Reanalysis (NARR) is a long-term atmospheric and hydrologic database that is used as a second predictor for the Cressman analysis. It has a high spatial and temporal resolution. It was generated with the numerical weather model ETA and developed by the National Center for Environmental Prediction (NCEP) of the National Oceanic and Atmospheric Administration (NOAA). Table 1 presents the main characteristics of the database that covers daily data from January 1st, 1979 to December 31st, 2008. The pixel length of the database is 0.375°15 (near 40 km). Tri-hourly reports from NARR are processed to estimate the values of daily accumulated precipitation and maximum and minimum temperature. Table 1. North American Regional Reanalysis (NARR) Element Characteristic Pixel size dx=dy=0.375° (~40km) Time reference Universal Coordinated Time (UTC) 3 hr (0-3, 3-6, 6-9, 9-12, 12-15, 15-18, 18-21 and Temporal resolution 21:00-0:00UTC every day) Initial date 01/01/1979 Final date Semi-Current (five days lag) Geographic reference system Geographical Coordinates of the lower left corner (pixel center) Latitude: 0.000°N; Longitude: -220.000°E Coordinates of the upper right corner (pixel center) Latitude: 89.625°N; Longitude: -0.625°E Source: “Gridded Analysis of Meteorological Variables for Hondurasâ€? (2010), and “Gridded Analysis of Meteorological Variables for Guatemalaâ€? (2010). The climatologies from the Ministry of Agriculture, Livestock and Nutrition of Guatemala (MAGA, acronym in Spanish) and also from the Climate Research Unit (CRU) are also included in the analysis to test for possible spatial inconsistencies in the information generated by regular grids. The climatology for precipitation and maximum and minimum temperature and evapo-transpiration from CRU have pixel length with low resolution (near 0.5°). 15 The resolution of NARR has increased recently. This was the resolution of NARR at the time Guatemala and Honduras analysis was conducted. 23 The National Meteorological Service (SMN acronym in Spanish) and the Secretariat of Natural Resources and Environment (SERNA acronym in Spanish) provide meteorological records for Honduras. The Institute of Seismology, Volcanology, Meteorology and Hydrology (INSIVUMEH, acronym in Spanish) is the source for Guatemala. 24 Appendix III. Implementation Methods Regular Grids for Temperatures and Precipitation The following description provides the basic steps for the implementation of regular grids for temperatures (Min and Max) and precipitation: 1. Average daily data: Estimation of daily fields of precipitation and temperatures (max and min) in agreement with the reading time of the local network based on NARR three-hourly data for the period and domain of interest. 2. NARR bilinear interpolation: Increasing the spatial resolution of NARR by bilinear interpolation16 to the resolution of interest. For example, for Honduras the pixel length of NARR (0.375° or around 40 km) is reduced through bilinear interpolation to 0.08° (precipitation) and 0.24° (temperature, ET and SR). 3. Use of Cressman algorithm: Computation of the Cressman iteration method (five iterations) using individual observations from weather stations and from the interpolated NARR from step 2. Allocation of the final iteration to each pixel based on Cressman (which corrects the initial interpolated NARR based on the observations), obtaining a higher resolution gridded dataset. Regular Grids for Evapo-transpiration (ET) ET is estimated using (1) below following Hargreaves method. Hargreaves depends only on latitude, Julian day, and maximum and minimum temperatures; and estimates ET for a crop of reference using evaporation rate of a pasture with a fixed height of 0.12 m, an albedo of 0.23, and a superficial resistance of 69 m*s -1. The equation is as follows: (1) E T = 0.0023 * Rext * (Tmax – Tmin )1/2 * (Tave+ 17.8), Where, Rext, represents extraterrestrial radiation in mm.d-1 which was also obtained from NARR; Tmax Tmin, corresponds to maximum and minimum temperatures based on the gridded dataset for maximum and minimum temperatures from Cressman Analysis method; Tave, represents the average temperature determined from Tave = 0.6 * Tmax+0.4 * Tmin Regular Grids for Solar Radiation (SR) The following description provides the basic steps for the implementation of regular grids for solar radiation (SR): 1. Average Daily Data: Download daily solar radiation from NARR and calculate averages from the three-hourly reports from 15:00UTC from the previous day to 15:00UTC of the day of interest. NARR estimates radiation using the NOAH, land surface model. The estimation is based on extraterrestrial solar radiation, atmospheric and terrestrial long wave radiations, sensible heat flux to and from the surface, soil heat flux, and internal soil heat flux. The model is able to implement the impact on solar radiation as it moves through the atmosphere, including the impact of clouds. 16 The method is documented at http://en.wikipedia.org/wiki/Bilinear_interpolation. 25 2. NARR bilinear interpolation: Apply bilinear interpolation of the average data of solar radiation from NARR to match the proposed resolution of the gridded analysis. 3. Kumar methodology: Kumar (1997) model for SR was also estimated for Guatemala. Kumar estimates solar radiation incidence on the surface assuming clear days with no clouds. The method takes into consideration the altitude, surface gradient (slope), and orientation (aspect). It estimates solar radiation at the top of the atmosphere based on the Julian day, the latitude and estimates of the solar declination, solar sunrise and sunset, solar altitude, and azimuth angles. The estimated solar radiation is then adjusted to account for the absorption by different gases in the atmosphere, molecular (or Rayleigh) scattered by the permanent gases, and aerosol (Mie) scattering due to particulates. Finally, the solar radiation is adjusted to take into consideration the slope of the surface. 26 Appendix IV. Skill Scores for the Evaluation of the Gridded Datasets The skill scores included in this paper are based on Hofstra et al. (2008) who documented the application of multiple skill scores for Europe. The objective of the empirical study was to evaluate the performance of several traditional interpolation methods calculated for precipitation, minimum and maximum temperature, and sea level pressure between 1961 and 1990. Table 1. Definition of Skill Scores Used Skill Score Equation ∑ (y k – ok)2 k=1 Compound relative error (CRE) CRE = n ∑ (o k – Å?)2 k=1 n Mean absolute error (MAE) MAE = 1 n ∑ yk – ok k=1 n Root mean squared error (RMSE) RMSE = 1 n ∑ (y k – ok)2 k=1 n n n ∑ ∑ ∑o 1 yk ok – n yk k k=1 k=1 k=1 Pearson correlation (R) R= 1/2 1/2 n n 2 n n 2 ∑y 2 k – 1 n ∑y k ∑o– ∑o 2 k 1 n k k=1 k=1 k=1 k=1 a+d Percent correct (PC) PC = a+b+c+d a Critical success index (CSI) CSI = a+b+c Note: Explanation of the variables: y is the series to evaluate (the value at the regular grid); o is the observation at the weather station, or reference series; k is the number of the day; n is the total number of days; a is the fraction of hits (e.g. wet (>0.5 mm) days in both the reconstructed gridded analysis and in the observed series); b is the fraction of false alarms (e.g. wet days in the reconstructed series but dry (<0.5 mm) days in the observed series); c is the fraction of misses (e.g. dry days in the reconstructed series but wet days in the observed series); and d is the fraction of correct rejection (e.g. dry days in the reconstructed and in the observed series). Source: Based on Hofstra et al., 2008. Compound Relative Error (CRE) CRE measures similarities between the regular grid and the observed values. It measures the mean square errors (MSE) relative to the variance of the observations. CRE is bounded below by 0, which indicates the best case, and unbounded above. CRE is unit-less. 27 Mean Absolute Error (MAE) MAE is a measure of average errors. MAE is bounded below by 0, which indicates the best case, and unbounded above. The units of MAE are the same of the variables of interest (e.g. mm for precipitation). Root Mean-Squared Error (RMSE) RMSE is another measurement of the deviations from the observed value. In this case it is measured as the standard deviation of the squared errors. Together with CRE, RMSE is sensitive to large outliers. Correlation Coefficient (R) R measures how the daily variability in time between the grid values and the observations are moving together. The statistic is standardized and can be compared across regions and months. Proportion Correctly Predicted (PC) PS measures the percentage of correct predictions of wet and dry days (See note Table 1 above). It is a measure of accuracy to determine if precipitation was predicted correctly. It may not be the best measure when the events are not symmetrically distributed (one of the events is less common than the other) as is the case for precipitation. Critical Success Index (CSI) CSI is more appropriate to determine success when the events are not symmetrically distributed (when one event is less common than the other). It is calculated by dividing the amount of correctly predicted events (but least/most common) by itself plus the amounts of incorrectly predicted events (least and most common). Thus, CSI is calculated for “lowâ€? and “highâ€? events. For precipitation CSI is only calculated for “highâ€? most common wet events. It attains a value of 1 when the number of false alarms and misses is cero; and a value of 0 when the number of hits is null. 28 Appendix V. Skill Scores for Individual Stations Table 1. Skill Scores for Precipitation and Maximum and Minimum Temperature, Honduras Precipitation Station ID NO CRE MAE RMSE R PC CSI Department A022 6,945 0.7705 0.2033 0.7705 0.9973 97.77 89.58 Yoro A037 9,653 0.5737 0.2000 0.5737 0.9985 98.15 95.25 Yoro A038 9,897 0.5819 0.1467 0.5819 0.9971 98.41 94.98 Olancho A039 151 0.4669 0.1417 0.4669 0.9580 96.03 79.13 Olancho A041 9,981 0.8924 0.2033 0.8924 0.9979 98.79 96.11 Colón A042 9,892 0.2741 0.0582 0.2741 0.9998 99.88 99.55 Colón A043 9,434 0.4630 0.1673 0.4630 0.9987 98.94 96.97 Yoro A045 7,183 0.3352 0.0909 0.3352 0.9989 97.97 91.41 Olancho A048 9,550 2.7725 0.9223 2.7725 0.9765 95.20 85.86 Yoro A049 9,685 0.6446 0.2127 0.6446 0.9991 98.64 96.97 Colón A050 7,647 0.5824 0.1713 0.5824 0.9984 99.16 97.07 Olancho A051 9,677 1.3155 0.4125 1.3155 0.9951 96.74 93.65 Colón A052 5,722 0.6739 0.2244 0.6739 0.9976 98.04 94.77 Olancho A053 1,096 2.0509 0.7678 2.0509 0.9767 90.15 76.00 Yoro A060 3,981 1.2015 0.3984 1.2015 0.9891 94.40 84.76 Yoro C001 10,165 0.2725 0.0951 0.2725 0.9994 98.95 96.70 Francisco Morazán C005 8,964 2.4505 0.9325 2.4505 0.9577 85.82 66.49 Francisco Morazán C006 10,560 0.3873 0.1410 0.3873 0.9994 98.09 93.44 La Paz C010 10,833 0.8961 0.2920 0.8961 0.9947 96.39 86.19 El Paraíso C012 7,883 1.4794 0.4143 1.4794 0.9847 98.44 91.72 El Paraíso C013 10,166 1.3068 0.5075 1.3068 0.9913 92.45 72.09 Francisco Morazán C014 10,202 2.1527 0.7361 2.1527 0.9796 93.84 80.67 El Paraíso C015 10.866 1.4292 0.5295 1.4292 0.9936 94.63 82.55 El Paraíso C016 10,527 1.6325 0.5913 1.6325 0.9865 90.12 65.19 El Paraíso C019 10,559 2.2608 0.7452 2.2608 0.9952 96.16 85.45 Choluteca C021 10,805 0.5741 0.1570 0.5741 0.9988 99.07 94.89 Francisco Morazán C023 8,481 7.3252 2.7016 7.3252 0.8641 88.13 67.27 Choluteca C036 8,358 3.6803 1.4296 3.6803 0.8794 84.95 62.09 Francisco Morazán C050 10,591 0.8794 0.2702 0.8794 0.9972 98.55 93.42 El Paraíso C063 10,253 2.0091 0.6725 2.0091 0.9978 94.70 83.47 Choluteca C064 6,301 2.4668 0.9627 2.4668 0.9830 90.32 70.91 Choluteca C084 4,502 6.7170 2.9709 6.7170 0.8119 90.43 84.40 Francisco Morazán C085 7,305 2.8785 1.2088 2.8785 0.9391 82.93 63.73 Francisco Morazán C086 7,588 5.5513 2.3098 5.5513 0.7488 75.82 49.70 Francisco Morazán G005 10,195 0.4867 0.1262 0.4867 0.9993 99.46 97.91 Valle H010 10,218 0.8523 0.2291 0.8523 0.9961 97.83 93.14 Santa Bárbara H011 10,925 4.4852 1.7145 4.4852 0.9516 89.64 76.79 Copán H018 10,411 2.2313 0.8199 2.2313 0.9722 90.28 75.89 Santa Bárbara H020 10,009 0.2115 0.0372 0.2115 0.9999 99.87 99.54 Santa Bárbara L007 1,826 0.2339 0.0611 0.2339 0.9999 99.78 99.49 Atlántida L011 7,398 20.4072 5.9630 20.4072 0.6487 82.97 62.48 Atlántida L012 8,788 1.4569 0.5398 1.4569 0.9995 97.10 93.98 Atlántida L013 9,804 6.5066 1.7193 6.5066 0.9848 95.48 89.68 Atlántida L211 9,769 0.9845 0.3095 0.9845 0.9972 98.35 94.86 Lémpira 29 L212 9,862 1.8706 0.8426 1.8706 0.9896 90.73 76.49 Lémpira L213 9,701 0.4835 0.1475 0.4835 0.9993 99.75 99.14 Lémpira L214 10.227 1.0574 0.3660 1.0574 0.9974 96.77 90.46 Lémpira L215 10,562 0.2704 0.0855 0.2704 0.9997 99.56 98.73 Lémpira N008 10,437 0.5826 0.1446 0.5826 0.9994 99.77 98.75 Valle N009 9,800 1.0223 0.3626 1.0223 0.9956 97.07 88.66 Francisco Morazán N011 6,940 0.8327 0.2254 0.8327 0.9983 99.34 97.00 Valle N012 91 0.6892 0.0879 0.6892 0.9968 100.00 100.00 Choluteca P003 10,353 0.5760 0.1450 0.5760 0.9978 98.65 96.45 Olancho P008 7,214 0.2831 0.0875 0.2831 0.9995 98.96 97.35 Olancho P009 10,194 0.3998 0.1159 0.3998 0.9988 98.63 96.42 El Paraíso P015 8,538 0.3411 0.1108 0.3411 0.9992 98.75 96.11 El Paraíso P021 5,479 0.8352 0.2121 0.8352 0.9960 97.43 90.75 Olancho P022 6,579 0.7003 0.1912 0.7003 0.9960 98.33 93.75 Olancho P026 2,557 0.3616 0.1019 0.3616 0.9983 98.67 94.83 Olancho P027 9,129 0.9230 0.3410 0.9230 0.9945 96.39 90.63 Olancho P028 6,183 0.0674 0.0067 0.0674 1.0000 99.95 99.88 Olancho P040 3,549 1.1437 0.4621 1.1437 0.9854 91.29 77.31 Olancho S004 4,579 0.2835 0.0894 0.2835 0.9992 99.28 98.17 Olancho U004 6,666 0.4892 0.1811 0.4892 0.9978 99.70 92.31 Intibuca U022 7,015 0.8370 0.2751 0.8370 0.9950 96.82 90.29 Yoro U024 7,662 1.0590 0.3935 1.0590 0.9889 94.91 82.25 Comayagua U026 10,225 0.4680 0.1825 0.4680 0.9984 97.05 89.63 Comayagua U056 6,359 0.2888 0.0650 0.2888 0.9994 98.98 96.84 Yoro U070 9,678 0.4988 0.1712 0.4988 0.9987 98.66 95.87 La Paz U080 10,926 0.4943 0.1729 0.4943 0.9984 97.68 92.38 Francisco Morazán U081 10,777 1.2160 0.4027 1.2160 0.9914 95.33 86.43 Francisco Morazán U084 9,891 5.6166 2.3237 5.6166 0.7116 82.65 58.75 Comayagua U088 10,035 0.8507 0.3155 0.8507 0.9963 97.86 93.41 Comayagua U093 6,362 0.7590 0.2666 0.7590 0.9952 98.05 94.44 Comayagua U095 10,075 5.4047 2.1232 5.4047 0.8426 85.01 63.44 Comayagua U096 8,584 6.7470 3.0207 3.7470 0.7818 88.71 72.86 Comayagua U144 5,718 0.2589 0.0491 0.2589 0.9995 99.51 98.32 Cortés U145 6,149 0.4608 0.1211 0.4608 0.9986 99.54 98.73 Comayagua U146 9,461 0.5130 0.1675 0.5130 0.9986 99.21 97.88 Yoro W102 10,958 0.5714 0.1508 0.5714 0.9984 99.32 96.82 Choluteca 78700 9,990 0.3650 0.0992 0.3650 0.9997 99.19 97.10 Valle 78701 5,423 0.0000 0.0000 0.0000 1.0000 100.00 100.00 Islas de la Bahía 78703 6,762 0.0000 0.0000 0.0000 1.0000 100.00 100.00 Islas de la Bahía 78704 2,564 0.7559 0.1445 0.7559 0.9996 98.75 96.89 Colón 78705 10,911 0.4249 0.1000 0.4249 0.9999 99.47 98.70 Atlántida 78706 10,859 0.0347 0.0026 0.0347 1.0000 99.94 99.86 Atlántida 78707 9,478 1.0282 0.3800 1.0282 0.9934 95.26 87.73 Yoro 78708 10,901 0.4640 0.1000 0,4640 0.9987 99.17 97.49 Cortes 78711 10,773 0.0000 0.0000 0.0000 1.0000 100.00 100.00 Gracias a Dios 78714 10,794 1.0822 0.3269 1.0822 0.9914 96.97 93.02 Olancho 78717 10,816 0.1716 0.0483 0.1716 0.9999 99.69 99.25 Copán 78718 6,274 0.2401 0.0900 0.2401 0.9997 99.14 97.44 Ocotepeque 78719 7,045 0.8363 0.3004 0.8363 0.9957 96.86 91.46 Intibuca 78720 10,806 1.5322 0.6268 1.5322 0.9781 89.86 71.94 Francisco Morazán Source: “Gridded Analysis of Meteorological Variables for Hondurasâ€? (2010). 30 Maximum Temperature Station ID NO CRE MAE RMSE R Department 78700 9,969 0.2924 0.2036 0.2924 0.9930 Valle 78703 6,798 0.0960 0.0544 0.0960 0.9989 Islas de la Bahía 78704 2,570 0.3568 0.2241 0.3568 0.9942 Colón 78705 10,915 0.1642 0.1079 0.1642 0.9983 Atlántida 78706 10,605 0.0776 0.0484 0.0776 0.9996 Atlántida 78707 9,460 0.7062 0.5905 0.7062 0.9908 Yoro 78708 10,878 0.1684 0.0541 0.1684 0.9991 Cortes 78711 10,762 0.0000 0.0000 0.0000 1.0000 Gracias a Dios 78714 10,794 0.1004 0.0494 0.1004 0.9992 Olancho 78717 10,831 0.2136 0.1377 0.2136 0.9984 Copán 78718 6,256 0.0937 0.0179 0.0937 0.9994 Ocotepeque 78719 7,061 0.0803 0.0178 0.0863 0.9995 Intibuca 78720 10,957 0.2525 0.2037 0.2525 0.9984 Francisco Morazán Source: “Gridded Analysis of Meteorological Variables for Hondurasâ€? (2010). Minimum Temperature Station ID NO CRE MAE RMSE R Department 78700 9,966 0.2707 0.1217 0.2707 0.9942 Valle 78703 6,803 0.0586 0.0202 0.0586 0.9996 Islas de la Bahía 78704 2,572 0.2985 0.2111 0.2985 0.9918 Colón 78705 10,917 0.1928 0.1454 0.1928 0.9956 Atlántida 78706 10,649 0.0889 0.0542 0.0889 0.9991 Atlántida 78707 9,462 0.5657 0.4336 0.5657 0.9832 Yoro 78708 10,873 0.3546 0.1933 0.3546 0.9894 Cortes 78711 9,001 0.0000 0.0000 0.0000 1.0000 Gracias a Dios 78714 10,277 0.2187 0.1796 0.2187 0.9983 Olancho 78717 10,835 0.2427 0.1626 0.2427 0.9969 Copán 78718 6,257 0.0698 0.0116 0.0698 0.9994 Ocotepeque 78719 7,062 0.0381 0.0051 0.0381 0.9999 Intibuca 78720 10,958 0.2400 0.1906 0.2400 0.9983 Francisco Morazán Source: “Gridded Analysis of Meteorological Variables for Hondurasâ€? (2010). 31 Table 2. Skill Scores for Precipitation, Maximum and Minimum Temperature, Guatemala Precipitation Station ID NO CRE MAE RMSE R PC CSI Department 1 7,587 4.14 1.73 4.14 0.8015 87.27 64.74 Chimaltenango 2 10,636 1.23 0.49 1.23 0.9923 95.87 85.59 Jutiapa 3 10,138 0.97 0.39 0.97 0.9967 97.03 93.87 Alta Verapaz 4 10,865 1.51 0.56 1.51 0.9974 97.42 94.24 Escuintla 5 10,677 0.75 0.28 0.75 0.9962 96.00 85.50 Chiquimula 6 10.327 0.53 0.17 0.53 0.9996 98.87 97.44 San Marcos 8 10,401 0.89 0.37 0.89 0.9963 97.52 93.42 Quiché 9 10.772 1.54 0.71 1.54 0.9874 93.36 83.67 Alta Verapaz 10 10,781 0.93 0.45 0.93 0.9906 86.43 59.92 Quiché 11 10,621 1.12 0.61 1.12 0.9956 95.17 91.39 Alta Verapaz 12 10,592 0.68 0.29 0.68 0.9955 94.20 83.02 Baja Verapaz 13 10,379 0.65 0.28 0.65 0.9935 95.84 87.09 Huehuetenango 14 10,408 0.89 0.36 0.89 0.9927 95.93 88.02 San Marcos 15 9,514 3.68 1.45 3.68 0.8628 90.12 71.81 Sololá 16 5,508 0.92 0.39 0.92 0.9941 96.04 89.17 Sololá 17 10,807 0.62 0.25 0.62 0.9984 97.23 92.24 Chiquimula 18 10,680 0.00 0.00 0.00 1.0000 100.00 100.00 Petén 19 10,802 0.29 0.12 0.29 0.9992 97.91 92.62 Huehuetenango 20 10,834 3.85 1.63 3.85 0.8706 87.35 67.70 Guatemala 21 10,903 0.98 0.36 0.98 0.9925 95.38 81.65 Jalapa 22 10,757 0.84 0.34 0.84 0.9904 92.93 73.40 Zacapa 23 10,197 4.53 1.87 4.53 0.7917 87.46 66.30 Sacatepéquez 24 10,820 1.16 0.50 1.16 0.9956 96.89 92.90 Zacapa 25 10,744 0.37 0.15 0.37 0.9979 98.21 94.08 Quetzaltenango 27 10,381 0.33 0.13 0.33 0.9996 98.75 97.08 Izabal 28 4,826 1.50 0.63 1.50 0.9909 94.94 87.98 El Progreso 29 10,463 0.57 0.22 0.57 0.9989 99.01 97.05 Santa Rosa 31 10,155 0.16 0.05 0.16 0.9999 99.31 97.28 Jutiapa 32 10,353 2.35 0.94 2.35 0.9372 89.36 68.41 El Progreso 33 10,055 1.22 0.60 1.22 0.9936 95.16 90.74 Quiché 34 10,656 1.12 0.42 1.12 0.9859 94.24 79.96 Quetzaltenango 35 8,200 2.15 1.06 2.15 0.9907 92.77 86.90 Alta Verapaz 36 10,388 1.07 0.43 1.07 0.9964 95.12 89.49 Alta Verapaz 37 10,830 1.12 0.40 1.12 0.9875 95.06 78.90 Zacapa 38 10,440 1.14 0.45 1.14 0.9918 95.43 86.53 Jalapa 39 10,717 0.29 0.14 0.29 0.9999 98.56 97.30 Izabal 40 10,603 0.67 0.22 0.67 0.9962 97.60 89.66 Jutiapa 41 10,605 1.31 0.59 1.31 0.9982 97.13 93.18 Retalhuleu 42 10,675 2.52 1.24 2.52 0.9895 91.21 82.08 Escuintla 43 6,690 0.14 0.05 0.14 0.9999 99.69 99.30 Alta Verapaz 44 10,834 1.23 0.50 1.23 0.9851 92.51 76.26 Baja Verapaz 32 45 10,665 1.51 0.61 1.51 0.9930 88.56 67.06 Escuintla 46 10,015 3.77 1.59 3.77 0.9014 89.61 72.99 Chimaltenango 47 9,729 1.31 0.50 1.31 0.9901 95.12 83.41 Guatemala 49 10,738 0.72 0.34 0.72 0.9962 96.82 92.21 Huehuetenango 50 10,745 1.22 0.58 1.22 0.9916 95.23 91.61 Huehuetenango 51 9,584 1.39 0.59 1.39 0.9749 93.60 81.61 Chimaltenango 52 9,363 3.91 1.55 3.91 0.8713 91.28 75.28 Sololá Source: “Gridded Analysis of Meteorological Variables for Guatemalaâ€? (2010). Maximum Temperature Station ID NO CRE MAE RMSE R Department 2 10,541 0.7284 0.6485 0.7284 0.9895 Jutiapa 3 10,109 0.3503 0.3039 0.3503 0.9984 Alta Verapaz 4 10,848 1.5174 1.3381 1.5174 0.9011 Escuintla 5 10,403 0.7340 0.6879 0.7340 0.9973 Chiquimula 6 9,540 0.4612 0.3803 0.4612 0.9878 San Marcos 8 10,158 0.5423 0.4281 0.5423 0.9909 Quiché 9 10,155 0.4513 0.3383 0.4513 0.9910 Alta Verapaz 11 10,554 0.7256 0.6608 0.7256 0.9954 Alta Verapaz 12 9,713 0.4543 0.4014 0.4543 0.9969 Baja Verapaz 13 10,166 0.1805 0.1123 0.1805 0.9981 Huehuetenango 17 10,467 0.9373 0.9108 0.9373 0.9979 Chiquimula 18 10,498 0.0000 0.0000 0.0000 1.0000 Petén 19 10,449 0.0948 0.0609 0.0948 0.9993 Huehuetenango 20 10,567 0.7913 0.7226 0.7913 0.9893 Guatemala 21 10,873 1.0405 0.9884 1.0405 0.9906 Jalapa 22 10,471 0.4206 0.3247 0.4206 0.9951 Zacapa 24 10,725 1.1393 1.0675 1.1393 0.9939 Zacapa 25 10,720 0.2842 0.2063 0.2842 0.9951 Quetzaltenango 27 9,880 0.1217 0.0996 0.1217 0.9997 Izabal 29 10,453 0.1007 0.0703 0.1007 0.9992 Santa Rosa 31 9,948 0.0402 0.0156 0.0402 0.9997 Jutiapa 32 10,231 0.8839 0.7453 0.8839 0.9800 El Progreso 33 10,620 0.3676 0.2481 0.3676 0.9936 Quiché 35 6,924 0.5713 0.4777 0.5713 0.9923 Alta Verapaz 36 8,340 0.3774 0.3109 0.3774 0.9959 Alta Verapaz 37 10,832 0.4087 0.3278 0.4087 0.9928 Zacapa 38 10,703 0.2469 0.0535 0.2469 0.9948 Jalapa 39 10,456 0.1099 0.0896 0.1099 0.9997 Izabal 41 10,487 0.4547 0.3939 0.4547 0.9929 Retalhuleu 44 10,798 0.5989 0.5135 0.5989 0.9929 Baja Verapaz 46 10,112 0.4076 0.3162 0.4076 0.9915 Chimaltenango 47 6,178 1.1534 1.1020 1.1534 0.9940 Guatemala Source: “Gridded Analysis of Meteorological Variables for Guatemalaâ€? (2010). 33 Minimum Temperature Station ID NO CRE MAE RMSE R Department 1 7,851 1.7068 1.2590 1.7078 0.9213 Chimaltenango 2 10,548 0.5594 0.4677 0.5594 0.9860 Jutiapa 3 10,137 0.2834 0.2183 0.2834 0.9964 Alta Verapaz 4 10,866 1.6993 1.5522 1.6993 0.9289 Escuintla 5 10,448 0.4950 0.4387 0.4950 0.9945 Chiquimula 6 8,249 0.7181 0.5331 0.7181 0.9525 San Marcos 8 10,181 0.9339 0.8093 0.9339 0.9855 Quiché 9 10,716 0.7149 0.5986 0.7149 0.9834 Alta Verapaz 10 9,825 0.3080 0.2337 0.3080 0.9964 Quiché 11 10,557 0.4330 0.3753 0.4330 0.9956 Alta Verapaz 12 10,027 0.4326 0.3955 0.4326 0.9983 Baja Verapaz 13 10,569 0.6016 0.5028 0.6016 0.9937 Huehuetenango 14 10,317 0.8394 0.5679 0.8394 0.9813 San Marcos 16 5,375 0.7443 0.6464 0.7443 0.9899 Sololá 17 10,708 0.4530 0.4058 0.4530 0.9945 Chiquimula 18 10,484 0.0000 0.0000 0.0000 1.0000 Petén 19 10,594 0.1307 0.1021 0.1307 0.9997 Huehuetenango 20 10,526 0.5889 0.4508 0.5889 0.9699 Guatemala 21 10,812 0.7962 0.6924 0.7962 0.9924 Jalapa 22 10,542 0.7783 0.6639 0.7783 0.9854 Zacapa 25 10,719 0.1912 0.1279 0.1912 0.9992 Quetzaltenango 27 10,016 0.0576 0.0294 0.0576 0.9997 Izabal 29 10,410 0.2085 0.1709 0.2085 0.9985 Santa Rosa 32 10,277 0.8017 0.6214 0.8017 0.9595 El Progreso 33 10,619 1.1808 1.0390 1.1808 0.9866 Quiché 35 6,694 0.5225 0.3746 0.5225 0.9838 Alta Verapaz 36 8,304 0.3616 0.2815 0.3616 0.9960 Alta Verapaz 37 10,769 0.6590 0.5918 0.6590 0.9918 Zacapa 38 10,247 0.2698 0.0648 0.2698 0.9972 Jalapa 39 10,470 0.0338 0.0105 0.0338 0.9999 Izabal 40 10,354 0.2453 0.1765 0.2453 0.9959 Jutiapa 41 10,107 0.5801 0.5307 0.5801 0.9829 Retalhuleu 44 10,802 0.3242 0.2547 0.3242 0.9943 Baja Verapaz 45 10,703 0.0847 0.0236 0.0847 0.9992 Escuintla 46 10,066 1.2207 0.8809 1.2207 0.8887 Chimaltenango 47 5,744 0.3941 0.3232 0.3941 0.9944 Guatemala 49 10,580 0.2882 0.2166 0.2882 0.9911 Huehuetenango Source: “Gridded Analysis of Meteorological Variables for Guatemalaâ€? (2010). 34 35 36 FIDES