Hydrol. Earth Syst. Sci., 19, 857–876, 2015 www.hydrol-earth-syst-sci.net/19/857/2015/ doi:10.5194/hess-19-857-2015 © Author(s) 2015. CC Attribution 3.0 License. 102436 Calibration approaches for distributed hydrologic models in poorly gaged basins: implication for streamflow projections under climate change S. Wi1 , Y. C. E. Yang1 , S. Steinschneider1 , A. Khalil2 , and C. M. Brown1 1 Department of Civil and Environmental Engineering, University of Massachusetts Amherst, USA 2 The World Bank, Washington, DC, USA Correspondence to: S. Wi (sungwookwi@gmail.com) Received: 10 August 2014 – Published in Hydrol. Earth Syst. Sci. Discuss.: 17 September 2014 Revised: 13 January 2015 – Accepted: 20 January 2015 – Published: 10 February 2015 Abstract. This study tests the performance and uncertainty equifinality does emerge. The results suggest that increased of calibration strategies for a spatially distributed hydrologic (excessive) parameter complexity does not always lead to in- model in order to improve model simulation accuracy and creased predictive uncertainty if structural uncertainties are understand prediction uncertainty at interior ungaged sites of present. The largest uncertainty in future streamflow results a sparsely gaged watershed. The study is conducted using a from variations in projected climate between climate models, distributed version of the HYMOD hydrologic model (HY- which substantially outweighs the calibration uncertainty. MOD_DS) applied to the Kabul River basin. Several cali- bration experiments are conducted to understand the bene- fits and costs associated with different calibration choices, including (1) whether multisite gaged data should be used 1 Introduction simultaneously or in a stepwise manner during model fit- ting, (2) the effects of increasing parameter complexity, and In an effort to advance hydrologic modeling and forecasting (3) the potential to estimate interior watershed flows using capabilities, the development and implementation of physi- only gaged data at the basin outlet. The implications of the cally based, spatially distributed hydrologic models has pro- different calibration strategies are considered in the context liferated in the hydrologic literature, supported by read- of hydrologic projections under climate change. To address ily available geographic information system (GIS) data and the research questions, high-performance computing is uti- rapidly increasing computational power. Distributed hydro- lized to manage the computational burden that results from logic models can account for spatially variable physiographic high-dimensional optimization problems. Several interesting properties and meteorological forcing (Beven, 2012), im- results emerge from the study. The simultaneous use of mul- proving simulations compared to conceptual, lumped mod- tisite data is shown to improve the calibration over a step- els for basins where spatial rainfall variability effects are sig- wise approach, and both multisite approaches far exceed a nificant (Ajami et al., 2004; Koren et al., 2004; Reed et al., calibration based on only the basin outlet. The basin out- 2004; Khakbaz et al., 2012; Smith et al., 2012) and for nested let calibration can lead to projections of mid-21st century basins (Bandaragoda et al., 2004; Brath et al., 2004; Koren et streamflow that deviate substantially from projections under al., 2004; Safari et al., 2012; Smith et al., 2012). The ben- multisite calibration strategies, supporting the use of caution efits of distributed modeling have been recognized by the when using distributed models in data-scarce regions for cli- U.S. National Oceanic and Atmospheric Administration’s mate change impact assessments. Surprisingly, increased pa- National Weather Service (NOAA/NWS) and demonstrated rameter complexity does not substantially increase the un- in the Distributed Model Intercomparison Project (DMIP) certainty in streamflow projections, even though parameter (Reed et al., 2004; Smith et al., 2004, 2012, 2013). Impor- tantly, distributed hydrologic models can evaluate hydrolog- Published by Copernicus Publications on behalf of the European Geosciences Union. 858 S. Wi et al.: Implication for streamflow projections under climate change ical response at interior ungaged sites, a benefit not afforded let gage (which is often all that is available in developing- by lumped models. The use of distributed hydrologic mod- country river basins). In the case of significant spatial vari- eling for interior point streamflow estimation is particularly ability in the basin properties that influence runoff generation relevant for poorly gaged river basins in developing coun- (e.g., permeability, vegetation, and slope), accurate runoff tries, where reliable predictions at interior sites are often predictions are unlikely at interior locations based only on required to inform water infrastructure investments. As in- the lumped information obtained at the basin outlet (Ander- ternational development agencies begin to integrate climate son et al., 2001; Cao et al., 2006; Breuer et al., 2009; Lerat et change considerations into their decision-making processes al., 2012; Smith et al., 2012; Wang et al., 2012). The extent (e.g., Yu et al., 2013), these investments need to be robust of this error and uncertainty is not well understood for het- under both current climate conditions and possible future cli- erogeneous basins due to the computational expense required mate regimes. to explore this issue. Finally, rarely have the implications of Despite their roots in physical realism, distributed hydro- these calibration issues been explicitly examined for possi- logic models can suffer from substantial uncertainty. A major ble future climate conditions, which is required in climate source of uncertainty originates from the proper identifica- change impact studies. This question has been explored for tion of parameter values that vary across the watershed, espe- lumped, conceptual models (Wilby, 2005; Steinschneider et cially when observed streamflow data is only available at one al., 2012), but has been difficult to evaluate for computation- or a few points (Exbrayat et al., 2014). Parameters can be dis- ally expensive distributed models. cretized across the watershed in several ways (Flugel, 1995; This study addresses the above research challenges by fo- Efstratiadis et al., 2008; Khakbaz et al., 2012): uniquely for cusing on the following four questions: (1) how does calibra- each grid cell or hydrologic response unit (fully distributed), tion procedure for using multisite data affect the accuracy based on sub-basins whose boundaries do not necessarily and uncertainty of distributed models used for streamflow ensure homogenous characteristics (semi-distributed) or, in predictions at ungaged sites; (2) what effects does increased the simplest case, a single parameter set for all model grid parameter complexity have on distributed model calibration cells (lumped). With limited data, the parameter identifica- and prediction; (3) how much degradation in model accuracy tion problem, particularly for the fully distributed case, can and uncertainty can be expected for interior flow estimation be impractical or infeasible (Beven, 2001). The parameteri- based on a calibration procedure using only the basin out- zation challenge has spurred substantial advances in under- let; and (4) how do different calibration formulations for a standing appropriate calibration techniques for distributed distributed model alter projections of streamflow at ungaged hydrologic models. Many studies have attempted to reduce sites under climate change conditions? These questions are the dimensionality of the calibration problem to alleviate the considered in an application of a distributed version of the issue of equifinality (Beven and Freer, 2001), which is the daily HYMOD hydrologic model to the Kabul River basin phenomenon whereby multiple parameter sets produce in- in Afghanistan and Pakistan. To address these research ques- distinguishable model performance. This work has found fa- tions, high-performance computing is utilized to manage the vorable results when the parametric complexity of the dis- computational burden that often hinders such explorations tributed model is aligned with the data available for calibra- (Laloy and Vrugt, 2012; Zhang et al., 2013). tion (Leavesley et al., 2003; Ajami et al., 2004; Eckhardt et al., 2005; Frances et al., 2007; Zhu and Lettenmaier, 2007; Cole and Moore, 2008; Pokhrel and Gupta, 2010; Khakbaz et 2 Study area al., 2012). There has also been extensive research exploring the use of multiple objectives and different operational proce- The Kabul River basin (67 370 km2 ) is a plateau sur- dures to understand parameter estimation tradeoffs and iden- rounded by mountains located in the eastern central part of tifiability for distributed model calibration, with great suc- Afghanistan (Fig. 1). It is the most important river basin of cess (Madsen, 2003; Efstratiadis and Koutsoyiannis, 2010; Afghanistan, containing 35 % of the country’s population. Li et al., 2010; Kumar et al., 2013). While it encompasses just 12 % of the area of Afghanistan, Despite these advances, important questions still persist. It the basin’s average annual streamflow (about 24 billion cu- still remains difficult to compare the uncertainty that emerges bic meters) is about 26 % of the country’s total streamflow from different operational calibration procedures for mul- volume (World Bank, 2010). tisite applications (i.e., whether gages in series should be Water resources from the basin are shared by Afghanistan used sequentially or simultaneously for calibration) and un- and Pakistan and serve as a water supply source for more than der different levels of parametric complexity. Due to the 20 million people. The shared use of transboundary water be- computational burden required to calibrate distributed mod- tween these two countries is central in establishing regional els, this uncertainty is problematic to explore. Furthermore, water resources development for this area (Ahmad, 2010). It in poorly gaged basins, it is challenging to quantify the lost is crucial to develop tools that can support engineering plans accuracy and increased uncertainty for interior flow estima- for existing and potential water infrastructure to take full ad- tion when a distributed model is calibrated only at an out- vantage of the water resources in the basin. The government Hydrol. Earth Syst. Sci., 19, 857–876, 2015 www.hydrol-earth-syst-sci.net/19/857/2015/ S. Wi et al.: Implication for streamflow projections under climate change 859 Figure 1. Kabul River basin. of Afghanistan has developed comprehensive plans for new 70 % of annual precipitation (475 mm) falls during the win- hydropower projects on the Kabul River owing to its advanta- ter season (November–April). While the dominant source of geous topography for the development of water storage and streamflow in winter is baseflow and winter rainfall, glaciers hydropower (IUCN, 2010), and recently reached an agree- and snow cover are the most important long-term forms of ment with the Pakistan government to work on a 1500 MW water storage and, hence, the main source of runoff during hydropower project on the Kunar River (one of major tribu- the ablation period for the basin (Shakir et al., 2010). In to- tary in the Kabul River basin) as part of the joint management tal, 2.9 % (1954 km2 ) of the basin is glacierized based on of common rivers between the two countries (DAWN, 2013). the Randolph Glacier Inventory version 3.2 (Pfeffer et al., The streamflow regime of the Kabul River can be classified as 2014). The meltwater from glaciers and snow produce the glacial with maximum streamflow in June or July and min- majority (75 %) of the total streamflow (Hewitt et al., 1989). imum streamflow during the winter season. Approximately Table 1 provides the climates and geophysical properties of www.hydrol-earth-syst-sci.net/19/857/2015/ Hydrol. Earth Syst. Sci., 19, 857–876, 2015 860 S. Wi et al.: Implication for streamflow projections under climate change Table 1. Streamflow gaging stations in the Kabul River basin. Data period Physiographic property Basin climate Data source Station River Start End Drainage Glacier Mean Mean Mean Mean name area (km2 ) area ( %) elev. (m) annual annual annual Prcp. mean flow (mm) Temp. (◦ C) (mm) USGS/ Dakah Kabul 2/1968 7/1980 67 370 2.9 2883 418 7.7 282 GRDC USGS/ Pul-i-Kama Kunar 1/1967 9/1979 26 005 7.3 3446 446 5.6 573 GRDC USGS Asmar Kunar 3/1960 9/1971 19 960 9.4 3716 483 4.1 651 GRDC Chitral Kunar 1/1978 12/1981 11 396 14.4 4126 518 2.1 698 USGS Gawardesh Landaisin 5/1975 6/1978 3130 2.1 3707 555 4.5 521 USGS/ Chaghasarai Pech 2/1960 2/1979 3855 0.4 3141 482 7.4 535 GRDC USGS/ Daronta Kabul 10/1959 9/1964 34 375 0.3 2722 350 8.0 165 GRDC each sub-watershed delineated by the stations located inside the Supplement). Thus, the APHRODITE precipitation was the Kabul Basin (Fig. 1). Two different climate patterns are bias-corrected by the precipitation product from the Univer- distinguishable across the sub-basins. The sub-basins on the sity of Delaware global terrestrial precipitation (UD) data set Kunar River tributary (Kama, Asmar, Chitral, Gawardesh, (Legates and Willmott, 1990). Daily series of bias-corrected and Chaghasarai) receive moderate annual precipitation and APHRODITE precipitation were coupled with APHRODITE are highly affected by snow and glacier covers. All of these temperature for 160 0.25 ◦ C grid cells to produce a climate sub-basins have high ratios of mean annual flow to mean an- forcing data set for the distributed domain of the Kabul River nual precipitation, with the ratios for the Kama, Asmar, Chi- basin model. tral, and Chaghasarai sub-basins larger than 1. Conversely, This study used the set of global climate change simula- the Daronta sub-basin contains only minimal glacial cover, tions from the World Climate Research Programme’s Cou- and is relatively dry. Daronta is also much less productive, pled Model Intercomparison Project Phase 5 (CMIP5) mul- with annual streamflow far below the other sub-basins with timodel ensemble (Talyor et al., 2012). Monthly climate an average of only 165 mm yr−1 . outputs of GCMs (general circulation models) were down- Issues of shared water resources between Afghanistan and scaled to a daily temporal resolution and 0.25 ◦ C spatial res- Pakistan in the Kabul River basin are becoming complex olution based on the bias-correction spatial disaggregation due to the impacts of climatic variability and change (IUCN, (BCSD) statistical downscaling method introduced by Wood 2010). The vulnerability of glacial streamflow regimes to et al. (2004). changes in temperature and precipitation (Stahl et al., 2008; Monthly streamflow observations for seven locations in Immerzeel et al., 2012; Radic et al., 2014) highlights the need the Kabul River basin (Fig. 1) were gathered between calen- to assess the impact of climate change on future water avail- dar years 1960 and 1981 from two data sources: the Global ability in this area. Runoff Data Centre (GRDC) database and the United States Geological Survey (USGS) database (Table 1). Streamflow data were not collected in Afghanistan after September 1980 3 Data and models until recently because stream gaging was discontinued soon after the Soviet invasion of Afghanistan in 1979 (Olson and 3.1 Data Williams-Sether, 2010). Though measurements were taken at Gridded daily precipitation and temperature products with a a daily time step, data are only made available for public use spatial resolution of 0.25 ◦ C were gathered between calendar at monthly aggregated levels, calculated using the mean of years 1961 and 2007 from the Asian Precipitation Highly the daily values. The available monthly streamflow observa- Resolved Observational Data Integration Towards Evalua- tions at each station were used for calibrating and validating tion (APHRODITE) data set (Yatagai et al., 2012). There has the distributed hydrologic model (Fig. 2). Kama and Asmar been some concern regarding underestimation of precipita- stations are treated as ungaged sites because they align with tion in APHRODITE for some regions of Asia (Palazzi et the potential dam project on the Kunar River tributary. The al., 2013); our preliminarily data analysis (intercomparison two gage stations are left out of the processes of multisite of precipitation products between five different databases) calibrations in order to evaluate the model’s ability to predict confirmed this for the Kabul River basin (shown in Fig. S1 in streamflow at interior ungaged sites. Furthermore, half of the Hydrol. Earth Syst. Sci., 19, 857–876, 2015 www.hydrol-earth-syst-sci.net/19/857/2015/ S. Wi et al.: Implication for streamflow projections under climate change 861 sent soil moisture accounting, evapotranspiration, snow pro- cesses, glacier processes and flow routing. The model op- erates on a daily time step and requires daily precipitation and mean temperature as input variables. The overall model structure of the HYMOD_DS and its 15 parameters are de- scribed in Fig. 3 and Table 2, respectively. Further details are provided below. The HYMOD conceptual watershed model has been ex- tensively used in studies on streamflow forecasting and model calibration (Wagener et al., 2004; Vrugt et al., 2008; Kollat et al., 2012; Gharari et al., 2013; Remesan et al., 2013). The HYMOD is a soil moisture accounting model based on the probability–distributed storage capacity con- Figure 2. Streamflow data usage for the model calibration and val- cept proposed by Moore (1985). This conceptualization rep- idation. resents a cumulative distribution of varying storage capaci- ties (C ) with the following function: B record at the Dakah station, located at the basin outlet, is also C F (C) = 1 − 1 − 0 ≤ C ≤ Cmax , (1) used for validation purposes. Cmax The Randolph Glacier Inventory version 3.2 (RGI 3.2) where the exponent B is a parameter controlling the degree data set (Pfeffer et al., 2014) was used to extract glacial cov- of spatial variability of storage capacity over the basin and erage in the Kabul River basin, which totaled 5.7 % of the Cmax is the maximum storage capacity. The model assumes basin area (Fig. S2). In the hydrological modeling process, that all storages within the basin are filled up to the same the model needs to be informed by reliable estimates on vol- critical level (C ∗ (t)), unless this amount exceeds the storage ume of water retained in glaciers, especially for future sim- capacity of that particular location. With this assumption, the ulations under warming conditions. We followed the method total water storage S(t) contained in the basin corresponds to proposed in Grinsted (2013), which uses multivariate scaling relationships to estimate glacier and ice cap volume based B +1 Cmax C ∗ (t) on elevation range and area. Specifically, the scaling law in- S (t) = 1− 1− . (2) B +1 Cmax cluding area and elevation range factors was applied to esti- mate glacier/ice cap volume when the glacier depth exceeded Consequently, two parameters are introduced for the runoff 10 m. Otherwise, glacier/ice cap volume was estimated with generation process with two components: the area–volume scaling law. The elevation range spanned  by each individual glacier is estimated using the global dig-  P (t) + C ∗ (t − 1) − Cmax if P (t) ital elevation model (DEM) from the shuttle radar topog- Runoff1 = +C ∗ (t − 1) ≥ Cmax , (3) 0 if P (t) + C ∗ (t − 1) < Cmax  raphy mission (SRTMv4) in 250 m resolution (Jarvis et al., 2008). Density of ice (0.9167 g cm−3 ) is applied to calculate  glacier/ice cap volume in meters of water equivalent.  (P (t) − Runoff1 ) + (S (t) − S (t − 1)) The database for land covers and soil types of the Kabul Runoff2 = if P (t) − Runoff1 ≥ S (t) − S (t − 1) , (4) River basin (Fig. 1) are provided by the Food and Agricul-  0 if P (t) − Runoff1 < S (t) − S (t − 1) ture Organization of the United Nations (Latham et al., 2014) and United States Department of Agriculture – Natural Re- where P (t) is precipitation, Runoff1 is surface runoff, and sources Conservation Service Soils (USDA-NRCS, 2005), Runoff2 is subsurface runoff. A parameter (α) is introduced respectively. to represent how much of the subsurface runoff is routed over the fast (Qfast ) and slow (Qslow ) pathway: 3.2 Distributed Hydrologic Model (HYMOD_DS) Qfast = Runoff1 + α · Runoff2 , (5) Qslow = (1 − α) · Runoff2 . (6) In this study the lumped conceptual hydrological model HY- MOD (Boyle, 2001) is coupled with a river routing model The potential evapotranspiration (PET) is derived based on to be suitable for modeling a distributed watershed system. the Hamon method (Hamon, 1961), in which daily PET in We name it HYMOD_DS denoting the distributed version of millimeters is computed as a function of daily mean temper- HYMOD. Snow and glacier modules have been introduced ature and hours of daylight: to enhance the modeling process for glacier and snow cov- T ered areas within the Kabul River basin. The HYMOD_DS 0.611 · exp 17.27 · (T +273.3) is composed of hydrological process modules that repre- PET = Coeff · 29.8 · Ld · , (7) T + 273.3 www.hydrol-earth-syst-sci.net/19/857/2015/ Hydrol. Earth Syst. Sci., 19, 857–876, 2015 862 S. Wi et al.: Implication for streamflow projections under climate change Table 2. HYMOD_DS parameters. Feasible range Parameter Lower Upper name Description bound bound Coeff Hamon potential evapotranspiration coefficient 0.1 2 Cmax Maximum soil moisture capacity (mm) 5 1500 B Shape for the storage capacity distribution function 0.01 1.99 α Direct runoff and base flow split factor 0.01 0.99 Ks Release coefficient of groundwater reservoir 0.00005 0.001 DDFs Degree day snowmelt factor (mm ◦ C day−1 ) 0.001 10 Tth Snowmelt temperature threshold (◦ C) 0 5 Ts Snow/rain temperature threshold (◦ C) 0 5 r Glacier melt rate factor 1 2 Kg Glacier storage release coefficient 0.01 0.99 Tg Glacier melt temperature threshold (◦ C) 0 5 N Unit hydrograph shape parameter 1 99 Kq Unit hydrograph scale parameter 0.01 0.99 Velo Wave velocity in the channel routing (m s−1 ) 0.5 5 Diff Diffusivity in the channel routing (m2 s−1 ) 200 4000 Figure 3. Distributed version of the HYMOD model (HYMOD_DS). where Ld is the daylight hours per day, T is the daily mean glacial area and runoff from glacial areas is regarded as sur- air temperature (◦ C), and Coeff is a bias correction factor. face flow. The runoff from each area is weighted by its area The hours of daylight is calculated as a function of lati- fraction within the basin to obtain total runoff. tude and day of year based on the daylight length estimation The time rate of change in snow and glacier volume gov- model (CBM model) suggested by Forsythe et al. (1995). erned by ice accumulation and ablation (melting and subli- The HYMOD_DS includes snow and glacier modules mation) is expressed by the degree day factor (DDF) mass with separate runoff processes, i.e., the runoff from the balance model (Moore, 1993; Stahl et al., 2008). The domi- glacierized area is calculated separately and added to runoff nant phase of precipitation (snow vs. rain) is determined by generated from the soil moisture accounting module cou- a temperature threshold (Tth ). The snowmelt Ms and glacier pled with the snow module. The implicit assumption here is melt Mg is calculated as that there is no interchange of water between soil layers and Hydrol. Earth Syst. Sci., 19, 857–876, 2015 www.hydrol-earth-syst-sci.net/19/857/2015/ S. Wi et al.: Implication for streamflow projections under climate change 863 outlet (Dakah), should be approached with caution. Given that a majority of the gages examined in this study are on an Ms = DDFs × (T − Ts ) , (8) underdeveloped branch of the Kabul River, issues of human Mg = DDFg × T − Tg , (9) interference on calibration are somewhat mitigated. with DDFs (Ts ) and DDFg (Tg ) applied separately for snow and glacier modules, respectively. To account for the higher 4 Methods melting rate of glaciers than snow owing to the low albedo (Konz and Seibert, 2010; Kinouchi et al., 2013), we intro- The purpose of this study is to explore the implications duced a parameter r > 1 to constrain DDFg to be larger than of different calibration strategies and choices for a compu- DDFs (i.e., DDFg = r × DDFs ). For the rain that falls on tationally expensive distributed hydrologic model. A vari- the glacierized area, the glacier parameter Kg determines the ety of calibration experiments are conducted, with the re- portion of rain becoming surface runoff as a multiplier for the sults from preceding experiments informing choices made rainfall. The remaining rainfall is assumed to be accumulated for subsequent ones. All calibration approaches are tested in to the glacier store. terms of their ability to predict flows at interior site gages The within-grid routing process for direct runoff is rep- that were left out of the calibration process. In all cases, resented by an instantaneous unit hydrograph (IUH) (Nash, the genetic algorithm (GA) introduced by Wang (1991) is 1957), in which a catchment is depicted as a series of N used as an optimization method for model parameter cali- reservoirs each having a linear relationship between storage bration, and the objective function is based simply on the and outflow with the storage coefficient of Kq . Mathemati- Nash–Sutcliffe efficiency (NSE) (Nash and Sutcliff, 1970), cally, the IUH is expressed by a gamma probability distribu- which is by far the most utilized performance metric in hy- tion: drological model applications (Biondi et al., 2012). A mul- tisite average of the NSE is used when evaluating perfor- Kq N −1 u (t) = Kq t exp −Kq t , (10) mance across multiple sites. We fully recognize that the use (N ) of one objective, such as the NSE, is inferior compared to multiobjective approaches that can identify Pareto optimal where is the gamma function. The within-grid groundwater solutions that provide good model performance across dif- routing process is simplified as a lumped linear reservoir with ferent components of the flow regime (Madsen, 2003; Efs- the storage recession coefficient of Ks . tratiadis and Koutsoyiannis, 2010; Li et al., 2010; Kumar et The transport of water in the channel system is described al., 2013). However, in this particular study daily hydrologic using the diffusive wave approximation of the Saint-Venant model simulations can only be compared against available equation (Lohmann et al., 1998): monthly streamflow records, reducing the number of viable ∂Q ∂Q ∂ 2Q objectives against which to calibrate. That is, statistics repre- +C − D 2 2 = 0, (11) senting peak flows, extreme low flows, and other daily flow ∂t ∂x ∂ x regime characteristics often used in multiobjective optimiza- where C and D are parameters denoting wave velocity (Velo) tion approaches are unavailable. We believe that the use of a and diffusivity (Diff), respectively. monthly NSE value as a single objective, while coarse, does Similar to most other hydrological models (Efstratisdis et not inhibit our ability to provide insight into the research al., 2008), HYMOD_DS is not designed to model water ab- questions posed. In addition to the NSE, the Kling–Gupta stractions for agricultural lands and dam operations within efficiency (KGE) (Gupta et al., 2009) is adopted as an al- the basin. According to the World Bank (2010), water de- ternative model performance metric, which equally weights mand for agricultural use is about 2000 million cubic me- model mean bias, variance bias, and correlation with obser- ters, or about 8.3 % of the total annual flow. The Naglu dam vations. (Fig. 1) upstream of the Daronta streamflow gage forms the In this study, three levels of parameter complexity are con- largest and most important reservoir in the basin, with an ac- sidered: lumped, semi-distributed, and fully distributed for- tive storage of 379 million cubic meters. In our hydrologic mulations (Fig. 4). The different levels of parameter com- modeling process, the water consumed by irrigated crop- plexity are defined according to the spatial distribution of lands is implicitly accounted for by the evapotranspiration unique hydrologic model parameters. In the lumped formu- module. We note that the degree of irrigation impact dur- lation a single parameter set is applied to the entire basin. ing the time frame used for calibration (1960–1981) is likely In the semi-distributed formulation, a unique parameter set much smaller than the current level. We also expect that using is assigned to each sub-basin, defined based on the location monthly data for calibration somewhat reduces the bias from of available streamflow gaging sites. The fully distributed human interference, particularly the daily operations of the parameter structure follows the spatial discretization of cli- Naglu dam. Nevertheless, the calibration results for the gage mate input grids, allowing for a unique parameter set for each below this dam (Daronta), and to a lesser extent the basin grid cell. No matter the parameterization scheme, the model www.hydrol-earth-syst-sci.net/19/857/2015/ Hydrol. Earth Syst. Sci., 19, 857–876, 2015 864 S. Wi et al.: Implication for streamflow projections under climate change Figure 4. Model structure based on climate input grids and three different parameterization concepts. structure follows the climate input grids; i.e., the hydrolog- and pooled approach. In the stepwise calibration, parameters ical water cycle within each grid cell is modeled separately. are calibrated for upstream gaged sub-catchments and subse- We note that a lumped model structure (i.e., no gridded or quently fixed during calibration of downstream points, while sub-unit structure) has often been considered as a baseline for the pooled approach, parameters are calibrated for multi- model formulation in the assessment of distributed model- ple sub-catchments simultaneously. Both approaches are as- ing frameworks (e.g., see Smith et al., 2013). However, the sessed for the semi-distributed formulation. The better of focus of our study is on ungaged interior site streamflow the two methods is identified for use in the second experi- estimation, making this formation somewhat inappropriate. ment, where the effects of increased parameter complexity Furthermore, preliminary tests comparing streamflow sim- are tested in terms of streamflow prediction accuracy and un- ulations at the basin outlet (Dakah) between a gridded and certainty. In the third experiment, we consider the situation basin-averaged structure, both with a lumped parameter for- where there is only data at the basin outlet for calibration. mulation, support the use of the distributed grid structure Here, the model is calibrated against the outlet gage under all (Fig. S3). levels of parameter complexity and is compared against the The parameter complexity will vary depending on the cal- best combination of calibration strategy (stepwise or pooled) ibration experiment being conducted but, for each exper- and parameter complexity (lumped, semi-distributed, or fully iment regardless of the parameterization, the optimization distributed) identified in the previous experiments. Finally, a is implemented 50 times using the GA algorithm to ex- subset of the calibration approaches deemed worthy of fur- plore calibration uncertainty. The considerably high compu- ther investigation are compared in terms of their projections tational cost required to perform a large number of calibra- of future streamflow under climate change to highlight how tions is managed using the parallel computing power pro- model calibration differences can alter the results of a climate vided by the Massachusetts Green High-Performance Com- change assessment for water resources applications. These puting Center (MGHPCC), from which several thousands of experiments are described in further detail below. processors are available. In the first modeling experiment, we explore two calibra- tion strategies for using multisite streamflow data, a stepwise Hydrol. Earth Syst. Sci., 19, 857–876, 2015 www.hydrol-earth-syst-sci.net/19/857/2015/ S. Wi et al.: Implication for streamflow projections under climate change 865 searches the entire parameter space at once to maximize the average NSE across all sites. This operational feature reduces the processing time spent on the GA implementation com- pared to the stepwise calibration strategy. To identify the bet- ter of the two multisite calibration approaches, the compar- ison focused on their ability to predict streamflow and cal- ibration uncertainties at two interior site gages (Kama and Asmar) that were assumed to be ungaged (Fig. 5), as well as for validation data at the basin outlet. It is important to note that the evaluation of these multi- site calibration strategies is somewhat weakened because of the lack of overlapping data periods among most of the sta- tions (Fig. 2). This drawback prevents the calibration meth- ods from accounting for simultaneous information from dif- ferent tributaries, which, if available, would better enable the calibration methods to account for heterogeneity of hydro- logical processes across the sub-basins. 4.2 Increased parameter complexity Figure 5. (a) Sub-basins corresponding to five gaging stations are In the second experiment, the better of the two approaches used for the multisite calibrations. (b) Two sub-basins (Kama and (stepwise or pooled) identified in the first experiment is fur- Asmar) are assumed to be ungaged and used for evaluating the cal- ther tested with respect to the three different levels of param- ibration approaches. eter complexity. In addition to the semi-distributed param- eter formulation considered in the first experiment, lumped and fully distributed parameter formulations are calibrated 4.1 Multisite calibration: stepwise and pooled for the selected approach to investigate the gain or loss aris- approaches ing from different levels of parameter complexity. Since the hydrologic model HYMOD employed in this study involves In the first experiment, the semi-distributed parameterization 15 parameters, the lumped version of the HYMOD_DS con- concept is compared under alternative multisite calibration tains a single, 15-member parameter set applied to all model strategies, the stepwise and pooled calibration approaches. grid cells. The semi-distributed conceptualization of HY- To conduct the stepwise calibration, a nested class of sub- MOD_DS contains a single parameter set for each sub- basins is defined corresponding to multiple gaging stations. basin, totaling 75 parameters. In the distributed parameteri- In the first step of the stepwise calibration, the optimiza- zation the number of parameters increases dramatically. With tion process is carried out with nested sub-basins at the low- 160 0.25 ◦ C grid cells, the number of parameters requiring est level (i.e., the most upstream sites). Once parameters of calibration reaches 2400. As the number of parameters in- nested sub-basins are determined, the parameters are fixed, crease across the parameterization schemes, calibration be- and the calibration procedure proceeds with nested basins at comes increasingly computationally expensive. The num- upper levels until parameters for the entire basin are deter- ber of model runs used in the GA optimization algorithm mined. In this particular application to the Kabul River basin, for the lumped, semi-distributed, and distributed parameter- five gaged sub-basins were selected and the stepwise calibra- ization schemes are 15 000 (150 populations × 100 gener- tion procedure for those sub-basins followed this direction: ations), 75 000 (750 × 100), and 480 000 (2400 × 200), re- Chitral → Gawardesh → Chaghasarai → Daronta → Dakah spectively. These population/generation sizes were supported (Fig. 5). The stepwise calibration approach involves a num- using convergence tests for each calibration. Again, 50 sep- ber of GA implementations corresponding to the number of arate GA optimizations were used to explore calibration un- gaging sites. The GA optimization was carried out a total of certainties for each parameterization scheme. To give a sense 250 times in this application, with 50 optimization runs con- of the computational burden of this experiment, we note that taining GA implementations for five sub-basin regions. 50 trials of the HYMOD_DS calibration under the distributed The pooled calibration strategy involves calibrating all pa- conceptualization required 1000 processors over 7 days on rameters of the model domain simultaneously against mul- the MGHPCC system. tiple streamflow gages within the watershed. This approach aims at looking for suitable parameters that are able to pro- duce satisfactory model results at all gaging stations in a single implementation of GA optimization. That is, the GA www.hydrol-earth-syst-sci.net/19/857/2015/ Hydrol. Earth Syst. Sci., 19, 857–876, 2015 866 S. Wi et al.: Implication for streamflow projections under climate change 4.3 Basin outlet calibration the model performance evaluated with the NSE, as well as an alternative metric, the KGE. The third experiment considers the situation where there is only gaged data at the basin outlet (Dakah) for calibration, 5.1 Pooled calibration vs. stepwise calibration a common situation when calibrating hydrologic models in data-scarce river basins. Here, we evaluate the potential of This section reports the results from the first experiment the basin outlet calibration to estimate interior watershed comparing the stepwise and pooled calibration approaches flows in terms of both accuracy and precision at all gaging for the semi-distributed model parameterization. Figure 6 stations. All levels of parameter complexity are considered shows the comparison between the Semi-Stepwise and Semi- for this calibration. The main purpose of this experiment is to Pooled with box plots representing the 50 trials of calibra- compare the veracity of a distributed hydrologic model cali- tion. Under the stepwise calibration the results for four sub- brated only using basin outlet data with results from multisite basins (Chitral, Gawardesh, Chaghasarai, and Daronta) are calibrations to better understand the degradation in model optimal because there is no interaction between those sub- performance under data scarcity. Other than the use of an basins. However, the calibrated parameter sets of each sub- NSE objective only at the basin outlet, all other GA settings basin act as constraints in the last step of the Semi-Stepwise for each level of parameter complexity are identical to the resulting in the degradation of model skill at the basin out- settings used in the second experiment. let (Dakah) and two left-out gages (Asmar and Kama). This becomes apparent when comparing the Semi-Stepwise to the 4.4 Climate change projections of streamflow Semi-Pooled results. The model skill under the Semi-Pooled is similar to that from the Semi-Stepwise with respect to the The fourth experiment investigates how the choice of cali- four upstream sub-basins, but it outperforms at the verifi- bration approach can alter the projections of future stream- cation gages. This is particularly true for the Asmar gage, flow under climate change. To explore this question, stream- which exhibits a downward bias and substantial variability flow simulations for the 2050s, defined as the 30-year period in performance under the Semi-Stepwise. The Semi-Pooled spanning from 2036 to 2065, are carried out using climate results suggest that small sacrifices of model performance projections from the CMIP5 (Talyor et al., 2012). A total of at certain sites can improve and stabilize basin-wide perfor- 36 different climate models run under two future conditions mance. Expected values of KGE from 50 calibrations are also of radiative forcing (RCP 4.5 and 8.5) are used. Streamflow provided (values in parenthesis in the bottom of Fig. 6) and projections are developed for the basin outlet (Dakah) and this performance metric also leads to the same conclusion. two interior gages left out of the calibration (Kama and As- Therefore, the Semi-Pooled was selected as the better multi- mar). By using 36 different GCMs and 50 optimization trials site calibration strategy and is considered for further analyses for each calibration scheme, this analysis compares the un- in the following sections. certainty in future streamflow projections originating from uncertainty in different hydrologic model parameterization 5.2 Pooled calibration with alternative schemes and under alternative future climates. parameterizations Streamflow projections are considered under all three parameterization schemes (lumped, semi-distributed, and Here we examine results for the three levels of parameter fully distributed) for both the basin outlet model and the complexity applied to the pooled calibration approach. Fig- best multisite calibration approach (stepwise or pooled). ure 7 shows the comparison of the pooled calibrations. Un- Multiple streamflow characteristics are evaluated, includ- surprisingly, streamflow predictions from the Lump-Pooled ing monthly streamflow, wet (April–September) and dry have the lowest accuracy and largest uncertainty at the cal- (October–March) season flows, and daily peak flow re- ibration sites, particularly for the Chaghasarai and Daronta sponse. The differences and uncertainty in these metrics sites. This demonstrates the well-known difficulty in rep- across calibration approaches will highlight the importance resenting flow characteristics of a spatially variable system of calibration strategy for evaluating future water availability with a homogenous parameter set (Beven, 2012). The pooled and flood risk. calibration substantially improves with increasing parame- ter complexity at the calibration sites. Both the Semi-Pooled 5 Results and Dist-Pooled produce NSE values above 0.8 for all cal- ibration sites; however, the Dist-Pooled shows a somewhat For the remaining part of the paper, we introduce the higher performance, undoubtedly from its greater freedom to following shorthand: Lump, Semi, and Dist indicate the overfit to the calibration data. However, the advantage of the lumped, semi-distributed, and fully distributed parameteriza- Dist-Pooled with respect to streamflow predictions at valida- tion schemes, and Outlet, Stepwise, and Pooled correspond tion sites becomes less clear. Only the Dist-Pooled at Kama to basin outlet, stepwise, and pooled calibrations. The com- shows marginally better predictions, while the results are am- parison between different calibration strategies is based on biguous at Dakah and Asmar. Overall, this likely suggests Hydrol. Earth Syst. Sci., 19, 857–876, 2015 www.hydrol-earth-syst-sci.net/19/857/2015/ S. Wi et al.: Implication for streamflow projections under climate change 867 Figure 6. Comparison of the stepwise and pooled calibrations under the semi-distributed parameterization. Each calibration is conducted 50 times. Values on the bottom represent expected values of NSE (in upper row) and KGE (within parenthesis in lower row) from 50 calibrations. Figure 7. Comparison of the pooled calibrations for the 3 parameterizations of lumped, semi-distributed, and distributed. Each calibration is conducted 50 times. Values on the bottom represent expected values of NSE (in upper row) and KGE (within parenthesis in lower row) from 50 calibrations. that the fully distributed conceptualization leads to overfit- the one for Asmar (1966–1971), which encompasses those ting of the model as compared to the Semi-Dist conceptu- two sub-basins. Instead, the validation at Asmar is mostly alization. We reached the same conclusion when examining affected by the calibration to Dakah because of the overlap- the KGE values, which rise with greater parameter complex- ping 4 years (1968–1971) between those two sites. This ex- ity at calibration sites but no longer follow this pattern strictly plains the reason why the Lump-Pooled shows high skill at at validation sites. Asmar despite the low skill at its sub-basins. However, the Interestingly, the Lump-Pooled performs well at the verifi- low model skill at Chaghasarai from the Lump-Pooled propa- cation sites despite its poor performance at calibration sites. gates to the validation result at Kama, as these two sites have The Lump-Pooled does not show significant degradation in a relatively long overlapping period (8 years, from 1967 to skill at Kama compared to the more complex parameteriza- 1974). tions, and the flow prediction at Asmar actually exhibits the best performance of all three model variants. A partial reason 5.3 Limitations of the basin outlet calibration for this unexpected result arises from different overlapping periods in the calibration and validation data (see Fig. 2). The In the third experiment the HYMOD_DS was calibrated periods used for the calibration for Chitral (1978–1981) and only to data at the basin outlet under all levels of parame- Gawardesh (1975–1978) have no overlapping periods with ter complexity, and streamflow records for all six sub-basins, as well as flows at Dakah not used during calibration, are www.hydrol-earth-syst-sci.net/19/857/2015/ Hydrol. Earth Syst. Sci., 19, 857–876, 2015 868 S. Wi et al.: Implication for streamflow projections under climate change Figure 8. Comparison of the basin outlet calibrations for the three parameterizations of lumped, semi-distributed, and distributed. Each calibration is conducted 50 times. Values on the bottom represent expected values of NSE (in upper row) and KGE (within parenthesis in lower row) from 50 calibrations. used for model validation. First, we consider the flows at the results indicate that any calibration based on basin outlet Dakah. During the calibration period, all three parameteriza- data should be used with substantial caution when predicting tion schemes produce very accurate streamflow predictions flows at interior basin sites. with NSE (KGE) values above 0.95 (0.96) (Fig. 8). High ac- After reviewing all of the calibration experiments, it be- curacy holds even under the Lump-Outlet, despite the spa- comes clear that the Semi-Pooled and Dist-Pooled calibra- tial heterogeneity of the basin. While NSE and KGE values tions provide more robust performance compared to the basin at Dakah rise marginally with greater parameter complexity outlet calibrations due to their improved representation of in- during calibration, this no longer holds during the validation ternal hydrologic processes across the basin. To further com- period, suggesting no benefit with an increase in parameter pare these calibration strategies against one another, we eval- complexity. uate the variability in optimal parameters resulting from the The validation results for the six sub-basins demonstrate 50 trials of the GA algorithm. Figure 9 shows the coefficient the danger in relying on outlet data alone when calibrating of variation (CV) of Cmax (a parameter for the soil moisture a distributed model for flow prediction at interior points. account module) over the basin from all combinations of cal- Streamflow predictions at interior sites exhibit low accu- ibration approaches (the outlet and pooled) and three param- racy and high uncertainty, with the worst performance at the eterization schemes. A clear pattern of increasing variabil- Daronta site (all NSEs and KGEs are negative). We note that ity (higher uncertainty in Cmax ) emerges as parameter com- the poor performance at Daronta is likely due in part to the plexity increases for both the outlet and pooled calibration impacts of water abstraction and the operation of Naglu dam. strategies. That is, the semi- and fully distributed parameter- Further examination (Fig. S4) showed that the HYMOD_DS izations lead to significantly variable parameter sets that pro- significantly overestimated streamflow at Daronta and un- duce similar representations of the observed basin response. derestimated flow at three sites in the eastern part of the Figure 9 also suggests that the equifinality can be alleviated basin (Chitral, Gawardesh, and Chaghasarai). Model perfor- to an extent by pooling data across sites. The pooled calibra- mance at Kama and Asmar is somewhat better than at the tion approaches consistently show lower variability in Cmax other validation sites, although improvements are not the compared to the outlet calibration at the same level of param- same across all parameterizations. The Lump-Outlet predic- eter complexity. These results are relatively consistent across tions at these sites still have low average accuracy (average the remaining 14 HYMOD_DS parameters. The implications NSE < 0.7 and average KGE < 0.6), while the Semi-Outlet of parameter stability on streamflow projections under cli- exhibits large uncertainty in performance across the 50 op- mate change is addressed in the next section. timization trials. Surprisingly, the over-parameterized Dist- Outlet shows promising results with high expected accuracy 5.4 Climate change projections of streamflow with at Kama and Asmar (mean NSE (KGE) of 0.84 (0.71) and uncertainty 0.90 (0.88), respectively) and comparable performance at many of the other sites. One exception is Gawardesh, where Here we explore how projections of future water availabil- the Lump-Outlet outperforms the other model variants, al- ity and flood risk under climate change are influenced by the though the reason for this is not immediately clear. Overall, choice of calibration approach. For the Kabul River basin, Hydrol. Earth Syst. Sci., 19, 857–876, 2015 www.hydrol-earth-syst-sci.net/19/857/2015/ S. Wi et al.: Implication for streamflow projections under climate change 869 Lump-Outlet. The historical monthly streamflow estimates from the outlet calibration strategies also tends to be highly uncertain for the months of June, July, August, and Septem- ber, especially compared to the Semi-Pool and Dist-Pool. Under future climate projections for the 2050s, the four calibration strategies show similar changes in monthly streamflow at Dakah, but the magnitudes of change are some- what different. All calibration strategies suggest reduction in streamflow for June, July, and August under both RCP 4.5 and 8.5 scenarios. Also, the peak monthly flow, which oc- curred in June or July in the historical period, is shifted to May at Dakah. However, the Lump-Outlet predicts less re- duction of flow in June and July and a greater reduction in August and September as compared to the other three cali- brations. Considering that all calibration schemes had simi- lar levels of good performance at this site for both calibration and validation periods, it is notable that they project future streamflow somewhat differently. Future monthly streamflow predictions at Kama and As- mar vary widely between the four calibration schemes, mostly an artifact of their historic differences (Fig. 10). Streamflow projections under the outlet calibration strate- gies tend to show large uncertainties at these two sites, Figure 9. Coefficient of variation (CV) of 50 optimal values of particularly the Lump-Outlet calibration. For three months, Cmax (parameter for the soil moisture accounting module in the July–September, the outlet calibration and pooled calibra- HYMOD_DS) from the basin outlet calibrations (left panel) and tion strategies provide substantially different insights about the pooled calibrations (right panel). future water availability at Kama and Asmar. The outlet cali- brations suggest less water with large uncertainties for those months as compared to the pooled calibrations. At Kama, the the CMIP5 GCM projections of monthly total precipitation pooled calibrations suggest significant changes in the pattern and mean temperature are shown in Fig. S5. According to of peak monthly flow timing under both RCP scenarios; in- the CMIP5 ensemble, precipitation projections show no clear stead of having a clear peak in July, streamflow from May to trend; the average precipitation change in monthly total pre- August show similar amounts of water. cipitation fluctuates between −10 and 10 mm. On the other To further understand the sources of uncertainty in future hand, temperature clearly shows an upward trend for both water availability, we evaluate the separate and joint influ- radiative forcing scenarios. The average changes in annual ence of uncertainties in parameter estimation and future cli- temperature are +2.2 and +2.8 ◦ C for RCPs 4.5 and 8.5, mate on seasonal streamflow projections across all calibra- which, using the Hamon method, correspond to an increase tion schemes. Figure 11 represents the uncertainty of wet in annual PET by approximately 100 and 150 mm, respec- and dry seasonal streamflow at Dakah from three sources: tively. (1) calibration uncertainty across the 50 trials, with future We first examine average monthly streamflow estimates climate uncertainty averaged out for each trial; (2) future cli- across four calibration strategies: the Semi-Pooled and Dist- mate uncertainty across the 36 projections, with calibration Pooled (most promising calibration strategies), as well as the uncertainty averaged out across the 50 trials; and (3) the com- Lump-Outlet (as a baseline) and Dist-Outlet (the best outlet bined uncertainty across all 1800 (50 × 36) simulations. The calibration strategy). Figure 10 shows the monthly stream- results suggest somewhat surprisingly that uncertainty reduc- flow estimates for the historical period with the whisker bars tion can be expected as parameter complexity increases and, indicating the uncertainty range across the 50 calibration tri- less surprisingly, by applying pooled calibration approaches. als. The monthly streamflow predictions are also provided for Another clear point is that the uncertainty resulting from dif- the 2050s under the RCP 4.5 and 8.5 scenarios. For the fu- ferent climate change scenarios substantially outweighs that ture scenarios, the whisker bars are derived by averaging over from calibration uncertainty. the 36 different climate projections for each of the 50 trials. Up to this point, there has been little difference between For the historical time period, all calibration schemes match the Semi-Pooled and Dist-Pooled model variants. These the observed monthly streamflow at Dakah well, but monthly two versions were further analyzed with respect to extreme streamflow is underestimated in most months at Kama and streamflow to see if distinguishing characteristics emerge. It Asmar under the basin outlet calibrations, particularly by the has been demonstrated that clear gains in predicting peak www.hydrol-earth-syst-sci.net/19/857/2015/ Hydrol. Earth Syst. Sci., 19, 857–876, 2015 870 S. Wi et al.: Implication for streamflow projections under climate change Figure 10. Historical and 2050s average monthly streamflow predictions at Dakah, Kama, and Asmar under four calibration strategies: Lump-Outlet, Dist-Outlet, Semi-Pooled, and Dist-Pooled. The error bars represent the streamflow ranges resulting from 50 trails of the HYMOD_DS calibration. For each of the 50 trials, the 2050s streamflow predictions are averaged over 36 GCM climate projections. Figure 11. Uncertainties in wet and dry season average streamflow predictions for 2050s are derived from the basin outlet and pooled calibrations for Dakah. Uncertainties are evaluated by the CV of average season streamflow predictions. Three uncertainty sources are considered: calibration uncertainty across 50 calibration trials (Par), climate uncertainty across GCM projections (Clim), and combined uncertainty (Joint). Hydrol. Earth Syst. Sci., 19, 857–876, 2015 www.hydrol-earth-syst-sci.net/19/857/2015/ S. Wi et al.: Implication for streamflow projections under climate change 871 flows from distributed models are noticeable (Reed et al., 2004) and spatial variability in model parameters signifi- cantly influence the runoff behavior (Brath and Montanari, 2000; Pokhrel and Gupta, 2011). The spatial variability of optimal parameters derived from the Semi-Pooled and Dist- Pooled is shown in Fig. S6, with larger variability across all parameters for the Dist-Pooled than for the Semi-Pooled. To understand the effects of spatial variability and calibration uncertainty of parameters on extreme event estimation, the 100-year daily flood event was calculated under the Semi- Pooled and Dist-Pooled for each of the 50 historic simula- tions and 1800 future simulations across both RCP scenar- ios. Although the intermodel comparison is intended to be a useful addition that provides a distinction between the pa- rameterization schemes in the pooled calibration approach, results from this analysis should be viewed in the context of a theoretical calibration exercise, not for decision-making purposes, because no observed daily streamflow is avail- able against which to compare the estimated 100-year daily flood events. Projections of the 100-year daily flood, esti- mated using a log-Pearson type III distribution fit to annual peaks of 30 years, differ somewhat between the Semi-Pooled and Dist-Pooled (Fig. 12). At three validation sites, extreme floods are consistently larger under the Semi-Pooled than the Dist-Pooled, and the mean difference in the 100-year daily Figure 12. Comparison of GCM average 100-year daily flood flood estimate between the two calibration approaches grows events derived from the semi-distributed and distributed pooled cal- between the historic runs and the RCP 4.5 and 8.5 scenar- ibrations. The uncertainty range is from 50 trials of the model cali- ios. This suggests that the flood-generation process is funda- bration. mentally different between the two parameterizations, with the Semi-Pooled formalization magnifying the effect of cli- mate change on extremes. Furthermore, there is substantially 6 Discussion and conclusion more uncertainty in the 100-year daily flood estimate un- der the Semi-Pooled. Figure 12 shows the combined uncer- In this study we examined a variety of calibration experi- tainty across both climate projections and calibrations, but ments to better understand the benefits and costs associated this uncertainty is broken down further in Fig. 13. Similar with different calibration choices for a complex, distributed to Fig. 11, three sources of uncertainty are evaluated for the hydrologic model in a data-scarce region. The goal of these 100-year daily flood, including calibration uncertainty alone, experiments was to provide insight regarding the use of mul- climate projection uncertainty alone, and their combined ef- tisite data in calibration, the effects of parameter complexity, fect. For both the Semi-Pooled and Dist-Pooled, calibration and the challenges of using limited data for distributed model uncertainty has a smaller influence than projection uncertain- calibration, all in the context of projecting future streamflow ties and, for all sites, the Dist-Pooled has a smaller uncer- under climate change. tainty range than the Semi-Pooled, even for calibration un- This study tested two multisite calibration strategies, the certainty alone. This was a truly surprising result, given the stepwise and pooled approaches, finding that the pooled ap- parametric freedom in the Dist-Pooled model and the fact proach using all data simultaneously provides improved cal- that no daily data were ever used in the calibration of either ibration results. This suggests that small sacrifices of model model. It appears that a lack of model parsimony does not performance at certain sites can improve and stabilize basin- necessarily lead to greater uncertainty in model simulations wide performance. The pooled calibration substantially im- under different climate conditions, somewhat counter to what proves with increasing parameter complexity at the calibra- would be expected of overfit models. One possible reason for tion sites, but similar streamflow predictions at the valida- this result would be if increased parametric freedom some- tion sites between the semi-distributed and distributed pooled how offset the effects of structural deficiencies in the model. calibrations were found, suggesting overfitting of the model However, further research is needed to investigate this issue. from the fully distributed conceptualization. It is worth not- ing that for the transformation of rainfall to runoff, up to five or six parameters can be identified on the basis of a single hydrograph (Wagner et al., 2001). Under this premise, the www.hydrol-earth-syst-sci.net/19/857/2015/ Hydrol. Earth Syst. Sci., 19, 857–876, 2015 872 S. Wi et al.: Implication for streamflow projections under climate change tury streamflow that deviate substantially from projections under multisite calibration strategies. From the test of impli- cations of the pooled calibration in the context of climate change, it was found that applying the pooled calibration with semi-distributed and distributed parameter formulations showed clear gains in reducing uncertainties in predictions of monthly and seasonal water availability as compared to the basin outlet calibrations. Surprisingly, increased parameter complexity in the calibration strategies did not increase the uncertainty in streamflow projections, even though parame- ter equifinality did emerge. The results suggest that increased (excessive) parameter complexity does not always lead to in- creased uncertainty if structural uncertainties in the model are present. Figure 13. Uncertainties in 100-year daily flood estimates for 2050s The semi-distributed pooled and distributed pooled cali- are assessed using the Semi-Pooled and Dist-Pooled calibrations. brations are very similar for monthly streamflow projections, Uncertainties are evaluated by calculating the CV of the 2050s 100- yet differ in their projections of extreme flows in part due to year flood estimates under three uncertainty sources: calibration their differences in the spatial variability of optimal parame- uncertainty across 50 calibration trials (Par), climate uncertainty ters, with the distributed pooled calibration showing less un- across GCM projections (Clim), and combined uncertainty (Joint). certainty for 100-year daily flood events. We evaluated the separate and joint influence of uncertainties in parameter esti- mation and future climate on projections of seasonal stream- number of the HYMOD_DS parameters being calibrated in flow and 100-year daily flood across calibration schemes and the semi-distributed approach remains realistic, but the fully found that the uncertainty resulting from variations in pro- distributed parameterization scheme likely causes poor iden- jected climate between the CMIP5 GCMs substantially out- tifiability of the parameters. Thus, pursuing a parsimonious weighs the calibration uncertainty. These results agree with configuration (e.g., optimization for a small portion of the other studies showing the dominance of GCM uncertainty in parameters) with an effort to increase the amount of informa- future hydrologic projections (Chen et al., 2011; Exbrayat tion (e.g., multivariable/multisite) is critical in the calibration et al., 2014). While the GCM-based simulations still have of watershed system models (Gupta et al., 1998; Efstratiadis widespread use in assessing the impacts of climate change et al., 2008). We also note the important role of experienced on water resources availability, the bounds of uncertainty re- hydrologists in designing a parsimonious hydrologic calibra- sulting from an ensemble of GCMs cannot be well-defined tion (e.g., Boyle et al., 2000). In this study, the feasible ranges because of the low credibility with which GCMs are able of the HYMOD_DS parameters were kept wide (as is often to produce time series of future climate (Koutsoyiannis et done in automatic hydrologic calibrations) without consider- al., 2008). This issue hinders a straightforward appraisal of ation of the physical properties of the basin; the judgment future water availability under climate change and has mo- of local hydrologic experts could help reduce the feasible tivated other efforts; e.g., performance-based selection of ranges used during the calibration and thus contribute to a GCMs (Perez et al., 2014). reduction of calibration uncertainty. In addition to the uncertainties surrounding model param- Calibration only based on data at the basin outlet is all too eters and future climate explored in this study, there is also common in hydrologic model applications and is sometimes significant uncertainty in streamflow projections stemming considered comparable to multisite calibrations even for pre- from structural differences between applied hydrologic mod- dictions at interior gauges (Lerat et al., 2012). In contrast, els, which can be especially pertinent where robust calibra- others have reported improvements in interior flow predic- tion is hampered by the scarcity of data (Exbrayat et al., tions by using internal flow measurements (Anderson et al., 2014). Furthermore, the residual error variance of hydrologic 2001; Wang et al., 2012; Boscarello et al., 2013). This is in model simulations would increase the effects of hydrologic agreement with the findings from this study, demonstrating model uncertainty as compared to that of the climate projec- the superiority of the pooled calibration approach to the basin tions (Steinschneider et al., 2014). These issues need to be outlet calibration in terms of its ability to represent interior addressed in future work for exploring a comprehensive un- hydrologic response correctly. This study shows the danger certainty assessment of climate change risk for poorly moni- in relying on an outlet calibration for interior flow prediction. tored hydrologic systems. It was shown that caution is needed when using an out- Successful automatic calibration algorithms for hydro- let calibration approach for streamflow predictions under fu- logic models are based primarily on global optimization al- ture climate conditions. This study showed that the basin gorithms that are computationally expensive and require a outlet calibration can lead to projections of mid-21st cen- large number of function evaluations (Kuzmin et al., 2008). Hydrol. Earth Syst. Sci., 19, 857–876, 2015 www.hydrol-earth-syst-sci.net/19/857/2015/ S. Wi et al.: Implication for streamflow projections under climate change 873 Although the speed and capacity of computers have in- Beven, J. 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P.: Long-Term Climate and Derived Sadeghi, A., Thomson, A. M., Sahajpal, R., Srinivasan, R., and Surface Hydrology and Energy Flux Data for Mexico: 1925– Arnold, J. G.: Efficient multi-objective calibration of a computa- 2004, J. Climate., 20, 1936–1946, 2007. tionally intensive hydrologic model with parallel computing soft- ware in Python, Environ. Modell. Softw., 46, 208–218, 2013. Hydrol. Earth Syst. Sci., 19, 857–876, 2015 www.hydrol-earth-syst-sci.net/19/857/2015/ Supplement of Hydrol. Earth Syst. Sci., 19, 857–876, 2015 http://www.hydrol-earth-syst-sci.net/19/857/2015/ doi:10.5194/hess-19-857-2015-supplement © Author(s) 2015. CC Attribution 3.0 License. Supplement of Calibration approaches for distributed hydrologic models in poorly gaged basins: implication for streamflow projections under climate change S. Wi et al. Correspondence to: S. Wi (sungwookwi@gmail.com) 1 Supplementary materials 2 3 4 Figure S1. Comparison of basin-wise average monthly precipitation and temperature for the Kabul 5 River basin. Sources of data sets: APHRODITE (Asian Precipitation High-Resolved 6 Observational Data Integration Towards Evaluation), CRU (Climatic Research Unit), GPCC 7 (Global Precipitation Climatology Centre), UD (University of Delaware). 8 1 9 10 Figure S2. Glacial coverage in the Kabul River basin based on the Randolph Glacier Inventory 11 version 3.2. Glacier volume scaling relationship proposed by Grinsted (2013) is applied to derive 12 glacier volume. Numbers in red represent glacier depths in meter of water for grid cells containing 13 glaciers. 14 2 15 16 Figure S3. (a) Basin outlet (Dakah) simulations of HYMOD and MYMOD_DS (with the lumped 17 parameterization) from 50 trials of calibration. The Box plots provide the performance evaluation 18 on 50 simulations of both models for both calibration and validation periods. (b) Performances of 19 the models at the interior points of the watershed are assessed. 20 3 21 22 23 Figure S4. HYMOD_DS streamflow simulations at sub-basins from 50 trials of the basin outlet 24 calibration under the lumped parameterization. 25 4 26 27 Figure S5. CMIP5 climate change projections of precipitation and temperature for the Kabul basin. 28 The changes in average monthly total precipitation and mean temperature for the future period 29 2050s (2036-2065) were calculated from the comparison with the historical period (1976-2005). 30 36 GCMs were employed in this analysis. 31 5 32 33 Figure S6. Spatial variability of the HYMOD_DS parameters. a) An example with Cmax showing 34 parameter ranges resulting from the single trail of Semi-Pooled and Dist-Pooled. b) Average 35 spatial variability across 50 trials of calibration for all 15 parameters. Error bar in b) represents the 36 range of parameter spatial variability from the 50 trails. 37 6 38 39 40 Figure S7. HYMOD_DS run time on parallel computing system. 41 7