Sensitivity of future continental United States water deficit projections to general circulation models , the evapotranspiration estimation method , and the greenhouse gas emission scenario

Projecting water deficit under various possible future climate scenarios depends on the choice of general circulation model (GCM), reference evapotranspiration (ET0) estimation method, and Representative Concentration Pathway (RCP) trajectory. The relative contribution of each of these factors must be evaluated in order to choose an appropriate ensemble of future scenarios for water resources planning. In this study variance-based global sensitivity analysis and Monte Carlo filtering were used to evaluate the relative sensitivity of projected changes in precipitation (P ), ET0, and water deficit (defined here as P –ET0) to choice of GCM, ET0 estimation method, and RCP trajectory over the continental United States (US) for two distinct future periods: 2030–2060 (future period 1) and 2070–2100 (future period 2). A total of 9 GCMs, 10 ET0 methods, and 3 RCP trajectories were used to quantify the range of future projections and estimate the relative sensitivity of future projections to each of these factors. In general, for all regions of the continental US, changes in future precipitation are most sensitive to the choice of GCM, while changes in future ET0 are most sensitive to the choice of ET0 estimation method. For changes in future water deficit, the choice of GCM is the most influential factor in the cool season (December–March), and the choice of ET0 estimation method is most important in the warm season (May–October) for all regions except the Southeast US, where GCMs and ET0 have approximately equal influence throughout most of the year. Although the choice of RCP trajectory is generally less important than the choice of GCM or ET0 method, the impact of RCP trajectory increases in future period 2 over future period 1 for all factors. Monte Carlo filtering results indicate that particular GCMs and ET0 methods drive the projection of wetter or drier future conditions much more than RCP trajectory; however, the set of GCMs and ET0 methods that produce wetter or drier projections varies substantially by region. Results of this study indicate that, in addition to using an ensemble of GCMs and several RCP trajectories, a range of regionally relevant ET0 estimation methods should be used to develop a robust range of future conditions for water resources planning under climate change.


Introduction
Climate change will result in significant impacts on hydrologic processes.The 2014 Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC) reported that climate change will significantly affect future precipitation (P ), temperature (T ), and reference evapotranspiration (ET 0 ), and these changes will affect the quantity and quality of water resources.The most recent report of the National Climate Assessment and Development Advisory Committee (NCADAC, Melillo et al., 2014) indicated that the average annual temperature in the United States (US) has increased by 0.7 to 0.9 • C since record keeping began in 1895 and is expected to continue to rise (Georgakakos et al., 2014;Walsh et al., 2014).The NCADAC report also indicated that Coupled Model Intercomparison Project 5 (CMIP5) general circulation model (GCM) precipitation projections show a consistent increase in Alaska and the far north of the continental US and a consistent decrease in the far Southwest US, but that GCM projections are inconsistent in the precipitation transition zone of the US continent.The uncertainty in climate change projections makes actionable water resources planning difficult in many regions.In order to predict changes in the hydrologic cycle, and future water supply and demand, estimates of changes in P , T , and ET 0 must be evaluated on a regional basis, and the uncertainty of these estimates must be quantified (Ishak et al., 2010).
Previous research has evaluated existing and potential future spatiotemporal changes in P , T , and ET 0 for various regions around the globe (e.g., Chaouche et al., 2010;Chong-Hai and Ying, 2012;Johnson and Sharma, 2009;Kharin et al., 2013;Maurer and Hidalgo, 2008;Quintana Seguí et al., 2010;Sung et al., 2012;Thomas, 2000;Wang et al., 2013;Xu et al., 2006).It is well known that future GCM projections of temperature and precipitation vary significantly due to both the different radiative forcing assumptions of carbon dioxide scenarios (e.g., the CMIP3 Special Report on Emissions Scenarios (SRES) and CMIP5 Representative Concentration Pathways; RCP trajectories) and different GCM model physics (Hawkins andSutton, 2009, 2010).Future ET 0 projections have been shown to depend on ET 0 estimation methods in addition to GCMs.For example, Wang et al. (2015) used projections from the CMIP3 HADCM3 model A2 scenario and found that the physically based Penman-Monteith equation, which uses less reliable GCM projection data (including vapor pressure and solar radiation), and the empirical temperature-based Hargreaves equation showed similar patterns but different magnitudes for future ET 0 changes over the Hanjiang River basin in China.Kingston et al. (2009) used five GCMs from the CMIP3 climate projections and six different ET 0 equations to estimate global ET 0 and found that the choice of ET 0 method contributes to different projections of the future state of water resources, which varies by region.They found that the Hamon and Jensen-Haise ET 0 estimates showed the greatest changes in both humid and arid regions, while the Penman-Monteith and Priestley-Taylor estimates frequently showed the smallest change.Similarly, McAfee (2013) used three ET 0 equations with 17 CMIP3 GCMs to evaluate the uncertainty of future global ET 0 projections and found that the Hamon equation showed more significant and consistently positive trends in ET 0 compared to the Priestley-Taylor and Penman methods.Models developed to estimate future water supply and demand as a result of projected climate change use many different types of ET 0 estimation methods (Zhao et al., 2013).Because the choice of ET 0 estimation method may be as important as the choice of GCM or RCP trajectory, better understanding of the contribution of each of these factors to the overall prediction uncertainty of future water availability or water deficit is necessary (Taylor et al., 2013).Kay and Davies (2008) compared the performance of the Penman-Monteith equation and a simple temperature-based ET 0 method using climate data from five global and eight regional climate models over Britain.They found that the two methods showed very different changes in ET 0 for the period 2071-2100 under the A2 emission scenario and different flow predictions for three catchments when the data were used to force a rainfall-runoff model.Kay and Davies results suggest that hydrological prediction uncertainty due to ET 0 formulation was smaller than that due to GCM structure or RCM structure for their study region.Bae et al. (2011) evaluated the uncertainty contributed by choice of GCM and hydrologic model for the Chungju Dam basin, Korea.They found that hydrologic model structural differences contributed greater uncertainty than GCM selection to winter runoff prediction.Koedyk and Kingston (2016) found that for the Waikaia River, New Zealand, the ET 0 method contributed more uncertainty than GCM selection when predicting ET 0 , but that runoff predictions were more sensitive to GCMs than to ET 0 methods.Thompson et al. (2014) evaluated the effect of using different GCMs and different ET 0 methods on discharge predictions for the Mekong River in Southeast Asia and found that GCM-related uncertainty was greater than the ET 0 method-related uncertainty.
In this study we perform a comprehensive evaluation of the relative sensitivity of future P , ET 0 , and water deficit (defined here as P -ET 0 ) projections to the choice of GCM, ET 0 method, and RCP trajectory over the continental USA using CMIP5 GCM model outputs to provide new insights that will inform more robust future water resources planning efforts.Variance-based global sensitivity analysis (Saltelli et al., 2010) and Monte Carlo filtering (Rose et al., 1991)   used to quantify the uncertainty and important input factors controlling these projections.Global sensitivity analysis (GSA) apportions the total output uncertainty simultaneously onto all the uncertain input factors described by marginal probability density functions, and thus is preferred over the local, one factor at a time, sensitivity analyses that have been previously reported (Homma and Saltelli, 1996;Saltelli, 1999).Monte Carlo filtering can identify sets of model simulations and input factors that meet a specified criterion or threshold.Thus global sensitivity analysis and Monte Carlo filtering offer an opportunity to gain insight into the sources of uncertainty and drivers of particular types of wet/dry behavior when estimating future water deficit under projected climate change.

Methods
All retrospective and future climate variables were obtained from the CMIP5 archive (accessible for download at http: //pcmdi9.llnl.gov/).The "historical" runs of CMIP5 were used for the retrospective period  and the same ensemble member runs (r1i1p1 ensemble) of CMIP5 were used for two future periods: future period 1 (2030-2060), and future period 2 (2070-2100).Data for three RCP trajectories, RCP2.6,RCP4.5, and RCP8.5, were included in the analyses.Taylor et al. (2012) described an overview of CMIP5 and RCP trajectories and compared the differences between CMIP5 and CMIP3 model projections.Data from the CMIP5 archive were used to calculate monthly mean P , ET 0 , and P -ET 0 (water deficit) for the retrospective and both future periods over each of the nine US climate regions identified by the National Climatic Data Center (Karl and Koss, 1984;Fig. 1).Future changes in monthly mean P , ET 0 , and P -ET 0 were estimated by subtracting the monthly mean value for the retrospective period from the monthly mean value for future period 1 or future period 2, as appropriate (Baker and Huang, 2014).
Variables directly used from the CMIP5 monthly model output included precipitation (pr, P in this study), maximum and minimum temperature (tasmax and tasmin), radiation (rlds, rlus, rsds, and rsus), air pressure (psl and ps), and wind speed (sfcWind).The abbreviations for these variables are as defined in the CMIP5 archive and explained in the PCMDI server (Program For Climate Model Diagnosis and Intercomparison, http://cmip-pcmdi.llnl.gov/cmip5/docs/standard_output.pdf).Other variables needed in the 10 reference evapotranspiration equations were calculated using the variables from CMIP5 monthly model output (for details, see Table 1).Monthly output that included all the variables needed for the Penman-Monteith reference evapotranspiration method (the most data-intensive method) was available for both the retrospective period and for the RCP2.6,RCP 4.5, and RCP8.5 trajectories for the future periods, for nine CMIP5 models.Table 2 lists the nine models from the CMIP5 archive that were used in this study.The sensitivity of changes in future P , ET 0 , and water deficit (defined here as P -ET 0 ) to the choice of GCM, ET 0 estimation method, and RCP trajectory was evaluated using the variance-based GSA method of Saltelli et al. (2010).Given a model of the form Y = f (X 1 X 2 , . ..X k ), with Y a scalar, the variance-based first-order effect for a generic factor X i can be written as (Saltelli et al., 2010) where X i is the ith factor (in our case either GCMs, ET 0 method, or RCP trajectory) and X ∼i is the vector of all factors except X i .The expectation operator E X ∼i (Y |X i ) indicates that the mean of Y is taken over all possible values of X except X i (i.e., X ∼i ) while keeping X i fixed.The variance, V X i , is then taken of this quantity over all possible values of X i .The first-order sensitivity coefficient is expressed as where V (Y ) is the total variance of Y over all X i .S i is a normalized index varying between 0 and 1, because varies between 0 and V (Y ) according to the identity (Mood et al., 1974) is called the residual.The total effect index, including firstorder and higher-order effects (i.e., interactions between factor X i and other factors) of the factor X i on the model output is calculated (Saltelli et al., 2010): The first-order sensitivity of estimated future changes in mean monthly P , ET 0 , and P -ET 0 to choice of GCM, ET 0 estimation method, and RCP trajectory was calculated over the nine US climate regions for each future period in order to evaluate the relative contributions of each of these factors in the uncertainty of future changes.A total of 270 simulations (9 GCMs × 10 evapotranspiration methods × 3 RCP trajectories) was used in the analysis.Sensitivity of projected changes in P was evaluated for both choice of GCM and choice of RCP trajectory.Sensitivity of projected changes in ET 0 and P -ET 0 was evaluated for choice of GCM, choice of ET 0 estimation method, and choice of RCP trajectory.For projected changes in water deficit (P -ET 0 ), Monte Carlo filtering (Saltelli et al., 2008) was used to identify whether projected wetter or drier future conditions (i.e., larger or smaller water deficit) could be attributed to specific GCMs, ET 0 estimation methods, or RCP trajectories.For each future period the ensemble of 270 projections of change in water deficit were categorized as either wet future condition (mean change in (P − ET 0 ) ≥ 0) or dry future condition (mean change in (P − ET 0 ) < 0).Next for each factor (X i = GCM, ET 0 method, RCP trajectory), the histograms of wet (f wet |X i ) and dry (f dry |X i ) future condi- tions over the range of possible values of that factor were estimated.To identify the factors that are most responsible for driving the model into projected wet or dry future conditions for each factor, X i , the distributions (f wet |X i ) and (f dry |X i ) were tested for significant difference using the X 2 two-sample test for categorical variables with α = 0.05 (Rao and Scott, 1981).If for a given factor X i the two distributions are significantly different, then X i is a key factor in driving into either a wet or dry condition (Saltelli et al., 2008).
Because GCM predictions are known to contain systematic biases (Hwang and Graham, 2013;Wood et al., 2002Wood et al., , 2004)), we evaluated the sensitivity of the mean monthly change in raw climate predictions between retrospective and future periods to the choice of GCM, ET 0 estimation method, and RCP trajectories.This is analogous to using the delta change GCM bias-correction method that involves shifting the mean of a series of observed climate data by the mean difference in raw GCM output between the corresponding observed time period and the desired future period.Teutschbein and Seibert (2012) pointed out that all bias-correction methods are based on the stationarity principle that assumes that  2014) found that the delta change GCM bias-correction method was more useful for simulating hydrologic extreme events than the quantile mapping bias-correction method, as it preserved daily climate variability better.In this study, we differenced raw rather than bias-corrected GCM outputs in order to prevent spurious alteration of the climate change signal between retrospective and future GCMs that might be induced by the bias-correction method.

Results
3.1 Projected P , ET 0 , and water deficit change in the 21st century Future P , ET 0 , and water deficit projections include large uncertainties stemming from different sources.Figures 2 and 3 present maps of the mean change (Fig. 2) and the standard deviation of change (Fig. 3) in annual P (top chart), ET 0 (middle), and water deficit (P -ET 0 ; bottom) over the continental US calculated over all GCMs, ET 0 estimation methods, and RCP trajectories for future period 2 (2070-2100).
Major portions of the West, Southwest, and South show a mean decrease in annual precipitation, while the rest of the continental US shows a mean increase (Fig. 2a).Future annual ET 0 shows a mean increase over retrospective annual ET 0 over the entire US (Fig. 2b), with the largest increase in the South region.Following the patterns of P and ET 0 , future annual water deficit (P -ET 0 ) shows a significant mean decrease in the West, Southwest, and South regions, and a slight decline or negligible change in most other regions (Fig. 2c).These mean changes in annual P , ET 0 , and P -ET 0 are relatively small compared to the standard deviation of changes in annual P , ET 0 , and P -ET 0 (Fig. 3).Water deficit in particular has a large standard deviation, resulting in coefficients of variation larger than 1 throughout the continental US.Similar results are shown in Figs.S1 and S2 for future period 1 (2030-2060) in the Supplement.
Figure 4 shows the seasonal changes in the monthly mean and standard deviation of water deficit (P -ET 0 ) over the nine US regions.Blue and red lines represent the changes in monthly mean water deficit for future period 1 and future period 2, respectively, and the error bars represent 1 standard deviation around each mean value.All regions of the continental US show drier conditions (negative mean changes) in the summer season (June-August).Southern regions (Southeast, South, Southwest, and West) show drier conditions throughout the year; however, northern portions of the US (i.e., the Northeast, Ohio Valley, Upper Midwest, Northern Rockies and Plains, and Northwest) show wetter conditions (positive mean changes) in the winter season.

Global sensitivity analysis of projected changes
Figure 5 shows the first-order sensitivity of change in P to GCMs and RCP trajectory over the nine US climate regions for future periods 1 and 2. For projected changes in P , the choice of GCM is generally more important than the choice of RCP trajectory for all regions and both future periods.First-order sensitivities of mean change in ET 0 to GCM, ET 0 method, and RCP trajectory are shown in Fig. 6.This figure clearly shows that the choice of ET 0 method is the most influential factor for projecting change in ET 0 for both future periods, except for the month of March in the Northeast, Upper Midwest, and Northern Rockies and Plains.High sensitivity of mean change in ET 0 to GCM selection occurs in spring for several regions (Northeast, Upper Midwest, and Northern Rockies and Plains), indicating a divergence of model predictions during this time.The influence of the RCP trajectory on ET 0 increases in future period 2 over future period 1, with a concomitant decrease in the influence of both ET 0 method and GCM.In future period 1 the GCM sensitivity coefficients are greater than the RCP trajectory sensitivity coefficients over most regions; however, in future period 2 the RCP sensitivity coefficients become more impor-tant.Figure 7 shows that projected change in water deficit depends strongly on both the choice of GCM and ET 0 estimation method.In all regions except the Southeast, projected change in water deficit is most sensitive to ET 0 estimation method in the warm season (May through October) and most sensitive to GCM in the cool season (December through March).For the Southeast region, the sensitivity coefficients for GCM and ET 0 method are quite similar throughout the year.The sensitivity coefficients for RCP trajectory are very low in future period 1, but increase in future period 2, becoming approximately equal to the GCM sensitivity coefficients in the summer season in future period 2.

Change in annual mean water deficit projections using different ET 0 methods
Figure 8 shows the change in annual mean water deficit over all nine GCMs for the RCP 4.5 trajectory in future period 1 (2030-2060) predicted by the 10 different ET 0 methods used in this study (a: Hargreaves; b: Blaney-Criddle; c: Hamon; d: Kharrufa; e: Irmak-Rn; f: Irmak-Rs; g: Dalton; h: Meyer; i: Penman-Monteith; j: Priestley-Taylor).This figure clearly shows that the changes in water deficit for future period 1 are diverse and depend strongly on the choice of ET 0 method.Except for the Hargreaves method (Fig. 8a), the temperature-based methods (e.g., Blaney-Criddle, Fig. 8b;

Monte Carlo filtering
Monte Carlo filtering (Saltelli et al., 2008) was conducted to further investigate whether projected wetter or drier future conditions (i.e., larger or smaller annual mean water deficit) could be attributed to specific GCMs, ET 0 estimation methods, or RCP trajectories.Figure 9 shows the histograms for wet conditions and dry conditions in future period 2 over the Southeast US by GCMs, the ET 0 method, and RCP trajectory for the example month of July. Figure 10 shows similar histograms for the Northern Rockies and Plains, a region with differing behavior from the Southeast US.Table 3 shows the P value results for the X 2 test for all months in both futures for the Southeast and Northern Rockies and Plains regions.P values greater than 0.05 (bold values) indicate the two histograms are not significantly different from each other.Tables 4-6 show the fraction of time that a particular GCM (Table 4), ET 0 method (Table 5), or RCP trajectory (Table 6) projected drier future conditions in each of the nine US climate regions for each month, with fractions higher than 0.5 shaded in grey.
The choice of GCM is generally more important than the choice of RCP trajectory for projected changes in P (Fig. 5).This is consistent with results found by Gaetani and Mohino (2013) and Knutti and Sedláček (2012), who showed significant differences in precipitation predictions among CMIP5 models.It should be noted that these results do not indicate that the choice of RCP trajectory does not affect the change in precipitation, only that the choice of RCP trajectory is less influential than the choice of GCM.There are no consistent seasonal patterns of the first-order sensitivity coefficients for either GCM or RCP trajectories in either future period.However, during the spring months, the sensitivity of change in P to the choice of RCP trajectory increases substantially in future period 2 compared to future period 1 in the Northeast, Ohio Valley, Upper Midwest, South, Southwest, and West regions.
Higher sensitivity of mean change in ET 0 to the choice of ET 0 estimation method than the choice of GCM (Fig. 6) is consistent with those found by Kingston et al. (2009), who showed that projected increase in ET 0 varied by more than 100 % between ET 0 methods, and Schwalm et al. (2013), who found that the choice of ET 0 estimation method is sensitive and even more influential than the choice of GCM in predicting ET 0 .However, neither of these studies looked at the influence of RCP trajectory on ET 0 projections, which increases in future period 2 over future period 1, causing a decrease in the sensitivity coefficient of both the GCM and the ET 0 method in future period 2. Burke and Brown (2008) evaluated uncertainties in the projection of future drought using several drought indices.They found that there are large uncertainties in regional changes in drought, and changes in drought are dependent on both index definition and GCM ensemble members.Similarly, our results for the projected change in water deficit vary by region and depend strongly on the choice of GCM and ET 0 estimation method, but are relatively less sensitive to RCP trajectory (Fig. 7).These findings are similar to results reported by Orlowsky and Seneviratne (2013), who found that the greenhouse gas emission scenario uncertainty is not as important as differences among GCMs or internal climate variability when predicting the Standardized Precipitation Index (SPI) and soil mois- ture (SMA).However, they also found that uncertainty due to greenhouse gas emission scenarios increased in later future periods.Taylor et al. (2013) showed the patterns of changes in future drought were similar between the A1B scenario in CMIP3 and the RCP2.6 trajectory in CMIP5, reinforcing our finding that the choice of RCP trajectory is less important than the choice of GCM and ET 0 estimation method when estimating future water deficit.
Similar to the results of Kay and Davies (2008) and Bae et al. (2011) the results of our GSA show that the choice of ET 0 method has important implications when making future ET 0 projections and future water deficit projections (Fig. 8).Kingston et al. (2009) recommended the use of different ET 0 equations to evaluate global ET 0 , and Wang et al. (2015) found that although different methods predict similar future ET 0 , there are important differences in uncertainties due to ET 0 estimation methods and input data reliability.Currently many hydrological models use a single evapotranspiration method for simulation, which may substantially increase the uncertainty and reduce the reliability of future projections.
Our results strongly indicate that an ensemble of ET 0 estimation methods should be used to understand potential future water availability and water deficit due to climate change.Monte Carlo filtering results (Fig. 9 and 10, Table 3) indicate that GCMs and ET 0 methods both produce statistically significant different wet condition and dry condition histograms in both the Southeast and Northern Rockies and Plains regions for almost all months in both future periods.This indicates that particular GCMs and ET 0 methods tend to systematically produce wet or dry conditions.Some GCMs (i.e., MIROC-ESM and BCC-CSM; Table 4) and ET 0 methods (i.e., Priestley-Taylor, Blaney-Criddle, and Kharrufa; Table 5) predict dry conditions the majority of the time for all regions in both future periods.However, the remaining GCMs and ET 0 methods project both wetter and drier fu-tures, depending on the region and future period.Results in Tables 4 through 6 show that for the South, West, and Southwest regions, drier conditions are predicted the majority of the time in both future periods by all GCMs and RCP trajectories, and by all ET 0 methods except Hargreaves.For RCP trajectory, P values indicate that the histograms are statistically significantly different in fewer cases than for either GCMs or ET 0 methods for both future periods 1 and 2 (Table 3).These results are consistent with the first-order sensitivity coefficient results that showed the RCP trajectory is not as important a factor as GCMs or ET 0 methods in driving differences in future projections, but that the sensitivity to choice of RCP trajectory increases in future period 2.
GCMs estimate some climate variables, such as temperature, with higher confidence than other variables (Randall et al., 2007).However, for some evapotranspiration estimation methods the effect of temperature on evaporation is smaller than other climate variables (Linacre, 1994;Roderick et al., 2009a, b;Thom et al., 1981).We found that temperature and  net radiation from the CMIP5 GCMs show increasing trends over the 2005-2100 time period, while wind speed and surface pressure are relatively constant (Fig. S3).Because we considered various ET 0 estimation methods our results include the impacts of the different physics represented in the ET 0 methods, the projected changes in each of the climate variables contributing to the different ET 0 methods, and the reliability of the predictions of each variable.
Future changes in precipitation and evapotranspiration will lead to changes in the hydrologic balance.This study clearly shows that the uncertainty caused by different GCMs, ET 0 methods, and RCP trajectories makes actionable water resources planning based on climate change projections difficult.Understanding and quantifying how these projected changes vary with choice of GCM, ET 0 method, and RCP trajectory is important for designing robust ensembles of scenarios to include in future water resources planning.This study assessed the future mean change in monthly precipitation, evapotranspiration, and water deficit (P -ET 0 ) projected by CMIP5 simulations over the continental US and analyzed the sensitivity of the projected changes to the choice of GCM, ET 0 estimation method, and RCP trajectory.Nine GCMs, 10 ET 0 estimation methods, and 3 RCP trajectories were included in the analyses.Variance-based global sensitivity analysis (Saltelli et al., 2010) was conducted in order to determine the relative contributions of the choice of GCMs, ET 0 estimation methods, and RCP trajectory to uncertainty in future prediction.Monte Carlo filtering was used to investigate whether particular GCMs, ET 0 methods, and/or RCP scenarios consistently led to wet or dry future projections.
The global sensitivity analyses showed that projected changes in precipitation are more sensitive to the choice of GCM than the choice of RCP trajectory over the entire continental US for both future periods.However, the choice of RCP trajectory becomes more important in future period 2. The most sensitive factor for the future ET 0 projections is the choice of ET 0 estimation method for all regions in both future periods.The first-order sensitivity of projected change in future ET 0 to the choice of RCP trajectory increases in future period 2 compared to future period 1, with a concomitant decrease in the first-order sensitivity to the choice of GCM.For projected change in future water deficit, the choice of ET 0 method constitutes the dominant source of uncertainty in warmer months (May through September), and the choice of GCM is the dominant source of uncertainty in the cooler months (November through March) over all regions except the Southeast, where the sensitivity of GCM and ET 0 method are roughly equal throughout the year.Sensitivity of change in future water deficit to RCP trajectory is very small for future period 1, but increased in future period 2.
Monte Carlo filtering results indicated that both GCMs and ET 0 methods produced statistically different histograms for wetter or drier future conditions (i.e., larger or smaller mean future water deficit) for almost all months in both future periods.Two GCMs (MIROC-ESM and BCC-CSM) and three ET 0 methods (Priestley-Taylor, Blaney-Criddle, and Kharrufa) predicted dry conditions the majority of the time for all regions in both future periods; however, the remaining GCMs and ET 0 methods projected both wetter and drier futures, depending on the region.
Results of this study indicate that when predicting the effects of future climate on water resources, the choice of evapotranspiration method should be carefully evaluated.Rather than the typical practice of using a single ET 0 method to drive a hydrologic model with future climate projections, an ensemble of ET 0 methods should be used in addition to an ensemble of GCMs and a variety of RCP trajectories.The GSA methodology adopted here assumed that all the GCMs, ET 0 methods, and RCP trajectories used in this study were equally appropriate for use in all US regions (i.e., the sensitivity coefficients were evaluated by equally weighting each GCM, ET 0 method, and RCP trajectory), which is likely not to be the case.When making future projections of potential climate change in water resources, reliability ensemble averaging (REA; Giorgi and Mearns, 2002) or Bayesian-based indicator-weighting (Asefa and Adams, 2013;Tebaldi et al., 2005;Xing et al., 2014) could be used to weight the results of an ensemble of GCMs and ET methods based on how close the retrospective GCM-ET 0 method predictions agree with past observations (bias criterion) and how well the future GCM-ET 0 -RCP projections agree with other future GCM-ET 0 -RCP predictions (convergence criterion).
This study assumed that ET 0 methods that have been developed and parameterized based on vegetation response to current CO 2 levels and climatic conditions will be valid under future CO 2 levels and climatic conditions.Future research should explore the validity of this assumption by incorporating potential changes in plant transpiration (e.g., stomatal conductance) to changing CO 2 levels into the ET 0 estimation methodologies.
The Supplement related to this article is available online at doi:10.5194/hess-20-3245-2016-supplement.

Figure 2 .
Figure 2. The change in the annual mean (a) P , (b) ET 0 , and (c) P -ET 0 over the US.All units are mm day −1 and the change is defined as the mean of 2070-2100 minus that of 1950-2005.These changes are averaged over all GCMs, ET 0 estimation methods, and RCP trajectories.

Figure 3 .
Figure 3.The standard deviation of the change in the annual mean (a) P , (b) ET 0 , and (c) P -ET 0 over the US.All units are mm day −1 and the change is defined as the average of 2070-2100 minus that of 1950-2005.The standard deviations are estimated over all GCMs, ET 0 estimation methods, and RCP trajectories.

Figure 4 .
Figure 4.The change in monthly mean water deficit (P -ET 0 ) over nine different regions.Blue lines represent future period 1 (2030-2060), and red lines represent future period 2 (2070-2100).Error bars represent 1 standard deviation of each value.The change is defined as the mean of future periods minus that of retrospective periods (1950-2005).

Figure 5 .
Figure 5. First-order sensitivity analysis results of change in precipitation.Solid lines represent future period 1 (2030-2060) and dotted lines represent future period 2 (2070-2100).Blue lines represent the first-order effect of GCMs and green lines represent the first-order effect of RCPs.

Figure 6 .
Figure 6.First-order sensitivity analysis results of change in reference evapotranspiration.Solid lines represent future period 1 (2030-2060) and dotted lines represent future period 2 (2070-2100).Blue lines represent the first-order effect of GCMs, red lines represent the first-order effect of ET 0 estimation methods, and green lines represent the first-order effect of RCPs.

Figure 7 .
Figure 7. First-order sensitivity analysis results of change in P -ET 0 .Solid lines represent future period 1 (2030-2060) and dotted lines represent future period 2 (2070-2100).Blue lines represent the first-order effect of GCMs, red lines represent the first-order effect of ET 0 estimation methods, and green lines represent the first-order effect of RCPs.

Figure 8 .
Figure 8.The change in the annual mean P -ET 0 of the RCP 4.5 scenario by 10 different evapotranspiration methods.All units are mm day −1 and the change is defined as the mean of 2030-2060 minus that of 1950-2005.(All results are interpolated to 1 • × 1 • grids and averaged over nine different GCMs.)

Figure 9 .
Figure9.Histograms for projected future period 2 wet conditions and dry conditions in the Southeast US by GCMs, the ET 0 method, and RCP trajectory for the month of July.

Figure 10 .
Figure10.Histograms for projected future period 2 wet conditions and dry conditions in the Northern Rockies and Plains US by GCMs, the ET 0 method, and RCP trajectory for the month of July.

Table 1 .
Description of reference evapotranspiration estimation methods used in this study (ET 0 : reference evapotranspiration).
1 Variables (estimated from CMIP5 outputs): G: soil heat flux (assumed 0); γ : psychrometric constant; T : average temperature; u 2 : wind speed at 2 m surface; e s : saturated vapor pressure; e a : actual vapor pressure; : slope vapor pressure; K T : Hargreaves-Samani coefficient; S 0 : extraterrestrial radiation (estimated by Julian date); δ T : difference between maximum and minimum temperature, p: percentage of total daytime hours (estimated by Julian date); R n : net radiation; R s : solar radiation; P t : saturated water vapor density; u: wind speed.

Table 2 .
Description of the CMIP5 models used in this study.

Table 3 .
P values of a Chi-square two-sample test for differences among wet condition vs. dry condition pdfs: Southeast US (SE US) and Northern Rockies and Plains (NRP; West North Central) US (bold values indicate that pdfs are not statistically significantly different at p = 0.05).

Table 4 .
The fraction of future dry conditions over all months by GCMs (future periods 1 and 2).

Table 5 .
The fraction of future dry conditions over all months by the ET 0 estimation method and region (future periods 1 and 2).

Table 6 .
The fraction of future dry conditions over all months by RCP trajectory and region (future periods 1 and 2).