Statistical Modeling to Predict Climate Change Effects on Watershed Scale Evapotranspiration

Abstract

Estimation of satellite-based remotely sensed evapotranspiration (ET) as consumptive use has been an integral part of agricultural water management. However, less attention has been given to future predictions of ET at watershed-scales especially since with a changing climate, there are additional challenges to planning and management of water resources. In this paper, we used nine years of total seasonal ET derived using a satellite-based remote sensing model, Mapping Evapotranspiration at Internalized Calibration (METRIC), to develop a Random Forest machine learning model to predict watershed-scale ET into the future. This statistical model used topographic and climate variables in agricultural areas of Lower Yakima, Washington and had a prediction accuracy of 88% for the region. This model was then used to predict ET into the future with changed climatic conditions under RCP4.5 and RCP8.5 emission scenarios expected by 2050s. The model result shows increases in seasonal ET across some areas of the watershed while decreases in other areas. On average, growing seasonal ET across the watershed was estimated to increase by +5.69% under the low emission scenario (RCP4.5) and +6.95% under the high emission scenario (RCP8.5).

1. Introduction

Water resources are severely stressed particularly in arid and semi-arid regions of the world with diverse competing pressures like agricultural, industrial, municipal, and environmental uses [1,2,3]. Climate change poses an additional risk to water stress and will probably exacerbate water management plans in the future [4,5]. This is because climate change is expected to alter the dynamics of spatiotemporal temperature and precipitation patterns, often resulting in increased evaporative demands [6]. With climate change expected to impose additional limitations on water management activities, it becomes increasingly necessary to predict changes in future agricultural water demands. Moreover, numerous studies have identified water quantity trading as a practical strategy for reducing the detrimental impact of climate change and water shortages [7,8,9,10]. However, uncertainty and complexity in the processes have repercussions in responding to climate change and water shortages [11]. Difficulty in estimating spatiotemporally varied evapotranspiration (ET) at field and watershed scales has led to inefficient water allocation, trading, and other planning operations, which are tremendous concerns in the face of climate variability, change and drought [12,13].

Irrigated agriculture accounts for approximately 80–85% of consumptive water use [14,15] making ET an important measure for agricultural water management. ET is a significant part of the water balance and is therefore essential for predicting water yields, designing water supply, and managing water quantity and quality in watersheds [16,17,18,19]. Therefore, accurate estimation of ET is critical for better agricultural water management both now and in the future. Despite continuing efforts to improve estimation procedures, watershed scale ET is still difficult to determine using measured data and even more difficult to predict due to its spatial and temporal complexity. ET can be modeled using data from weather stations and can be measured directly with high accuracy at specific points using lysimeter or eddy covariance stations [20,21,22]. However, spatially explicit information is more useful to water resource managers. Moreover, being able to determine future ET values as a result of climate modeling efforts is required for strategic planning purposes [23]. Traditional methods for estimating watershed-scale ET addresses these needs by estimating crop coefficients (K_c) over the watershed and multiplying them by a reference ET value at the nearest weather station. Since variability of watershed properties and crop growth stages cannot be accommodated completely into one factor of K_c, alternative approaches for estimating watershed scale ET has been employed—such as the Antecedent Precipitation Index, Advection-Aridity actual ET model [24,25,26] or physically based spatial models like VIC-CropSyst [27] or remote sensing models like METRIC, SEBAL, TSEB, etc. [28,29,30]. Empirical models predicting actual ET and physically-based spatial models, when being used on a larger watershed scale, however, require huge amounts of data, careful consideration of assumptions based on the region of study, and extensive calibration effort [22,27]. Remote sensing approaches have been shown to overcome some of these limitations of physically-based models and perform consistently better with less effort towards calibration or requirement for additional data [31,32]. However, physically-based models have been used extensively in the prediction of ET into the future but use of remote sensing methods to do the same is not yet possible. This study presents a unique approach to use remote sensing with statistical modeling to predict ET into the future that requires much less computational effort than physically-based models.

Due to the complexity of ET estimation, there is increasing interest in the use of machine learning algorithms for robust prediction. Several studies have used statistical and machine learning approaches to predict reference ET and energy balance processes [19,33,34,35]. However, as described by Kumar et al. [36] these models are unable to describe the physical relationship between different components of the process due to the nature of machine learning techniques. Therefore, a model trained with inputs from a specific location cannot be used in a different region without local training Jain et al. [37]. Additionally, these approaches still require extrapolation of ET from point to watershed-scale using K_c. ET values resulting from these models represent the climatic conditions of the locations close to the weather station while the K_c are estimated for specific crop conditions based on the time in the growing season. A few studies have attempted to upscale point measurements of ET to regional scale using climatic predictors and machine learning [38,39] but these studies have used hourly or sub-hourly temporal scale climate variables to estimate regional ET. Since it is impossible to predict climate variables at such fine temporal scale several years into the future, these upscaling methods are not feasible for future prediction of watershed scale ET. Similarly, a few studies have used machine learning techniques to estimate ET between days when satellite imagery is available [40], but these models cannot predict the future due to the lack of imagery. To our knowledge, there are no studies that have used remote sensing models to predict future water consumption in a watershed. A key research question of this paper is to develop a model based on remote sensing information to predict crop consumptive use in agricultural watershed. However, as pointed out by Hindman [41], robust model prediction requires a good set of both response data and predictor variables.

Multiple approaches for determining evapotranspiration using remote sensing technologies have been proposed in the literature [29,42,43,44]. One of these approaches, an energy balance model that uses Landsat imagery called Mapping Evapotranspiration at Internalized Calibration (METRIC) [45], has been used to quantify agricultural consumptive use for decision-making where the results were even upheld in the courts [46,47]. METRIC [45] is specifically designed and parametrized for agricultural areas and has been proven to be reliable as an operational model for producing ET maps at field resolutions across large regions [32]. Here, we use the METRIC ET as the response variable to train a machine learning model to predict the consumptive use of water. Similarly, predictor variables are chosen ranging from topographical, climatic and crop, based on the watershed properties.

The objective of this paper is to develop a predictive model for crop consumptive use in agricultural watersheds and subsequently predict the effect of climate change on crop consumptive use. We developed a random forest model using topographic, climate and crop variables as predictors and METRIC ET as the response. The predictors thus determined are used for estimating the effects of climate change on future consumptive use of water using forecasted climate variables. To provide proof-of-concept for potential watershed-scale forecasting, we focused on agricultural area of Lower Yakima River Basin in Washington State where we trained the Random Forest (RF) model using a growing period dataset of 2008–2014 and tested using the growing period dataset of 2015 and 2016. We make a significant advance on previous studies by developing a framework to predict regional scale ET estimates using climate, topographic and cropping patterns. Using 2008–2014 as the baseline period, we estimated the change in ET in the 2050s with climate projection data for two greenhouse gas emission scenarios (RCP4.5 and RCP8.5). Our study can have multiple uses including better prediction of future water demands and identification of the probable areas for water markets.

2. Materials and Methods

2.1. Study Area

While we believe our approach would be valid for most arid and semi-arid regions, this study focused on the Lower Yakima River basin in the Pacific Northwest U.S. This area is a highly developed watershed for irrigated agriculture and has multiple stakeholders which makes water management a complex issue. There are five upstream reservoirs in the Yakima River basin that account for holding 30% of the mean annual runoff of the system [9]. Moreover, an estimated 97% of water withdrawals from the Yakima River is used in irrigated agriculture [48]. Thus, predicting the impact of climate change on consumptive use of water would be useful to the water managers in the region as storage is highly susceptible to climate change. Besides, the heterogeneity of crops, water rights, irrigation practices, and management decisions of different irrigation districts would make the study applicable in more watersheds.

The 7606 km² (~3000 square miles) watershed located in southcentral Washington encompasses one of the most productive agricultural areas in the State (Figure 1). This region supports a USD 3 billion irrigated agriculture industry and significant crops include apple, corn, alfalfa, hops, grapes and wheat [9]. The region receives an average rainfall of 212 mm (8.35 inches) and snowfall of 584 mm (23 inches). For this study, we focus only on the agricultural areas of the watershed.

2.2. Data

2.2.1. Landsat Imagery

Landsat images were used to map ET for our study area due to the high spatial and temporal resolution required. All available Landsat images with cloud cover less than 30% within the Yakima River basin for the growing period of 2008–2016 (mid-April to mid-October) were used. This resulted in Landsat images with path-row 45–28 and 44–28 that covered the agricultural area of the watershed (Figure 1). Google Earth Engine (GEE) [49] was used to access and analyze Landsat data from the public catalog GEE provides using the process implemented in Dhungel and Barber [50].

2.2.2. Weather Data

Hourly and daily weather data required for ET estimation using the METRIC methodology were extracted from two US Bureau of Reclamation (USBR) Agrimet Network weather stations at Harrah (HRHW) and Legrow (LEGW) (

Table 1. Weather station detail used in this study.

Site Descriptors	HRHW	LEGW
Latitude (N)	46.38472	46.20527
Longitude (W)	120.57444	118.93611
Elevation (m)	259.1	176.784
Data availability period	1987–current	1986–current
Source of data	USBR Agrimet	USBR Agrimet

).

2.2.3. Gridded Climate Data

Gridded climate data at 4 km resolution required for the Random forest model were extracted from the PRISM dataset [51].

2.2.4. Climate Projection Data

Gridded climate projections (MACAv2-METADATA) from 20 global climate models downscaled using the Multivariate Adaptive Constructed Analogs approach [52] were extracted for two Representative Concentration Pathway (RCP) scenarios (RCP4.5 and RCP8.5). The GCMs considered in evaluating predictive model performance are: bcccsm1-1, bcccsm1-1, BNU-ESM, CanESM2, CCSM4, CNRM-CM5, CSIRO-Mk3-6-0, GFDL-ESM2G, GFDL-ESM2M, HadGEM2-CC365, HadGEM2-ES365, inmcm4, IPSL-CM5A-LR, IPSL-CM5A-MR, IPSL-CM5B-LR, MIROC5, MIROC-ESM, MIROC-ESM-CHEM, MRI-CGCM3, and NorESM1-M. Instead of choosing a single GCM for prediction, we took the equally weighted multi-model mean of the 20 climate models as the multimodal ensemble average outperforms any individual model [53,54,55].

2.2.5. Elevation and Land Use Data

Digital Elevation Model (DEM) data at 30 m resolution was obtained from the USGS National Elevation Dataset. We also used 30 m resolution agricultural land-use pixels and pasture land-use pixels from the 2006–2011 period obtained from the USGS National Land Cover Database to calibrate the model.

2.2.6. Crop Data

The Cropland Data Layer (CDL), available in the GEE catalog from the US Department of Agriculture (USDA) National Agriculture Statistics Service (NASS), was used to identify the five major crops in the study area based on acreage (corn, alfalfa, hops, grapes, apples).

2.3. METRIC Model

METRIC [46] is an image processing tool for mapping regional ET as a residual of energy balance at the surface (Equation (1)).

$$LE=R_n-G-H$$

(1)

where LE is the latent heat flux (W·m⁻²), R_n is the net radiation (W·m⁻²), G is the soil heat flux (W·m⁻²), and H is the sensible heat flux (W·m⁻²). LE is divided by latent heat of vaporization to get instantaneous ET. The fraction of ET (ETrF, assumed Constant within one day) is calculated by dividing instantaneous ET by the reference ET (ETr, calculated from the nearby weather station, here computed using the American Society of Civil Engineers (ASCE) standardized alfalfa-based reference ET method). To calculate daily ETrF cubic spline interpolation is performed between ETrF of day of satellite overpass, which is multiplied with daily reference ETr for seasonal ET calculation.

Net Radiation (R_n) is estimated from the sum of the difference between the incoming (R_s ↓) and the reflected outgoing shortwave solar radiation (R_s↑), and the difference between the downwelling atmospheric (R_L↓) and the surface-emitted and -reflected longwave radiation (R_L ↑) (Equation (2)).

$$R_n=R_s\downarrow -R_s\uparrow +R_L\downarrow -R_L\uparrow$$

(2)

The ground heat flux (G) is calculated as the fraction of net radiation using the following equation:

$$\frac{G}{R_n}=\left(T_s-273.15\right)\left(0.0038+0.0074\propto \right)\left(1-0.98 NDV{I}^4\right)$$

(3)

where T_s is surface temperature, $\propto$ is albedo and NDVI is Normalized vegetation index. The sensible heat flux (H) is the rate of heat loss to the air by convection and conduction due to a temperature difference, which can be calculated as:

$$H={\varrho }_{air}{C}_p\frac{dT}{r_{ah}}$$

(4)

where ${\varrho }_{air}$ is the density of air (kg·m⁻³), C_p is the air specific heat (=1004 J·kg⁻¹·K⁻¹), while dT is the difference between the air temperature and the aerodynamic temperature near the surface, (dT = T_a − T_s), and rah is the aerodynamic resistance.

METRIC uses two anchor pixels (hot and cold) for internal calibration and to fix boundary conditions for energy balance eradicating the need for in-depth atmospheric correction of surface temperature and reflectance. The calibration is done by choosing the hot and cold pixels to define the vertical temperature gradient range above the surface. Typically, cold conditions correspond to well-irrigated alfalfa fields ET = ETr (reference evapotranspiration over standardized 0.5 m tall alfalfa) whereas hot conditions correspond to dry bare agricultural fields ET = 0. These two pixels are used as boundary conditions to find temperature gradients (dT) at each pixel which is then used to determine the coefficients of a linear relationship (Equation (5)) to be used to calculate dT across the entire image and subsequently the sensible heat flux.

$$dT=a{T}_s+b$$

(5)

where a and b are empirical constants and are determined using extreme end conditions i.e., with cold pixel (representing maximum LE) and hot pixel (representing zero LE). An iterative solution approach is then applied at these two anchor pixel locations to determine dT followed by the relationship between dT and T_s. For the selection of anchor pixel locations, we followed the process outlined by Dhungel and Barber [50] where a detailed analysis was performed on the effect of anchor pixel selection on the relationship of dT vs. T_s and subsequently on sensible heat flux (H). This approach provides better understanding of the uncertainty and error in METRIC results due to variability in anchor pixel selection process, which is one of the major sources of error in METRIC.

The iterative process and series of steps in the METRIC process requires large data storage and computational engine. We used Google Earth Engine (GEE) [49] and the associated Python API to develop and implement METRIC in an entirely web-based environment that does not require the use of a personal computational engine. GEE is a cloud-based geospatial processing platform that uses per-pixel algebraic functions with a powerful computational infrastructure optimized for parallel processing of large geospatial datasets. Readers are referred to Dhungel and Barber [50] for more details on the process.

2.4. Random Forest Model

We used the Random Forest (RF) [56] algorithm to develop a predictive model for our study as it has been used to predict climate change effects [57,58] and has been shown to perform better than similar other machine learning techniques Fernández-Delgado et al. [59]. RF has been successfully used in similar activities such as predicting the effect of climate change on species distribution [57,58] and land use/cover classification [60,61].

Random forest is a machine learning technique that can be used for both classification and regression. For our purpose, we use it as a regression tool. RF creates a large number of individual decision trees, each based on a bootstrapped sample of the training data [56,62]. As an ensemble machine learning method, RF is relatively insensitive to noise. Further, as long as the individual decision tree models are kept simple, it does not overfit [63] even when the number of records is not large which is the case for our study. Further, splits within each tree are based on different subsamples of the available variables to reduce correlation between trees and to allow the model to explore minor correlations that might otherwise be ignored. As only a subsample of the observations are used to build each tree, the remaining set of observations (out-of-bag; OOB) can be used to test the model. Model predictive error is quantified by comparing OOB predictions with original response variable. The final prediction model is based on the average of an ensemble of decision trees.

2.5. Model Development

Random Forest model development was done using the “randomForest” [62] package available in R, a statistical programming language [64]. Based on Snow Water Equivalent (SWE) and Palmer Drought Severity Index (PDSI) there were two wet years (2011 and 2016) and two dry years (2014 and 2015) in the period of analysis. Thus, the observed nine years dataset (2008–2016) was split into a training set (2008–2014) and a testing set (2015 and 2016) to evaluate the final model performance. Cross-validation was performed on the training data prior to testing final performance by splitting it into training and testing datasets (train: 80% and test: 20%).

For this study, the annual growing season ET computed using METRIC was used as the response variable and watershed and climate properties were used as the predictor variables. A total of 33 predictor variables were selected based on process and basin characteristics that we assumed could affect ET (

Table 2. Input and output variables used in Random Forest model.

S.N.	Variable Name	Variable Description	Variable Acronym	Source
1	Apples area	Crop area of apple	Apples_ac	USDA, CDL
2	Alfalfa area	Crop area of alfalfa	Alfalfa_ac	USDA, CDL
3	Corn area	Crop area of corn	Corn_ac	USDA, CDL
4	Grapes area	Crop area of grapes	Grapes_ac	USDA, CDL
5	Hops area	Crop area of hops	Hops_ac	USDA, CDL
6	Aspect	Aspect	Asp	USGS, NED
7	Elevation	Elevation	Elev	USGS, NED
8	Slope	Slope	Slp	USGS, NED
9	Spring precipitation	Average precipitation of March, April and May	pptMAM	PRISM
10	Summer precipitation	Average precipitation of June, July and August	pptJJA	PRISM
11	Fall precipitation	Average precipitation of September, October and November	pptSON	PRISM
12	Winter precipitation	Average precipitation of December, January and February	pptDJF	PRISM
13	Precipitation standard deviation	Standard deviation of annual precipitation	ppt_sd	PRISM
14	Sum precipitation	Annual precipitation	sumppt	PRISM
15	Spring maximum temperature	Average maximum temperature of March, April and May	tmaxMAM	PRISM
16	Summer maximum temperature	Average maximum temperature of June, July and August	tmaxJJA	PRISM
17	Fall maximum temperature	Average maximum temperature of September, October and November	tmaxSON	PRISM
18	Winter maximum temperature	Average maximum temperature of December, January and February	tmaxDJF	PRISM
19	Maximum temperature standard deviation	Standard deviation of annual maximum temperature	tmax_sd	PRISM
20	Spring minimum temperature	Average minimum temperature of March, April and May	tminMAM	PRISM
21	Summer minimum temperature	Average minimum temperature of June, July and August	tminJJA	PRISM
22	Fall minimum temperature	Average minimum temperature of September, October and November	tminSON	PRISM
23	Winter minimum temperature	Average minimum temperature of December, January and February	tminDJF	PRISM
24	Minimum temperature standard deviation	Standard deviation of annual minimum temperature	tmin_sd	PRISM
25	Spring maximum vapor pressure deficit	Average maximum vapor pressure deficit of March, April and May	vpdmaxMAM	PRISM
26	Summer maximum vapor pressure deficit	Average maximum vapor pressure deficit of June, July and August	vpdmaxJJA	PRISM
27	Fall maximum vapor pressure deficit	Average maximum vapor pressure deficit of September, October and November	vpdmaxSON	PRISM
28	Winter maximum vapor pressure deficit	Average maximum vapor pressure deficit of December, January and February	vpdmaxDJF	PRISM
29	Spring minimum vapor pressure deficit	Average minimum vapor pressure deficit of March, April and May	vpdminMAM	PRISM
30	Summer minimum vapor pressure deficit	Average minimum vapor pressure deficit of June, July and August	vpdminJJA	PRISM
31	Fall minimum vapor pressure deficit	Average minimum vapor pressure deficit of September, October and November	vpdminSON	PRISM
32	Winter minimum vapor pressure deficit	Average minimum vapor pressure deficit of December, January and February	vpdminDJF	PRISM
33	Sum of monthly temperature	Sum of total monthly temperature	dailyTsum	PRISM
34	Evapotranspiration	Total growing seasonal evapotranspiration	ET	METRIC

). These were derived using temperature, precipitation, crops and elevation data of the watershed. Table 2 provides detailed information about the input and response variable for the Random Forest model, while

Table 3. Summary statistics of input and output variables for both training and testing datasets.

S.N.	Variable Name	(2008–2014)	2015	2016
		Mean, Sd	Mean, Sd	Mean, Sd
1	Apples area	306.65, 334.60	306.06, 382.35	335.88, 403.90
2	Alfalfa area	114.72, 151.80	148.11, 219.25	156.00, 212.04
3	Corn area	182.28, 286.31	193.29, 327.81	192.94, 307.522
4	Grapes area	272.438, 391.80	256.01, 421.42	263.92, 441.73
5	Hops area	85.56, 179.02	138.86, 275.71	172.88, 320.87
6	Aspect	175.10, 101.60	175.10, 101.60	175.10, 101.60
7	Elevation	342.57, 154.12	342.57, 154.12	342.57, 154.12
8	Slope	6.51, 7.58	6.51, 7.58	6.51, 7.58
9	Spring precipitation	18.78, 2.19	19.24, 2.6	18.78, 4.61
10	Summer precipitation	9.33, 1.51	0.21, 0.44	4.89, 1.39
11	Fall precipitation	15.96, 1.85	11.21, 2.08	32.49, 3.40
12	Winter precipitation	23.13, 4.30	23.20, 5.57	44.93, 9.62
13	Precipitation standard deviation	12.84, 1.45	21.29, 4.22	21.38, 3.17
14	Sum precipitation	171.25, 18.88	128.54, 16.67	227.40, 27.57
15	Spring maximum temperature	16.93, 1.09	19.62, 1.13	19.63, 1.06
16	Summer maximum temperature	29.45, 0.97	31.96, 0.93	29.44, 0.94
17	Fall maximum temperature	17.66, 0.86	18.19, 0.86	17.74, 0.87
18	Winter maximum temperature	4.76, 0.67	6.78, 0.63	5.99, 0.76
19	Maximum temperature standard deviation	9.81, 0.16	9.97, 0.17	9.54, 0.17
20	Spring minimum temperature	2.79, 0.85	4.58, 0.74	5.17, 0.77
21	Summer minimum temperature	12.25, 1.06	14.11, 1.05	11.96, 1.09
22	Fall minimum temperature	4.00, 0.87	4.45, 0.96	5.68, 0.94
23	Winter minimum temperature	−3.95, 0.59	−0.78, 0.58	−1.66, 0.9
24	Minimum temperature standard deviation	6.47, 0.26	6.12, 0.26	5.92, 0.19
25	Spring maximum vapor pressure deficit	1.57, 0.13	1.64, 0.40	1.50, 0.47
26	Summer maximum vapor pressure deficit	3.58, 0.60	5.11, 1.88	3.59, 1.42
27	Fall maximum vapor pressure deficit	1.43, 0.39	1.33, 0.54	0.96, 0.49
28	Winter maximum vapor pressure deficit	3.58, 0.28	3.77, 0.34	3.42, 0.40
29	Spring minimum vapor pressure deficit	1.57, 0.13	1.64, 0.40	1.50, 0.47
30	Summer minimum vapor pressure deficit	3.58, 0.60	5.11, 1.88	3.59, 1.42
31	Fall minimum vapor pressure deficit	1.43, 0.39	1.33, 0.54	0.96, 0.49
32	Winter minimum vapor pressure deficit	0.41, 0.06	0.40, 0.14	0.22, 0.07
33	Sum of monthly temperature	3363.00, 179.02	3729.19, 151.30	3547.07, 162.77
34	Evapotranspiration	572.32, 337.07	609.24, 390.13	626.23, 391.09

provides the summary statistics of these variables for both training and testing dataset. Correlations between these predictor variables and their correlation with seasonal ET are shown in Figure 2. While summer maximum temperatures, summer maximum vapor pressure deficits, and crop acreage have higher positive correlation, spring minimum vapor pressure deficits and elevation show a slightly higher negative correlation with ET. These variables are expected to perform better in the random forest model. The correlation plot provides the idea about which predictor value could be deterministic in predicting the ET. However, as RF methods model non-linear relationships which may not be apparent from a linear correlation, we used all the predictor parameters for initial model development and implemented a variable selection routine to select the final variable set.

The 30 m scale ET was upscaled to 4 km scale to have the same scale with climate predictor variables. The upscaling was performed by calculating the total ET from each of the agricultural pixels within the climate variable pixel. As METRIC ET performs well for agricultural areas we masked the METRIC ET with USDA crop layer and used ET values only from agricultural areas.

The next step in model development was selection of model parameters. Variable selection and tuning of model parameters were done using the Variable importance plot and tuneRF method available in the “randomForest” R package [62]. Among all of the variables used in the model, a subset was chosen based on their effect on reduction of Mean Square Error. (MSE) provided as the variable importance plot by the Random Forest package. Since model errors do not decrease significantly after the addition of around 17 variables we selected those 17 variables for our final model. Similarly based on output of tuneRF (Figure 3), we selected tuning parameters the maximum number of terminal nodes (maxnodes) as 10 and number of trees for the forest (ntree) as 100. Since we have a smaller dataset increased number of trees does not affect the computational efficiency and choosing a greater number of trees ensures that every input row gets predicted at least few times.

2.6. Projecting Future Evapotranspiration

Future climate data derived from 20 GCMs for 2051–2060 and for two Representative Concentration Pathway (RCP) scenarios (RCP4.5 and RCP8.5) were used to calculate climate predictor variables identified as important predictors for RF model. To focus only on the effect of climate change we kept the same crop and topographical parameters from the observed period 2008–2014. This was further motivated by the fact that we assume that the crop pattern of major crops (alfalfa, hops, apples, grapes, corn) is unlikely to change substantially over a short period of time. Using the identified current crop and topographical parameters and the projected climate variables, future consumptive uses were computed under present (2008–2014) as well as future time periods and scenarios (2051–2060 for RCP4.5 and RCP8.5). This step was conducted using the “predict” function available in the “randomForest” package in “R” [62]. Here, future predicted evapotranspiration is superimposed on the current evapotranspiration map to assess how climate projections would impact the consumptive use of water.

3. Results

3.1. Historical ET

Figure 4 depicts the METRIC ET values for the growing seasons of 2008–2016 at 4 km scale. METRIC ET was computed at pixel size of Landsat imagery (30 m), but for the purposes of developing the statistical model, it was upscaled from 30 m to 4 km by calculating total ET from each agricultural pixel with the 4 km grid. The spatial variation of evapotranspiration within the watershed and between different years is evident. Evapotranspiration is affected by both climate and supply systems. From Figure 4 we can observe that there are reductions in ET during non-drought periods which could be attributed to the effects of climate change. Similarly, the effects of the supply system on consumptive use are also evident as there are relatively higher ET values on the northern side of the watershed, which is served by the Roza Irrigation District.

Figure 5 presents the boxplot of the METRIC ET across the study period. From the figure, we can observe that the test dataset of 2015–2016 are in the range of the training dataset of 2008–2014. Since RF model can predict within the range of input variables only. We can expect that the good performance of RF model on test and training dataset. Similarly, variation in the distribution of ET across the years will help in the generalization of the model.

3.2. Important Predictors of Watershed ET

Using the variable analysis tools available from the Random Forest package in R, a variable importance plot as shown in Figure 6 was used for selecting the most important variables for the model. The variable importance plot shows the increase in Mean Square Error (MSE) with iterative removal of each predictor in random forest model and sorting them. This results in variables that are considered to have the largest impact on model error to be identified as important predictors. Based on Figure 6, we can identify the important variables for the model which are—(1) apple crop area, (2) corn crop area, (3) hops crop area, (4) slope, (5) grapes crop area, (6) elevation, (7) alfalfa crop area, (8) maximum vapor pressure deficit from September to November, (9) minimum vapor pressure deficit from September to November, (10) minimum temperature from September to November, (11) standard deviation of precipitation, (12) minimum temperature from June to August, (13) aspect, (14) maximum vapor pressure deficit from March to May, (15) standard deviation of maximum temperature, (16) maximum temperature from March to May, and (17) minimum vapor pressure deficit from June to August. These 17 variables were selected as the most important model parameters since additional variables added to the model did not produce significant decreases in the mean square error (MSE). Based on the variable importance plot (Figure 6), we can infer that the most important predictor variables for ET are crop area, basin topography and spring, summer and fall climatic variables. Since the ET values were calculated only from crop pixels, we assume that crop area would have a significant effect on ET. The basin topography parameters slope and aspect determine the amount of radiation received, a major driver of ET. Similarly, temperature is affected by the elevation and thus ET. Since the evaporation from a basin depends upon the precipitation and the temperature, these variables were expected to be important predictors. In addition, the model selected summer and fall climatic variables as important predictors, which is consistent with general consensus that much of the growth and irrigation water application occurs during this time. We also examined the correlation among these variables (Figure 2)and found that all these variables had a correlation coefficient of less than 0.6.

3.3. Model Evaluation

The RF model developed in this study could explain about 89% of ET variability using climate and watershed properties. The model’s Out-of-Box (OOB) error levels off as shown in Figure 6 with 80 trees. Figure 7 presents the comparison of RandomForest-predicted-ET with METRIC-ET for two years (2015 and 2016). Overall RF-predicted-ET compared well with METRIC-ET with a Standard Error of Estimate (SEE) of 65 mm (R²: 0.9, slope: 0.74). While 2015 had a SEE of 8.7 mm (R²: 0.92 slope: 0.8), 2016 had a SEE of 83 mm (R²: 0.89, slope: 0.7). Although R² was ~0.9 for both cases, we can observe from the figure that higher values of ET are underpredicted and lower values of ET are overpredicted by the RF model. This is because prediction by the RF model is based on the average values at the final nodes causing the model to either increase the lowest values or decrease the highest peak values. Therefore, the RF model developed is not good for predicting peak ET values. Nevertheless, it provided a reasonable estimation of the spatial distribution of water use across the watershed. The average difference between METRIC and RF predicted ET for 2015 and 2016~3.5 mm, which is ~0.5% of mean METRIC ET.

3.4. Historical and Projected Climate

Table 4. Average maximum and minimum temperature in °C.

Variable	Season	Observed, 2008-14	RCP4.5, 2008-14	RCP8.5, 2008-14	RCP4.5, 20051-60	RCP8.5, 20051-60
Maximum Temperature	Winter	4.76	6.49	6.26	7.49	7.84
	Spring	16.93	19.79	19.65	20.42	20.76
	Summer	29.45	30.65	30.84	32.88	33.93
	Fall	17.66	17.13	17.21	19.73	20.91
Minimum Temperature	Winter	−3.95	−2.06	−2.18	−0.70	−0.26
	Spring	2.79	5.31	5.24	6.02	6.38
	Summer	12.25	13.26	13.44	15.10	15.98
	Fall	4.00	3.93	3.93	5.99	6.94

shows the seasonal average of maximum and minimum temperatures observed for 2008–2014, and the average GCM ensemble maximum and minimum temperatures projected for 2008–2014 and 2051–2060 for our study area. Both the observed and projected temperatures show similar trends although the projected temperatures are slightly higher than the observed. Winter and spring have greater departures whereas summer and fall have the least departures for both maximum and minimum temperatures. In comparison to the 2008–2014 GCM projections, the average increase in maximum temperature projections for RCP4.5 and RCP8.5 for 2051–2060 are 1.62 °C and 2.35 °C, respectively. Similarly, the average increase in minimum temperature for RCP4.5 and RCP8.5 are 1.49 °C and 2.15 °C respectively. As expected, this shows that there is more temperature rise under RCP8.5 (maximum temperature: 0.73 °C, minimum temperature: 0.66 °C) compared to RCP4.5 for 2051–2060.

Figure 8 presents the observed and projected precipitation values. While the projected and observed precipitation for the 2008–2014 period are similar during the spring and summer seasons, projected precipitation substantially exceeds the observed precipitation during the fall and winter seasons. A comparison of the projected precipitation for 2008–2014 with 2051–2060 shows that there is little or no change in precipitation during the spring and summer seasons. Whereas, under both scenarios, the precipitation is expected to increase during the winter season. Based on Table 4 and Figure 8 we can expect that our study area will be hotter and drier during the summer and wetter and warmer during the winter.

As depicted in Table 4 and Figure 8, the RCP4.5 and 8.5 climate projections have errors in replicating historic climate conditions. To reduce the impacts of these discrepancies in the climate model projections, we compared the effect of climate change using the low emission scenario RCP4.5 for 2008–2014 data as the baseline and the future forecasted data as the future data. The choice of RCP4.5 is motivated by the fact that it is reasonably close to the original data compared to RCP4.5 for our baseline study.

3.5. Change in Consumptive Use of Water under Future Projected Climate

Figure 9 below shows the predicted change in seasonal consumptive use of water between 2008–2014 and 2051–2060 predicted using the Random Forest statistical model for RCP4.5 and RCP8.5 scenarios. We found that on average the ET increases by 5.69% under RCP4.5 and 6.95% under RCP8.5 scenarios, this is consistent with the increase of temperature for 2051–2060 as shown in Table 4. This will increase the total water demand in the watershed approximately by 130 and 164 million cubic meters of water under the low and high emission scenarios, respectively. The higher value of change in RCP8.5 with respect to RCP4.5 may be because of the effect of a rise in temperature and increasing precipitation in winter. Across the study region, we found that expected change in ET ranges −9.71% to +32.81% when RCP4.5 climate projections are used and between −9.16% to +33.78% when RCP8.5 projections are used. The decrease in ET is noticed around the bottom western region of the study area whereas the increase does not show any discernable pattern. The boxplot in Figure 9 depicts that the distribution of change in ET is expected to be wider under RCP8.5 compared to RCP4.5 scenarios.

4. Discussion

Our results show that the future water demand in a watershed increases with the change in climate. We found that in the 2050s there will be an additional water demand of about 130 million cubic meters (110 thousand acre-ft) and about 164 million cubic meters (130 thousand acre-ft) water under the low and high emission scenarios, respectively. With warmer summer and wetter winter projections [65], it can be expected that there will be more water demand in the future, especially during the growing season. This analysis does not factor in any changes in planting dates that may occur due to climate change. Similarly, warmer winter results in less snowfall, quicker snowmelt, and more rainfall. Therefore, it is expected that while there will be an increase in water demand, supplies could dwindle. This necessitates careful and deliberate management of water for future water projects within the watershed. Various water management strategies such as increasing reservoir storage, adopting differing crop patterns, changing management practices, facilitating partial leasing of water rights, groundwater storage and recovery, and improving irrigation efficiency can be employed to manage future water demand [10,66].

Additionally, our results demonstrate that the RF regression model is highly effective for forecasting future evapotranspiration at the watershed scale. A statistical measure of the strength of prediction of future ET using crop acreages and climate data for 2015 and 2016 from this model showed SEE of 65 mm and R² values greater than 0.9 (Figure 7). The model identified the 17 important variables which influence consumptive use within the selected watershed. Unlike models to estimate potential evapotranspiration, which depends mostly on climate variables, our study showed accurate estimation of actual watershed ET depends on cropping patterns, climate and topography of the area. Removal of any of these variables significantly reduces the accuracy of the model. Moreover, the RF model can also provide useful information about the underlying process and determine the important variables for predicting watershed ET. Another advantage of this model is that, unlike other statistical spatial ET model (support vector machine, extreme learning machine) products [67] which predict potential ET, and requires assumptions of crop coefficients for predictions of actual ET, it provides a direct measure of actual crop ET of the entire watershed. However, there are some limitations to our model.

The Random Forest model developed for our study consistently underpredicted the high values of ET and overpredicted the low values of ET (Figure 7). This is because prediction of regression for the RF model is based on the average of decision trees as well as the inability of the RF model to extrapolate beyond the range of input variables. Thus, the RF model cannot be used to predict peak values in the watershed. Nevertheless, it provides a reasonable estimation of the spatial distribution of water use across the watershed. Although our study is focused on the Yakima region, the model is generalizable to other regions with the understanding that the identified predictor variable will vary. While magnitude and timing of effect of climate change may vary significantly from one basin to another depending upon crop mix, topographical properties of the basin, the results are useful for context such as those in the Yakima River basin where summers are expected to be hotter and winters are expected to be wet and warmer (Table 4 and Figure 8).

Finally, it is important to acknowledge the several necessary simplifications in the decision-making process that were considered beyond the scope of this project. We used the ensemble average mean of the 20 climate models for the projection. This could result in error as only one model could be suitable for the study area and ignores the variation among these, which is a measure of inter-GCM uncertainty. Similarly, we used the METRIC ET as the true ET value. However, there is uncertainty associated with ET estimation using remote sensing model like error due to error in the selection of hot and cold pixel. Nevertheless, we selected hot pixel that had maximum dT and cold pixel that had minimum dT from candidate pixel as the METRIC’s overall performance is better using this selection, we assume that our model is less impacted by error in ET estimation [50]. Besides, in our model, we assume that the ET depends only on the hydrologic characteristics of a particular pixel. However, the supply of water into this basin is not based only on the hydrology of this area but also depends on the reservoir release from the upstream watershed (Upper Yakima), outside our study area. Since statistical models operate only within the bounds of predictor and response space, any change in ET due to change in supply patterns from outside the model space cannot be predicted by this model. In addition, for predicting the future ET we used the same cropping pattern of 2008–2014. While this may not represent the exact change in ET as the cropping pattern may change over time, this will help in predicting the potential change in ET due to the effect of change in the climate.

5. Conclusions

Climate change is likely to alter the dynamics of future water supply and demand around the globe, and thus increase the water stress. While leasing of water rights has been shown to reduce the levels of water stress, the lack of insightful temporal and spatial information on consumptive uses has affected trade flexibility in many watersheds. Information regarding how much water demand will there be in future would allow the better management of water resources with water trading. With the use of Random Forest statistical modeling with a remote sensing model, we have successfully demonstrated the possibility of reliable estimation of future consumptive use of water in facilitating water quantity trading. Superimposing the output of the Random Forest model on observed consumptive use, we predicted the possible change in water demand. We found that on average the future water demand for 2051–2060 will increase by 5.69% and 6.95% percentage under low emission and high emission scenarios respectively.

Researchers and water managers continue finding ways to mitigate the impact of climate change on agricultural water supply and demand. In the future, we hope that this research will lead to alleviating climate change induced water shortage in the watershed. Although this model has been developed for a small area, the same modeling principle can be used to create models in larger spatial domains. This could provide better predictions of change in future actual ET at regional scales. More research and innovations are needed to cope with the climate change induced water shortage.