Characterizing Spatial Heterogeneity in Reservoir Evaporation within the Rio Grande Basin Using a Coupled Version of the Weather, Research, and Forecasting Model

Kathleen D. Holman aTechnical Service Center, Bureau of Reclamation, Denver, Colorado

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Kristin M. Mikkelson aTechnical Service Center, Bureau of Reclamation, Denver, Colorado

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Dagmar K. Llewellyn bUpper Colorado Basin Regional Office, Bureau of Reclamation, Salt Lake City, Utah

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Abstract

Increasing evaporative demand from storage reservoirs is aggravating water scarcity issues across the American West. In the Rio Grande basin, open water evaporation estimates represent approximately one-fifth of all water losses from the basin. However, most estimates of reservoir evaporation rely on outdated methods, point measurements, or simplistic models. Warming temperatures and increasing atmospheric evaporative demand are stressing overallocated resources, increasing the need for improved evaporation estimates. In response to this need, we develop open water evaporation estimates at Elephant Butte Reservoir (EBR), New Mexico, using three evaporation models and field measurements. Few studies quantify spatial heterogeneity in evaporation rates across large reservoirs; we therefore focus our efforts on using the Weather Research and Forecasting Model coupled to an energy budget lake model, WRF-Lake, to simulate evaporation across EBR over the course of two years. We compare results from WRF-Lake, which simulates lake heat storage, to results from the Complementary Relationship Lake Evaporation (CRLE) model and the Global Lake Evaporation Volume dataset (GLEV). Results indicate that monthly and annual evaporation totals from WRF-Lake and GLEV are similar, while CRLE overestimates annual evaporation totals, with monthly peak evaporation offset compared to WRF-Lake and GLEV. While WRF-Lake and GLEV appear to capture monthly and annual evaporation totals, only WRF-Lake simulates differences in evaporation totals across the reservoir surface. Average annual evaporation at EBR was approximately 1487 mm, yet annual totals differed by up to 545 mm depending on location. This study improves understanding of open water evaporation and elucidates limitations of extrapolating point in situ or bulk evaporation estimates across large reservoirs.

Significance Statement

Changes in climate are amplifying the loss of stored water in reservoirs due to increases in evaporation. Water managers need to account for this water loss, but many current methods do not accurately reflect the temporal and spatial variability in evaporation across large, heterogeneous reservoirs. To address this gap, we use a numerical weather prediction model coupled to a lake model to simulate spatial heterogeneity in reservoir evaporation on a subdaily time step. Our results suggest that bulk evaporation models may be sufficient for estimating evaporation at smaller, more homogeneous reservoirs, but more complex formulations may be more appropriate for estimating evaporation rates at large, complex reservoirs and for better understanding the heat storage affects that influence temporal variability of evaporation.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kathleen Holman, kholman@usbr.gov

Abstract

Increasing evaporative demand from storage reservoirs is aggravating water scarcity issues across the American West. In the Rio Grande basin, open water evaporation estimates represent approximately one-fifth of all water losses from the basin. However, most estimates of reservoir evaporation rely on outdated methods, point measurements, or simplistic models. Warming temperatures and increasing atmospheric evaporative demand are stressing overallocated resources, increasing the need for improved evaporation estimates. In response to this need, we develop open water evaporation estimates at Elephant Butte Reservoir (EBR), New Mexico, using three evaporation models and field measurements. Few studies quantify spatial heterogeneity in evaporation rates across large reservoirs; we therefore focus our efforts on using the Weather Research and Forecasting Model coupled to an energy budget lake model, WRF-Lake, to simulate evaporation across EBR over the course of two years. We compare results from WRF-Lake, which simulates lake heat storage, to results from the Complementary Relationship Lake Evaporation (CRLE) model and the Global Lake Evaporation Volume dataset (GLEV). Results indicate that monthly and annual evaporation totals from WRF-Lake and GLEV are similar, while CRLE overestimates annual evaporation totals, with monthly peak evaporation offset compared to WRF-Lake and GLEV. While WRF-Lake and GLEV appear to capture monthly and annual evaporation totals, only WRF-Lake simulates differences in evaporation totals across the reservoir surface. Average annual evaporation at EBR was approximately 1487 mm, yet annual totals differed by up to 545 mm depending on location. This study improves understanding of open water evaporation and elucidates limitations of extrapolating point in situ or bulk evaporation estimates across large reservoirs.

Significance Statement

Changes in climate are amplifying the loss of stored water in reservoirs due to increases in evaporation. Water managers need to account for this water loss, but many current methods do not accurately reflect the temporal and spatial variability in evaporation across large, heterogeneous reservoirs. To address this gap, we use a numerical weather prediction model coupled to a lake model to simulate spatial heterogeneity in reservoir evaporation on a subdaily time step. Our results suggest that bulk evaporation models may be sufficient for estimating evaporation at smaller, more homogeneous reservoirs, but more complex formulations may be more appropriate for estimating evaporation rates at large, complex reservoirs and for better understanding the heat storage affects that influence temporal variability of evaporation.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kathleen Holman, kholman@usbr.gov

1. Introduction

Atmospheric evaporative demand is increasing in water-scarce regions of the world, particularly in the American West (McCabe and Wolock 2015; Ficklin et al. 2015; Albano et al. 2022). These observed increases are more pronounced in the Rio Grande basin, where annual reference evapotranspiration has increased by upward of 229 mm (9 in.) from 1980 to 2020 (Albano et al. 2022). The Rio Grande basin covers approximately 471 896 km2 (182 200 mi2), spanning three U.S. states and four Mexican states (Fig. 1). Waters of the Rio Grande River, which support tribes, municipal and industrial users, agriculture, environmental needs, and recreation, have been considered fully appropriated since the year 2000 (e.g., Harding and McCord 2005). Increasing population, growing water demands, variable inputs, emerging protections for endangered species, and increasing water temperatures are stressing an already scarce water supply (Ward et al. 2006).

Fig. 1.
Fig. 1.

(a) WRF modeling domains (1–3) used in the current study. The green polygon represents the Rio Grande basin. The inset map shows water depth (m) across Elephant Butte Reservoir as simulated by WRF-Lake during the full simulation (0000 UTC 1 Jan 1994–2300 UTC 31 Jan 1996). Within the inset, the pink dot over land represents the location of the Class A pan, and the orange dot represents the location of the marina, Marina Del Sur. (b),(c) Monthly average maximum and minimum air temperatures (°C; solid purple and solid green lines, respectively) and monthly total precipitation (mm; solid blue line), respectively. Observations are valid at the Elephant Butte Dam weather station between 1 Jan 1994 and 31 Jan 1996. Dashed lines represent the historic average monthly climatological values from 1 Jan 1980 through 31 Dec 2019.

Citation: Journal of Hydrometeorology 24, 9; 10.1175/JHM-D-22-0210.1

Elephant Butte Reservoir (EBR; Fig. 1), along the Rio Grande River in south-central New Mexico, is the principal storage facility of the Bureau of Reclamation’s (Reclamation) Rio Grande Project, with a surface area of 145 km2 (35 786 acres) at full capacity. This reservoir, known colloquially to New Mexicans as the place “where we hang our water out to dry” (Belknap 2003; Fleck 2015), serves as the delivery point from the State of New Mexico to the State of Texas under the Rio Grande Compact. Previous studies have cited annual evaporative volumes from EBR of over 0.247 km3 (200 000 acre feet), which is about half the total annual consumptive allocation to the state of New Mexico under the Rio Grande Compact.

Current methods of estimating evaporation from many managed reservoirs across the American West, including EBR, rely on Class A pan measurements (Moreno 2008; Blythe and Schmidt 2018), energy budget models (Tschantz 1965), the eddy covariance (EC) method (Bawazir and King 2003), bulk aerodynamic mass transfer methods (Tschantz 1965; Bawazir and King 2003), or combinations thereof. While in situ techniques can provide reliable estimates of open water evaporation rates at point locations and serve as critical validation datasets for alternative approaches, the methodologies alone do not provide detail on spatial variability of evaporation, nor do they always represent the temporal effects of heat storage on evaporation rates over large bodies of water, particularly Class A pans.

To improve understanding of open water evaporation beyond point measurements, researchers are expanding estimation techniques to include the use of spatially distributed data such as remotely sensed variables and numerical weather prediction (NWP) model output. For example, Bawazir et al. (2007) combine remotely sensed surface temperature data from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) with observations from an offshore EC tower to estimate evaporative losses across EBR on 22 December 2001. Results suggest that on this day in 2001, total daily evaporative loss rates across the reservoir surface range from 0 to 2.7 mm, with higher losses observed across the southernmost portion of the reservoir where water depth is greatest. This finding is consistent with results from Spence et al. (2011), who show large evaporation totals in deeper portions of Lake Superior that occur after the peak evaporation season, a finding that may be related to residual heat storage in deeper regions of the lake.

Remotely sensed imagery is also being used to develop spatial estimates of water surface temperature and ultimately open-water evaporation across large bodies of water. For example, Lofgren and Zhu (2000) produce spatial estimates of latent heat flux across Lake Huron between 1992 and 1995 using a bulk aerodynamic method applied to Advanced Very High Resolution Radiometer (AVHRR) measurements of surface temperature. Melesse et al. (2009) develop spatial estimates of latent heat flux across Lake Ziway in the Rift Valley region of Ethiopia by combining the Abtew method for estimating evapotranspiration (Abtew 1996) with two instantaneous Landsat images of surface temperature. Similarly, Hassan (2013) produces instantaneous estimates of open-water evaporation across Lake Nassar in Egypt using seven Landsat scenes combined with a surface energy budget approach originally developed for estimating evapotranspiration (i.e., Bastiaanssen et al. 1998). Sima et al. (2013) use Moderate Resolution Imaging Spectroradiometer (MODIS) imagery to estimate daytime and nighttime water surface temperatures of Urmia Lake in northwestern Iran between 2007 and 2010. The authors use daytime images of water surface temperature in conjunction with the Bowen ratio energy budget method to estimate maximum monthly evaporation rates across the lake surface. While these studies, among others, demonstrate large advancements with remote sensing technology, study limitations often exist related to overpass frequency, image contamination, and spatial and temporal resolutions.

In contrast to remotely sensed imagery, NWP models can support evaporation estimation techniques across water bodies at continuous, subdaily temporal resolutions and time scales ranging from hourly to century-long. Spence et al. (2011) combine a monthly-mean transfer coefficient estimated with EC observations and 15 km forecast model climate data from Environment Canada’s deterministic NWP system, the Global Environment Multiscale (GEM) model, with the bulk mass transfer equation to estimate evaporative losses across Lake Superior between August 2008 and March 2009. The authors compute evaporation at each GEM grid cell separately to illustrate spatial and temporal variability. Similarly, Rahaghi et al. (2019) estimate the spatial distribution of surface heat flux, including latent heat flux, across Lake Geneva in western Europe between 2008 and 2014 using a combination of NWP output and satellite imagery of lake surface temperature. The authors combine assimilated output from the Swiss Federal Office’s NWP model run on a roughly 2.2-km grid with lake water surface temperature from AVHRR satellite imagery. While the authors do not explicitly illustrate spatial variability in evaporation, they do illustrate spatial variability in surface heat flux. Results suggest that surface heat flux can vary by up to 80 W m−2 across the surface of Lake Geneva during the winter months. Both of these studies demonstrate the ability of NWP models to support evaporation estimation techniques across large water bodies in humid regions. However, research has yet to expand or test these methodologies on reservoirs in more water-limited environments.

To address this gap, we utilize the WRF Model coupled to a lake model, WRF-Lake, and simulate evaporation from EBR during a 2-yr period of record high water levels in the mid-1990s. WRF-Lake has been shown to accurately simulate surface water temperatures at managed reservoirs that experience large and frequent inflows and outflows (Guo et al. 2022), and thus, could be a useful tool for estimating evaporative losses from managed reservoirs across the western United States. Our main goals throughout this study are to 1) demonstrate the application of WRF and WRF-Lake to a common water management challenge in the Rio Grande basin (Friedrich et al. 2018), specifically estimating open water evaporation; 2) characterize spatial variability in evaporation rates across EBR; and 3) compare simulated evaporative losses with field measurements and two alternative evaporation models of varying complexity. The additional estimates of reservoir evaporation include Class A pan observations, output from an energy balance model more commonly used in water operations and management, and recently released satellite and model based estimates from Zhao et al. (2022).

2. Data and methods

We develop spatially distributed estimates of reservoir evaporation from EBR using the WRF Model coupled to WRF-Lake. No in situ estimates of evaporation exist during our period of simulation; however, we calibrate WRF-Lake using in situ observations of surface water temperature. We compare simulated evaporation estimates from WRF-Lake with three alternative data sources described below.

a. Coupled WRF Model

We utilize version 4.2.0 of the WRF Model (Skamarock et al. 2019) coupled to the default lake model to simulate open-water evaporation across EBR. We use the Advanced Research version of WRF (ARW) dynamical core, which solves the fully compressible, Eulerian, nonhydrostatic fluid equations on an Arakawa C horizontal grid and terrain-following sigma (vertical) coordinate (Skamarock et al. 2008). The full model domain is shown in Fig. 1. Spatial resolution increases from 9 km in domain 1 to 3 km in domain 2 to 1 km in domain 3. EBR is located within domain 3. The model time step in domain 1 is 45 s and decreases by a factor of 3 in each subsequent domain (e.g., from 45 to 15 to 5 s). The number of vertical levels is set to 50 for each domain, extending from the surface to 50 hPa. The full simulation spans 0000 UTC 1 January 1994–0000 UTC 1 February 1996, where we treat the first month as model spinup (Gu et al. 2015).

Following Vivoni et al. (2009), who utilize WRF to simulate land–atmosphere coupling in southwestern U.S., we employ the Rapid Radiative Transfer Model longwave radiation scheme (Mlawer and Clough 1997), the Dudhia shortwave radiation scheme (Dudhia 1989), the planetary boundary layer scheme based on Mellor–Yamada–Janjić approach (Janić 2001), the unified Noah land surface model (Chen and Dudhia 2001), and the Kain–Fritsch cumulus parameterization scheme (Kain and Fritsch 1990) in the outermost domain (domain 1) only. We force the WRF Model with initial and boundary conditions from the Climate Forecast System Reanalysis dataset (Saha et al. 2010), available every 6 h on a 0.31° × 0.31° horizontal grid (approximately 38 km) with 38 vertical levels. See Wang et al. (2017) for a list of forcing variables. We apply spectral nudging (Stauffer and Seaman 1990) to air temperature, wind speed, and geopotential height outside the planetary boundary layer of domain 1 by nudging wavelengths greater than 1700 km in the x direction and greater that 1116 km in the y direction based on recommendations from Gómez and Miguez-Macho (2017) and NCAR (2018).

1) One-dimensional lake model

The default lake scheme in WRF, WRF-Lake, is a one-dimensional (1D) eddy diffusion lake model based on concepts from Henderson-Sellers et al. (1983), Henderson-Sellers (1985), and Hostetler et al. (1993) and adapted from the lake component within the Community Land Model (Oleson et al. 2004, 2010; Subin et al. 2012; Gu et al. 2015). While complex 3D lake models have been developed in recent decades for the purpose of investigating lake dynamics (e.g., Ye et al. 2019) and lake–atmosphere interactions (Xue et al. 2017), these models require more computational resources due to the complex hydrodynamics and enhanced spatial resolutions (Wu et al. 2020). One-dimensional lake models are still being used in coupled regional climate models for their computational efficiency, consideration of heat storage, and ability to simulate features of the regional climate system (e.g., Notaro et al. 2013; Bennington et al. 2014; Guo et al. 2022). Thus, we utilize a version of the 1D lake model available in the WRF modeling system, WRF-Lake (Gu et al. 2015), and provide estimates of reservoir evaporation across the entire surface of EBR (inset of Fig. 1).

Xu et al. (2016) provides a detailed description of WRF-Lake, which is summarized here. WRF-Lake is a 1D energy balance model that simulates water temperature at 10 levels distributed throughout the water column. Energy transport under ice-free conditions is divided into two components: surface layer heat exchange and subsurface layer heating. The surface energy budget is calculated by
β(KK)+(LL)=QH+QE+QG,
where β is the fraction of shortwave radiation absorbed in the surface layer, K and K are the incoming and outgoing shortwave radiation (W m−2), L and L are the incoming and outgoing longwave radiation (W m−2), QH is the sensible heat flux (W m−2), QE is the latent heat flux (W m−2), and QG is the heat storage term (W m−2). The surface layer absorbs a fraction of the net shortwave radiation β, while the remaining amount penetrates and is absorbed by subsurface layers following the Beer–Lambert law. The value of β is set to a constant value of 0.4 in the model (Oleson et al. 2010; Wang et al. 2019). The remaining 60% of net shortwave radiation penetrates subsurface layers and decays at a rate that is a function of η, a light extinction coefficient. The default representation of η in WRF-Lake follows Håkanson (1995),
η=1.1925d0.424,
where d represents lake depth (m).
Water surface temperature Tg (K) at the first simulated time step is received by the atmospheric boundary layer and at the next time step is computed as
ΔTg=(KK)(LL)QHQEQG(LL)Tg+QHTg+QETg+QGTg.
The momentum, heat, and water vapor fluxes are solved at the same time that the surface temperature equation is solved using the Crank–Nicolson thermal diffusion solution (Subin et al. 2012; Gu et al. 2015). The lake model time step is the same as the associated domain time step of the WRF Model.
Water temperature (K) in subsurface layers is governed by
Tt=z[(Km+Ke)Tz]+1cliqdϕdz,
where Km is the molecular diffusion coefficient (fixed at 1.433 × 10−7 m2 s−1), Ke is the eddy diffusion coefficient (m2 s−1), cliq is the heat capacity of water (J kg−1 K−1), z is the depth from the surface (m), and ϕ is the subsurface solar radiation heat source term (W m−2) defined as
ϕ=[1β(KK)]exp[η(zza)],
where η is the light extinction coefficient defined in Eq. (2), and za is the thickness of the surface layer (m). The wind-driven eddy diffusion coefficient Ke for layer i follows the Henderson-Sellers parameterization (Henderson-Sellers et al. 1983; Henderson-Sellers 1985) and is defined as
Ke={1.0×102u2kziP0(1+37Ri2)exp(k*zi)Tg>Tf0TgTf,
where i is the layer index (1 ≤ i ≤10), k is the von Kármán constant of 0.4, u2 is the 2-m wind speed (m s−1), zi is the node depth (m), P0 is the neutral value of the turbulent Prandtl number, Ri is the gradient Richardson number, k*=6.6u21.84|sinϕ|, and Tf is the freezing temperature of water (°C). In addition to molecular diffusion and wind-driven eddy diffusion, mixing within the water column also results from convective overturning (Hostetler and Bartlein 1990). More specifically, the convective mixing module within WRF-Lake (Hostetler and Bartlein 1990) assumes that no temperature instability can be maintained in the water column. At the end of every numerical time step, if there is denser water overlying lighter water, convective mixing happens immediately, mixing the water column from surface to the unstable layers (Hostetler and Bartlein 1990; Wang et al. 2019).
Turbulent fluxes of sensible and latent heat are calculated between the water surface and the lower atmosphere using Monin–Obukhov similarity theory (Oleson et al. 2004, 2010), where the residual energy flux at the water surface is then used as a top boundary condition for thermal diffusion in the snow, lake body, and sediment. According to Subin et al. (2012), upward sensible heat flux (W m−2) from the water surface is computed as
H=ρatmcpTgθatmrah,
while upward latent heat flux (W m−2) from the water surface is computed as
E=λρatmqgqatmraw,
where ρatm is moist atmospheric air density (kg m−3), cp is the specific heat of air at constant pressure (J kg−1 K−1), Tg is the water surface temperature (K), θatm is the potential temperature (K) at the atmospheric reference height with respect to the surface (normalized to the reference height with an assumed lapse rate; Subin et al. 2012), rah is the aerodynamic resistance with respect to sensible heat (s m−1), λ is the latent heat of vaporization or sublimation (dependent on the surface temperature; J kg−1), qg is the saturated specific humidity at the surface temperature (kg kg−1), qatm is specific humidity at the reference height (kg kg−1), and raw is the aerodynamic resistance with respect to latent heat (s m−1). The aerodynamic resistances (rah and raw) are computed following Oleson et al. (2004, 2010), except the roughness length scales for temperature and humidity (z0h and z0w, respectively), which are set to a constant value equal to the roughness length of momentum, z0m = 0.001 m (Gu et al. 2015; Charusombat et al. 2018).

WRF-Lake is not a mass-balance model (e.g., volumetric lake water content is fixed; Subin et al. 2012) and therefore does not simulate time-varying water levels. This can be problematic when applying WRF-Lake at reservoirs with highly variable and managed water storage volumes (e.g., Almeida et al. 2022; Guo et al. 2022). Consequently, we focus our simulation on a historical period during which water levels at EBR are relatively constant, 1 January 1994–1 February 1996. Average daily water surface elevation recorded at the dam during this period is 1342.69 m (4405.15 ft), while the standard deviation of daily water surface elevation over the same time period is 0.26 m (0.87 ft). The average reservoir surface area during this time is 145 km2, which we maintain within the coupled modeling framework by using 145, 1 km × 1 km water grid cells within domain 3. We define spatially varying depth of the water column (inset of in Fig. 1) using bathymetry data obtained from a 1999 reservoir survey performed by Reclamation (Reclamation 1999). Water column depth is computed by subtracting two-dimensional bathymetry observations from the average water surface elevation during the simulation period. The thickness of the top lake layer of each water grid cell is fixed at 0.1 m, while the thickness of each of the remaining nine lake layers constitutes an equal percentage of the total remaining depth. Average observed monthly air temperature (minimum and maximum; °C) and precipitation (mm) during the simulation period are shown in the right panel of Fig. 1. These data are valid at Elephant Butte Dam, New Mexico, (ID: USC00292848), a station in the Global Historical Climatology Network (GHCN). Average monthly conditions during the simulation are shown as solid lines, while climatological averages valid during the 40-yr period from 1 January 1980 and 31 December 2019 are shown as dashed lines. These observations suggest that the selected years are fairly average years with respect to average monthly air temperatures. During 1994, monthly total precipitation was below average during the monsoon season and above average during the cool season. During 1995, monthly precipitation was slightly below normal during most of the year, where September was slightly above average.

The WRF Preprocessing System (WPS) sets the surface temperature of inland grid cells designated as water by interpolating sea surface temperatures from the closest water point in the forcing dataset (Skamarock et al. 2008). This practice can result in unrealistic water surface temperature values or sharp gradients around inland water bodies (Mallard et al. 2014, 2015). At EBR, the WPS assigned a water surface temperature of 18.4°C to the reservoir on 0000 UTC 1 January 1994. Instead of using this value, we initialize water surface temperatures across EBR using water temperature observations recorded at Marina Del Sur, a marina located near the dam (see Fig. 1; B. Kalminson 2020, personal communication). Staff from the Bureau of Reclamation’s Elephant Butte Field Division recorded water temperature using a thermocouple temperature reader dropped approximately 0.3 m (1 ft) down from the water surface at the edge of the marina walkway. The location was approximately 22.9 m (75 ft) from the water’s edge at all times; however, the marina moved during the observational record, which varied the observation point in space (B. Kalminson 2020, personal communication). Lake temperatures were recorded on a weekly basis between 1 January 1988 and 9 September 2010. We force surface water temperatures across the entire reservoir to the value recorded on 31 December 1993, which is 7.78°C (280.93 K). Initial water temperatures below the surface layer (i.e., layers 2 through 10; 2 ≤ i ≤ 10), are calculated as a function of water surface temperature, Tg,
Ti=Tg+(277.0Tg)/(depthc×zi),
where depthc is set to 50 m.
A clear benefit of using a NWP model coupled to an energy budget lake model is the ability to estimate available energy for evaporation, a term that is often quantified as net radiation minus change in heat storage of the water column, Rn − ΔQG (Lenters et al. 2005; Gan and Liu 2020). In this study, we define Rn as the net solar radiation (incoming minus outgoing) plus the net longwave radiation (incoming minus outgoing) at the water surface at time step t = tN and ΔQG as the change in simulated heat storage in the water column between two consecutive time steps (tN+1tN),
ΔQG=ρwcliq(z=1z=10TtN+1dzz=1z=10TtNdz),
where ρw is the density of water (kg m−3). We retain the spatial dimension across the reservoir surface by quantifying available energy, Rn − ΔQG, at each grid cell separately and averaging hourly fluxes on a monthly basis.

2) Calibration simulations

Default model parameters in WRF-Lake are based on modifications from Gu et al. (2015), who focus on the Great Lakes, specifically Lake Superior and Lake Erie. Wu et al. (2020) note that these improvements are specific to large, deep (depth > 50 m), freshwater lakes located in the midlatitudes and may not be appropriate for alternative settings. This argument is supported by findings from Xu et al. (2016), Huang et al. (2019), Wu et al. (2020), and Guo et al. (2022), who document large biases in simulated lake surface temperatures at Erhai Lake, Lake Nam Co, and Miyun Reservoir in China using the default WRF-Lake configuration. The authors reduce simulated water temperature biases by modifying lake model parameters such as the fraction of absorbed shortwave (β), the light extinction coefficient (η), surface roughness (z0m), the eddy diffusion coefficient (Ke), maximum water density, and reservoir bathymetry. Wu et al. (2020) argue that the light extinction term and the wind-driven eddy diffusion term are critical for determining the vertical distribution of lake temperatures. We utilize appropriate bathymetry observations to define water column depth across the reservoir and focus our WRF-Lake calibration tests on the two parameters called out in Wu et al. (2020), the leading coefficient of the light extinction equation [i.e., Eq. (2)] and the leading coefficient of the wind-driven eddy diffusion equation [i.e., Eq. (6)].

From section 1, we see that η controls the rate at which solar radiation decays as a function of depth below the water surface [Eq. (2)] and is related to water quality (Cole and Wells 2006; Shatwell et al. 2016). Decreasing η allows more solar radiation to penetrate below the water surface and heat deep water layers, which results in lower lake surface temperature and a deepened thermocline (Wu et al. 2020). This is consistent with lakes that contain fewer aquatic plants (Wu et al. 2020). The wind-driven eddy diffusivity term Ke is a function of water column depth and influences water temperature via mixing of vertical temperature gradients [Eqs. (4) and (6)]. We explore the role of η and Ke in influencing simulated water surface temperature at EBR by comparing results from default simulations [i.e., simulations based on default formulations of η and Ke in Eqs. (2) and (6), respectively] with results from simulations where the leading coefficients in both equations are modified. We test two coefficients in the formulation of η, while allowing the leading coefficient of Ke to vary. Table 1 lists the coefficient values tested and the reference names associated with each parameter set.

Table 1.

WRF-Lake parameter coefficients considered in this study. Only leading coefficients in Eqs. (2) and (6) are changed. Units represent coefficient units. RMSE and MAE values are based on differences between water temperature observations at Marina Del Sur, NM, and simulated water surface temperatures at the grid cell closest to that location between 0000 UTC 15 Jul 1993 and 2300 UTC 30 Sep 1993.

Table 1.

The selected coefficients of η listed in Table 1 include the default value of 1.1925 from Eq. (2) and a value of 0.45 from Cole and Wells (2006). The default η coefficient comes from Subin et al. (2012). More specifically, Subin et al. (2012) defines the leading light extinction coefficient in WRF-Lake by combining the Poole–Atkins regression expression from Idso and Gilbert (1974) with historical Secchi depth estimates from 88 Swedish lakes presented in Håkanson (1995). The 88 lakes included in Håkanson (1995) are part of the Liming-Mercury-Cesium project and have variable physical/morphometric/chemical properties that influence Secchi depth. The trophic status of each lake is not listed. The second η coefficient (i.e., 0.45) represents pure water and is used in other WRF-Lake studies, including those by Xu et al. (2016) and Almeida et al. (2022). The test coefficients of Ke are based on arguments from Subin et al. (2012), who suggest that large values, such as those used in simulations of the Great Lakes, may result in excessively mixed conditions and degrade simulation quality for shallow lakes. The default coefficient of Ke in WRF-Lake [i.e., the leading coefficient of Ke in Eq. (6)] is 1.0 × 102. Following Wang et al. (2019), we decrease this value by four and five orders of magnitude due to the small surface area of EBR relative to the Great Lakes. In all test simulations, the functions for η and Ke are unchanged; we only test variations of the leading coefficients.

We compare water temperature output from calibration simulations with water temperature observations recorded at the local marina located on the reservoir, Marina Del Sur. We identify the reservoir grid cell located closest to the marina’s location, where the simulated depth is 36.23 m (see Fig. 1a). We focus on comparison metrics of root-mean-square error (RMSE) and mean absolute error (MAE). While other studies, such as Charusombat et al. (2018), focus on η and Ke, among others (including roughness length), a lack of high resolution in situ water temperature and latent heat flux observations restricts additional calibration potential at EBR. If alternative overwater and/or evaporation observations were made available, we could expand our approach to the lake model calibration.

b. Complementary Relationship Lake Evaporation model

In addition to WRF-Lake, we simulate evaporation from EBR using the Complementary Relationship Lake Evaporation (CRLE) model (Morton 1979, 1983, 1986). We include the CRLE model as a comparison to the WRF-Lake model as CRLE can support long-term water resource investigations due to its minimal meteorological input and computational resources requirements. The CRLE model has previously been used in multiple water resource studies to provide estimates of monthly reservoir evaporation across the United States (Huntington and McEvoy 2011; Reclamation 2015) and beyond (Melesse et al. 2009).

CRLE runs on a monthly time step and relies on a numerical energy-aerodynamic approach to estimate open-water evaporation. The core concept behind the “complementary relationship” (CR) in the CRLE model centers on the feedbacks that occur between land and the near-surface boundary layer. Changes in air temperature and humidity occur as an air mass passes from land to open water, and the air becomes cooler and wetter. The CR relies on these feedbacks between the air mass that passes over an evaporative surface and between evaporation (E) and potential evaporation (Ep). In CRLE, parameterizations of Ep and wet environment evaporation (Ew) are based on a modified Priestly–Taylor equation for computing Ew. This modified approach is less sensitive to differences in air temperature, humidity, and wind speed from land to water, thus overcoming the shortcomings of other estimation methods that require accurate overwater humidity and wind speed. The CRLE model instead relies on the strength of the available energy approach, in which wind speed is not used directly.

The equations used in the CRLE model are discussed at length in Morton (1983) and therefore, only a brief summary is provided here. CRLE iteratively solves energy balance and vapor transfer equations to estimate Ep, which is further used to estimate the equilibrium wet surface temperature. This equilibrium wet surface temperature is then used to estimate the slope of the saturation vapor pressure curve (Δw; kPa °C−1) used in a modified Priestly–Taylor equation that calculates reservoir or lake evaporation (Ew; mm) and is computed as
Ew=b1+b2Δw(RnG)(Δw+γ).
In this modified Priestly–Taylor equation used to estimate open-water evaporation, Rn is the net radiation for a water surface and b1 and b2 are calibration constants set to 13 W m2 and 1.12 (dimensionless), respectively (Huntington and McEvoy 2011). The calibration constants, b1 and b2, along with the net radiation constants required to estimate Rn, are calibrated by Morton (1983) using water budget estimates of lake evaporation across nine lakes in North America. These are once-calibrated constants and do not change with simulation location. The psychrometric constant is represented by γ (kPa °C−1), and G is a heat storage term. The heat storage term G is solved using an approach outlined by Morton (1983, 1986), where absorbed shortwave solar radiation is lagged by t months, where t is a function of salinity and average water body depth. Similar to Muskingum’s routing method (dos Reis and Dias 1998), a linear heat storage reservoir is used to lag the absorption of the shortwave radiation.

Application of the CRLE model requires local weather data, specifically solar radiation, air temperature, and dewpoint (or relative humidity) from land-based weather stations or gridded climate data near the reservoirs and lakes of interest. For this study, we force the CRLE model with data extracted from the coupled WRF simulation. Specifically, we average hourly WRF output of air temperature, solar radiation, and dewpoint temperature over all land grid cells located within a 3-km buffer of EBR during each month of the simulation. The 3-km buffer is intended to represent a typical distance from the water body for identifying possible meteorological stations from which to obtain forcing data.

In addition to the time-varying inputs, CRLE requires static data on reservoir location, depth, and salinity of the water (i.e., total dissolved solids). We set the average salinity in EBR simulations to 300 ppm based on Turner et al. (2003), though the CRLE model is insensitive to changes in salinity less than 5000 ppm (Morton 1986). Average reservoir depth is set to 15.45 m, which is the average depth of all WRF-Lake grid cells across EBR during the simulation period. Antecedent solar and water borne energy inputs for the CRLE model were determined by first running the model in an initializing mode and using model results from that run as initial conditions in the final model run. We run CRLE monthly from February 1994 through January 1996 and compare output to aggregated monthly results from WRF-Lake.

c. Global Lake Evaporation Volume data

Zhao et al. (2022) produce monthly evaporation volume and area estimates from 1.42 million lakes and reservoirs across the globe between 1985 and 2018. For each lake, evaporation volume (VE) is calculated as a function of the evaporation rate (Elake), the lake surface area (As), and the fraction of ice duration (fd,ice). The fraction of ice duration is defined as the time percentage of a month when a lake is fully covered by ice. The lake surface area is defined using a Landsat-based global surface water dataset. The evaporation rate Elake is computed using the Lake Evaporation Model (LEM) of Zhao and Gao (2019), which uses the Penman combination equation
Elake=Δ(RnδU)+γλ(a+bu2)Lf0.1(esea)λ(Δ+γ)
with heat storage
δU=ρwcwh¯TwTw0Δt,
where Elake is the lake evaporation rate (mm day−1); Δ is the slope of the saturation vapor pressure curve (kPa °C−1); Rn is the net radiation (MJ m−2 day−1); δU is the heat storage change of the water body (MJ m−2 day−1); a and b are wind function coefficients set to 2.33 and 1.65, respectively; u2 is 2-m wind speed (m s−1); Lf is the average fetch length of the water body (m); es is the saturated vapor pressure at air temperature (kPa); ea is the air vapor pressure (kPa); λ is the latent heat of vaporization (MJ kg−1); γ is the psychrometric constant (kPa °C−1); h¯ is the average water depth (m); Tw is the water column temperature at the current time step (°C); Tw0 is the water column temperature at the previous time step (°C); and Δt is the time step of 30 days (Zhao et al. 2022). The water column temperatures are estimated from air temperature measurements following methods in Zhao and Gao (2019). Authors force the LEM with surface downward shortwave radiation, surface air temperature, surface humidity, and wind speed from three different meteorological datasets to understand impacts of forcing uncertainty in evaporation estimates (Zhao and Gao 2019). Final evaporation estimates are averaged over the three forcing datasets. In this study, we compute evaporation rates for EBR by dividing monthly lake evaporation volumes by monthly surface area from the GLEV dataset between February 1994 and January 1996. Results are referred to as GLEV. We refer to both the CRLE model and LEM as bulk evaporation models because they simulate reservoir-average evaporation estimates (with no spatial component to the output).

d. Class A pan data

The final evaporation dataset that we consider in comparison with WRF-Lake model output includes field measurements taken at a Class A pan located on the southwestern side of EBR. Evaporation measurements from the pan are scaled by a reservoir coefficient of 0.7 to develop EBR-specific values, where the reservoir coefficient is based on historical recommendations (Rohwer 1934). This dataset is important because values are used as direct inputs into the Upper Rio Grande Water Operations Model, URGWOM (Roach and Tidwell 2007). URGWOM is a RiverWare model used to support water management and operations decisions in the Upper Rio Grande basin. We consider daily pan observations from the same time period as the WRF simulation, 1 February 1994–31 January 1996.

3. Results

a. Calibration

The intent of the calibration simulations is to identify an appropriate coefficient of η and Ke from those values listed in Table 1 for simulating conditions at EBR in the presence of limited water temperature observations. The top plot in Fig. 2 shows hourly simulated water surface temperature at the grid cell closest to Marina Del Sur from all eight combinations of lake coefficients listed in Table 1 between 15 and 31 July 1993, while the middle plot shows daily average simulated water surface temperature at the same location, along with observed instantaneous values recorded at the marina. Hourly temperatures are dominated by the diurnal cycle, while daily mean temperatures more easily demonstrate differences among simulations with respect to observations. Results in both plots suggest that the light extinction coefficients considered here primarily influence the diurnal range of surface temperatures, specifically, the nighttime minimum, such that the daily mean water surface temperatures in simulations with the modified η coefficient (dashed lines) are lower by the end of the simulation period compared to water temperatures with the default η coefficient. Daily average simulated water surface temperature values from the modified η coefficient simulations are closer to the observed values recorded on 19 and 26 July 1993.

Fig. 2.
Fig. 2.

(a) Hourly simulated surface water temperature (°C) at the grid cell closest to Marina Del Sur between 0000 UTC 15 Jul 1993 and 2300 UTC 31 Jul 1993 from each test simulation. (b) Daily mean water surface temperature (°C) at the same grid cell between 15 and 31 Jul 1993 from each test simulation and observations. (c) Average water temperature (°C) as a function of depth between 0000 UTC 15 Jul 1993 and 2300 UTC 31 Jul 1993 from each test simulation.

Citation: Journal of Hydrometeorology 24, 9; 10.1175/JHM-D-22-0210.1

To further characterize the influence of the leading η coefficient on simulated water temperature at the grid cell located closest to Marina Del Sur, we plot average water temperature as a function of depth below the surface during the two week period of the simulation (2300 UTC 15 and 31 July 1993; Fig. 2). Although we do not have observations of water temperature with depth, this figure allows us to examine lake model behavior and differences below the water surface. The simulated water temperature profiles in the right panel of Fig. 2 suggest that the default coefficient of η results in a shallower thermocline, more energy stored in the upper layers of the water column, and higher surface water temperatures relative to the modified η coefficient simulations. This finding is true for three of the eight simulations listed in Table 1 (e.g., k2ed, k663ed, and k3ed). Simulated thermocline depths from the other five simulations show some agreement with observed and simulated July thermocline depths presented in Nielsen (2005). As a result, we eliminate three parameter sets from further consideration and perform additional testing with five of the eight simulations (e.g., kded, kde45, k2e45, k663e45, and k3e45).

We aim to distinguish WRF-Lake model behavior among the five parameter sets by extending the simulation duration. Specifically, we extend the simulation from 2300 UTC 31 July 1993 to 2300 UTC 30 September 1993 for models based on five of the eight parameter sets in Table 1. Hourly water temperatures as a function of depth for the longer simulation duration are shown in the first five plots of Figs. 3a–e. These plots demonstrate a few key findings. First, hourly water temperatures among the five simulations range from 10.4° to 30.0°C, where differences in peak water surface temperature among the five simulations reach 4°C. Second, the two simulations with the default eddy mixing coefficient do not develop a well-defined thermocline (e.g., kded, kde45) even though simulated and observed temperature data from Nielsen (2005) suggest that a thermocline can and does develop in EBR. The lack of a clear thermocline in these two simulations is likely caused by too strong vertical mixing for such a small reservoir (Subin et al. 2012; Gu et al. 2015). These two simulations also produce warmer water temperatures at depth compared to the three simulations with reduced vertical mixing. Finally, maximum upper-level water temperatures increase as the eddy mixing coefficient decreases (from k2e45 to k663e45 to k3e45) as more heat is retained in surface layers. Daily average water surface temperatures among all five simulations are shown in Fig. 3f (valid from 15 July to 30 September 1993), along with the instantaneous observations from B. Kalminson (2020, personal communication). RMSE is greatest for the kde45 and kded simulations (1.56° and 1.57°C, respectively) and is lowest for the k663e45 simulation (0.83°C). Similarly, MAE is greatest for the kde45 and kded simulations (1.36° and 1.37°C, respectively) and is lowest for the k663e45 simulation (0.64°C). See Table 1 for the remaining values. Some water quality studies, such as Buccola et al. (2016), consider MAE values less than 1.5°C acceptable. Overall, water temperatures from the k663e45 simulation parameter set show the smallest RMSE and MAE values relative to observations among the five test simulations.

Fig. 3.
Fig. 3.

(a)–(e) Hourly simulated water temperature (°C) as a function of depth at the grid cell closest to Marina Del Sur, NM, from five of the eight test simulations (kde45, kded, k2e45, k663e45, and k3e45, respectively) between 15 Jul and 30 Sep 1993. (f) Hourly simulated water surface temperature (°C) between 0000 UTC 15 Jul 1993 and 2300 UTC 17 Sep 1993 at the same grid cell from the same five test simulations along with instantaneous observations.

Citation: Journal of Hydrometeorology 24, 9; 10.1175/JHM-D-22-0210.1

Given the lack of observational water temperature data with which to further calibrate leading coefficients of η and Ke, we investigate how sensitive surface evaporation is to variations in these two WRF-Lake parameters. We present evaporation totals between 15 July and 30 September 1993 for three (e.g., k2e45, k663e45, and k3e45) of the eight test simulations with similar RMSE and MAE metrics (e.g., Table 1). Results are shown in Fig. 4, where values in the upper-left corner of each subplot represent the reservoir average total evaporation and values in the lower-right corner of each subplot represent the range of evaporation totals (among lake grid cells) for each given time period. Among individual months and simulations, we see that evaporation totals in the northern half of the reservoir generally exceed evaporation totals in the southern half of the reservoir, where depths are largest. We also see that reservoir average evaporation totals are greatest during August. The range of evaporation totals across the reservoir surface is also greatest during August. For example, reservoir average total evaporation in August among these three simulations ranges from 172 mm (k3e45) to 190.1 mm (k2e45), a difference of 11% relative to the k3e45 total.

Fig. 4.
Fig. 4.

Total evaporation (mm) across Elephant Butte Reservoir during (first column) 15–31 Jul, (second column) 1–31 Aug, (third column) 1–30 Sep, and (fourth column) 15 Jul–30 Sep 1993 from simulations based on the (top) k2e45, (middle) k663e45, and (bottom) k3e45 parameter set. Values in the upper-left corner of each plot (μ; mm) represent the average over the reservoir surface. Values in the lower-right corner of each plot represent the maximum grid cell total minus the minimum grid cell total during each time period (R; mm).

Citation: Journal of Hydrometeorology 24, 9; 10.1175/JHM-D-22-0210.1

The fourth column of Fig. 4 represents total evaporation over the full calibration simulation duration, 15 July–30 September 1993. These plots show similar results to the monthly plots; evaporation totals are lower in the southern half of the reservoir and are higher in the northern, narrow portion of the reservoir. Reservoir average evaporation totals range from 402.9 mm (k3e45) to 452.1 mm (k2e45), for a difference of 12% relative to the k3e45 total. However, the range of evaporation totals across the reservoir surface varies from 156.1 mm (k2e45) to 160.4 (k3e45) for a difference of only 3% relative to the k3e45 simulation. Collectively, the results in Fig. 4 suggest that average evaporation totals are influenced by the two parameters modified here, while the range of totals (and hence, the spatial variability) is not. In light of these results and water temperature performance discussed above, we complete the 2-yr coupled WRF and WRF-Lake simulation using the k663e45 parameter set.

b. Full simulation

The fully coupled WRF and WRF-Lake simulation performed for this study runs from 0000 UTC 1 January 1994 to 0000 UTC 1 February 1996, where we treat the first month as model spinup. Thus, all results are valid between 1 February 1994 and 31 January 1996. The left plot of Fig. 5 shows daily average simulated water surface temperature (valid at between 0 and 0.1 m below the water surface) at the grid cell closest to Marina Del Sur along with weekly observations from the B. Kalminson (2020, personal communication) dataset, while the right plot shows average difference between the two time series (computed as simulated minus observed) as a function of month. Results in the left plot demonstrate that simulated water surface temperatures at the grid cell closest to the marina reach similar warm-season peaks, yet decrease more rapidly than observations during the cool season, a finding that occurs during both simulated years. Results in the right plot show that simulated water surface temperatures are cooler than observations between September and March and are warmer than observations during the warm season, specifically April–August. The largest average monthly difference occurs during December (−4.89°C). The average difference between the two datasets over the full simulation period is −1.3°C, indicating that there is a slight cool bias in the lake model relative to the instantaneous water temperature observation dataset considered here (see section 4 for more detail on this result).

Fig. 5.
Fig. 5.

(left) Time series of surface water temperature observed weekly at Marina Del Sur and simulated daily average values from the grid cell located closest to the marina (°C). (right) Average monthly difference in surface water temperatures (°C) computed as simulated minus observed.

Citation: Journal of Hydrometeorology 24, 9; 10.1175/JHM-D-22-0210.1

Average monthly simulated surface water temperature across EBR is shown in Fig. 6. During the first 12 months of simulation, surface water temperature warms from February 1994 to August 1994 and cools from August 1994 to January 1995. Differences in surface water temperature across the reservoir during this 12-month window peak during May and November with a relative minimum during February and August. During the second 12 months of simulation, surface water temperatures warm from January 1995 to August 1995, when they peak. A minimum is reached again the following January. Unlike the first 12-month window, differences in surface water temperature across the reservoir surface peak during October, November, and December. Results in Fig. 6 indicate that during periods of warming (i.e., March–June 1994 and March–August 1995), surface water temperatures in deeper portions of the reservoir are generally cooler than shallower portions of the reservoir. One explanation for why surface water temperatures in deep regions are lower than surface water temperatures in shallow regions during periods of warming could be variations in volumetric heat capacity (over the water column) and ultimately stratification. Water temperatures in shallow regions may warm throughout the column, whereas in deep regions, the warming may be restricted to upper portions of the water column.

Fig. 6.
Fig. 6.

Average monthly surface water temperature (°C) across Elephant Butte Reservoir between February 1994 and January 1996 based on output from the WRF Model coupled to a 1D energy budget lake model. Values in the upper-left corner of each plot (μ; °C) represent the average over the reservoir surface.

Citation: Journal of Hydrometeorology 24, 9; 10.1175/JHM-D-22-0210.1

Monthly evaporation totals across EBR during the simulation are shown in Fig. 7. The reservoir-average total, as indicated by μ, is shown in the upper-left corner of each plot. The range R of evaporation totals (computed as grid cell maximum minus grid cell minimum) is shown in the lower right of each plot. Between February and July 1994, there is an increase in reservoir-average evaporation, with a decline in reservoir-average evaporation from July to December 1994. During this first year of simulation, the largest difference in monthly evaporation totals across the reservoir surface occurs during September (R = 135.6 mm), with June (R = 121.7 mm) second, and May (R = 110.9 mm) third. During the second year of simulation, evaporation totals increase from February to September 1995 and decline again from September to December 1996. Unlike the first year, the range of evaporative losses across the reservoir peaks during May (R = 119.1 mm), with June (R = 107.5 mm) second, and October (R = 106.7 mm) third.

Fig. 7.
Fig. 7.

Monthly evaporation totals (mm) across Elephant Butte Reservoir between February 1994 and January 1996 based on output from the WRF Model coupled to a 1D energy budget lake model. Values in the upper-left corner of each plot (μ; mm) represent the average over the reservoir surface, while values in the lower-right corner of each plot (R; mm) represent the maximum grid cell total minus the minimum grid cell total during each month of the study.

Citation: Journal of Hydrometeorology 24, 9; 10.1175/JHM-D-22-0210.1

Available energy in the water column, Rn −ΔQG, is considered a significant driver of lake and reservoir evaporation (Gan and Liu 2020; Earp and Moreo 2021). We compute this term for each month of the coupled WRF simulation, with results shown in Fig. 8. From this figure, we see that during the first year of simulation, available energy across the reservoir surface increases from February to July 1994 and declines from July 1994 to a relative minimum in December 1994. We see a similar pattern during the second year of simulation, where available energy increases from the December 1994 minimum to a maximum in September 1995. Available energy decreases from September 1995 to January 1996. Results in Fig. 8 also include spatial correlations (sCor; right label of each subplot) between monthly total evaporation and monthly average available energy. We compute sCor using Pearson correlation, where the sample dimension is space rather than time. The spatial correlation values in Fig. 8 suggest that the spatial distribution of evaporation is most strongly correlated (sCor ≥ 0.8) with the spatial distribution of available energy during June–November of the first year and June–September and December of the second year. This relationship may be related to accumulated energy in the water column and variations across the water body that occur after the onset of stratification. The sign of the correlation is reversed during February of both years, which suggests that evaporation totals are high in regions of the reservoir where available energy is low during this time of year (i.e., opposite of most other months).

Fig. 8.
Fig. 8.

Average monthly available energy, Rn − ΔQG (W m−2), across Elephant Butte Reservoir between February 1994 and January 1996 based on output from the WRF Model coupled to a 1D energy budget lake model. Values in the upper-left corner of each plot (μ; W m−2) represent the average over the reservoir surface. Values in the lower right (R; W m−2) represent the maximum grid cell total minus the minimum grid cell total in each month. The sCor values indicate the spatial correlation between average monthly available energy and monthly total evaporation from Fig. 7.

Citation: Journal of Hydrometeorology 24, 9; 10.1175/JHM-D-22-0210.1

Monthly differences in evaporation across the reservoir surface accumulate over time. Annual simulated evaporation totals across EBR are shown in Fig. 9. The reservoir-average evaporation total (μ) during the first and second year is 1463.7 and 1509.1 mm (4.8 and 4.95 ft), respectively. Results show that annual evaporative losses in the southern portion of the reservoir, where water depth is generally greater, tend to be lower than annual evaporative losses in the northern reaches of the reservoir. This finding is true for both years. Finally, results show that annual evaporation across EBR can vary by upward of 482.1 mm (first year) and 545 mm (second year), depending on location.

Fig. 9.
Fig. 9.

Total evaporation (mm) across Elephant Butte Reservoir between (a) 1 Feb 1994 and 31 Jan 1995 and (b) 1 Feb 1995 and 31 Jan 1996 based on output from the WRF Model coupled to a 1D energy budget lake model. Values in the upper-left corner of each plot (μ; mm) represent average over the reservoir surface, while values in the lower-right corner of each plot (R; mm) represent the maximum grid cell total minus the minimum grid cell total during each 12-month period.

Citation: Journal of Hydrometeorology 24, 9; 10.1175/JHM-D-22-0210.1

c. Model comparisons

A comparison of monthly and annual evaporation totals from four different methods is shown in Fig. 10, where Nash–Sutcliffe efficiency and percent bias metrics relative to Class A pan observations are summarized in Table 2. Monthly evaporation totals from the Class A pan peak during summer, specifically June, similar to the seasonal cycle of incoming solar radiation. Monthly evaporation totals from the CRLE model peak in August during both years, which represents a lag of two months relative to the Class A pan peaks. The lag in CRLE estimates relative to Class A pan data is likely related to the heat storage formulation in CRLE, which is defined as a function of average lake depth and salinity (Huntington and McEvoy 2011). The largest monthly totals from CRLE exceed the largest monthly totals from the Class A pan. Reservoir-average evaporation from WRF-Lake peaks in July during the first year and in September during the second year. Monthly evaporation estimates from the GLEV dataset (Zhao et al. 2022) closely resemble estimates from WRF-Lake in that they peak during July of the first year; however, they peak during October during the second year (one month later than WRF-Lake). Monthly evaporation estimates from WRF-Lake and GLEV may differ because of differences in heat storage formulation between the two methods.

Fig. 10.
Fig. 10.

(top) Monthly and (bottom) annual evaporation (mm) totals from the coupled WRF modeling system, the CRLE model, Class A pan estimates with a pan coefficient of 0.7, and GLEV estimates.

Citation: Journal of Hydrometeorology 24, 9; 10.1175/JHM-D-22-0210.1

Table 2.

Performance metrics of three datasets relative to Class A pan data based on the Nash–Sutcliffe performance efficiency (NSE) and percent bias (Pbias).

Table 2.

While differences in evaporation are clear among methods at the monthly time step, annual totals show better agreement. The largest difference in annual evaporation totals occurs between CRLE and WRF-Lake during 1994 and is 203 mm (0.66 ft). This discrepancy largely stems from higher monthly totals from the CRLE model during summer and fall months. Class A pan totals exceed totals from WRF-Lake during both years and exceed or equal totals from the GLEV dataset during both years. Annual totals from WRF-Lake are lower than all other methods, which may reflect the impact of spatially varying depth, available energy (or heat storage), and heterogeneity in evaporation rates on accumulated reservoir average totals. Annual totals from the CRLE model exceed all other methods during both years. This finding is consistent with Huntington and McEvoy (2011), who note an overestimation of annual evaporation totals from CRLE relative to in situ estimates at Lake Tahoe (among other locations). These authors suggest that the differences may be related to a lack of wind in the formulation of evaporation or the simplistic heat storage employed within CRLE. Overall, results in the bottom plot of Fig. 10 demonstrate that agreement in annual evaporation totals among methods can occur at the expense of compensating monthly differences.

4. Discussion

In this study, we utilize the WRF Model coupled to a 1D energy budget lake model, WRF-Lake, to simulate open water evaporation rates across EBR during a 2-yr period of record high water levels and volumetric evaporative losses. This study is the first application of a NWP model coupled to a lake model to understand how evaporation varies spatially across a large storage reservoir in the western United States, while also comparing results to field observations and two other bulk evaporation models. Results from the 2-yr simulation indicate that reservoir evaporation varies spatially and temporally at EBR. The range of WRF-Lake evaporation totals across the reservoir surface can reach upward of 135 mm (0.44 ft) in a given month. Aggregated to an annual time scale, differences across the reservoir surface can reach 545 mm (1.8 ft). Spatial differences in evaporation totals across the reservoir surface have implications for interpreting evaporation totals from point, in situ methods employed at managed reservoirs across the western United States (Reclamation 2015) and for accurately quantifying the volume of water lost to evaporation across large reservoirs with varying depths.

In addition to providing spatial estimates of evaporation, WRF-Lake also provides information on temporal fluctuations of reservoir evaporation on time scales ranging from hourly to annual. The timing of peak reservoir-average evaporation from WRF-Lake does not agree with the timing of peak evaporation from the Class A pan and the CRLE model, a finding that is consistent with evaporation estimates from other deep lakes in the literature (Morton 1979; Croley 1992; Moreo and Swancar 2013; Friedrich et al. 2018; Zhao et al. 2020). Better agreement exists between the peak timing of evaporation from WRF-Lake and GLEV. The largest differences between these two datasets (e.g., WRF-Lake and GLEV) occur during the cool season of the second year of simulation. These differences may be related to the fact that the GLEV dataset is a global dataset forced by gridded meteorological data (an average among three different forcing datasets), only uses one reservoir-average depth, and runs on a monthly time step. Differences between these two models may also be related to biases in WRF-Lake (i.e., mixing within the water column), impacts of heat storage, and/or advected inflows/outflows. Heat storage effects have been strongly linked to temporal variability of evaporation in deep lakes (Morton 1979; Blanken et al. 2011), but have recently been found important in shallow lakes as well (Gan and Liu 2020). Specifying real bathymetry within WRF-Lake allows the user to capture variations in available energy in time and spatially across the reservoir (though the volume of water remains fixed).

While using WRF-Lake to simulate reservoir evaporation at EBR helps elucidate differences in spatial totals across the reservoir surface, limitations associated with the modeling framework exist. For example, the limited calibration dataset relies on surface water temperature observations based on weekly, point temperature measurements taken at a single location on the reservoir (B. Kalminson 2020, personal communication). The authors are unaware of alternative water temperature observations valid at the surface and/or below the surface during the study period. Charusombat et al. (2018) note that improvements to any modeling system are limited by the quality and spatial extent of observations. We therefore argue that our modifications to WRF-Lake represent an improvement over the default parameters for simulating conditions at EBR, while acknowledging that alternative lake model parameter sets could be identified in the presence of additional observations.

Although the average simulated water temperature bias reported here (−1.3°C) is on the same order of magnitude as biases reported between lake surface water temperatures derived from MODIS and in situ water temperature measurements (e.g., Crosman and Horel 2009; Xiao et al. 2013; Liu et al. 2015), monthly differences between simulated and observed temperatures can be even larger. One possible explanation for this behavior in simulated water temperature biases relates to measurement depth. Namely, the historical observations are valid at 0.3 m below the water surface, while WRF-Lake simulates surface water conditions in the water layer that extends from 0 to 0.1 m below the surface. Lazhu et al. (2022) suggest that differences between skin temperature (defined over micrometers of water depth) and bulk temperature (up to 1 m of water depth) can be on the order of several degrees. A second explanation for this bias is that during the warming phase of each year, energy in WRF-Lake does not sufficiently transfer into deep layers. Calibration simulation results (e.g., Fig. 3) suggest that water temperatures in the deepest layer of the lake model (at the grid cell closest to Marina Del Sur, New Mexico) are warmer by the end of the test simulations with larger leading Ke coefficients (e.g., within kde45 and kded simulations). This finding may suggest that the selected leading Ke coefficient used in the full 2-yr simulation (e.g., 6.6 × 10−3) restricts energy transfer from shallow to deep portions of the water column. However, more broadly, the bias in WRF-Lake is consistent with recent findings from Wang et al. (2023), who demonstrate a cool bias in WRF-Lake simulated surface water temperatures relative to in situ observations at a deep lake in eastern China.

A second limitation of the employed modeling framework relates to simulated inflows and outflows and horizontal circulations. WRF-Lake is an energy budget model (as opposed to water budget model) and treats reservoir volumetric water content as fixed. No reservoir inflows or outflows are considered, nor does one water column communicate with a neighboring water column. These aspects of the model could influence evaporation estimates by modifying the volume of water in the reservoir and the heat storage content, particularly if outflow water temperatures are drastically different from inflow water temperatures (e.g., Lake Mohave; Earp and Moreo 2021). Guo et al. (2022) explore how neglecting inflows and outflows at a regulated reservoir in China influences simulated water temperatures. Results from their study suggest that WRF-Lake, with appropriate modifications to model parameters, is able to adequately simulate surface water temperatures without inclusion of inflows and outflows. Alternatively, Almeida et al. (2022) suggest simulated water temperatures can vary substantially from observed values when neglecting inflows and outflows in coupled, climate model–lake model simulations. These conflicting findings suggest that additional analysis is needed in other managed systems. Nonetheless, we acknowledge that the lack of simulated reservoir inflows/outflows and the lack of horizontal circulations likely allow us to mimic behavior of the real system at the expense of possibly unbalancing the coupled model’s response to certain forcings.

In the absence of in situ evaporation estimates at EBR during our simulation time period, we have no data for a direct comparison with observations. However, in situ evaporation estimates at EBR exist over differing time periods. For example, Moreno (2008) presents 24-h evaporation totals at a single point on EBR between January 2006 and December 2007 based on a bulk aerodynamic approach and the EC method. During these two years, daily EC estimates range from near zero to 14 mm day−1, while daily aerodynamic estimates range from near zero to almost 17 mm day−1 with average monthly rates reaching 6 mm day−1 (May 2006) and 5 mm day−1 (October 2007). The daily and monthly evaporation rates from WRF-Lake compare favorably to the Moreno (2008) estimates with daily evaporation ranging from near 0 to 20 mm day−1 and monthly average rates close to 6 mm day−1. Beyond EBR, reservoir average evaporation estimates from the coupled WRF system align with other in situ estimates from reservoirs located in arid climates (Moreo and Swancar 2013; Earp and Moreo 2021).

5. Conclusions

Water in the western United States is a limited resource and heavily managed in order to provide for the growing municipal and agricultural demands. Climate change is exacerbating challenges with managing this limited resource, and the need for accurate estimates of evaporative losses at reservoirs in these arid environments is growing. In this study, we simulate evaporation across a large reservoir in New Mexico [Elephant Butte Reservoir (EBR)] using WRF coupled to WRF-Lake. We adjust reservoir bathymetry in WRF-Lake based on observations from a reservoir bathymetric survey (e.g., Reclamation 1999) and calibrate WRF-Lake using a water surface temperatures dataset by B. Kalminson (2020, personal communication). We note that average reservoir evaporation is more sensitive to the WRF-Lake model parameter choices than differences in evaporation totals across the reservoir surface. This suggests that spatial variability in reservoir evaporation may be driven by conditions that are consistent across calibration test simulations, including reservoir bathymetry (and heat storage), regional topography, and meteorological forcings. Finally, we document how surface water temperatures and evaporation from the reservoir vary throughout the 2-yr simulation, with spatial differences in annual evaporation totals reaching 545 mm (1.8 ft) dependent on location in the reservoir.

In addition to modeling reservoir evaporation using WRF-Lake, we also compare monthly evaporation from two bulk evaporation models and one observational dataset. Current hydrologic modeling efforts at EBR are based on the Upper Rio Grande Water Operations Model (URGWOM) model (Roach and Tidwell 2007), which uses Class A pan data to estimate evaporation from the reservoir. While annual evaporation estimates from the Class A pan are similar to annual evaporation estimates from WRF-Lake and GLEV, the monthly distribution of evaporation totals from the pan does not agree with timing from WRF-Lake and GLEV and does not vary substantially from year to year, neglecting intra- and interannual variability. Updating reservoir evaporation estimates in URGWOM to incorporate estimates from other methods, including results from the modeling effort presented in this paper, could improve water budget estimates and water allocation plans.

Acknowledgments.

This research was funded by the Bureau of Reclamation’s Water Resources and Planning Office under the work order identification F316A. WRF simulations were performed with the USGS Advanced Research Computing System, specifically Denali (USGS 2021). Analysis was completed using the freely available software NCL (NCAR 2016) and R (R Core Team 2020). The authors would like to acknowledge the useful information shared by the Bureau of Reclamation’s Albuquerque Area Office staff. Finally, the authors thank two anonymous reviewers for their feedback, which helped improve the overall manuscript.

Data availability statement.

Daily GHCN data at Elephant Butte Dam, NM, are available at https://www.ncdc.noaa.gov/cdo-web/datasets/GHCND/stations/GHCND:USC00292848/detail. Class A pan data and output from WRF-Lake are available for public download at https://data.usbr.gov/. GLEV data are available at https://zeternity.users.earthengine.app/view/glev.

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