A Simple Turbulent Exchange Approach for Estimating Reservoir Evaporation in Managing Water for Irrigation Using Remote Sensing and Ground Measurements

Abstract

Effective management of reservoir water for irrigation is crucial in arid regions prone to drought and water shortages. However, evaporation losses from reservoirs remain poorly understood. Direct measurements typically quantify evaporation only at the measurement site rather than across the entire reservoir. This study introduces the Turbulent Exchange Approach for Reservoir Evaporation Estimation (TEAREE). The TEAREE is a simple model that integrates a bulk aerodynamic formulation with Landsat 8–9 satellite water-surface temperature data and meteorological observations to estimate spatially distributed daily reservoir evaporation. The TEAREE model was first evaluated at Elephant Butte and Caballo reservoirs in NM, USA, and subsequently applied across multiple reservoirs with diverse climatic conditions to demonstrate its applicability for estimating open-water evaporation. Daily evaporation was obtained by upscaling satellite overpass-time evaporation estimates using the daily-to-instantaneous vapor pressure deficit ratio (k_e) and wind speed. The model performed strongly across 12 lakes (R² = 0.91–0.99; RMSE = 0.27–0.85 mm/day) compared with the bulk aerodynamic (B_AER) method. Comparison with eddy covariance (EC) evaporation also showed good agreement. Monte Carlo analysis indicated moderate uncertainty associated with k_e variability, supporting the operational use of a constant k_e = 0.95 for daily upscaling.

1. Introduction

Reservoirs play a crucial role in storing water for consumption, irrigation, and industrial use, as well as in flood control and, in certain instances, hydropower generation. These bodies of water offer numerous benefits, including regulating river flows, supporting recreational activities, and providing habitats for fish, among others. Reservoirs have significantly improved water security for irrigation, supplying water to vast areas of irrigated land worldwide. Therefore, the effective management of reservoir water is vital, particularly in arid regions susceptible to drought and water shortages. One of the primary causes of water loss from lakes and reservoirs is evaporation, and accurately quantifying these losses remains a challenge. Direct measurement of evaporation within the reservoirs is not only expensive and time-consuming but also involves major logistical challenges in installing and maintaining sensors (aka instrumentation) above the water to collect good data. Several methods have been used to estimate reservoir evaporation losses: water balance methods [1,2], Class A evaporation pan [2,3,4,5], energy balance approaches [6,7,8,9], bulk aerodynamic formulations [7,10,11], eddy covariance measurements [9,12], and combination equations such as Penman [7,13,14] and the Priestley–Taylor method [15,16,17]. While these methods provide valuable insights, they often provide point-based estimates that do not capture the spatial variability of evaporation across large lakes and reservoirs [18]. The energy balance method is often considered the most accurate approach for estimating evaporation [19]. The pan evaporation method, although widely used, tends to overestimate evaporation because shallow pans respond more rapidly to environmental changes than large reservoirs. Empirical models, while relatively simple to implement, require site-specific calibration, which limits their transferability [20]. These limitations highlight the need for approaches capable of providing spatially distributed evaporation estimates over large water bodies. In this context, satellite remote sensing has emerged as a promising alternative.

Remote sensing technologies offer a practical alternative by providing spatially distributed, temporally consistent observations of water bodies across large areas [21]. Remote sensing models such as SEBAL (Surface Energy Balance Algorithm for Land) [22,23], METRIC (Mapping Evapotranspiration at High Resolution with Internalized Calibration) [24,25], SEBS (Surface Energy Balance System), and ETWatch [26] have been used to estimate evapotranspiration (ET) over vegetated landscapes. However, these models face significant challenges when applied to water surfaces, where energy-flux dynamics differ from those on land [27]. Among these approaches, SEBAL has been among the most widely tested in lakes and reservoirs. Studies have shown that SEBAL can be used to estimate evaporation from lakes using Landsat 5 TM and 7 ETM+. For example, SEBAL estimated evaporation at Lake Naivasha, Kenya, and the results were reasonably close to pan measurements [28]. Similar results were reported for the Rift Valley lakes in Ethiopia [29]. However, these studies were typically based on data from only one or a few satellite overpasses. The SEBAL model was not evaluated for seasonal dynamics or interannual variability in open-water evaporation at these lakes.

Subsequent analyses revealed variable performance when evaluating large reservoirs. Using Landsat 5 TM and Landsat 8 OLI imagery, Losgedaragh and Rahimzadegan [27] assessed the SEBAL, METRIC, and SEBS models over the Amirkabir Reservoir in Iran. They found that SEBAL performed poorly at estimating evaporation relative to pan evaporation measurements (R² = 0.36; RMSE = 5.1 mm/day). In contrast, METRIC showed moderate agreement with pan evaporation (R² = 0.57; RMSE = 2.02 mm/day) [27]. In Egypt, Hassan [30] applied the SEBAL model using Landsat 5 TM imagery over Lake Nasser and found a moderate correlation with the Priestly Taylor method (R² = 0.48). A similar study using NOAA-AVHRR imagery demonstrated reasonable agreement with Penman–Monteith estimates (R² = 0.78) [31]. Similarly, Evans et al. [32] utilized SEBAL with Landsat 5 TM and MODIS imagery over the Menindee Lakes system in Australia, reporting moderate agreement with water-balance estimates (R² = 0.65–0.71). In contrast, the SEBS model showed improved performance in open water compared with SEBAL and METRIC at the Amirkabir Reservoir, achieving an R² of 0.93 and an RMSE of 0.62 mm/day [27]. However, broader validation under different climatic conditions has revealed more moderate performance. For example, Xiao et al. [33] used Landsat 5 TM, 7 ETM+, and 8 OLI imagery over the Tarim River Basin in China, validated their results against pan evaporation, and reported moderate agreement for open-water evaporation (r = 0.62; RMSE = 1.63 mm/day). Similarly, Chinyepe [34] applied the SEBS model using Terra MODIS imagery over Lake Mutirikwi, Zimbabwe, and found no statistically significant difference from Class A pan evaporation.

Although SEBS (Sensible Heat and Evaporation from the Surface) has shown some improvement in estimating evaporation, it does not explicitly account for water’s physicochemical properties. Recent studies have highlighted the importance of factors such as salinity in influencing evaporation rates. In 2016, Abdelrady et al. [35] developed the AquaSEBS model, which incorporates salinity to account for its effects on water density and the latent heat of vaporization. Validation of AquaSEBS at Lake Tana in Ethiopia against Bowen-ratio energy balance and eddy covariance measurements showed good agreement with observed data, yielding an RMSE of 35.6 W/m² and a relative RMSE (rRMSE) of 10.3%. Additionally, Abdelrady et al. [35] validated the AquaSEBS model against the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis product at Lake Victoria in Africa, reporting reasonable agreement with an RMSE of 1.5 mm/day and an rRMSE of 7.4%. The AquaSEBS model was also applied to four tropical reservoirs in Northeast Brazil using Landsat 5 TM and Landsat 8 OLI imagery and validated against pan evaporation and Penman–Monteith estimates. This validation yielded R² values ranging from 0.51 to 0.65 and RMSE values between 0.8 and 1.25 mm/day. These results suggest that AquaSEBS provides moderately accurate, spatially distributed estimates of open-water evaporation, making it suitable for trend analysis in data-scarce regions [36]. Fisher et al. [37] conducted a multi-site global evaluation of AquaSEBS across 19 lakes using Landsat 5 TM, Landsat 7 ETM+, and Landsat 8 OLI, as well as Terra MODIS imagery. They validated the model against in situ evaporation measurements, including eddy covariance, Bowen ratio, and bulk mass transfer methods. Their daily validation statistics, pooled across three lake observations, indicated moderate agreement for MODIS (R² = 0.47, RMSE = 1.5 mm/day) and slightly higher agreement for Landsat (R² = 0.56, RMSE = 1.2 mm/day).

In addition to salinity effects, recent advances have underscored the importance of lake heat storage in regulating evaporation. Zhao et al. [38] developed the Lake Temperature and Evaporation Model (LTEM), which uses Terra MODIS data to account for lake heat storage. The model was applied to 11 lakes worldwide and validated against in situ measurements, including eddy covariance and Bowen ratio data. The LTEM performed well, with an average R² of 0.84, ranging from 0.67 to 0.98. Furthermore, Dias et al. [39] developed the STAEBLE model using Aqua and Terra MODIS data and applied it to Lake Mead in the USA. Validation against in situ latent heat flux measurements yielded a correlation coefficient (r) of 0.69 and an RMSE of 62 W/m².

Accurately estimating spatially distributed evaporation from large water bodies remains challenging despite methodological refinements. Models such as METRIC and SEBAL often underestimate or overestimate evaporation because they rely on land-based temperature and roughness parameters [33,40]. Meanwhile, SEBS requires further refinement for application to water surfaces. Additionally, many remote sensing-based approaches focus on achieving full closure of the surface energy balance, thereby increasing model complexity and limiting their operational use for routine reservoir management. From the perspective of agricultural water management, these uncertainties in evaporation estimates directly affect reservoir water balance calculations, which are essential for irrigation allocation, drought planning, and seasonal release scheduling. These limitations underscore the need for an efficient model to estimate open-water evaporation. In this study, we present the Turbulent Exchange Approach for Reservoir Evaporation Estimation (TEAREE). This physically based model combines a mass-transfer or bulk-aerodynamic framework with Landsat 8–9-derived water-surface temperature to estimate daily open-water evaporation. The study aims to: (i) determine whether the TEAREE model accurately captures the spatial and temporal variability of reservoir evaporation by validating it against independent bulk aerodynamic (B_AER) and eddy covariance (EC) measurements; (ii) evaluate the TEAREE model across different seasons and years in estimating open-water evaporation; (iii) evaluate the TEAREE model across multiple reservoirs and lakes with diverse climatic conditions to demonstrate its applicability.

2. Study Site Descriptions and Meteorological Measurements

Two reservoirs, the Elephant Butte Reservoir (EBR) (33°15′0″ N; 107°10′12″ W; WGS84) and the Caballo Reservoir (CBR) (32°55′36.48″ N; 107°17′46.32″ W; WGS84), located along the Rio Grande (Rio is river) in NM, USA (Figure 1), were studied to develop the simple TEAREE model. Both reservoirs are located in the Rio Grande’s main channel. The reservoirs are part of the Rio Grande Project in south-central New Mexico. They store water for irrigating about 55,000 hectares of land along the river valley, including land in El Paso County, TX, USA, and land in the Republic of Mexico bordering the USA. The two reservoirs were selected for their extensive offshore evaporation measurements using the EC and B_AER methods, and for their large and small sizes, respectively. On-shore weather data in the vicinity of the reservoirs were also monitored.

The EBR extends approximately 64.4 km north–south, with a width ranging from 3.22 km to 6.44 km [41]. It covers 14,482.08 ha and has a total storage capacity of 2.46 km³ (USBR Technical Report No. ENV-2020-019). The CBR is smaller and shallower than the EBR. It covers 4667 ha, has a total storage capacity of 0.37 km³, is about 26.9 km long, and is 1.77 km wide [42]. However, these storage capacities have been reduced by sedimentation from upstream erosion since the dams were constructed. Overall, these reservoirs play a critical role in regional water infrastructure by storing, regulating, and distributing water for agricultural, municipal, and ecological uses.

2.1. Climate of the Region

The climate in this region is semi-arid, characterized by low annual rainfall, pronounced daily and seasonal temperature swings, low humidity, and abundant sunshine [43]. Monsoon rain typically falls from July to September, accounting for about 50% of the annual precipitation. Long-term data from Truth or Consequences (1951–1980), a nearby city, show maximum daily temperatures ranging from 36.7 °C to 41.1 °C, minimum temperatures from −20 °C to −27.2 °C, and an average annual precipitation of 223.5 mm [44]. Prevailing winds generally come from the southwest and northwest, funneling through the valley where the reservoirs are located. The average frost-free period is about 210 days and has been steadily increasing. The area’s dry climate creates high evaporative demand.

2.2. In Situ Measurement

Meteorological data required for the TEAREE model were collected from two flux stations (Figure 1): the onshore Elephant Butte Bulk-Aerodynamic flux station (EB-2), representing atmospheric conditions near EBR, and the offshore Caballo Eddy Covariance flux station (CB-1), representing overwater atmospheric conditions at CBR. The offshore CB-1 station was selected for CBR because no nearby onshore weather station accurately represented CBR’s climatic conditions. These flux stations provided the meteorological parameters required for the model inputs, capturing site-specific weather variations. The collected meteorological data included instantaneous measurements recorded as hourly averages between 10.00 and 11:00 am local time (Coordinated Universal time (UTC-7)) in NM, USA to match the satellite overpass time, which occurs between approximately 10:30 and 11:00 AM. These measurements included air temperature, relative humidity, wind speed at 10 m, and barometric pressure above the water surface. In addition to these instantaneous values, the daily mean wind speed at 10 m was also recorded as a model input. Water surface temperature is one of the parameters used to calculate instantaneous evaporation. In situ water surface temperatures for EBR and CBR were measured using high-precision infrared sensors mounted at the Elephant Butte eddy covariance station (EB-1) and the CB-1 station. These measurements were used to validate satellite-derived surface temperatures and open-water B_AER evaporation calculations. Daily evaporation measurements used in the TEAREE model validation were obtained from the offshore eddy covariance systems at EB-1 and CB-1, which directly measured evaporation over open water using B_AER and EC methods. These independent datasets provided reference evaporation against which model outputs were evaluated.

3. Methodology

3.1. TEAREE Model Development

The TEAREE model estimates daily evaporation by integrating satellite-derived instantaneous observations and ground-based meteorological data. The framework is based on the physical processes of turbulent vapor transport between the open-water surface and the overlying atmosphere. It treats turbulent vapor exchange and wind speed as the dominant controls on open-water evaporation and explicitly derives daily evaporation from instantaneous satellite overpass water-surface temperature, vapor pressure deficit, and wind speed. The formulation is based on the most direct description of water vapor transport, following Fick’s first law of diffusion. This applies to evaporation from the open-water surface in the absence of advection and changes in heat storage. Figure 2 outlines the model’s workflow, from identifying water bodies to calculating daily evaporation. This framework applies to Landsat 4, 5, 7, 8, and 9 Collection 2 Level 2 satellite imagery with green, shortwave infrared, and thermal infrared bands. Although this study focused on Landsat data, other satellites, such as MODIS, that provide thermal data can also be used in the TEAREE model. However, the use of coarse spatial resolution thermal sensors may reduce the accuracy in small water bodies due to mixed pixel effects (land–water) and loss of spatial detail.

Satellite images from the Landsat 8 and 9 Operational Land Imager (OLI) and Thermal Infrared Sensor (TIRS) Collection 2 Level 2 (C2 L2) datasets were acquired as GeoTIFF files for EBR and CBR. These images were retrieved from the USGS Earth Explorer platform (https://earthexplorer.usgs.gov/ (accessed on 1 August 2024)). The C2 L2 datasets were chosen for their high location accuracy, eliminating the need for georectification and internal atmospheric correction. Only images with clear skies over the reservoirs during the satellite overpass, between 10:30 am and 11:00 am local time (UTC-7) in New Mexico, were used in the model to estimate evaporation. However, thin clouds, which are harder to detect, may occasionally be present in the imagery. To avoid the thin clouds, a value of zero percent “cloud cover range” was set in USGS Earth Explorer platform during the image downloading process. The satellite images were provided in the WGS84/UTM Zone 13N projected coordinate system (EPSG:32613). From the Landsat imagery, bands 3 (green), 6 (SWIR1), and 10 (thermal infrared) were used. Bands 3 and 6 have a spatial resolution of 30 m, while band 10 is acquired at 100 m resolution and resampled to 30 m. A total of 280 images were collected from March 2021 to July 2024 at both reservoirs. These datasets were used to calculate the Modified Normalized Difference Water Index (MNDWI) for water body delineation and to estimate water surface temperatures, following Xu [45].

Water bodies were extracted from satellite images using MNDWI, a proven method for separating water surfaces from land, vegetation, and urban features [45]. The index improves the visibility of waterbodies and reduces misclassification of vegetation and urban areas [45,46]. The MNDWI (Equation (1)) was calculated from Landsat 8 and 9 C2 L2 imagery using bands 3 (green, 0.53–0.59 µm) and 6 (shortwave infrared or SWIR 1, 1.57–1.65 µm). This method separates water bodies by calculating the MNDWI for each pixel, classifying values greater than zero as water and values less than or equal to zero as non-water (land or vegetation). This step ensured that evaporation calculations were applied only to open-water pixels. The resulting water mask was used as input for estimating water surface temperature.

$$MNDWI={\displaystyle \frac{Green-SWIR1}{Green+SWIR1}}$$

(1)

Water Surface Temperature (Ts) is derived from the thermal infrared (TIR) band 10 (10.60–11.19 µm) of Landsat 8 and 9, where brightness temperatures are recorded as digital numbers (DNs). These DN values are converted to temperature in Kelvin using Equation (2), a calibration equation provided in the Landsat 8 and 9 Collection 2 data processing guidelines.

$$\mathit{Ts}=\left(0.00341802\right)\mathit{DN}+149.0$$

(2)

This process generates a high-resolution dataset of water surface temperatures, which serves as a primary input for estimating evaporation. Satellite-derived water surface temperatures were compared with in situ precision infrared radiometer (Model SI-111 by Campbell Scientific Inc., Logan, UT, USA) measurements at EB-1 and CB-1 stations. For comparison, the average satellite water surface temperature within a 3 × 3-pixel grid (90 m × 90 m) near the measurement location was compared with the infrared measurements. A linear regression was then used to correct the satellite-derived water surface temperatures to match the infrared sensor measurements. Similar approach (aka linear regression) can be applied in different reservoirs and environments to correct satellite surface temperature estimates by using infrared sensors, temperature sensors mounted on buoys or drones to measure the surface temperature of water during the satellite over pass. It is important that the measured temperature of water reflects the satellite temperature footprint at the measured location to avoid edge effect and land influences. For example, the General Lake Model, which utilizes meteorological parameters can also be used to indirectly estimate water surface temperature [47].

3.1.1. Instantaneous Evaporation Estimation

Instantaneous evaporation from the reservoir’s free water surface at the time of satellite overpass is estimated using the B_AER method, expressed as latent heat flux density (LE) in Equation (3), as described by Dingman [48] and others (e.g., Kondo [49], Sene et al. [50]). The evaporation rate (E) (Equation (4)) is determined by dividing the right-hand side of Equation (3) by the latent heat of vaporization of water (λ) and the density of water (${\rho }_w$). The saturation vapor pressure (e_s) of the evaporating surface is determined from Tenen’s Equation [51] using the water surface temperature (T_s) (Equation (5)). The vapor pressure of the overlying air (e_a) is determined from the overlying saturated vapor pressure using the air temperature and relative humidity (RH) (Equations (5) and (6)). In this study, we define “instantaneous” as hourly data at the time of satellite overpass, reflecting the readily available hourly weather information in many locations. However, another time interval can be considered. For simplicity, the coefficient (C_e) in Equation (7), which reflects the efficiency of vertical transport of water vapor by the turbulent eddies of the wind [48], is assumed to remain constant during the satellite overpass and the rest of the day. It is assumed that the density of water, the density of air, atmospheric pressure, and the depth of the reservoir water (or the height of wind measurements above the water) will remain constant over the course of the day, as these factors do not vary significantly. A near-neutral atmospheric stability condition is assumed; however, stability corrections for momentum and water vapor can be incorporated into Equation (3).

$$LE=\lambda \times {\displaystyle \frac{0.622{\rho }_a}{P}}\times {\displaystyle \frac{k^2}{{\left[\mathit{ln}\left(\frac{z-d}{z_o}\right)\right]}^2}}\times U_{10}\times \left(e_s-e_a\right)$$

(3)

$$E={\displaystyle \frac{0.622{\rho }_a}{P{\rho }_w}}\times {\displaystyle \frac{k^2}{{\left[\mathit{ln}\left(\frac{z-d}{z_o}\right)\right]}^2}}\times U_{10}\times \left(e_s-e_a\right)$$

(4)

$$e_s=0.6108\times e^{\left({\displaystyle \frac{17.27T}{T+237.3}}\right)}$$

(5)

$$e_a=e_s\times \left({\displaystyle \frac{RH}{100}}\right)$$

(6)

$$Ce={\displaystyle \frac{0.622{\rho }_a}{P{\rho }_w}}\times {\displaystyle \frac{k^2}{{\left[\mathit{ln}\left(\frac{z-d}{z_o}\right)\right]}^2}}$$

(7)

where LE is the latent heat flux density [MT⁻³], λ is the latent heat of vaporization of water [L²T⁻²], k is von Karman’s constant equal to 0.41, ${\rho }_a$ is the density of air [ML⁻³], ${\rho }_w$ is the density of water [ML⁻³], P is the atmospheric pressure [ML⁻¹T⁻²], $z$ is the height of the wind speed measurement [L] (z = 10 m in this study) above the surface, d is the zero-plane displacement height [L], $z_o$ is the roughness height of the surface [L], U₁₀ is the average wind speed [LT⁻¹] at 10 m height above the water surface, e_s and e_a are the saturated and actual vapor pressure, respectively [ML⁻¹T⁻²], RH is the relative humidity (%), and T is the air temperature in degrees Celsius [θ].

3.1.2. Daily Evaporation Estimation

Daily evaporation is estimated by scaling the instantaneous evaporation derived at the satellite overpass time. Instantaneous evaporation represents vapor exchange between the water surface and the atmosphere at the time of satellite overpass. However, evaporation varies throughout the day due to changes in meteorological drivers such as wind speed and humidity. Daily evaporation depends on how these atmospheric controls evolve over the full diurnal cycle. The TEAREE model uses the following algorithm to scale instantaneous evaporation (E_i) to daily evaporation (E_daily) by taking their ratio (Equation (8)).

$${\displaystyle \frac{E_{daily}}{E_i}}=24\times {\displaystyle \frac{{{(U}_{10})}_{daily}}{{{(U}_{10})}_i}}\times {\displaystyle \frac{{(e_s-e_a)}_{daily}}{{(e_s-e_a)}_i}}$$

(8)

Setting the daily-to-instantaneous vapor pressure deficit (VPD) ratio as a dimensionless constant, k_e,

$$k_e={\displaystyle \frac{{(e_s-e_a)}_{daily}}{{(e_s-e_a)}_i}}$$

(9)

and by substituting equation k_e into Equation (8), E_daily is then determined as (Equation (10)).

$$E_{daily}=24\times k_e\times E_i\times \left[{\displaystyle \frac{{{(U}_{10})}_{daily}}{{{(U}_{10})}_i}}\right]$$

(10)

where E_daily is the daily evaporation (mm/day) calculated from the instantaneous evaporation (E_i) in mm/h. The ${{(U}_{10})}_i$ and ${{(U}_{10})}_{daily}$ are the instantaneous and daily-average wind speeds at 10 m, respectively, in m/s. The factor 24 converts hourly evaporation (mm/h) to daily (mm/day) evaporation. If the measurement were collected at a 30-min time scale during the satellite overpass, then the factor 24 should be replaced by 48 to convert from a 30-min to a daily scale. The constants, C_e (Equation (7)), cancel out for both daily and instantaneous calculations. The ratio k_e reflects how representative the evaporative demand at the satellite overpass is relative to the average evaporative demand for the entire day. A k_e value close to 1 indicates that the atmospheric conditions at the time of the overpass closely resemble the daily average. Values greater than 1 suggest that the air’s evaporation demand for the remainder of the day is higher than during the overpass. Conversely, when k_e values fall below 1, it signifies that the evaporation demand at the time of the overpass exceeds that of other times throughout the day.

4. Results and Discussion

4.1. Water Surface Temperature

The comparison of satellite-derived and in situ water surface temperature (Ts) using linear regression at EBR and CBR from March 2021 to July 2024 shows strong agreement with in situ measurements at both reservoirs (Figure 3). These results indicate that Landsat-derived Ts data captured more than 98% of the temporal variability in observed Ts across seasonal and interannual conditions.

Despite the strong correlation, a consistent bias was observed. Regression slopes below unity (0.84 at EBR and 0.93 at CBR) and slightly negative intercepts indicate that satellite-derived Ts tend to overestimate actual Ts measurements. The RMSE values were 3.59 °C at EBR and 2.24 °C at CBR. The higher RMSE at EBR likely reflects a combination of factors, including its larger surface area, longer fetch length, greater depth, and bathymetric variability, as well as increased discrepancies between satellite-derived and in situ Ts measurements. The magnitude of the observed error falls within the broader range reported in the literature for Ts. For example, Kozlov et al. [52] validated Terra/Aqua MODIS-derived sea surface temperature against in situ buoy and coastal-station observations in the Baltic Sea, reporting a bias ≤ 0.49 °C, an RMSD ≤ 1.31 °C, and an R² ≥ 0.78. Over inland lakes, Terra and Aqua MODIS products were evaluated across multiple Italian lakes by Virdis et al. [53], who reported R² of 0.95 and RMSE of 2.34 °C. Their results are comparable to those at CBR. Similarly, Zhao et al. [38] reported that MODIS-derived Ts are generally biased and require empirical correction prior to application in energy balance models. The higher RMSE values observed in this study, particularly for EBR, highlight the challenges of capturing Ts for large reservoirs such as EBR. Tavares et al. [54] recommended using thermal data from the Landsat 7 ETM+ sensor for smaller lakes due to its relatively high spatial resolution, which produced an error of 1.05 °C in their study. These observations emphasize that although Landsat-derived Ts reliably capture temporal variability, pixel-wise regression correction is necessary to minimize systematic bias and prevent error propagation into vapor pressure deficit and evaporation calculations in the TEAREE model. Applying the site-specific regression adjustments in this study ensures that satellite-derived Ts are physically consistent with in situ measurements while preserving its spatial variability across the reservoir surface, thereby strengthening the robustness of the TEAREE evaporation framework.

4.2. Instantaneous Evaporation Estimates

To evaluate TEAREE’s initial accuracy at the satellite overpass time, satellite-derived instantaneous evaporation estimates were compared with in situ measurements at both reservoirs. For validation against in situ measurements of B_AER, instantaneous TEAREE-derived evaporation estimates were extracted using a 3 × 3-pixel grid averaging near the flux station measurements in the EBR and CBR. Satellite-derived and in situ instantaneous evaporation estimates exhibited strong agreement at both EBR and CBR. Statistical analysis confirms the model’s robustness, with R² values exceeding 0.96 at both sites. At EBR, the regression slope of 1.08 indicated a slight overestimation of satellite-derived estimates, though errors remained low (RMSE = 0.032 mm; MAE = 0.024 mm). The TEAREE model performed better at estimating instantaneous evaporation at CBR, a smaller reservoir, than EBR (R² = 0.9847; slope = 1.08, RMSE = 0.021 mm; MAE = 0.013 mm). This high accuracy at CBR can be attributed to the closer comparison between satellite-derived and in situ Ts at this site, which minimized bias in the evaporation estimates. Minor discrepancies at higher evaporation rates were due to the residual differences between corrected satellite-derived and in situ Ts [55].

These results are consistent with previous studies of satellite-based ET and evaporation models. Dhungel et al. [56] compared instantaneous satellite-based surface energy balance ET with the Penman–Monteith method and found a high correlation (R² ≈ 0.96–0.99). Similar performance has been observed in recent applications of the LakeVap tool by Matta et al. [57], where instantaneous evaporation estimates achieved R² = 0.92 and NSE = 0.83 compared with in situ observations. Overall, these findings demonstrate the robustness of satellite-derived evaporation estimates across varying reservoir conditions and highlight the importance of accurate Ts retrievals to minimize residual uncertainty.

4.3. Vapor Pressure Deficit Ratio (k_e)

Estimating daily evaporation with the TEAREE model requires assessing how representative the Vapor Pressure Deficit (VPD) at the satellite overpass is of the daily VPD. Analysis of data from March 2021 to July 2024 at the EBR and CBR shows k_e values ranging from 0.80 to 1.17, with most clustering around 0.95 (Figure 4).

At EBR, the mean k_e is 0.95 (median 0.95, SD 0.08, n = 1083 days), while at CBR it is 0.96 (median 0.95, SD 0.08, n = 1199 days), with values ranging from 0.81 to 1.18. The 5th to 95th percentile intervals for k_e are 0.841 to 1.100 at EBR and 0.842 to 1.109 at CBR, indicating that about 90% of days fall within a narrow range around unity. Notably, the mean k_e values are significantly below 1 (p < 0.001), suggesting that the instantaneous VPD from satellite overpasses is generally higher than the daily average at both sites.

The seasonal k_e values were evaluated using data collected from March 2021 to July 2024 at EBR and CBR. The results are presented in the boxplot in Figure 5. The whiskers represent the non-outlier max and min values of k_e, with the crossbars in the middle indicating the means. The results show a seasonal effect: the mean k_e is about the same (k_e ~ 95) in spring and summer for both reservoirs, but varies slightly between EBR and CBR. In fall, EBR exhibited a higher mean k_e of 0.98 (n = 265 days) than the smaller, shallower CBR (k_e = 0.95; n = 273 days). In winter, however, k_e values were similar between the reservoirs, with CBR showing a slightly higher mean k_e of 0.99 (n = 295 days) than EBR (k_e = 0.97; n = 266 days). Also, the k_e values for both reservoirs were higher during wintertime, approaching unity. This higher k_e in wintertime compared to summertime could be attributed to the reservoir’s heat storage and the rate of heating and cooling during the day, thereby changing the boundary-layer VPD above the free water surface.

Overall, the statistical analysis of the data shows that k_e is below 1 and remains around 0.95–0.96 across seasons at both reservoirs. The 95% confidence interval for the long-term mean of k_e was narrow, indicating the reliability of using a k_e of 0.95 in the TEAREE model application. Seasonal consistency of k_e values at EBR and CBR further supports the robustness of this ratio. Therefore, selecting a constant k_e of 0.95 provides a conservative estimate of daily evaporation for upscaling E_i to E_daily in the TEAREE framework.

4.4. Performance of the TEAREE Model Across Multiple Lakes

The performance of the TEAREE model was evaluated at EBR, CBR, and 10 other reservoirs to assess its transferability and robustness across diverse climatic and geographic contexts (

Table 1. Geographic coordinates (WGS84) of the twelve reservoirs with diverse climatic and geographic conditions where the TEAREE model was validated; [* natural lakes].

SN	Reservoir	Latitude and Longitude (WGS84)
1	Elephant Butte Reservoir (EBR), USA	33°15′0″ N, 107°10′12″ W
2	Caballo Reservoir (CBR), USA	32°55′36.48″ N, 107°17′46.32″ W
3	Cochiti Lake, USA	35°37′41.63″ N, 106°19′1.78″ W
4	Lake Mead, USA	36°02′46″ N, 114°44′30″ W
5	Lake Mohave, USA	35°25′50″ N, 114°39′7″ W
6	Lake Powell, USA	37°03′28.01″ N, 111°18′11.95″ W
7	Lake Okeechobee, USA *	26°55′0″ N, 80°46′27″ W
8	White Bear Lake, USA *	45°04′38″ N, 92°58′34.6″ W
9	Corumba Lake, Brazil	17°46′12″ S, 48°33′36″ W
10	Lake Erken, Sweden *	59°50′45.6″ N, 18°35′13.2″ E
11	Taihu Lake, China *	31°10′1.2″ N, 120°09′0″ E
12	Lake Taupo, New Zealand *	38°48′13.82″ S, 175°54′0.95″ E

). In addition to the primary sites, EBR and CBR, the evaluation was conducted across multiple reservoirs and lakes in the United States and on other continents, with varying numbers of validation days due to limited in situ data availability and cloud-covered satellite images. Consistent with the approach applied at EBR and CBR, satellite-derived Ts at all validation sites were corrected using site-specific linear regression to account for systematic bias prior to evaporation estimation. For the TEAREE model validation against in situ measurements of B_AER and EC, daily TEAREE-derived evaporation estimates were extracted using a 3 × 3-pixel grid averaging near the flux station measurement in the water and within the footprint of EC measurements.

4.4.1. TEAREE Model Validation Against Bulk Aerodynamic Method

The statistical analysis comparing TEAREE-modeled and measured B_AER evaporation across various reservoirs and lakes, using in situ meteorological and evaporation data, is presented in

Table 2. Summary of TEAREE daily evaporation performance across 12 lakes, validated against in situ bulk aerodynamic (B_AER) evaporation. Y-Int denotes the intercept of the linear regression equation.

Reservoir	Period	N (Days)	Reg. Equation		R2	RMSE (mm/Day)	NSE	RSR	Performance Rating
			Slope	Y-Int
Elephant Butte Reservoir (EBR), USA	2021–2024	122	1.03	−0.08	0.9574	0.46	0.95	0.22	Very good
Caballo Reservoir (CBR), USA	2021–2024	131	1.02	−0.14	0.9574	0.50	0.95	0.22	Very good
Cochiti Lake, USA	2018–2019	24	0.91	0.21	0.9492	0.36	0.94	0.23	Very good
Lake Mead, USA	2013–2016	38	0.98	0.10	0.9797	0.56	0.98	0.14	Very good
Lake Mohave, USA	2013–2016	35	0.94	0.40	0.9710	0.62	0.97	0.17	Very good
Lake Powell, USA	2019	9	0.91	0.08	0.9673	0.32	0.95	0.22	Very good
Lake Okeechobee, USA	2014–2016	17	0.90	0.57	0.9103	0.85	0.90	0.30	Very good
White Bear Lake, USA	2015–2016	12	1.07	−0.16	0.9930	0.30	0.98	0.10	Very good
Corumba Lake, Brazil	2005	6	1.02	−0.23	0.9623	0.27	0.93	0.24	Very good
Lake Erken, Sweden	2008	6	1.16	−0.28	0.9694	0.31	0.93	0.24	Very good
Taihu Lake, China	2016	5	0.94	0.46	0.9846	0.48	0.97	0.15	Very good
Lake Taupo, New Zealand	2015–2016	11	0.91	0.21	0.9649	0.29	0.96	0.19	Very good

and Figure 6. The TEAREE model shows a strong correlation with measured evaporation across all reservoirs. This close agreement highlights TEAREE’s effectiveness and extends its reliability beyond the primary calibration sites of EBR and CBR. For the majority of reservoirs analyzed, the regression slope is approximately 1, with minimal scatter. This outcome indicates that the TEAREE framework consistently delivers reliable performance across reservoirs with diverse climatic and geographic contexts. To illustrate the spatial capability of the TEAREE model, Figure 7 presents an example map of daily evaporation for EBR and CBR. The spatial patterns demonstrate the model’s ability to capture heterogeneity in evaporation driven by variations in water surface temperature across the reservoir surface.

Statistical analysis of TEAREE validation shows that R² is generally high, exceeding 0.96, and that RMSE is between 0.46 and 0.50 mm/day for EBR (n = 122 days) and CBR (n = 131 days) when TEAREE model results are compared with evaporation estimated using measured parameters in the B_AER method (Table 2). The regression slopes at EBR and CBR were close to unity (1.02–1.03), with Nash–Sutcliffe efficiency (NSE) values of 0.95 and the ratio of RMSE to standard deviation (RSR) values of 0.22 at both reservoirs. The remaining US reservoirs, including Cochiti Lake (n = 24 days), Lake Mead (n = 38 days), Lake Mohave (n = 35 days), Lake Powell (n = 9 days), Lake Okeechobee (n = 17 days), and White Bear Lake (n = 12 days), were also validated against in situ B_AER measurements. TEAREE consistently showed strong performance, with R² values ranging from 0.91 to 0.98 and RMSE below 0.62 mm/day. Lake Okeechobee showed a slightly higher RMSE of 0.85 mm/day (Table 2). The regression slope for these reservoirs/lakes ranged from 0.90 to 1.07, indicating minimal bias between measured and TEAREE-modeled evaporation. Reservoirs (named lakes) with more available validation days, such as Cochiti Lake, Lake Mead, and Lake Mohave, exhibited higher performance, with NSE values ≥ 0.95 and RSR values ≤ 0.23, reflecting TEAREE’s well-constrained performance under more robust data availability. In contrast, the number of validation days was lower due to limited in situ data availability and cloud-free satellite observations at Lake Powell, Lake Okeechobee, and White Bear Lake. These lakes still showed NSE values of 0.90–0.98 and RSR values of 0.10–0.30. They also demonstrated low RMSE values comparable to those of lakes with a larger number of samples, indicating no bias in TEAREE’s performance regardless of the number of samples.

Validation at international lakes, including Corumba Lake (Brazil), Lake Erken (Sweden), Taihu Lake (China), and Lake Taupo (New Zealand), further demonstrates the TEAREE model’s transferability and robustness across diverse climatic and geographic regions. Despite fewer validation samples (n = 5–11 days) at these lakes due to limited in situ measurements and frequent cloud cover during satellite overpasses, TEAREE showed strong agreement with in situ B_AER evaporation. Across international lakes, the regression slope ranged from 0.91 to 1.02, with a higher slope of 1.16 observed only at Lake Erken (n = 6 days), which may reflect the limited sample size for validation. Despite this higher slope, the model performed well at Lake Erken (R² = 0.97, RMSE = 0.31 mm/day, NSE = 0.93, and RSR = 0.24). TEAREE also showed strong performance at other international lakes, with R2 values ranging from 0.96 to 0.98, RMSE values below 0.48 mm/day, NSE values exceeding 0.93, and RSR values remaining below 0.24, indicating TEAREE’s high and realistic predictive performance despite the limited sample sizes.

The TEAREE model’s performance was evaluated using NSE and RSR, following the criteria proposed by Moriasi et al. [58]. Moriasi et al. [58] consider NSE values between 0.75 and 1 or RSR values between 0 and 0.50 to indicate “very good” performance. Across the validated lakes, NSE ranged from 0.90 to 0.98, and RSR ranged from 0.10 to 0.30. Performance at all validated lakes falls under a “very good” rating. This consistent performance across primary calibration sites, regional U.S. lakes, and international lakes demonstrates TEAREE’s robustness, reliability, and transferability beyond the calibration sites under varying data availability and diverse climatic and geographic conditions. The TEAREE model employs the B_AER formulation, coupled with satellite-derived water-surface temperature, to estimate daily evaporation, requiring fewer input variables and enabling more robust application across reservoirs, large or small, and in different environments.

4.4.2. TEAREE Validation Against the Eddy Covariance Method

Validation against EC measurements was conducted to assess further TEAREE’s performance at EBR, CBR, and White Bear Lake (Figure 8). Evaporation measurements using the EC method were measured at the primary sites, EBR and CBR, from March 2021 to March 2023. At White Bear Lake, EC-based evaporation measurements were obtained from the University of Minnesota Biometeorology Group data archive [12] to validate the model. No EC-based evaporation from other reservoirs (Table 1) was available for validation.

The statistical analysis showed that the TEAREE model’s evaporation estimates are in better agreement with the B_AER than with the EC method (Figure 8). Validation against EC-based evaporation yielded lower R² (about 0.84) and higher RMSE (1.06–1.15 mm/day) than the B_AER method at EBR and CBR. Corresponding NSE values were about 0.65, and RSR values were about 0.59 at both reservoirs, indicating a “good” model performance rating according to the criteria of Moriasi et al. [58]. A similar pattern was observed at White Bear Lake, where validation showed strong agreement (R² = 0.94; RMSE = 1.33 mm/day; NSE = 0.78; RSR = 0.45) but with a more negative slope, which falls within the “very good” performance rating category. The slightly higher R² at White Bear Lake than at the primary sites is likely due to the difference in sample size. The difference in evaporation estimates between B_AER and EC are due to methodological differences. The B_AER is known to be more sensitive to higher winds than the EC, leading to occasional higher evaporation estimates. Minor deviations were mostly during summer peaks, when TEAREE slightly overestimated evaporation relative to EC due to high horizontal wind speeds. Previous intercomparison studies demonstrate that B_AER and EC estimates exhibit strong correlations but do not agree perfectly. For example, Metzger et al. [59] reported a slope of 1.13 (r ≈ 0.94) at the Dead Sea, while at Base Mine Lake, they observed an R2 of around 0.76 between the B_AER and EC methods. Similarly, Shevnina et al. [60] reported correlation coefficients of 0.87–0.88 between the two methods, and Holman et al. [61] reported a strong correlation (r ranging from 0.89 to 0.91) between the B_AER and EC methods at Lake Powell.

4.5. Uncertainty Analysis of TEAREE Model

The Monte Carlo uncertainty analysis quantified the uncertainty introduced by a single daily-to-instantaneous vapor pressure deficit ratio (k_e) in the TEAREE framework. In this analysis, k_e was treated as a variable parameter and repeatedly sampled via bootstrap resampling (with replacement) from observed k_e at EBR and CBR (Section 4.3). For each lake and validation day, daily TEAREE evaporation was recalculated using 5000 Monte Carlo simulations. In each simulation, the k_e value from the bootstrap sample was used to compute daily evaporation, and the result was compared with in situ B_AER evaporation to quantify uncertainty in model performance. The distribution of RMSE values across the simulations provides a direct estimate of the uncertainty in model performance due to day-to-day variability in k_e.

Figure 9 presents a summary of the Monte Carlo results, showing the actual RMSE with a k_e value of 0.95, the mean RMSE from 5000 simulations, and the 95% uncertainty range for RMSE. The actual RMSE across all lakes ranges from 0.27 to 0.85 mm/day, while the Monte Carlo mean RMSE varies from 0.34 to 0.92 mm/day, suggesting a slight increase in error due to variability in k_e. The uncertainty in RMSE across sites ranges from 0.14 to 0.43 mm/day, with the narrowest uncertainty band observed at EBR, CBR, Cochiti, and Lake Taupo, and wider bands at White Bear Lake (0.43 mm/day) and Lake Okeechobee (0.38 mm/day). The wider uncertainty bands are associated with limited validation sample sizes in these locations. In summary, the Monte Carlo results indicate that uncertainty stemming from k_e variability is moderate and does not significantly compromise model performance, as lakes with low RMSE values continue to show low errors. The narrow RMSE bands observed across various reservoirs suggest that using a single k_e value of 0.95 for daily upscaling is operationally sound.

5. Conclusions

The physically based TEAREE model, which uses corrected water-surface temperature measured by Landsat 8–9 satellites and is coupled with in situ meteorological measurements via the bulk aerodynamic method, was developed to estimate daily open-water evaporation from reservoirs accurately. The model was validated against independent evaporation estimates from the bulk aerodynamic (B_AER) and eddy covariance (EC) methods using data from EBR and CBR in NM, USA. The TEAREE model captured the spatial and temporal variability of reservoir evaporation, including seasonal dynamics and interannual variability. The model was also evaluated across multiple reservoirs with diverse climatic conditions to demonstrate its applicability in estimating open-water evaporation. Regression analysis showed a strong correlation (R² > 0.91; RMSE < 0.85 mm/day; NSE > 0.90) between the model’s evaporation estimates and measurements across various reservoirs.

The TEAREE model is simple to use and can be applied to estimate open-water evaporation in routine reservoir assessments, regional water accounting, and management. The uncertainty associated with the daily-to-instantaneous vapor pressure deficit ratio (k_e) is generally moderate, supporting the operational use of a single coefficient, k_e = 0.95, for daily upscaling. A key limitation is that Landsat-derived water surface temperature exhibits site-dependent bias and therefore requires local correction. In addition, the TEAREE model is not applicable during periods of ice cover due to sublimation process.