Estimating reservoir evaporation using numerical weather prediction: Omo Gibe III reservoir in Ethiopia

Water resource management plays a crucial role in promoting sustainable development and protecting the environment. However, estimating evaporation rates in complex terrains, such as the Omo Gibe III Reservoir area, poses significant challenges due to limited data availability and the influence of natural formations on local weather patterns. To solve this problem Weather Research and Forecasting (WRF) model employed. The WRF model employs the European Centre for Medium-Range Weather Forecasts (ECMWF) Fifth generation of atmospheric reanalysis (ERA5) climate dataset to simulate key meteorological parameters. The simulation period covers 2014 to 2020, with a one-month spin-up period (December 1–30, 2013) to ensure model stability. To evaluate the model performance, various metrics such as Mean Squared Error (MSE), Nash-Sutcliffe Efficiency (NSE), Pearson correlation coefficient (r), Kling-Gupta Efficiency (KGE), and Mean Absolute Error (MAE) are employed. Reservoir evaporation is estimated by employing the mass transfer method and using WRF simulated meteorological variables. The findings highlight the WRF model-based estimatessuperiority over the MOD16 dataset, displaying lower MSE (85.22 versus 168.13) and higher NSE (0.91 versus 0.82), and signifying better agreement with observed evaporation patterns. Both models exhibit robust positive correlations with observed data (r: WRF − 0.97, MOD16–0.98), effectively capturing overall trends. The WRF model calculates a mean monthly average evaporation rate of 72.79 mm, which falls between Wolaita Station’s estimate (76.70 mm) and is lower than MOD16 (86.61 mm). The standard deviation values indicate that MOD16 exhibits the highest variability (36.67 mm), whereas the WRF model-based estimates(26.58 mm) and estimates of observed Station at Wolaita (30.91 mm) show comparatively lower variability, suggesting more consistent estimates. The research emphasizes the importance of the WRF model in estimating evaporation rates at Gibe III Reservoir, assisting in water allocation, reservoir operation, and environmental preservation. Furthermore, its applicability in climate resilience and sustainable development.


Introduction
Effective management and planning of water resources are crucial for promoting sustainable development and safeguarding the environment (Loucks 2000, Maurya andSingh 2021). Water resources management and planning are vital for meeting the needs of present and future generations while mitigating harm to ecosystems. Efficient water resource utilization is crucial in achieving these objectives. Accurate estimation of reservoir evaporation plays a pivotal role in this regard. However, estimating evaporation rates in regions with unique topography poses significant challenges. One such area is the Gibe III Reservoir valley, characterized by diverse topographical features such as valleys and canyons. These natural formations can greatly influence local weather reach with a height of 243 meters and a total installed capacity of 1,870MW from ten Francis turbines. The total reservoir area will have a storage capacity of 14.7 km 3 with active capacity of 11.75 km 3 and 2.95 km 3 capacity of dead storage. The reservoir has catchment area is approximately 34,150 km 2 .During the rainy season (June to September), the reservoir level rises and falls during the dry season (February-May)(Giorgio Pietrangeli Alessandro Cagiano 2016). The Omo Gibe Basin and the reservoir location is shown below in the Figure 1 obtained from (https://ethiogis-mapserver.org/dataDownload.php).

WRF model
The Weather Research and Forecasting (WRF) model is a state-of-the-science mesoscale weather prediction model serving the needs of both operational forecasts and atmospheric research. Recently, the model has been developed to conduct simulations of regional climate for studies focused on the finer-scale impacts of climate change. The WRF model is known for its ability to simulate meteorological processes at high spatial and temporal resolutions, allowing for detailed representation of terrain features, land cover, and atmospheric interactions. This allows the model to capture the effects of topography on wind patterns, temperature gradients, and other atmospheric processes in valley and gorge regions, which can influence the estimation of evaporation and other meteorological variables (Soares et al 2012). The WRF model can simulate relevant meteorological parameters that affect evaporation from reservoir surfaces. The model incorporates advanced atmospheric dynamics, surface physics parameterizations, and solar radiation parameterizations to provide accurate and high-resolution simulations for research and practical applications in hydrological studies(Chen and Dudhia 2001, Grell and Devenyi 2002, Teixeira et al 2016, Skamarock et al 2019.The model serves a wide range of meteorological applications across scales from tens of meters to thousands of kilometers. WRF can produce simulations based on actual atmospheric conditions (i.e., from observations and analyses) or idealized conditions (Skamarock et al 2019).
One of the key advantages of the WRF model is its adaptability, which permits users to customize model configurations for their specific research or operational needs. It can be configured for different domains, resolutions, and time steps and has the ability to assimilate a broad range of observational data, including surface observations, radar data, and satellite data, to enhance forecast precision. The WRF model has been extensively used in various applications, including weather forecasting, climate research, air quality modeling, and hydrological modeling.

WRF domain configuration
The WRF (Weather Research and Forecasting) Model was set up using geographical data from WPS V4 Geographical Static Data, which was obtained from the official WPS website at https://2.mmm.ucar.edu/wrf/ users/download/. The model utilized the Mercator projection and was centered at 7.008N latitude and 37.312E longitude. The domain configuration consisted of two grids, with an inner nested grid nested within the outermost grid. The outermost grid had a horizontal resolution of 4 kilometers and covered the South West of Ethiopia and the Northern part of Lake Turkana. It was composed of 100 grid points in the x-direction and 136 grid points in the y-direction. On the other hand, the nested grid featured a higher resolution of 1.3 kilometers and covered the boundaries of the Gibe III Catchment. It was defined by 199 grid points in the x-direction. The computational domain is shown in the figure 2 below. The topography is downloaded (https://ethiogismapserver.org/dataDownload.php).

Metrological forcing
The WRF Model simulation covering the years 2014 to 2021 begins with the utilization of the ERA5 dataset to establish the initial of conditions the atmosphere. This dataset serves as the foundation the for model, representing properly the state of the Earth's climate during the chosen simulation period. The ERA5 data includes various meteorological variables such as temperature humidity, wind, pressure, precipitation, and radiation essential for driving the model's simulations (Hersbach et al 2020). To ensure a smooth and accurate start to the simulation a spin-up time of one month, starting from December 1-30 2013 is implemented. During this one-month period the WRF Model is run to allow the atmospheric conditions to stabilize and reach a representative state. This spin-up time enables the model to minimize initial biases and transients setting the stage for a more reliable and realistic simulation. Once the one-month spin-up period is complete in January 2014 the WRF Model is ready to be driven by the meteorological forcing data from ERA5 for the remaining simulation years (2014 to 2021).

Parametrization and physics options
The model simulation of the basin catchments involved the selection of parameterization options to handle physical processes. Physics components were developed, such as microphysics, Radiation Options, Planetary Boundary Layer, Land Surface Options, and Surface Layer Options. The parameterization options were chosen based on previous studies. That were under taken in tropical region and defaults of the model.
Physics options are used to represent various atmospheric and surface processes. These options include microphysics, radiation, planetary boundary layer (PBL), land surface, and surface layer schemes, among others. Microphysics schemes simulate the formation and precipitation of atmospheric particles, radiation schemes represent the interactions between solar and terrestrial radiation, PBL schemes simulate turbulence and mixing near the Earth's surface, land surface schemes model energy and water exchanges with the land surface, and surface layer schemes represent fluxes of heat, moisture, and momentum at the lowest level of the atmosphere. The careful selection of physics options involves choosing suitable schemes that align with the particular operational needs. Various factors, such as the geographical area being simulated, the study's temporal and spatial scales, the computational resources available, and the desired level of precision, all influence the decisionmaking process. (Kessler 1969, Chou and Max 1999, Pleim 2006, Niu et al 2011. Table 1 displays the selected physics options for the WRF model, organized into distinct schemes and their corresponding values, accompanied by references. These choices are made by considering factors such as the geographical region under simulation.

Area-volume-elevation curve
To estimate the reservoir surface corresponding to the water elevation reached in Omo Gibe III Reservoir, a 30 m resolution Digital Elevation Model (DEM) provided by SRTM was classified into 1 m elevation bands over the reservoir and surrounding area. Each elevation band's surface area was calculated to provide an estimate of the reservoir surface at the corresponding water elevation. To understand the relationship between the reservoir surface area and elevation in Omo Gibe III Reservoir, a second-order polynomial equation was used to model the relationship. This allowed for the estimation of both the area elevation and volume elevation relationship for the reservoir since the plot area-elevation volume curve derived from Digital Elevation Model (DEM) shows parabolic nature. This type of model assumes that the relationship between the height and area (or height and volume) can be approximated hence by a quadratic equation.
Where A is the Area of the Reservoir, V is storage of the reservoir and h is the height of the water in the reservoir, and a, b, c, d, e, and f are coefficients that are determined by fitting the model to observed data. Once the coefficients are known, the equation can be used to make predictions about the surface area or volume of the reservoir at elevations that have not been measured directly.

Water level data
To estimate the water levels over Gibe III Reservoir, radar altimetry-based water surface elevations were used. These elevations were acquired from the operational satellite altimetry Hydro web database. Radar altimetry is a remote sensing technique that uses radar pulses to measure the distance between a satellite and the Earth's surface. By measuring the time it takes for the radar pulse to travel to the surface and back to the satellite, the satellite can determine the elevation of the surface with a high degree of accuracy (Kittel et al 2021). The Hydro web database provides access to a range of data products derived from satellite altimetry, including water surface elevations These data products are based on measurements taken by various satellite missions, including Jason-2, Jason-3, and Sentinel-3.By using these water surface elevation data products, it is possible to estimate the water levels over Gibe III Reservoir. This information is useful for managing the reservoir, predicting water levels, and planning water resource management activities. (Schwatke et al 2020). In order to simplify computation, missing data were filled by average method and monthly data were averaged into monthly data.

Observational data
The evaporation rate of Gibe III Reservoir is determined at Wolaita Station using the Hargreaves method, which utilizes observational data obtained from the Ethiopian National Meteorological Agency. The Hargreaves method is a commonly used approach for estimating evaporation based on temperature data. The Hargreaves method calculates ET0 using only temperature data. The equation takes into account the daily mean temperature (T mean ) and the difference between the maximum temperature (T max ) and the minimum temperature (T min ) from (Hargreaves and Samani 1985).
here: ET 0 is evapotranspiration (mm/day), T mean is Daily mean temperature (°C) , ΔT is Difference between maximum and minimum temperature (T max -T min ) (°C) and Ra is Extraterrestrial radiation (MJ/m 2 /day).

MOD16 dataset
The MOD16 dataset is a global evapotranspiration (ET) product developed by NASA for the MODIS sensor on the Aqua and Terra satellites. It calculates terrestrial ecosystem ET over global vegetated land regions with an 8-day temporal resolution and a spatial precision of 0.5 km. The MOD16 method employs the Penman-Monteith equation and takes as inputs daily meteorological reanalysis data and remotely sensed vegetation dynamics from MODIS. The dataset has been widely used in a variety of applications, including hydrological modeling, climate change research, and ecological monitoring (Mu et al 2007).The use of MOD16 products can provide improved accuracy in estimating evaporation from lakes in Romania, compared to traditional methods (Stan et al 2017).

Lake evaporation
Estimating the evaporation of lakes and reservoirs is a complex task due to various factors that influence it, including climate, physiography, and surroundings. Valley lakes, in particular, present unique challenges in this regard. They are affected by steep terrain that alters wind patterns and reduces exposure to solar radiation, resulting in lower evaporation rates compared to open lakes. Additionally, their shallower depth leads to faster warming and cooling, further impacting evaporation. To accurately estimate evaporation from valley lakes, it is crucial to consider factors such as available energy, momentum, mass, and energy transfers. Developing accurate models that incorporate these factors is essential for estimation, and the Mass Transfer Method is one the approaches used for this purpose (Hamblin et al 2002, Finch andCalver 2008) .

Mass transfer method
The mass transfer method operates on the principle that the rate of evaporation from the surface of a lake is directly related to the difference in vapor pressure between the lake surface and the surrounding atmosphere. The mass transfer coefficient, which governs this relationship, can vary depending on factors such as wind speed and atmospheric stability. The simplicity and straightforwardness of the mass transfer method make it attractive for practical applications, as it only requires basic meteorological data such as air temperature, relative humidity, and wind speed to calculate evaporation rates. This makes it especially useful in situations where detailed information about the lake and its surroundings may not be readily available. Furthermore, the widespread usage and validation of this method in different regions and climates have proven its accuracy and reliability in estimating lake evaporation rates. (Valipour 2017).The Mass Transfer Method for quantifying evaporation from lakes, was explained in (Finch and Calver 2008) prepared for the World Meteorological Organization's Commission for Hydrology .The bulk transfer equation for Evaporation from a tropical lake (Harbeck 1962, Sene et al 1991, Finch and Calver 2008 has the form Where C is the mass transfer coefficient, u 2 the wind function for wind is speed at 2-m height, e s is the saturation vapor pressure in kPa at water surface temperature and e a is the actual vapor pressure in kPa at air temperature. On the basis of an extensive measurement on reservoirs Harbeck suggested an expression for C that incorporated the area of the water body (Harbeck 1962). In appropriate units (Shuttleworth 1993) The transfer equation is; Where E is evaporation (mm/ day). e s is the saturation vapor pressure in kPa at water surface temperature, e s is the actual vapor pressure in kPa at air temperature A is lake surface area in m , 2 u 2 is the wind speed at 2m in m/s. Harbeck coefficient is suitable for lakes in the range of A 50 m 100 km 0.5

< <
This holds true for the area of Omo Gibe III reservoir.
The saturation vapor pressure and the actual vapor pressure are estimated from WRF simulation data .as saturation vapor pressure is related to air temperature, it can be calculated from the air temperature. The relationship is expressed by; Where, e T is saturation vapor pressure at the air temperature T, kPa and T in°C. The actual vapor pressure can computed as: Where T dew is dew Temperature.

Performance metrics
The performance measures for evaluating meteorological data typically consist of MAE (Mean Absolute Error), MSE (Mean Square Error), and correlation coefficient (r). These metrics are commonly used to assess the accuracy and effectiveness of the model in predicting meteorological conditions (Willmott 1982, Gleckler et al 2008. Similarly, for hydrological data, the evaluation metrics for predictive models include NSE (Nash-Sutcliffe 4. The Nash-Sutcliffe Efficiency (NSE), is a statistical measure commonly used to evaluate the performance of hydrological models. It is particularly useful in assessing how well a model simulates observed data, The NSE is calculated using the following formula: Where O i is the observed value at time step i (observed evaporation), S i is the simulated value at time step i (simulated evaporation) and, O is the mean of the observed values.
5. Kling-Gupta Efficiency (KGE) is a performance metric used in hydrology to evaluate the goodness-of-fit of hydrological models. It is a modification of the Nash-Sutcliffe Efficiency (NSE) that takes into account the variability of the simulated and observed data .The KGE is calculated as follows: Where ED is the Euclidean distance between the simulated and observed data, and 1 is the ideal value. The Euclidean distance is defined as; Where r is the linear correlation between observations and simulations, α a measure of the variability error, and β a bias, therefore Kling-Gupta performance for hydrological data calculated from (Gupta et al 2009); Where obs s is the standard deviation in observations, sim s the standard deviation in of simulated data, sim m is the simulation of mean, and obs m is the mean of observation. Table 2 displays comparison of basic statistical measures for both minimum and maximum temperatures, showcasing the performance of the WRF model in simulating meteorological data at the Wolaita Sodo station (37.75E, 6.79N). The table 2 compares observed and simulated minimum (Tmin) and maximum (Tmax) temperatures. The observed minimum temperature (Tmin) has a mean of 13.92°C, while the simulated Tmin has a higher mean of 14.84°C and greater variability. Simulated temperatures consistently exceed observed values across all percentiles and the observed maximum temperature (Tmax) has a higher mean (28.58°C) and lower standard deviation (2.45°C) compared to the simulated Tmax with a lower mean (26.22°C) and higher standard deviation (2.99°C). The simulated data tends to exceed observed values at higher percentiles, suggesting higher temperatures in the upper range.

Performance metrics of selected metrological fields
Performance metrics for temperature in the WRF model are used to assess the accuracy of its predictions compared to reference data. Commonly used metrics include Mean Square Error (MSE), Mean Absolute Error (MAE) and Pearson Correlation Coefficient (r). Table 3 shows model's predictions for the Minimum Temperature show better accuracy and stronger correlation (MAE = 1.3403, r = 0.7093) compared to the Maximum Temperature (MAE = 2.545, r = 0.8315) based on the provided performance metrics (MSE, MAE, and r). Figure 3 above depicts how well the simulated maximum and minimum temperatures align with observed values at the reservoir site, demonstrating a notable correlation in capturing the overall trends. Table 4 illustrates the average annual statistics of evaporation estimations in millimeters (mm) sourced from three different data sources: MOD16, WRF model-based simulation estimates, and Observational estimate from Wolaita Station with Hargreaves method. The mean annual evaporation estimation is greatest for MOD16 at 86.61 mm, followed by Observational estimate from Wolaita Station with Hargreaves method at 76.70 mm and WRF model-based simulation estimates at 72.79 mm. The standard deviation signifies the degree of variability in  Table 5 as well as Figure 4 presents a comparison of monthly evaporation estimates in millimeters (mm) obtained from data: MOD16, WRF model-based, and Wolaita Station. In January, the lowest estimate (22.76 mm) is observed at Wolaita Station, closely followed by MOD16 (23.80 mm) and WRF model-based (27.71 mm). Moving to February, the estimates gradually increase, with Wolaita Station exhibiting the highest estimate (24.23 mm) among the three methods. From March to May, MOD16 consistently shows the highest evaporation estimates and reaches its peak in May with 116.69 mm, while Wolaita Station and WRF follow suit. In June, the estimates from MOD16 and Wolaita Station are quite similar, whereas WRF has slightly lower estimates. From July to September, MOD16 remains the method with the highest estimates, followed by Wolaita Station and WRF. Notably, WRF presents the lowest estimate (79.29 mm) in August. Switching to October, Wolaita Station records the highest estimate (101.21 mm), trailed by MOD16 and WRF. Finally, in November and December, MOD16's estimates experience a significant decrease and become the lowest among the three methods, while   figure 5 shows MOD16, WRF, and Wolaita Station, show that MOD16 and Wolaita Station methods have higher median and upper quartile (75th percentile) values compared to WRF method, indicating potentially higher evaporation values. However, all three methods have relatively small interquartile ranges (IQR), indicating less variability in the data.   To assess the accuracy, goodness-of-fit, and bias of the models, selected evaluation metrics were employed, including Mean Squared Error (MSE), Nash-Sutcliffe Efficiency (NSE), Pearson correlation coefficient (r), Kling-Gupta Efficiency (KGE), and Mean Absolute Error (MAE). Table 6 shows a comprehensive analysis of the evaluation of evaporation estimates derived from two different data sources mainly MOD16 and the WRF evaporation estimates.

Performance metrics of evaporation estimate
Upon examining table 6, it becomes apparent that the WRF evaporation estimate outperforms the MOD16 data source in various aspects. The MSE value for the WRF evaporation estimate (85.22) is lower than that of MOD16 (168.13), indicating that the WRF model's predictions closely align with the observed evaporation values. Additionally, both models demonstrate positive NSE values, surpassing the mean value as a benchmark. However, the WRF estimate exhibits a higher NSE (0.91) compared to MOD16 (0.82), indicating a better capture of the observed evaporation patterns.
The Pearson correlation coefficient (r) further highlights the strong linear relationship between the predicted and observed evaporation values. Both models display high positive correlations, with MOD16 achieving an r value of 0.98 and the WRF estimate obtaining 0.97, confirming their ability to capture the general trends in the observed evaporation data.
Furthermore, the KGE considers correlation, variability ratio, and bias ratio to assess the overall performance of the models in reproducing the observed evaporation values. The WRF estimate exhibits a higher KGE value (0.73) compared to MOD16 (0.57), indicating its excellence in reproducing the mean, variability, and pattern of the observed evaporation data.
Lastly, the Mean Absolute Error (MAE) provides insights into the absolute differences between the predicted and observed evaporation values. The WRF estimate displays a smaller MAE (7.13) in comparison to MOD16 (10.09), suggesting its capability to provide more accurate estimates with less deviation from the observed values. Figure 6 provides statistical information on the meteorological conditions at the Reservoir site from 2014 to 2021. The data includes the minimum and maximum temperatures, as well as wind speed measurements. The table shows that the mean minimum temperature was 14.79°C, with a standard deviation of 1.73°C, and the lowest recorded temperature was 9.38°C, while the highest was 18.43°C. The mean maximum temperature was 26.23°C, with a standard deviation of 2.97°C, and the lowest and highest recorded maximum temperatures were 22.13°C and 33.15°C, respectively. The mean wind speed was 0.97 m s −1 , with a standard deviation of 0.21 m s −1 , and the lowest and highest recorded wind speeds were 0.42 m s −1 and 1.49 m s −1 , respectively. The percentiles presented in the show that 25% of the observations for minimum temperature were below 14.01°C, 50% were below 15.18°C, and 75% were below 15.91°C. Similarly, 25% of the observations for maximum temperature were below 23.69°C, 50% were below 25.46°C, and 75% were below 28.04°C. Finally, 25% of the observations for wind speed were below 0.85 m s −1 , 50% were below 0.97 m s −1 , and 75% were below 1.13 m s −1 .

Metrological condition of reservoir site
3.4. Reservoir water level, area and volume AVE curve of the Gibe III is obtained by processing a digital elevation model and the shape area of the lake using the storage capacity tool of ArcGIS. This curve provides valuable information about the relationship between elevation, area, and volume of the reservoir, which is crucial for the efficient operation of the hydroelectric power plant. The area elevation curve is shown in the in figure 7 below.
The relationship between the height and area/volume of a reservoir plays a crucial role in determining the changes in the water's expansion or contraction. The shape and size of the reservoir changes as the level of water increases or decreases, which significantly affects the amount of water it can contain. To estimate this  relationship, a second-order polynomial approximations is usually formulated, assuming that the height and area/volume are linked by a quadratic equation. This approximation proves to be accurate enough for practical applications while being simple mathematically. By using this model, we can estimate the change in the reservoir's area or volume based on changes in its height, which can be useful in a variety of applications, such as predicting how much water will be available for irrigation or hydropower generation. Additionally, this model can help us understand the relationship between the different variables involved and can aid in the design and management of reservoirs. Figure 8 represents an estimated curve that shows the correlation between area, volume, and elevation.
From (Schwatke et al 2020), and from processed area volume elevation curve of the reservior, it has been noted that the reservoir level climbed from 142 meters when the dam initially began to function to 207.9 meters when it reached its highest peak. During the study period, the reservoir increased by 65.9 meters. This enhanced the reservoir's capacity to store water from 4 billion cubic meters to 10.62 billion cubic meters, while also increasing the area from 82.2 km 2 to 122.00 km 2 . Figure 9 portrays the fluctuations in the temporal dimensions of Omo Gibe III Reservoir, encompassing its volume, area, and water level.

Reservoir evaporation
The monthly reservoir evaporation data for Omo Gibe III Reservoir is obtained by processing meteorological data obtained from WRF (Weather Research and Forecasting) Simulation data using the Mass transfer method and MOD16 dataset. The WRF simulated data provides meteorological variables such as temperature, humidity, wind speed, and solar radiation, which are processed using the Mass transfer method to calculate the evaporation values. The MOD16 dataset contains pre-processed evapotranspiration data derived from satellite observations. Table 7 presents the evaporation data from the Gibe III Reservoir using WRF simulated data for the years 2014 to 2020. The evaporation values are given in millimeters (mm) for each month of the year. The highest monthly evaporation values are observed in May and April, ranging from 131 to 160.9 mm in 2014, 142 to 153   From the Figure 10 the evaporation data from the Omo Gibe III Reservoir demonstrate monthly fluctuation between the WRF estimate data and MOD16 observations. The largest evaporation levels are often noticed from April to August, while the lowest values are observed from January to March and December. The data from both sources may be important for understanding the water balance and hydrological dynamics of the Oom Gibe III Reservoir, and may have consequences for water resource management and planning in the region. Further data analysis and comparison could provide insights into long-term trends and patterns in evaporation behavior, as well as improve decision-making processes connected to water resources in the research area.   Table 9 presents the statistical values of Omo Gibe III Reservoir evaporation based on WRF simulated data. The average evaporation for each month ranges from 29.38 mm in January to 43.50 mm in December. The standard deviation ranges from 25.37 mm in January to 32.58 mm in December. The lowest recorded evaporation is 2.00 mm in January, while the highest is 157.00 mm in October. The 25th percentile (25%) of evaporation spans from 8.25 mm in January to 73.00 mm in October, while the 75th percentile (75%) goes from 42.25 mm in January to 157.00 mm in October. Table 10, on the other hand, depicts the statistical values of Gibe III Reservoir evaporation based on MOD16 data. The monthly average evaporation ranges from 22.40 mm in January to 37.61 mm in December. In February, the standard deviation is 13.06 mm, while in December, it is 29.29 mm. The lowest recorded evaporation is 3.20 mm in December, while the highest is 160.90 mm in April. Evaporation ranges from 6.68 mm in January to 102.58 mm in October at the 25th percentile (25%) and from 28.73 mm in January to 136.10 mm in October at the 75th percentile (75%).
Upon comparing the data presented in tables 9 and 10 along with Fgure 11, it becomes evident that table 8 (WRF simulated data) typically exhibits elevated mean and standard deviation values in contrast to table 10 (MOD16 data) across most months. Distinct fluctuations in minimum, maximum, and percentile values between the two tables can also be noted across various months. Specifically, the minimum evaporation figures tend to be greater in table 9, while the maximum evaporation values hold higher positions in the same table. These disparities can be attributed to disparities in data sources, methodologies, and assumptions employed in the WRF simulation and MOD16 data computation.

Seasonality
The seasonality of evaporation is a critical factor in reservoir operation, impacting various aspects such as storage capacity, water supply planning, hydropower generation, flood control, and climate change adaptation. Reservoir managers must be aware of the seasonal patterns of evaporation and adjust their operational strategies accordingly. This may involve scheduling water releases, conserving storage during periods of high evaporation, and prioritizing water uses. Additionally, considering the potential impacts of climate change on evaporation patterns is crucial for long-term planning and effective water resources management. Figure 12 illustrates the Patterns in Seasonal Evaporation Estimations, displaying the variations in evaporation rates across four distinct seasons: DJF (December-February), MAM (March-May), JJA (June-July-August), and SON (September-November). The graph provides a visual representation of how evaporation levels change. Table 11 succinctly explains the numerical differences in the magnitude of Seasonality of Evaporation estimates at Wolaita Sodo Station. It provides data on mean, median, standard deviation, minimum, and maximum evaporation values for four seasons: DJF (December-February), MAM (March-May), JJA (June-July-August), and SON (September-November). Figure 12 visually represents these variations, highlighting the seasonal patterns in evaporation rates throughout the year. Table 12 illustrates the evaporation trends at Wolaita Sodo Station using the Hargreaves method for four different seasons. Notably, the evaporation rate is at its lowest during the DJF season (35.36 mm) with moderate variations, reaching its highest point during MAM (104.67 mm) with relatively low fluctuations. JJA shows consistently elevated evaporation (95.71 mm) with minimal variability, while SON displays moderate evaporation (86.39 mm) accompanied by higher fluctuations, indicating distinct seasonal patterns of evaporation.
From Table 13 we can see that the highest mean evaporation rate observed using the WRF method is during the MAM (March-May) season with a value of 104.62 mm. The lowest mean evaporation rate is during the JJA (June-July-August) season with a value of 79.19 mm. The DJF (December-February) season has a slightly higher mean evaporation rate of 39.14 mm, while the SON (September-November) season has a mean evaporation rate of 68.24 mm.
The seasonal summary of evaporation rates from Omo Gibe III Reservoir using two different methods, Hargreaves and WRF, and compare them with the evaporation rates from Wolaita Station. From the analysis, it can be observed that the MAM (March-May) season has the highest evaporation rates for both Hargreaves and WRF methods in Gibe III Reservoir. The mean evaporation rates are relatively consistent across seasons and methods, with low standard deviations indicating less variability. However, there are some differences in the minimum and maximum values, with the WRF method showing higher maximum values during the SON (September-November) season.
Based on the data presented in Table 13 and Figure 13, we can observe the seasonal evaporation patterns of both the WRF Model and MOD16 data. Notably, the highest average evaporation rate, as calculated by the MOD16 data, occurs during the JJA (June-July-August) season, reaching 118.24 mm. Conversely, the lowest average evaporation rate is recorded during the DJF (December-February) season, measuring 37.58 mm. The MAM (March-May) season demonstrates a relatively higher mean evaporation rate of 110.72 mm, while the SON (September-November) season exhibits an average evaporation rate of 79.94 mm.

Discussion
Effective water resource management and planning are crucial for sustainable development and environmental protection. Estimating evaporation rates in regions with unique topography, like the Gibe III Reservoir with its diverse features such as valleys and canyons, poses significant challenges. These natural formations greatly influence local weather conditions, including temperature, humidity, wind speed, and precipitation variations. The complexity of estimating reservoir evaporation in such areas is compounded by the lack of consistent data representing the exact reservoir location. Additionally, the inadequate positioning of measurement gauges in nearby towns instead of at precise reservoir sites introduces inaccuracies in evaporation estimations, compromising the reliability of the data and hindering effective water management. To address these challenges, innovative solutions that integrate hydrology, data science, and computational techniques prove to be powerful approaches for tackling complex water management problems. Leveraging these interdisciplinary tools enhances the accuracy of evaporation estimates and leads to improvements in water resource planning.
Researchers utilized the Weather Research and Forecasting (WRF) model to estimate reservoir evaporation rates in the unique topographic conditions of the Gibe III Reservoir area. The WRF model simulates meteorological parameters like temperature, humidity, wind speed, and solar radiation, considering local topography and site-specific factors. This enables the creation of high-resolution meteorological data even in regions with complex terrain or limited accessibility. The simulation period was from 2014 to 2020, and a 1-month spin-up period at the start of the simulation ensured model stability.
Evaluation of performance metrics revealed that the WRF model outperformed MOD16 in estimating reservoir evaporation in the Gibe III Reservoir valley. The WRF model demonstrated its superiority in accuracy, goodness-of-fit, and capturing observed evaporation patterns, as evidenced by lower Mean Squared Error,   Comparison was made between three different data sources for evaporation estimation: the WRF model's meteorological data, observed meteorological data, and the MOD16 dataset. To estimate evaporation rates, researchers employed the mass transfer method in conjunction with the WRF model. This method relies on the difference in vapor pressure between the lake surface and the surrounding atmosphere and requires basic meteorological data, such as air temperature, relative humidity, and wind speed, making it suitable for areas with limited lake information. Examining the data reveals noticeable differences in the monthly evaporation predictions among the three references. Broadly, both MOD16 and WRF model-based simulation estimates tend to present greater estimates in contrast to the actual measurements obtained from the Wolaita Station. More specifically, MOD16 consistently calculates higher rates of evaporation compared to both WRF modelbased simulation estimates and the observed data, particularly in the months of March, April, May, and June.
The mean annual statistics of evaporation estimates further supported the superior performance of the WRF model-based simulation estimates, MOD16 provided a mean annual evaporation estimate of 86.61 mm, while the WRF model-based simulation estimates gave a lower estimate of 72.79 mm. Wolaita Station fell in between with a mean annual estimate of 76.70 mm. The standard deviation values showed that MOD16 had higher variability (36.67 mm) compared to both the WRF simulation (26.58 mm) and Wolaita Station (30.91 mm), indicating more consistency in their estimates.
Across different months, the WRF model-based simulation estimates consistently showed strong performance, closely aligning its estimates with observed evaporation values. In contrast, MOD16 often overestimated evaporation in certain months, while Wolaita Station provided estimates with varying degrees of  accuracy throughout the year. Overall, the WRF model provided more reliable and acceptable estimates of evaporation across different months compared to MOD16. The research findings demonstrate the superiority of the Weather Research and Forecasting (WRF) model over the MOD16 dataset in estimating reservoir evaporation in the challenging topographic conditions of the Gibe III Reservoir valley. The WRF model-based simulation estimates higher accuracy, reflected in lower Mean Squared Error, higher Nash-Sutcliffe Efficiency, higher Pearson correlation coefficient, higher Kling-Gupta Efficiency, and smaller Mean Absolute Error values, makes it a valuable tool for water management and planning. By considering local topography and meteorological data, the WRF model provides reliable evaporation estimates, enabling informed decision-making for water allocation, reservoir operation, irrigation planning, environmental conservation, and more. Moreover, its potential applications in climate resilience, policy formulation, investment decisions, and promoting sustainable development underscore its significance as a versatile tool in water resource management beyond the Omo Gibe III Reservoir valley.

Conclusion
Through the in-depth analysis conducted earlier, the study arrived at conclusions that effectively condense the essential insights and results.
• Challenges in Estimating Evaporation in Unique Topography: estimating evaporation rates in regions with distinct topography, like the Gibe III Reservoir with valleys and canyons, presents difficulties due to their influence on local weather conditions. Inaccuracies arise from inconsistent data representing the reservoir's location and inadequate positioning of measurement gauges in nearby towns, impeding effective water management.
• Interdisciplinary Approaches for Complex Water Management: Innovative solutions for complex water management challenges arise from integrating hydrology, data science, and computational techniques. Employing interdisciplinary methods enhances the accuracy of evaporation estimation, thereby contributing to improve planning of water resources.
• Enhanced Accuracy through Mass Transfer Method with WRF Model metrological estimate: Researchers combined the mass transfer method with the WRF model to estimate evaporation rates. This approach, relying on basic meteorological data and vapor pressure differences, proved effective in regions with limited lake information, significantly enhancing accuracy in evaporation estimates.
• Implications for Water Management and Planning: The research findings emphasize the WRF model's crucial role in accurately estimating evaporation for effective water management and planning. Its precise estimates, tailored to local topography and meteorological data, facilitate informed decision-making for purposes like water allocation, reservoir operation, irrigation planning, and environmental preservation.
• Adaptability beyond OmoGibe III Reservoir: The significance of the WRF model extends beyond the Gibe III Reservoir valley. Its potential applications encompass climate resilience, policy development, investment decision-making, and sustainable development, highlighting its versatility as a valuable tool in water resource management.