Reference Evapotranspiration Retrievals from a Mesoscale Model Based Weather Variables for Soil Moisture Deficit Estimation.

: Reference Evapotranspiration (ETo) and soil moisture deﬁcit (SMD) are vital for understanding the hydrological processes, particularly in the context of sustainable water use efﬁciency in the globe. Precise estimation of ETo and SMD are required for developing appropriate forecasting systems, in hydrological modeling and also in precision agriculture. In this study, the surface temperature downscaled from Weather Research and Forecasting (WRF) model is used to estimate ETo using the boundary conditions that are provided by the European Center for Medium Range Weather Forecast (ECMWF). In order to understand the performance, the Hamon’s method is employed to estimate the ETo using the temperature from meteorological station and WRF derived variables. After estimating the ETo, a range of linear and non-linear models is utilized to retrieve SMD. The performance statistics such as RMSE, %Bias, and Nash Sutcliffe Efﬁciency (NSE) indicates that the exponential model (RMSE = 0.226; %Bias = − 0.077; NSE = 0.616) is efﬁcient for SMD estimation by using the Observed ETo in comparison to the other linear and non-linear models (RMSE range = 0.019–0.667; %Bias range = 2.821–6.894; NSE = 0.013–0.419) used in this study. On the other hand, in the scenario where SMD is estimated using WRF downscaled meteorological variables based ETo, the linear model is found promising (RMSE = 0.017; %Bias = 5.280; NSE = 0.448) as compared to the non-linear models (RMSE range = 0.022–0.707; %Bias range = − 0.207– − 6.088; NSE range = 0.013–0.149). Our ﬁndings also suggest that all the models are performing better during the growing season (RMSE range = 0.024–0.025; %Bias range = − 4.982– − 3.431; r = 0.245–0.281) than the non − growing season (RMSE range = 0.011–0.12; %Bias range = 33.073–32.701; r = 0.161–0.244) for SMD estimation.


Study Area and Datasets
The Brue catchment (135.5 km 2 ) is used as a study area, having an elevation of 105 m above mean sea level, positioned in the south-west of England (51.11 • N and 2.47 • W) (Figure 1). Land use/land cover of the area comprises of pastureland (94.34%), followed by forest (3.48%), and urban settlements (2.18%). It is a predominantly a rural catchment with spring-fed headwaters rising in the Mendip Hills and Salisbury Plain. The DEM created from Digimap, an EDINA service (data library service at the University of Edinburgh) UK. indicates that most of the area shows a modest relief and hence comes under non-complex topography area. The high-resolution soil texture map from LandIS (national computerised database system) of Soil Survey and Land Research Centre (SSLRC) indicates that the most of the area comprises of clayey soil type (49%), followed by coarse loam 29%, and silt 21%. All of the required station based dataset were provided by the Natural Environment Research Council and the British Atmospheric Data Centre, United Kingdom for the calculation of ETo and SMD. For benchmark SMD, a probability distributed model or PDM is employed using the locally measured flow, rainfall, and Evapotranspiration. PDM is used in the UK for both operational and design purposes and successfully employed in other parts of the world [27,28]. The calibration of the model involves two years of hourly data from 1 February 2009 to 31 January 2011 is used, while for validation, one year of data is taken into account for the period 1 February 2011 to 31 January 2012. The SMD obtained during the validation is considered for all of the models development. The overall analysis of PDM indicated a satisfactory performance with NSE value of 0.84 and 0.81 during the calibration and validation respectively. The detailed information on PDM calibration, validation, sensitivity, and uncertainty analysis over Brue is reported in [26]. An overview of the methodology adopted in present study is depicted in Figure 2.
Sustainability 2017, 9,1971 3 of 16 3 delivers the results and provides a discussion of those in the context of the available literature, followed by the conclusions in Section 4.

Study Area and Datasets
The Brue catchment (135.5 km 2 ) is used as a study area, having an elevation of 105 m above mean sea level, positioned in the south-west of England (51.11° N and 2.47° W) (Figure 1). Land use/land cover of the area comprises of pastureland (94.34%), followed by forest (3.48%), and urban settlements (2.18%). It is a predominantly a rural catchment with spring-fed headwaters rising in the Mendip Hills and Salisbury Plain. The DEM created from Digimap, an EDINA service (data library service at the University of Edinburgh) UK. indicates that most of the area shows a modest relief and hence comes under non-complex topography area. The high-resolution soil texture map from LandIS (national computerised database system) of Soil Survey and Land Research Centre (SSLRC) indicates that the most of the area comprises of clayey soil type (49%), followed by coarse loam 29%, and silt 21%. All of the required station based dataset were provided by the Natural Environment Research Council and the British Atmospheric Data Centre, United Kingdom for the calculation of ETo and SMD. For benchmark SMD, a probability distributed model or PDM is employed using the locally measured flow, rainfall, and Evapotranspiration. PDM is used in the UK for both operational and design purposes and successfully employed in other parts of the world [27,28]. The calibration of the model involves two years of hourly data from 1 February 2009 to 31 January 2011 is used, while for validation, one year of data is taken into account for the period 1 February 2011 to 31 January 2012. The SMD obtained during the validation is considered for all of the models development. The overall analysis of PDM indicated a satisfactory performance with NSE value of 0.84 and 0.81 during the calibration and validation respectively. The detailed information on PDM calibration, validation, sensitivity, and uncertainty analysis over Brue is reported in [26]. An overview of the methodology adopted in present study is depicted in Figure 2.

WRF-Noah LSM Downscaling of Surface Temperature
The WRF-Noah Land Surface Model (LSM), which is based on eta-coordinate modeling system, is used for downscaling surface temperature from ECMWF Re-Analysis (ERA: ECMWF Re-Analysis) interim global reanalysis dataset. In total, 28 terrain following the eta levels in the vertical direction from surface are used following a two-way nesting scheme [29,30]. The WRF physical scheme is shown through Table 1. The WRF-Noah LSM includes an explicit canopy resistance design given by [31], and a surface runoff scheme is provided by [32]. A comprehensive explanation of the WRF-Noah LSM can be found in [33]. The WRF-Noah LSM model is used with three nested provinces having horizontal grid resolutions of 81 km (D1), 27 km (D2), and 9 km (D3). The D1, D2, and D3 consist of 18 × 18, 19 × 19, and 22 × 22 horizontal grids, respectively. The area with 9 km resolution is used after dynamical downscaling, as others also found that WRF dynamical downscaling improves the estimation of weather data from global reanalysis datasets [34][35][36].

WRF-Noah LSM Downscaling of Surface Temperature
The WRF-Noah Land Surface Model (LSM), which is based on eta-coordinate modeling system, is used for downscaling surface temperature from ECMWF Re-Analysis (ERA: ECMWF Re-Analysis) interim global reanalysis dataset. In total, 28 terrain following the eta levels in the vertical direction from surface are used following a two-way nesting scheme [29,30]. The WRF physical scheme is shown through Table 1. The WRF-Noah LSM includes an explicit canopy resistance design given by [31], and a surface runoff scheme is provided by [32]. A comprehensive explanation of the WRF-Noah LSM can be found in [33]. The WRF-Noah LSM model is used with three nested provinces having horizontal grid resolutions of 81 km (D1), 27 km (D2), and 9 km (D3). The D1, D2, and D3 consist of 18 × 18, 19 × 19, and 22 × 22 horizontal grids, respectively. The area with 9 km resolution is used after dynamical downscaling, as others also found that WRF dynamical downscaling improves the estimation of weather data from global reanalysis datasets [34][35][36].

Probability Distributed Model and Soil Moisture Deficit
The Probability Distributed Model (PDM) comes under the category of lumped model for depicting rainfall runoff relationship developed by the Centre of Ecology and Hydrology (CEH) Wallingford. It is employed in this study for SMD simulation using the ground based inputs of rainfall and reference evapotranspiration (ETo) [28]. It has a better representation of soil moisture computation and is equipped with appropriate time steps for hydrological modelling. Through this model, the SMD can be estimated using the relationship below [37]: is the ratio of actual ET to potential ET; and (S max − S(t)) is Soil Moisture Deficit; b e is an exponent in the actual evaporation function; S max is the total available storage; and, S(t) is storage at a particular time t. The model structure of PDM is further discussed in [37]. Sensitivity analysis (SA) and uncertainty analysis (UA) are considered important to explore the high dimensional parameter spaces, structural uncertainty, and also to understand the sources of uncertainty [38,39].
After a rigorous and careful calibration of the PDM following the Generalized Likelihood Uncertainty Estimation (GLUE), the SMD is extracted. The model parameters for PDM calibration are provided in the study conducted by [29].

Reference Evapotranspiration or ETo
The study site is predominantly grassland with short green cover of uniform height, completely shading the ground, and with adequate water status in the soil profile. In the case of grasslands, ETo closely resembles the physical condition, as described for PET. Hence, at grassland, both PET and ETo can be safely assumed as equivalent to each other (see the FAO56 criteria for ETo and PET). Many studies have confirmed that Hamon provides a stable and reasonable output as compared to the Thornthwaite, Hargreaves, and Samani methods [40,41], therefore it is also used in the current study to estimate the ETo. Hamon [17] proposed an equation to calculate ETo by providing day length and mean air temperature [42]. It shows the relationships among potential evapotranspiration, saturation vapor pressure, and the possible incoming radiant energy by means of the prevailing air temperature. The hours of sunlight can be used as an index for the maximum possible incoming radiant energy, while the absolute humidity at saturation is used for the estimating the moisture-holding capacity of air. It uses the mean daily temperature and sunshine hours for ETo calculation. The saturation vapor pressure, e s , is then determined directly from the mean air temperature. One typical feature of this method is that when mean air temperature is lesser than 0 • C, the ETo does not drop up to zero; instead, it provides effectively the same as annual total of the Thornthwaite method [6]. In the Hamon technique, ETo (mm/day) is estimated as follows: where: T = Temperature (degree centigrade); L day = Day time length (Unitless); e s Saturation Vapor Pressure (mb) at given T can be computed using: The L day was obtained from the website http://www.soda-pro.com/ by providing the information of solar declination and latitude. The observed ETo is calculated by using the station based dataset following the Hamon's method as described above.

Performance Analysis
In the present study, SMD assessed from the WRF and observed ETo are validated with PDM SMD. The performance statistics Nash Sutcliffe Efficiency (NSE) [43], Root Mean Square Error (RMSE), and %Bias and Correlation (r) are used to understand the model performances. The %Bias, NSE, and RMSE can be calculated using Equations (4)- (6).
where n is the number of observations; x is the perceived variable and y is the simulated variable.

Evaluation of Hydro-Meteorological Variables
The WRF-Noah LSM downscaled temperature data is evaluated by utilising the observed temperature measured at the meteorological station. The trends in the WRF and observed temperature are represented through Figure 3a, while the association between the SMD and rainfall are indicated in Figure 3b. Both of the plots are used to understand the relationship between the SMD behavior and the hydro-meteorological parameters (rainfall and temperature). A direct appraisal of the temperatures from WRF with the other hydro-meteorological variables showed that these results are comparable to those obtained in the past and with the other data sets collected in this catchment. The analysis of WRF estimated and observed temperature showed a strong correlation of 0.95 between both datasets. In spite of some minor mismatches in the data, the plot indicates a general covenant between the Sustainability 2017, 9,1971 7 of 17 temporal trend of the WRF and observed temperatures with seasons and the declining trend of the rainfall throughout the observation period. A significant optimistic relationship between the SMD and temperature are also evident in the Figure 3a,b. All of the plots exhibit a close match with the seasonal changes from winter to autumn. There is a gradual rise in temperature observed, when progressing from the winter to spring and summer seasons, followed by gradual decrease in temperature on arrival of the autumn season. Similar behavior can be seen in the SMD pattern also, as a rise in temperature causes an increase in SMD values. Some spikes in the temporal plots can be attributed to some sporadic rainfall or storm events. These short duration storms cause a change in SMD and create spiky fluctuations in temperature. It is also evident from the figure that after a rainfall event, there is some lag time for SMD changes for nearly~1-2 days. Therefore, in overall, there are significant relationships that exist between the temperature and the SMD in the Brue catchment.
Sustainability 2017, 9,1971 7 of 16 are comparable to those obtained in the past and with the other data sets collected in this catchment. The analysis of WRF estimated and observed temperature showed a strong correlation of 0.95 between both datasets. In spite of some minor mismatches in the data, the plot indicates a general covenant between the temporal trend of the WRF and observed temperatures with seasons and the declining trend of the rainfall throughout the observation period. A significant optimistic relationship between the SMD and temperature are also evident in the Figure 3a,b. All of the plots exhibit a close match with the seasonal changes from winter to autumn. There is a gradual rise in temperature observed, when progressing from the winter to spring and summer seasons, followed by gradual decrease in temperature on arrival of the autumn season. Similar behavior can be seen in the SMD pattern also, as a rise in temperature causes an increase in SMD values. Some spikes in the temporal plots can be attributed to some sporadic rainfall or storm events. These short duration storms cause a change in SMD and create spiky fluctuations in temperature. It is also evident from the figure that after a rainfall event, there is some lag time for SMD changes for nearly ~1-2 days. Therefore, in overall, there are significant relationships that exist between the temperature and the SMD in the Brue catchment.  The ETo, calculated by using the temperature data from WRF and ground based observations, are shown using the correlation matrix plots along with the SMD in Figure 4. Hydro-meteorological variables used for ETo estimation are temperature, sunshine hour, and saturation vapor pressure  The ETo, calculated by using the temperature data from WRF and ground based observations, are shown using the correlation matrix plots along with the SMD in Figure 4. Hydro-meteorological variables used for ETo estimation are temperature, sunshine hour, and saturation vapor pressure following the Hamon method. The Hamon model is grounded on coefficient derived from an empirically determined model. The time series of both the observed and WRF ETo are ranges from 0.0005 mm/day to 0.0040 mm/day. There is a no major difference found between the WRF and the observed dataset when plotted against SMD. The r and rs correlations indicates a value of 0.75 for both WRF and observed ETo, which indicates that the WRF downscaled surface temperature when used with Hamon method can provide an accurate estimates of ETo for various applications. Some lower performances in correlation can be attributed to the high precipitation in the Brue catchment and the influence of temperate maritime climate. Further, slight overestimation of ETo over wet areas indicates that a correction factor is needed in the Hamon model. Sustainability 2017, 9,1971 8 of 16 following the Hamon method. The Hamon model is grounded on coefficient derived from an empirically determined model. The time series of both the observed and WRF ETo are ranges from 0.0005 mm/day to 0.0040 mm/day. There is a no major difference found between the WRF and the observed dataset when plotted against SMD. The r and rs correlations indicates a value of 0.75 for both WRF and observed ETo, which indicates that the WRF downscaled surface temperature when used with Hamon method can provide an accurate estimates of ETo for various applications. Some lower performances in correlation can be attributed to the high precipitation in the Brue catchment and the influence of temperate maritime climate. Further, slight overestimation of ETo over wet areas indicates that a correction factor is needed in the Hamon model.

Comparison of SMD Estimated Using Different ETo Products
For utilization of dataset for hydrological applications, the relationship between PDM and ETo based SMD is examined using various linear and nonlinear algorithms. To segregate the data for calibration and validation, the dataset is distributed into two-third and one-third parts. The first two third parts are considered for model calibrations, while the remaining part is for the models validation. This method has its own significance as it represents the data for all of the seasons. In total, five linear and non-linear models are employed to estimate the relationships for SMD assessment using the perceived and WRF ETo viz linear, second and third order polynomial, exponential, and logarithmic algorithms (Figures 5 and 6). In Table 2, the performances of the diverse models in terms of R 2 are indicated by using the ETo derived from WRF and Observed dataset. The model results indicate that the observed ETo and SMD indicate a higher performance in comparison to WRF ETo. Among all of the techniques, 0.749 is the best NSE obtained with 3rd order polynomial regression technique, implies that the relationship between PDM, SMD, and observed ETo can be

Comparison of SMD Estimated Using Different ETo Products
For utilization of dataset for hydrological applications, the relationship between PDM and ETo based SMD is examined using various linear and nonlinear algorithms. To segregate the data for calibration and validation, the dataset is distributed into two-third and one-third parts. The first two third parts are considered for model calibrations, while the remaining part is for the models validation. This method has its own significance as it represents the data for all of the seasons. In total, five linear and non-linear models are employed to estimate the relationships for SMD assessment using the perceived and WRF ETo viz linear, second and third order polynomial, exponential, and logarithmic algorithms (Figures 5 and 6). In Table 2, the performances of the diverse models in terms of R 2 are indicated by using the ETo derived from WRF and Observed dataset. The model results indicate that the observed ETo and SMD indicate a higher performance in comparison to WRF ETo. Among all of the techniques, 0.749 is the best NSE obtained with 3rd order polynomial regression technique, implies that the relationship between PDM, SMD, and observed ETo can be best represented Sustainability 2017, 9,1971 9 of 17 by third order polynomial. Other than this logarithmic and second order polynomial models are also produced satisfactory R 2 values of 0.689 and 0.722 respectively. On the other hand, the linear and exponential model does not provide good results as compared to other techniques. The performance statistics between WRF ETo and PDM SMD indicates a marginally lower performance in contrast to the observed ETo ( Table 2). As expected, in the case of WRF, the R 2 for different regression techniques gives the similar values, as observed ones with the highest in case of 3rd order polynomial (0.739) followed by 2nd order polynomial (0.731), logarithmic (0.689), exponential (0.549), and linear (0.616) during the calibration. It is evident from the R 2 statistics that WRF simulated surface temperature data could be used for SMD in absence of ground-based observations. However, an exact accuracy of the dataset is needed for operational applications. The validations of linear and non-linear models for SMD estimation are presented with their performance statistics in Table 3. The statistical indices such as NSE, RMSE, and %Bias test are used to understand the model performances during the validation, while the behavior of the dataset can be seen in Figure 7. Different algorithms provide different NSE values, which ranges from 0.013 to 0.448. From the results, it is evident that the linear regression technique has good NSE (0.448) as compared to all of the other models. The high performance of linear model herein can be revealed by analyzing the Pearson's and Spearman's correlation statistics between PDM SMD, observed and WRF ETo. From the Spearman's correlation statistics, it is clear that that there is no strong non-linearity exists between the dataset and therefore, the proposed linear model could be used for SMD estimation, because of its simplicity. Sustainability 2017, 9,1971 9 of 16 best represented by third order polynomial. Other than this logarithmic and second order polynomial models are also produced satisfactory R 2 values of 0.689 and 0.722 respectively. On the other hand, the linear and exponential model does not provide good results as compared to other techniques. The performance statistics between WRF ETo and PDM SMD indicates a marginally lower performance in contrast to the observed ETo ( Table 2). As expected, in the case of WRF, the R 2 for different regression techniques gives the similar values, as observed ones with the highest in case of 3rd order polynomial (0.739) followed by 2nd order polynomial (0.731), logarithmic (0.689), exponential (0.549), and linear (0.616) during the calibration. It is evident from the R 2 statistics that WRF simulated surface temperature data could be used for SMD in absence of ground-based observations. However, an exact accuracy of the dataset is needed for operational applications. The validations of linear and non-linear models for SMD estimation are presented with their performance statistics in Table 3. The statistical indices such as NSE, RMSE, and %Bias test are used to understand the model performances during the validation, while the behavior of the dataset can be seen in Figure 7. Different algorithms provide different NSE values, which ranges from 0.013 to 0.448. From the results, it is evident that the linear regression technique has good NSE (0.448) as compared to all of the other models. The high performance of linear model herein can be revealed by analyzing the Pearson's and Spearman's correlation statistics between PDM SMD, observed and WRF ETo. From the Spearman's correlation statistics, it is clear that that there is no strong non-linearity exists between the dataset and therefore, the proposed linear model could be used for SMD estimation, because of its simplicity.

Performance with Growing and Non-Growing Seasons
Many studies indicated that vegetation plays an important role in the differences of soil water content. Authors have reported that the transformation in seasons specially growing and nongrowing season have significant impact on SMD. In an earlier study, it has been found that growing and non-growing seasons behave differently. Therefore, for proper assessment and understanding of SMD inclusion of growing and non-growing seasons are important. During the growing season, crops create problems in the estimation of actual values of ETo, as they do not have a proper correction factor to differentiate between the growing and non-growing seasons. For understanding the data in an efficient way, the dataset is divided conferring to the growing and non-growing seasons. As per the UK met office, temperature is an important parameter for deciding the growing and non-growing seasons. When the temperature of five consecutive days exceeds 5 °C, there will be an onset of growing season, while it ends when the temperatures fall below 5 °C for five consecutive days [27]. The 1971 to 2000 average season length was 280 days (~9.3 months) (Source: http://www.metoffice.gov.uk/climate/uk/averages/ukmapavge.html). Therefore, in the current

Performance with Growing and Non-Growing Seasons
Many studies indicated that vegetation plays an important role in the differences of soil water content. Authors have reported that the transformation in seasons specially growing and non-growing season have significant impact on SMD. In an earlier study, it has been found that growing and non-growing seasons behave differently. Therefore, for proper assessment and understanding of SMD inclusion of growing and non-growing seasons are important. During the growing season, crops create problems in the estimation of actual values of ETo, as they do not have a proper correction factor to differentiate between the growing and non-growing seasons. For understanding the data in an efficient way, the dataset is divided conferring to the growing and non-growing seasons. As per the UK met office, temperature is an important parameter for deciding the growing and non-growing seasons. When the temperature of five consecutive days exceeds 5 • C, there will be an onset of growing season, while it ends when the temperatures fall below 5 • C for five consecutive days [27]. The 1971 to 2000 average season length was 280 days (~9.3 months) (Source: http://www.metoffice.gov.uk/ climate/uk/averages/ukmapavge.html). Therefore, in the current study, the entire season of winter (December-February) is taken as non-growing (average temperature < 5 • C), while March-November is chosen as growing season (average temperature > 5 • C).
Box plots are used to understand the variations in SMD values during the growing and non-growing seasons, as shown in Figure 8. In non-growing season, the SMD from WRF ETo is showing a good match with benchmark SMD in terms of distribution as it is capturing good variations. The results of WRF ETo based SMD is found to be comparable with the observed ETo based SMD. The upper and lower minima of WRF and observed dataset based SMD are found on the same levels. Growing season is also providing the similar types of results, which indicates a comparable performance between the WRF and observed dataset based SMD. In non-growing season during December, January, and February, the range of SMD lies between 0.017 and 0.038 m. This is likely to be because of lower temperature, low evaporation, and lesser solar radiation that leads to high soil moisture in the non-growing season and hence low SMD. During the growing season from March to November, there is a steady rise in SMD observed with recorded highest value of 0.10 m in the month of June.
Sustainability 2017, 9,1971 12 of 16 study, the entire season of winter (December-February) is taken as non-growing (average temperature < 5 °C), while March-November is chosen as growing season (average temperature > 5 °C). Box plots are used to understand the variations in SMD values during the growing and nongrowing seasons, as shown in Figure 8. In non-growing season, the SMD from WRF ETo is showing a good match with benchmark SMD in terms of distribution as it is capturing good variations. The results of WRF ETo based SMD is found to be comparable with the observed ETo based SMD. The upper and lower minima of WRF and observed dataset based SMD are found on the same levels. Growing season is also providing the similar types of results, which indicates a comparable performance between the WRF and observed dataset based SMD. In non-growing season during December, January, and February, the range of SMD lies between 0.017 and 0.038 m. This is likely to be because of lower temperature, low evaporation, and lesser solar radiation that leads to high soil moisture in the non-growing season and hence low SMD. During the growing season from March to November, there is a steady rise in SMD observed with recorded highest value of 0.10 m in the month of June.  Figure 9 is showing seasonality in the PDM, WRF, and observed ETo. For pastoral landscape, the demand of water is mostly depends on the exposure of the land and thickness of the grass type. The vegetation covers over the surface of soil reduces the loss of the moisture from the soils because of reduced exposure to the sunlight. The extent of non-growing period is lesser than that of the growing season and the accessibility of environmental variable, such as soil moisture is highly variable and depends on the factors such as climate, soil (texture) and vegetation. For the nongrowing period (mostly a bare soil or snow covered), the SMD from WRF ETo is slightly overestimated in comparison to PDM SMD. In the growing season, it might be because of the roughness of the soil and high soil moisture variability, there is an overestimation recorded in the months of late February to mid May, whereas an underestimation is found all through the months of mid May to August, tailed by the November month ( Figure 9). The SMD from WRF ETo matches closely to PDM SMD throughout the year except for the last week of July where it is showing an underestimation when compared with the SMD using the Obs ETo. Further, during June, although both WRF and observed ETo based SMD follows a close pattern, there is some sharp drops that occurred that might be due to some short duration storms in the area.
The three evaluation statistics are used to assess the influence of growing and non-growing seasons on SMD ( Table 4). The performance statistics indicates that during the growing season, the SMD estimated using the WRF ETo (RMSE = 0.025, r = 0.245) has lower performance than the SMD using the observed ETo (RMSE = 0.024, r = 0.281). However, during the non-growing season, some lower performances are detected in terms of %Bias and r in the datasets as related to the growing season. On the other hand, a better performance is evidenced during the non-growing season as compared to the growing season with lower value of RMSE in the former case than the latter. The  Figure 9 is showing seasonality in the PDM, WRF, and observed ETo. For pastoral landscape, the demand of water is mostly depends on the exposure of the land and thickness of the grass type. The vegetation covers over the surface of soil reduces the loss of the moisture from the soils because of reduced exposure to the sunlight. The extent of non-growing period is lesser than that of the growing season and the accessibility of environmental variable, such as soil moisture is highly variable and depends on the factors such as climate, soil (texture) and vegetation. For the non-growing period (mostly a bare soil or snow covered), the SMD from WRF ETo is slightly overestimated in comparison to PDM SMD. In the growing season, it might be because of the roughness of the soil and high soil moisture variability, there is an overestimation recorded in the months of late February to mid May, whereas an underestimation is found all through the months of mid May to August, tailed by the November month (Figure 9). The SMD from WRF ETo matches closely to PDM SMD throughout the year except for the last week of July where it is showing an underestimation when compared with the SMD using the Obs ETo. Further, during June, although both WRF and observed ETo based SMD follows a close pattern, there is some sharp drops that occurred that might be due to some short duration storms in the area. during the growing season, an underestimation is recorded in the both the dataset. Even though there is some mismatch between the model performances during the two seasons, by comparing the %Bias the datasets indicates a satisfactory performance. Therefore, the ETo derived from the WRF temperature can be utilised for SMD estimation in absence of ground based information. The analysis reveals that there is profound effect of growing and non-growing season on the SMD simulation. Therefore, separate algorithms are needed to represent the responses of both the seasons.  The three evaluation statistics are used to assess the influence of growing and non-growing seasons on SMD ( Table 4). The performance statistics indicates that during the growing season, the SMD estimated using the WRF ETo (RMSE = 0.025, r = 0.245) has lower performance than the SMD using the observed ETo (RMSE = 0.024, r = 0.281). However, during the non-growing season, some lower performances are detected in terms of %Bias and r in the datasets as related to the growing season. On the other hand, a better performance is evidenced during the non-growing season as compared to the growing season with lower value of RMSE in the former case than the latter. The performance statistics during the non-growing season reveals a slight lower efficiency of the linear model in case of WRF ETo based SMD (RMSE = 0.012, r = 0.161) as compared to observed ETo based SMD (RMSE = 0.011, r = 0.244). The PDM and simulated SMD during the growing and non-growing seasons with 1:1 equiline are shown in Figure 10. By looking over the %Bias of the model, both the growing and non-growing seasons indicates a similar performance. A high bias is recorded in the dataset from the SMD simulated using the WRF ETo during the non-growing season. Similarly, during the growing season, an underestimation is recorded in the both the dataset. Even though there is some mismatch between the model performances during the two seasons, by comparing the %Bias the datasets indicates a satisfactory performance. Therefore, the ETo derived from the WRF temperature can be utilised for SMD estimation in absence of ground based information. The analysis reveals that there is profound effect of growing and non-growing season on the SMD simulation. Therefore, separate algorithms are needed to represent the responses of both the seasons.

Conclusions
The mesoscale model-WRF-Noah LSM is a sophisticated model for the numerical weather prediction that can be used for downscaling of global hydro-rological variables into finer spatio-temporal resolutions, and thus can be used for ETo estimation. In this work, the Hamon method has been employed to calculate ETo from WRF downscaled surface temperature data and station observations. The trend indicates marginal differences in the WRF and station based ETo when plotted against SMD. Similar results are also reported by correlation statistics between the station and WRF derived ETo for SMD prediction. Among many linear and non-linear techniques used in this study, the exponential model (RMSE = 0.226; %Bias = −0.077; NSE = 0.616) is found to be useful for SMD estimation by using the Observed ETo, while in case of WRF, the linear model is found to be promising with RMSE = 0.017; %Bias = 5.280, and NSE = 0.448 values. On the other hand, all of the models are performing better during the growing season than the non-growing season for SMD estimation.
The changes in ETo are dependent on the climatic and geographical factors, which affects the spatial distribution of ETo. Therefore, more analysis is needed in this direction for different geographical areas to estimate the changes in ETo in terms of spatial and temporal distributions of temperature, precipitation, location, and the elevation. This study indicates a reliable relationship between the temporal variability of ETo flux and SMD in the region that is influenced by temperate maritime climate. The ETo derive in this study can be further improved by providing the physical characteristics of locations (e.g., climate, topography, etc.), so that a modified Hamon model for ETo would be available for different applications. Therefore, future work will focus on providing a correction factor in the Hamon method, which is expected to result to a more accurate ETo estimation that is particularly suited for hydrological applications.