# Novel Approaches for the Empirical Assessment of Evapotranspiration over the Mediterranean Region

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## Abstract

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## 1. Introduction

_{M}), Hamon (HM), modified Hamon (HM

_{M}), Hargreaves–Samani (HS), Kharrufa (KH), Romanenko (RM), Schendel (SC), Thornthwaite (TH), and Penman–Monteith at 0.5 m (PM

_{0.5}), were evaluated at daily and monthly temporal resolution in Kahramanmaras province and its eleven districts and compared to the reference PM method. In addition, the effect of modified techniques on evapotranspiration estimates was investigated over the region.

## 2. Materials and Methods

_{0.5}), Blaney–Criddle (BC), modified Blaney–Criddle (BC

_{M}), Hamon (HM), modified Hamon (HM

_{M}), Hargreaves–Samani (HS), Kharrufa (KH), Schendel (SC) methods, and the reference Penman–Monteith (PM) at daily temporal resolutions, whereas monthly and annual ET values were derived by taking the averages. The Thornthwaite (TH) and Romanenko (RM) techniques were utilized to compute monthly ET values and produce yearly ET values. Days with missing data and ET values equal to zero were excluded from computation.

#### 2.1. Study Area and Data Sets

^{2}, and is situated between 37–39 northern parallels and 36–38 eastern meridians. The province’s northern regions are quite mountainous, with landforms mostly consisting of mountains that are extensions of the Taurus Mountains in the southeast and the depressions that separate them (Figure 2). Digital elevation model (DEM) data for the study area were obtained from the US Geological Survey (USGS) website [39]. After adjusting the required projections and coordinate system as well as delineating the area, the acquired data were examined using the Arc-GIS program, a scalable integrated geographic information system software developed by ESRI. Figure 2 was obtained by processing the coordinate information of the relevant stations shown in Table 1 into the program. As can be seen from the figure, the altitude of the study area ranges from 130 to 3075 m, and the regions where stations S3 and S10 are located have the highest altitude, while the areas where stations S2 and S11 are located have the lowest elevation. Although the altitude values in the territories containing stations S4 and S9 are relatively close to one another, the high-elevation difference between the regions where stations S1 and S3 are located can be seen in Figure 2.

_{max}, °C), minimum temperature (T

_{min}, °C), average relative humidity (RH, %), maximum relative humidity (RH

_{max}, %), minimum relative humidity (RH

_{min}, %), average wind speed at 2 m height (${\mathrm{u}}_{2}$, m s

^{−1}), and sunshine duration (n, hr) for each station, were acquired from the MEVBIS module at daily temporal resolution within the scope of this study. In this study, multi-paradigm numerical calculation software developed by MathWorks r2006a MATLAB program was utilized in a holistic sense with Microsoft 365 Excel program for manipulations on the obtained data sets, preparation of required time series, ET calculations, and graphing.

#### 2.2. Evapotranspiration Estimation Methods

#### 2.2.1. FAO Penman–Monteith Method (PM)

^{−1}, and adequately irrigated at a height of 0.12 m [1,23,24]. The ET

_{PM}in the equation expresses the reference evapotranspiration in mm d

^{−1}, and Δ (kPa °C

^{−1}) denotes the slope of the vapor pressure curve at average air temperature and is calculated using Equations (2) and (3). In these equations, G symbolizes the soil heat flux density (MJ m

^{−2}d

^{−1}) and can be considered zero for daily calculations, T is the daily average air temperature (°C), u

_{2}denotes the wind speed at 2 m height (m s

^{−1}), e

_{s}emblematizes the saturated vapor pressure (kPa), e

_{a}stands for actual vapor pressure (kPa), γ represents the psychrometric constant (kPa °C

^{−1}), and e°(T) indicates the saturated vapor pressure (kPa) at air temperature T (°C).

_{n}(MJ m

^{−2}d

^{−1}) refers to the net radiation at the crop surface and is equal to the difference between the incoming net shortwave radiation (R

_{ns}) and the outgoing net longwave radiation (R

_{nl}). While R

_{ns}is also known as net solar radiation and can be calculated using Equation (4), R

_{s}is the part of solar radiation that is not reflected from the surface. The value 0.23 in the equation indicates the albedo coefficient for green grass surfaces. R

_{s}(Solar radiation) can be derived as suggested by Hargreaves–Samani [45] and is shown in Equation (5) when there is no measured data of solar radiation. In the equation, K

_{rs}symbolizes the calibration coefficient and can be taken as 0.16, whereas R

_{a}indicates extraterrestrial radiation (MJ m

^{−2}d

^{−1}). T

_{max}and T

_{min}are the maximum and minimum absolute temperatures over 24 h, respectively. Net outgoing longwave radiation R

_{nl}, the difference between the outgoing and incoming longwave radiation, is computed according to Equation (6).

^{−9}MJ m

^{−2}d

^{−1}K

^{−4}. $\mathsf{\u03ad}$ represents the air humidity correction factor and is defined as in Equation (7), while R

_{so}expresses the clear-sky solar radiation (MJ m

^{−2}d

^{−1}) and is calculated as shown in Equation (8). In the following equation, E

_{1}represents the station elevation above sea level (m).

_{sc}is the solar constant and has a value of 0.082 MJ m

^{−2}min

^{−1}. d

_{r}is the inverse relative distance factor for the Earth–Sun and is unitless (Equation (10)), w

_{s}indicates sunset hour angle in radians (Equation (11)), δ refers to solar declination in radians (Equation (12)), ϕ symbolizes station latitude (L) in radians (Equation (13)), and i stands for the Julian day of the year.

^{−1}. On the other hand, in cases where the u

_{2}data required in Equation (1) are unavailable, the wind speed data measured at various altitudes can be converted to the wind speed at 2 m height using Equation (16). In the equation, z

_{w}(m) denotes the height of the measurement location from the ground, while u

_{z}(m s

^{−1}) indicates the wind speed at height z

_{w}. Lastly, the saturated (e

_{s}) and actual vapor pressures (e

_{a}), can be calculated using daily e°(T

_{min}), e°(T

_{max}), minimum relative humidity (RH

_{min}), and maximum relative humidity (RH

_{max}) data by Equations (17) and (18), respectively. e°(T

_{min}) and e°(T

_{max}) represent the saturation vapor pressure (kPa) at the daily minimum and maximum temperatures, respectively.

_{PM}in cases where the measured climatic parameters are insufficient or missing in the Penman–Monteith method (Equation (1)), which requires various climatic parameters, Hargreaves–Samani [45] and Allen et al. [1] proposed auxiliary equations from Equations (2)–(18) in the FAO Irrigation and Drainage Paper 56. Alternative approaches are being investigated because PM-driven ET and all of these supplementary equations are laborious and time-consuming.

#### 2.2.2. FAO Penman–Monteith 0.5 m Method (PM_{0.5})

_{0.5}method was recommended for ${\mathrm{E}\mathrm{T}}_{{\mathrm{P}\mathrm{M}}_{0.5}}$ in mm d

^{−1}, which will occur on a tall plant-covered surface with a height of approximately 50 cm, as given in Equation (19).

#### 2.2.3. Blaney–Criddle Method (BC)

_{BC}denotes Blaney–Criddle-driven ET values in mm d

^{−1}in the equation that uses the daily average air temperature parameter, whereas the symbol p can be used to define the mean daily percentage of annual daylight hours, which varies based on latitude. In the given equation, the seasonal crop coefficient, k, was considered to be 0.85.

#### 2.2.4. Modified Blaney–Criddle Method (BC_{M})

_{min}, n (actual sunshine duration), and N (maximum possible sunshine duration), while the b value varies depending on the daily average daytime wind speed (U) (m s

^{−1}), in addition to RH

_{min}and n/N ratio (Equation (23)). In cases where daytime wind speed data are unavailable, 1.33 times the average wind speed can be considered for the u value. For the coefficients e

_{0}, e

_{1}, e

_{2}, e

_{3}, e

_{4}, and e

_{5}employed in Equation (23), the values of 0.81917, −0.0040922, 1.0705, 0.065649, −0.0059684, and −0.0005967 were used, respectively [1,31,50,51].

#### 2.2.5. Hamon Method (HM)

_{HM}symbolizes Hamon-driven ET estimations. The constant C in the equation has a value of 0.0055 and was converted from inches to mm and utilized as 0.1397 in the computations. While D, which indicates the 12 h possible sunshine duration (N/12), is estimated as in Equation (25), P

_{t}is the saturated water vapor density at the daily average temperature and can be calculated using Equation (26).

#### 2.2.6. Modified Hamon Method (HM_{M})

_{t}values using the modified Hamon technique. After the daily evapotranspiration estimations were determined using the Hamon and modified Hamon techniques, in this study, a local calibration coefficient of 1.2 was set based on the suggestions of previous studies [54,55,56].

#### 2.2.7. Hargreaves–Samani Method (HS)

_{HS}denotes evapotranspiration predictions based on the Hargreaves–Samani approach, and the coefficient λ

^{−1}(0.408) was used to convert evapotranspiration values into mm d

^{−1}.

#### 2.2.8. Kharrufa Method (KH)

_{KH}in the equation represents Kharrufa-driven daily evapotranspiration predictions.

#### 2.2.9. Schendel Method (SC)

_{SC}symbolizes the evapotranspiration values obtained according to the Schendel technique.

#### 2.2.10. Romenenko Method (RM)

_{RM}values were derived monthly using temperature (T

_{mth}, °C) and relative humidity (RH

_{mth}, %) monthly average climatic data.

#### 2.2.11. Thornthwaite Method (TH)

_{TH}), the ij symbol denotes the monthly temperature index (Equation (34)); the letter I symbolizes the annual temperature index, which is the sum of monthly temperature indices; the coefficient α is determined by the annual temperature index (Equation (35)).

#### 2.3. Statistical Metrics

_{M}, HM, HM

_{M}, HS, KH, PM

_{0.5}, and SC-driven ET performances were evaluated using CRMSE, PCC, DET, MAE, MRE, MSE, NSCE, NNSCE, Bias, and RMSD statistical indices at a daily temporal resolution. The random error between the simulations and the reference values to the mean reference value was assessed using CRMSE. It can be calculated using Equation (36), and its values vary from 0 to +∞. A lower CRMSE indicates better consistency, whereas a value of zero signifies no random error between the time series [65,66]. PCC is the covariance of the two variables divided by the product of their standard deviations and can be calculated using Equation (37). It measures the strength and direction of the linear relationship between two variables. If PCC is close to 1 (−1), it suggests a strong positive (negative) correlation, while converging to 0 indicates no systematic linear relationship between the estimations and references. However, it is important to note that a zero correlation does not necessarily imply the absence of any relationship between the variables; it simply means that there is no linear relationship [67]. DET quantifies the model’s goodness of fit and can be expressed as shown in Equation (38). It is a statistical metric that determines the proportion of the variance in the dependent variable that is explained by the independent variables in a regression model. Its value ranges from 0 to 1; convergence to 1 indicates that the simulation explains a greater proportion of the variability in the dependent variable [68]. The absolute value of the variation between the simulated ET magnitude and PM was defined as the MAE and calculated using Equation (39). The MAE values vary between 0 and +∞, with a value of 0 denoting perfect predictions. The MRE was utilized to evaluate the average relative difference between the estimated ET values relative to PM (Equation (40)). It is particularly useful for evaluating the accuracy of predictions in simulations in terms of over/under estimations and varies from −∞ to +∞ [64,69]. The MSE was preferred to measure the average squared difference between the estimated ET relative to the PM simulation. Equation (41) can be used to obtain this accuracy metric, and its values range from 0 to +∞. A zero MSE implies that the alternative ET methods perfectly match PM-driven ET values. MAE treats all errors equally, unlike MSE, which squares the errors and may assign more weight to large errors [63,70,71]. The NSCE is a widely used metric for assessing the performance of hydrological applications and can be expressed as shown in Equation (42). NSCE ranges from −∞ to 1, with higher values indicating better model performance and 1 being the ideal simulation [72]. The NNSCE error metric can be obtained by dividing the NSCE by a normalization factor to ensure that it remains between 0 and 1 (Equation (43)). The normalizing process makes the NSCE more interpretable, and the NNSCE is less affected by the scale of the data and is confined to a consistent range. The average tendency of the ET simulations to be larger or smaller than the reference ET can be measured by Bias (Equation (44)), and its values vary from −∞ (underestimation) to +∞ (overestimation) [73]. RMSD describes the difference between model simulations and reference ET in the units of the variable. Its values, which range from 0 to +∞, close to zero imply a perfect fit, while increases indicate an increment in the error in ET predictions [62,64].

_{r,ti}denotes the evapotranspiration values obtained based on the PM reference method at ti

^{th}day, ET

_{p,ti}symbolizes the evapotranspiration estimates obtained according to the alternative estimation method at ti

^{th}day, while $\overline{{\mathrm{E}\mathrm{T}}_{\mathrm{p}}}$ and $\overline{{\mathrm{E}\mathrm{T}}_{\mathrm{r}}}$ express the mean evapotranspiration values of the prediction and reference methods, respectively.

## 3. Results

_{0.5}, BC, BC

_{M}, HM, HM

_{M}, HS, KH, and SC techniques, resulting in the box plot shown in Figure 3. A box plot visualizes the five-number summary of the dataset: the minimum, first quartile, median, third quartile, and maximum. The box plot was produced using the fourth-generation programming language MATLAB. Alternative methods are shown on the horizontal axis of the box plot in Figure 3, whereas evapotranspiration values in mm d

^{−1}predicted using these approaches are displayed logarithmically on the vertical axis. As shown in the figure, days with missing data and negative ET values were not evaluated, while the extreme ET values and estimates between these values produced by each approach were presented with values from 0.001 to 100 mm d

^{−1}. As can be seen from the figure, PM-driven simulations were overestimated by the PM

_{0.5}-based approach over all districts, but the HM method, which displays a symmetrical box plot distribution, consistently underestimates the references in the study area. The positive results of the modifications to the BC method are shown in the graph. For example, the BC

_{M}approach yielded more effective outcomes than the BC method, which gave ET values within a narrow range when compared to the reference method over the region. Additionally, at numerous stations, the results acquired by the HM

_{M}technique were comparable to those obtained by the reference ET

_{PM}values, with higher performance than the HM approach, revealing the importance of modifications made to the HM equation.

^{−1}(between the lower and upper quartiles) at Kahramanmaras station (S1), where 22 years of comprehensive data are available, which means that half of all ET values are in this range, considering the PM technique used as reference. The PM

_{0.5}approach results reveal that it slightly overestimates the ET values with respect to the reference PM method. The BC-driven ET values, shown in black, were aggregated in a narrower range at the S1 station relative to the reference method. The BC method simulated the minimum (maximum) ET values with overestimation (underestimation). It can be seen that the methods that give results close to the reference method at the S1 station are the HM

_{M}and HS approaches, although there are slight differences in the values of the whiskers. It is clear from the box plot of the HM approach with the best performance, shown in blue, that its quarters are distributed uniformly, and there is no skewness in the data to the PM technique. The upper outlier and interquartile range of the ET simulations produced by the BC

_{M}and KH methods—which are represented in gray and orange, respectively—produced similar findings to those of the reference method, but they had a longer minimum outlier owing to the underestimation of the small ET values. Overestimation is dominant in the maxima of SC-based ET predictions, whereas the opposite is true for smaller values less than one.

^{−1}. The BC

_{M}and SC techniques yield ET values within a similar range; nevertheless, the values obtained by both methods simulate the minimal ET values with strong underestimation. It can be seen that while the PM

_{0.5}approach produces ET values with a comparable distribution to the reference method, as in the S1 station, it continually produces a slight overestimation. The findings can be made more accurate by multiplying the values by the calibration coefficients to minimize this bias. The BC-based ET values generated for the Dulkadiroglu district were clustered in a narrower range, similar to the results at the S1 station. Although different distributions are attained in the HM, HM

_{M}, HS, and KH approaches, where the maximum ET values are estimated to be close to each other, it has been observed that the underestimations are predominant compared with the PM reference method.

_{0.5}technique was examined in terms of distribution, it was observed that it was quite similar to the reference method, although it tended to yield slightly higher ET values compared to the reference method. The convergence of the BC-driven ET time series in the first and third quartiles clearly shows a concentration in a narrower range, similar to those from other stations. It has been noted that the BC, BC

_{M}, and KH approaches underestimated the minimum values for quartiles smaller than 0.05 at the S3 station. However, the BC

_{M}and KH approaches performed well in the interquartile range and higher whisker values. Although the HM and HM

_{M}methods capture ET values with very small variations in a negative way from the reference values, their distributions are similar to those in the PM.

_{M}techniques were close to the reference values, it was observed that both stations estimated ET values with a slight constant underestimation in the interquartile range compared to the reference values. The BC

_{M}and SC methods produce overestimation (underestimation) ET values in the upper (lower) whisker compared to the reference method at both stations, while PM

_{0.5}-driven ET simulations overestimated ET values in all quartiles.

_{PM}values, varying between 1.8 and 4 mm d

^{−1}for the interquartile range, were clustered in a narrower range relative to other stations, and they were captured using the HM

_{M}, HS, and SC approaches at the S6 station. While the PM

^{0.5}and BC methods produce higher ET values for values between the 25th and 75th percentiles with respect to the PM technique, ET

_{BC}values are concentrated in a narrower range. Although it was discovered that the ET

_{HM}results were close to the reference for extreme values, these estimations clustered with underestimation until the median. Although BC

_{M}-based ET estimates produce values close to the PM, it has been monitored that this method underestimates ET values smaller than the 25th percentile. As can be seen from the figure, the box plot produced by the KH approach has a wider spread with a higher standard deviation, and ET

_{KH}values are simulated with a significant degree of bias in comparison to the reference method.

_{PM}values are close to each other, it is seen that the ET

_{BC}simulations are similar to the other stations with the clustered in a narrower range. The ET values estimated by these two approaches are close to one another, and their maximum (minimum) values are simulated less (more) than those of the reference method. The PM

_{0.5}model overestimated the reference ET values with a slight difference, similar to the previous six stations. In the Pazarcik and Caglayancerit districts, the formula that yielded the closest results to the reference method was the HS approach. The BC

_{M}, KH, and SC approaches, which simulated the minimum ET values up to the first quartiles with a high deviation compared to the reference method, captured the ET

_{PM}values at both stations for the values interquartile range. It can also be seen from Figure 3 that the evapotranspiration values obtained via the HM and HM

_{M}techniques had a more symmetrical distribution, even though the ET values at both stations underestimated the reference values.

^{−1}, and the best performance was acquired with the ET

_{HS}formula. In the Ekinozu district, although the BC

_{M}, KH, and SC approaches underestimated the minimum ET values in the lower whisker with high deviation compared with the reference method, ET

_{PM}values were captured between the 25th and 75th percentiles. Underestimation is dominant in HM and HM

_{M}-driven predictions, and BC-driven simulations are concentrated in a narrower range with a small standard deviation, whereas KH-based values are spread over a wider range with a high standard deviation. In addition, while the ET

_{BC}values are in a narrower range with a small standard deviation in Nurhak and Turkoglu, the PM

_{0.5}technique tends to overestimate evapotranspiration time series compared to the reference method, as in the other stations in general.

_{KH}and ET

_{SC}values had high variance compared to ET

_{PM}, both methods underestimated evapotranspiration smaller than the median value, and strong overestimation was dominant in ET

_{SC}values greater than the median. The BC

_{M}approach revealed the most accurate results relative to the reference method at the S10 station (except for the lower whisker), while the best performance was obtained with HS at the S11 station, with insignificant underestimations in the upper whisker. Another result obtained from the figure is that HS, HM, and HM

_{M}-based estimates in the Nurhak district have a symmetric distribution and simulate ET values slightly less than the reference values. In the Turkoglu district, ET values in the interquartile range were captured by the BC

_{M}, HM, HM

_{M}, and KH approaches in addition to the ET

_{HS}formula. The graph also shows that the values in the lower than 25th percentile are underestimated by the BC

_{M}, KH, and SC techniques.

_{PM}values are found in S4, located in Afsin, even though the slopes of the S4 and S5 stations are close to one another when Figure 3 and Figure 4a are examined together. However, it becomes clear from the aspect map in Figure 4b that Afsin has more southern slopes and that these slopes have a positive impact on ET.

_{PM}values (Figure 3) than Turkoglu because of the dominance of the southern slopes and high solar radiation. Moreover, when the slopes in Figure 4a of S1 (572 m) and S2 stations with similar heights were examined, it was revealed that the S1 station had a greater slope but exhibited lower ET values. This is because Dulkadiroglu has stronger solar radiation and more southern slopes, as shown in Figure 4b,c, and these two factors have a linear effect on ET.

^{−1}for the reference PM and alternative approaches, respectively. In addition, the calculated monthly correlation value and linear trend line with its formula between the reference PM and other methods are displayed in the plots.

_{0.5}method has a strong positive correlation with the reference PM method with a PCC value of 0.99, while it estimates high ET values on a monthly basis more so than the references. While the BC-driven simulation revealed a correlation of 0.95, it overestimated (underestimated) low (high) ET

_{PM}values. This discrepancy became wider for values greater than 6 mm d

^{−1}. On the other hand, a significant improvement is observed in the BC

_{M}technique compared to the original method, and it estimates the reference values slightly higher with a strong correlation (0.98). Additionally, the scatter plots of the HM and HM

_{M}methods reveal similar results, with a correlation of 0.94 in both methods. Unlike other methods, the two equations, which include water vapor density, tend to underestimate ET

_{PM}values.

_{TH}simulation underestimates the reference ET

_{PM}values, while it has a lower standard deviation in its distribution compared to the other monthly methods, RM, and a strong PCC value of 0.93.

_{M}-based simulations at the S2 station produced the lowest CRMSE of 10.63% among all values, whereas the HS technique at stations S1, S3, S4, S5, and S9 reached the lowest value. The best results in terms of CRMSE performance are seen to be the KH method, with values of 19.73% and 19.16% at stations S7 and S8, respectively. Moreover, the PM

_{0.5}, BC

_{M}, and HM methods produced lower CRMSE values than the other methods at stations S6, S10, and S11, respectively. It was also noted that the SC technique, which ranged from 34.94 to 91.69%, showed the worst performance compared with other approaches at all stations.

_{0.5}approach is the most consistent with the reference method, having the highest DET values (0.94–1) at all stations. On the other hand, the obtained results detect that the SC technique has the lowest DET values ranging from 0.61 to 0.82. The highest DET values, after PM

_{0.5}simulations, were produced with the BC method at the S1 station; the HS method at stations S3, S4, and S5; and the BC

_{M}method at the other seven stations.

^{−1}) as evapotranspiration, is shown in Figure 6c. Even though the BC

_{M}has the lowest MAE values at S2, S8, and S10, the HS technique is the most successful approach since it shows the least absolute difference at the other eight stations. Although the methods with the highest MAE differ depending on the station, the SC technique has the worst MAE performance at the six stations.

_{M}showed the best overall result (Figure 6d). The HM

_{M}method has the highest accuracy, with an MRE value of 0.0 at station S1, whereas negative MRE values indicate an underestimation tendency at other stations. In general, the PM

_{0.5}and SC (HM and KH) techniques with positive (negative) MRE values overestimated (underestimated) ET compared to the reference method.

_{0.5}values are the highest MSEs after SC. Upon examining the results per station, it is seen that the BC

_{M}approach at stations S2, S8, and S10; the KH method at station S7; and the HS technique at the other seven stations have the least error with MSE values closest to zero.

_{M}method exhibited the best performance at stations S2, S7, S8, and S10, this method reached the highest NSCE value at station S2 with a value of 0.98. The HS method produced the closest result to the reference values for the other seven stations.

_{0.5}in S2, and the SC method in the other nine stations. At stations S2, S7, S8, and S10, the BC

_{M}method yields accurate results by giving the NNSCE value closest to one, and the KH method converges to 0.9 at station S7. As can be observed from the NNSCE index, the HS technique worked well for the remaining seven stations.

_{M}, PM

_{0.5}, and SC methods, overall, take positive Bias values, indicating a tendency to overestimate, underestimation is more dominant in KH, HM, and HM

_{M}approaches with general negative Bias values. Another noteworthy point when the results are examined in terms of the Bias error metric is that the BC

_{M}and KH methods have performances closest to zero at the majority of the stations.

_{0.5}method, ranging between 0.97 and 1.00, while the lowest is the SC technique, varying between 0.78 and 0.91.

_{M}method performed better than the other empirical formulae with RMSD values closest to zero at stations S2, S8, and S10, the KH approach showed a successful performance at station S7. The figure indicates that for the other seven stations, the HS method produced RMSD values with a discrepancy of only a maximum of 1 mm d

^{−1}. The HS (SC) method achieved the best (worst) performance among all the methods at station S3 (S10) with an RMSD value of 0.49 (4.80) mm d

^{−1}.

## 4. Discussion

_{M}, KH, and SC-based ET simulations underestimated minimum values smaller than the 25th percentile relative to the ET

_{PM}. Saud et al. [75] analyzed the spatiotemporal variation of several methods over Al-Anbar province, western Iraq. They found that the Kharrufa equation tended to underestimate ET values, similar to the above-mentioned finding. On the other hand, the SC method tends to predict maximum extreme ET values larger than the third quartile than the reference method. The performance of the PM

_{0.5}approach was higher for the minimum ET values, which were especially smaller than the lower quartile. However, it produces more ET values, albeit with a slight difference, at larger ET values compared with the reference technique. Additionally, the ET

_{BC}values were clustered in a narrower range than the reference ET values with smaller standard deviations. It was concluded that the BC

_{M}method produced more successful results than the BC method, showing values close to those of the PM method for values greater than the lower quartile. As a matter of fact, in this sense, the positive effect of the modifications on the BC-based ET equation was observed, as in the previous studies [14,76]. It is also understood that the ET values obtained with the HM and HM

_{M}approaches have a more symmetrical distribution; however, the HM method underestimates ET

_{PM}at all stations, whereas the modified HM method achieves more successful results than the original HM method. The results of these two modified equations support the importance of adjustment in the original formulae [77,78,79]. For example, Proutsos et al. [19] evaluated 127 ET approaches in Mediterranean urban green sites and concluded that the adjusted models performed more accurate ET simulations overall compared to the original equations. Compared to other techniques, the HS method produces results that are closest to the reference ET

_{PM}when examining the box plot of the method at all stations.

_{PM}reference values, while an overestimation tendency was observed for the PM

_{0.5}method, although the highest correlation was achieved with it. As stated in the methodology section, the modified Blaney–Criddle approach applies parameters computed using the minimum relative humidity, ratio of actual sunshine to the maximum possible sunshine duration, and daytime wind speed instead of the seasonal crop coefficient used in the original method. This resulted in a significant improvement in the evapotranspiration estimations, as seen from the scatter plot. In the Hamon methods, which tend to underestimate ET, the modified version produced better ET values than the original equation. This graph reveals the importance of modification analysis more clearly and supports the results of previous studies [14,76,77,78]. Another important result obtained from the scatter plot is that the KH method, which tends to predict lower daily ET minimum extremes, showed a high performance in monthly simulations across the city. Additionally, the HS method produced the best result by providing a high correlation, although it underestimated the maximum extreme values.

_{PM}. Conversely, negative NSCE values indicate that for SC-driven simulations at the stations, the mean of the ET

_{PM}values is a better predictor than the SC empirical method. The main difference for NNCSE lies in the normalization of the NSCE value, which helps NNSCE to be less sensitive to the variability in the reference data and allows for better comparison across other empirical approaches, regardless of its variance. The highest NSCE and NNSCE values were obtained with BC

_{M}-driven simulations in S2, S8, and S10, whereas the best results were yielded with ET

_{HS}estimations in S7, and it is the HS method at the other seven stations. The obtained findings were observed more clearly in the NNSCE graph. It is essential to note that while the NSCE is a crucial error metric for measuring predictive accuracy, it has some limitations. For instance, it gives equal weight to both overestimation and underestimation errors, which might not always reflect the true importance of such errors in the direction of discrepancy. In comparison to ET

_{PM}, in general, the underestimation is more dominant in Hargreaves–Samani, Kharrufa, and both Hamon equations with negative MRE values, whereas the BC

_{M}, PM

_{0.5}, and SC techniques overestimated the reference values with positive MRE indices. These results are seen more clearly in the Bias metric. Additionally, overall, HS, BC

_{M}, and KH-driven simulations yielded the best MSE, CRMSE, and RMSD results, while the PM

_{0.5}(SC) method had the highest (lowest) value at all stations according to the DET metric. All approaches, excluding SC, have strong positive correlations greater than the PCC value of 0.9 at all stations except for S6. The BC (HS) technique exhibits the highest PCC values in S1 (S3, S4, and S5) after the PM

_{0.5}approach, while the BC

_{M}method, in S2 and the six stations between S6 and S11, is secondary in terms of PCC performance.

## 5. Conclusions

_{0.5}, BC, BC

_{M}, HM, HM

_{M}, HS, and KH, along with SC methods, and assessments were conducted on a station basis. The HM method, which shows a symmetrical box plot distribution, underestimated the ET

_{PM}over the region, while the PM

_{0.5}method overestimated the reference ET

_{PM}values at all stations. In contrast to the BC method, which produced ET values in a narrow range compared with the reference method in the 11 districts, the BC

_{M}method produced more successful results. The HM

_{M}method, which has a symmetrical box plot distribution, produced results close to those of the reference method at some of the stations, indicating that the modification of the HM method was positively reflected. Additionally, underestimation is dominant in minimum whisker ET values obtained from BC

_{M}, KH, and SC-driven simulations. In the Onikisubat district, the HM, HM

_{M,}and HS methods yielded the highest performances among the other methods. Although the BC

_{M}, KH, and SC techniques underestimated the minimum extremes, they generally overestimated ET values compared to the reference method. In Dulkadiroglu, where the highest ET values were produced among all stations, the approaches that gave the closest results to the reference method for the interquartile range were the BC

_{M}, KH, and SC. In the Goksun district, BC

_{M}, HS, KH, and SC-based ET simulations captured ET

_{PM}variations greater than the 25th percentile, whereas they predicted the minimum ET values to be lower. It was concluded that the HS and KH approaches, which underestimated the minimum outliers, provided the closest results to the reference method in the districts of Afsin and Elbistan, where similar ET values were achieved. For Andirin, where ET fluctuations were in the lowest range among all stations, the HS and SC methods produced the most accurate results for ET

_{PM}values in the interquartile range. The HS method, which slightly underestimated the reference ET values, exhibited the highest accuracy in Pazarcik, Caglayancerit, and Ekinozu districts. In Nurhak, the BC

_{M}method was the most successful, slightly underestimating the minimum ET

_{PM}outliers, while the second-highest performance belonged to the HS simulations with underestimation relative to the reference method. Finally, in the Turkoglu district, the HM

_{M}and HS methods produced results similar to those of the reference method.

_{M}approach achieved the highest performance in Dulkadiroglu and Nurhak. Additionally, KH resulted in the smallest CRMSE in Pazarcik and Caglayancerit, whereas PM

_{0.5}and HM were the best in Andirin and Turkoglu, respectively. The PM

_{0.5}approach performed well at all stations based on the DET and PCC metrics because of its similarity with the reference method, although SC-based simulations produced the lowest values. After the PM

_{0.5}-driven performance, the methods showing the highest correlations are the HS method at Onikisubat, Goksun, Afsin, and Elbistan, similar to the CRMSE metric, whereas the BC

_{M}approach has the highest at other stations. Moreover, the most successful results were obtained via the BC

_{M}approach in Dulkadiroglu, Caglayancerit, as well as Nurhak, and the HS method yielded MAE values less than 0.5 mm d

^{−1}at other stations, while the SC and PM

_{0.5}formulae produced strong discrepancy in terms of MAE. An underestimation tendency is observed in the HM, HM

_{M}, and KH methods with negative MRE and Bias indices, while the PM

_{0.5}and SC methods overestimated the ET

_{PM}values. Additionally, the BC

_{M}and HS techniques are generally the ones that are closest to zero, while the methods with the least error vary based on the stations in terms of MRE and Bias metrics. MSE and MRE produced comparable outcomes, and SC-based ET simulations performed the poorest in terms of both statistical indices. The RMSD values more clearly displayed inconsistencies and corroborated those derived from the MSE index. Additionally, the lowest performances were obtained with SC and PM

_{0.5}formulae, while other methods generally received NSCE values greater than 0.7 and BC

_{M}, HS as well as KH-driven ET predictions exhibited the best NSCE values. The negative NSCE values in the SC-driven simulations indicated that the model did not capture the variability and patterns present in the reference value. This finding typically means that SC predictions perform poorly and might be less accurate than simply using the mean of the ET

_{PM}data as a prediction. NNSCE performances support these results and reveal the variation in accuracy/discrepancy on a station basis more clearly.

_{0.5}approach, with the strongest correlation value of 0.99 for the reference among the alternative methodologies. The approach that generates the ET value at a height of 50 cm is likely to have been overestimated as a result of the standardized as a result of coefficient modifications in the original PM equation. The ET

_{BC}values were clustered, ranging from 1.82 to 6.15 mm d

^{−1}, and the BC model overestimated low ET values, whereas it underestimated high ET values relative to ET

_{PM}values. On the other hand, the modified BC version used the “a” and “b” coefficients computed depending on various climatic parameters (i.e., relative humidity, wind speed, and sunshine duration) instead of the “k” seasonal crop coefficient in the formula and yielded significant improvement in the results. After this adjustment, it was concluded that the BC

_{M}approach, which has the second highest correlation with a PCC value of 0.98, can be used as an alternative to the PM method over many districts in the region. Although the HM and HM

_{M}techniques involving water vapor density underestimated the ET

_{PM}values with an identical PCC (0.94), unlike other alternative methods, the modified version produced better results than the original Hamon formula. Furthermore, even though the 1.2 local calibration coefficient improved the results in the equations of both techniques, it is anticipated that regional and seasonal modifications to the included coefficient will improve the accuracy of the ET estimations. In addition, the HS approach produced ET values that were similar to the reference method throughout Kahramanmaraş, demonstrating a successful performance with a low bias between ET

_{PM}and ET

_{HS}and a high correlation of 0.96 PCC. The KH technique, in which the linear trend line is close to that of the PM method with a PCC value of 0.94, produced accurate ET

_{PM}at some stations, although it had higher noise in overall ET estimates. Moreover, the TH method, which underestimates ET values compared to the reference method, showed a high correlation with a PCC value of 0.93. Among all alternative empirical approaches, SC and RM methods generated the highest deviation in the simulations relative to the ET

_{PM}values and smallest PCC values of 0.88 and 0.89, respectively. Additionally, both methods tended to overestimate the evapotranspiration time series compared with the reference method. Examining the equations for both methods revealed that ET values were derived only from the average temperature and relative humidity data. However, the majority of other alternative formulae are functions of sunshine duration in addition to the aforementioned parameters, and coefficients derived depending on sunshine duration are also enhanced in the correlation.

_{M}and HS approaches can be utilized as alternatives to the PM method in estimating evapotranspiration values over Kahramanmaras province. Additionally, the KH technique, which only employs temperature data, can be listed as an alternative for accurately capturing ETs. While the worst results in the region were obtained with SC-driven ET simulations, the PM

_{0.5}method consistently overestimated the ET

_{PM}values despite having a high correlation. Investigating the effectiveness of the alternative empirical methodologies assessed in this study in other locations with features comparable to the region is another matter that can attract attention. The obtained ET results will play a significant role in the planning of areas for agriculture and forestry, in determining the usable water potential of dams, in the accurate estimation of water losses in rainfall-runoff simulations, and in hydrometeorological applications such as forecasting drought or flood predictions.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Box plots of evapotranspiration from the various approaches for the 11 stations at the daily temporal resolution.

**Figure 4.**(

**a**) Kahramanmaras slope map; (

**b**) Kahramanmaras aspect geography map; (

**c**) Kahramanmaras solar radiation map.

**Figure 5.**Scatter plots of evapotranspiration from the various approaches and reference (PM) at the monthly average.

**Figure 6.**Variation of statistical metrics. (

**a**) centered root mean square error; (

**b**) determination coefficient; (

**c**) mean absolute error; (

**d**) mean relative error; (

**e**) mean squared error; (

**f**) Nash–Sutcliffe coefficient of efficiency; (

**g**) normalized Nash–Sutcliffe coefficient of efficiency; (

**h**) percent bias; (

**i**) Pearson’s correlation coefficient; (

**j**) root mean square deviation.

Station Number | Station Name | District | Coordinates | Elevation (m) | Available Time Period |
---|---|---|---|---|---|

S1 | 17255-Kahramanmaras | Onikisubat | 37.58 36.92 | 572 | 01.01.2000–31.12.2021 |

S2 | 17256-Kahramanmaras Airport | Dulkadiroglu | 37.54 36.97 | 525 | 01.01.2017–31.12.2021 |

S3 | 17866-Goksun | Goksun | 38.02 36.48 | 1344 | 01.01.2000–31.12.2021 |

S4 | 17868-Afsin | Afsin | 38.24 36.92 | 1230 | 01.01.2000–31.12.2021 |

S5 | 17870-Elbistan | Elbistan | 38.20 37.20 | 1137 | 01.01.2000–31.12.2021 |

S6 | 18156-Andirin | Andirin | 37.59 36.36 | 1108 | 01.01.2013–31.12.2021 |

S7 | 18157-Pazarcik | Pazarcik | 37.47 37.24 | 787 | 01.01.2013–31.12.2021 |

S8 | 18279-Caglayancerit | Caglayancerit | 37.75 37.37 | 1001 | 01.03.2014–31.12.2021 |

S9 | 18280-Ekinozu | Ekinozu | 38.05 37.1872 | 1246 | 01.03.2014–31.12.2021 |

S10 | 18281-Nurhak | Nurhak | 37.96 37.45 | 1368 | 01.03.2014–31.12.2021 |

S11 | 18282-Turkoglu | Turkoglu | 37.38 36.84 | 535 | 01.03.2014–31.12.2021 |

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## Share and Cite

**MDPI and ACS Style**

Uzunlar, A.; Dis, M.O.
Novel Approaches for the Empirical Assessment of Evapotranspiration over the Mediterranean Region. *Water* **2024**, *16*, 507.
https://doi.org/10.3390/w16030507

**AMA Style**

Uzunlar A, Dis MO.
Novel Approaches for the Empirical Assessment of Evapotranspiration over the Mediterranean Region. *Water*. 2024; 16(3):507.
https://doi.org/10.3390/w16030507

**Chicago/Turabian Style**

Uzunlar, Ali, and Muhammet Omer Dis.
2024. "Novel Approaches for the Empirical Assessment of Evapotranspiration over the Mediterranean Region" *Water* 16, no. 3: 507.
https://doi.org/10.3390/w16030507