Novel Approaches for the Empirical Assessment of Evapotranspiration over the Mediterranean Region
It is necessary to conduct studies to ascertain the suitability and accuracy of empirical techniques for different regions that have emerged from investigations conducted in local areas with soil structure as well as certain climatic and environmental characteristics. Several empirical approaches can be used with varying degrees of success, owing to the unique characteristics of each place and the availability of a limited number of measurable climatic and environmental factors. Hydrological studies are significant for the effective management of water resources in Kahramanmaras, given their considerable water potential. Unfortunately, ET measurements are not available for Turkiye, and these values vary spatiotemporally. However, no comprehensive ET study has been conducted in the city, and a district-based ET study was implemented for the first time in the region. Additionally, the city has complex climate zones, varying vegetation cover, and uneven distribution of elevation gradient.
In this study, the quantitative determination of ET, one of the most significant water losses of the hydrological cycle, can contribute to studies in this field and will also play an important role in various hydrological planning studies, such as agricultural irrigation projects and basin management, to be carried out in the study area. Data-scarce ET time series were assessed utilizing ten climatological-driven ET approaches relative to the PM method over eleven districts of Kahramanmaras region, Turkiye. In this study, the performances of ten empirical evapotranspiration approaches, namely Blaney–Criddle (BC), modified Blaney–Criddle (BCM), Hamon (HM), modified Hamon (HMM), Hargreaves–Samani (HS), Kharrufa (KH), Romanenko (RM), Schendel (SC), Thornthwaite (TH), and Penman–Monteith at 0.5 m (PM0.5), 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.
The ET values obtained were clustered in the range of 1 to 6 mm d−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 PM0.5 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 HMM 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 BCM 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.
Additionally, the reference ET values for the S2 station, which had the least amount of accessible climatic data, were concentrated between 2 and 9.5 mm d−1. The BCM 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 PM0.5 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, HMM, 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.
Moreover, as can be seen in the box plot of the S3 station, it can be seen that the HS method, shown in green, produces results substantially closer to the reference approach, although it slightly underestimates the minimum outlier. Although the ET values generated by the SC approach remained in the interquartile range compared to the reference method, the absolute values of the extreme ETs were higher. When the PM0.5 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, BCM, and KH approaches underestimated the minimum values for quartiles smaller than 0.05 at the S3 station. However, the BCM and KH approaches performed well in the interquartile range and higher whisker values. Although the HM and HMM 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.
In addition, when looking at the box plot of stations S4 and S5, the extreme ETs were close to one another, and the ET values computed using the reference technique were concentrated in a similar range. It was observed that the ET values acquired by the HS and KH techniques at both stations were concentrated in a similar range and captured the majority of the reference values, although the ET values smaller than the lower quartile were predicted with underestimation. Although the extreme ET values in whiskers simulated with the HM and HMM 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 BCM and SC methods produce overestimation (underestimation) ET values in the upper (lower) whisker compared to the reference method at both stations, while PM0.5-driven ET simulations overestimated ET values in all quartiles.
Additionally, ETPM 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 HMM, HS, and SC approaches at the S6 station. While the PM0.5 and BC methods produce higher ET values for values between the 25th and 75th percentiles with respect to the PM technique, ETBC values are concentrated in a narrower range. Although it was discovered that the ETHM results were close to the reference for extreme values, these estimations clustered with underestimation until the median. Although BCM-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 ETKH values are simulated with a significant degree of bias in comparison to the reference method.
At the S9 station, the interquartile range of reference ET values varies between 1.8 and 6 mm d−1, and the best performance was acquired with the ETHS formula. In the Ekinozu district, although the BCM, KH, and SC approaches underestimated the minimum ET values in the lower whisker with high deviation compared with the reference method, ETPM values were captured between the 25th and 75th percentiles. Underestimation is dominant in HM and HMM-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 ETBC values are in a narrower range with a small standard deviation in Nurhak and Turkoglu, the PM0.5 technique tends to overestimate evapotranspiration time series compared to the reference method, as in the other stations in general.
When the box plot of the S10 station was examined, while ETKH and ETSC values had high variance compared to ETPM, both methods underestimated evapotranspiration smaller than the median value, and strong overestimation was dominant in ETSC values greater than the median. The BCM 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 HMM-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 BCM, HM, HMM, and KH approaches in addition to the ETHS formula. The graph also shows that the values in the lower than 25th percentile are underestimated by the BCM, KH, and SC techniques.
The performances of the ET approaches on a daily scale were computed and graphed using ten various statistical criteria to enhance the evaluation of the methods to be more detailed and sensitive for each station. As can be seen from the NSCE results, a value higher than 0.5 demonstrates that alternative approaches (except SC) can sufficiently replicate the variability of the ETPM. Conversely, negative NSCE values indicate that for SC-driven simulations at the stations, the mean of the ETPM 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 BCM-driven simulations in S2, S8, and S10, whereas the best results were yielded with ETHS 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 ETPM, in general, the underestimation is more dominant in Hargreaves–Samani, Kharrufa, and both Hamon equations with negative MRE values, whereas the BCM, PM0.5, and SC techniques overestimated the reference values with positive MRE indices. These results are seen more clearly in the Bias metric. Additionally, overall, HS, BCM, and KH-driven simulations yielded the best MSE, CRMSE, and RMSD results, while the PM0.5 (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 PM0.5 approach, while the BCM method, in S2 and the six stations between S6 and S11, is secondary in terms of PCC performance.
However, this study has some limitations; for instance, in addition to the aforementioned factors, ET may also be affected by elements such as vegetation cover, soil map, land use, and land cover belonging to the relevant study area, and they were not evaluated within the scope of this study. Despite these limitations, the results of this study can help future studies mitigate the effects of drought and the prejudice of hydrological modeling results over the study area. Furthermore, the findings motivate future studies to analyze how well alternative empirical approaches are performed in other areas with features comparable to the analyzed region.
Empirical approaches for calculating ET values hold a significant place in the literature because of their advantages, such as simplicity of use when utilizing meteorological data and obtaining results in a short time. Evapotranspiration may be quantitatively assessed using a variety of techniques. Numerous studies have been conducted to find the most straightforward and accurate method that can be applied in various study regions, and these have been updated in response to evolving circumstances. In this study, evapotranspiration simulations carried out various techniques such as Penman–Monteith, Penman–Monteith at 0.5 m, Blaney–Criddle, modified Blaney–Criddle, Hamon, modified Hamon, Hargreaves–Samani, Kharrufa, Schendel, Romanenko, and Thornthwaite using daily meteorological data from stations in 11 districts of Kahramanmaras province. In evaluating the alternative methods at daily and monthly temporal resolutions, the Penman–Monteith method, recommended by the Food and Agriculture Organization for use worldwide, was considered as a reference.
A box plot was generated using ET values derived from daily scale estimations utilizing the PM, PM0.5, BC, BCM, HM, HMM, 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 ETPM over the region, while the PM0.5 method overestimated the reference ETPM 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 BCM method produced more successful results. The HMM 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 BCM, KH, and SC-driven simulations. In the Onikisubat district, the HM, HMM, and HS methods yielded the highest performances among the other methods. Although the BCM, 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 BCM, KH, and SC. In the Goksun district, BCM, HS, KH, and SC-based ET simulations captured ETPM 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 ETPM 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 BCM method was the most successful, slightly underestimating the minimum ETPM outliers, while the second-highest performance belonged to the HS simulations with underestimation relative to the reference method. Finally, in the Turkoglu district, the HMM and HS methods produced results similar to those of the reference method.
To evaluate the statistical performance of the methods on a daily scale, the central square mean error, determination coefficient, mean absolute error, mean relative error, mean squared error, Nash–Sutcliffe efficiency coefficient, normalized NSCE, percentage error, Pearson’s correlation coefficient, and root mean square error metrics were applied. According to the CRMSE index, the HS method had the lowest values in Onikisubat, Goksun, Afsin, Elbistan, and Ekinozu, whereas the BCM approach achieved the highest performance in Dulkadiroglu and Nurhak. Additionally, KH resulted in the smallest CRMSE in Pazarcik and Caglayancerit, whereas PM0.5 and HM were the best in Andirin and Turkoglu, respectively. The PM0.5 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 PM0.5-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 BCM approach has the highest at other stations. Moreover, the most successful results were obtained via the BCM 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 PM0.5 formulae produced strong discrepancy in terms of MAE. An underestimation tendency is observed in the HM, HMM, and KH methods with negative MRE and Bias indices, while the PM0.5 and SC methods overestimated the ETPM values. Additionally, the BCM 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 PM0.5 formulae, while other methods generally received NSCE values greater than 0.7 and BCM, 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 ETPM data as a prediction. NNSCE performances support these results and reveal the variation in accuracy/discrepancy on a station basis more clearly.
In this study, the monthly averages of ET values generated by the TH and RM techniques—which can compute ET on a monthly scale—as well as the daily ET values produced by other methods, were utilized to build a scatter plot. An overestimation tendency is observed for the PM0.5 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 ETBC 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 ETPM 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 BCM 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 several districts in the region. Although the HM and HMM techniques involving water vapor density underestimated the ETPM 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 ETPM and ETHS 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 ETPM 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 ETPM 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.
Within the scope of this study, where the impact of terrain characteristics and altitude on ET was also assessed, a slope, aspect geography, and solar radiation map of the study area were prepared. It was concluded that altitude has an adverse effect on ET, although the evaluation of altitude alone might not be comprehensive except in rare circumstances. Upon evaluating the aspect, slope, and solar radiation maps in this manner on a station basis, it was observed that the slope positively impacted ET. While the southern slopes of the slope are another factor that increases ET, it has been detected that interconnected solar radiation raises ET. Along with these elements in terrain characteristics, examining the effects of land use and vegetation on ET can motivate future studies.
In light of all examinations and evaluations, it can be concluded that the BCM 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 PM0.5 method consistently overestimated the ETPM 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.
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