Prediction of daily reference evapotranspiration with M5P, Gaussian process regression and Support vector regression methods

Background and Objectives: Indiscriminate use of water resources and the occurrence of drought in recent years have caused many problems in the country's water resources. The increasing shortage of water resources and high irrigation costs require developing new irrigation methods for optimal water consumption, which can minimize the amount of water used to produce yields. Evapotranspiration is one of the most important parameters needed to estimate the water balance in any ecosystem. Evapotranspiration is an essential parameter in the hydrological cycle process in natural ecosystems, which links the water and energy balance of the earth's surface with the atmosphere. Reference evapotranspiration (ET0) plays an important role in the availability of water resources and stimulating the hydrological effect of climate change. Accurate estimation of ET0 is necessary for forecasting climate changes, predicting and monitoring droughts, assessing the lack of availability of water resources, assessing crop water needs, and planning irrigation. FAO's Penman-Monteith method is known as a standard reference method for estimating ET0. However, this model and, in general, water balance-based assessment methods require accurate and long-term meteorological data, which are not always and everywhere available. Therefore, alternative methods for predicting ET0 at different temporal and spatial scales should be developed, which are easily applied and require fewer input data without compromising the estimation accuracy. Also, due to the high rate of evapotranspiration in the coastal and central stations of the country, so far, few studies have predicted the ET0 parameter. Therefore, this study was carried out to predict daily reference evapotranspiration in Isfahan and Astara stations.
Methodology: The current study is forecasting daily reference evapotranspiration in two stations of Astara and Isfahan using Gaussian Process Regression (GPR), Support Vector Regression (SVR), M5P tree model, and M5Rules linear regression. For this purpose, the daily meteorological data of the stations including average temperature, minimum temperature, maximum temperature, average relative humidity, minimum relative humidity, maximum relative humidity, wind speed, and sunshine hours during the period of 1990-2021 as inputs to the models was used. Also, to evaluate the effectiveness of the models, the evaluation criteria of determination coefficient (R2), root mean square error (RMSE), Nash-Sutcliffe coefficient (NS), and Wilmott's index of agreement (WI) were used.
Findings: The evaluation of the results of different scenarios of the GPR model in Astara station showed that the fifth scenario was recognized as the best scenario of this model due to having a lower error value (RMSE=1.52 mm day-1). For the M5Rules model, the fifth scenario has performed better than the other scenarios of the M5Rules model due to having fewer inputs and similar errors compared to the sixth to eighth scenarios (RMSE=1.42 mm day-1). In the M5P model, the fifth scenario has a higher accuracy than the other scenarios due to having a lower error value (RMSE=1.42 mm day-1). For the SVR model, the sixth scenario with the least error (RMSE=1.58 mm day-1) was selected as the best scenario compared to other scenarios of the SVR model. For the Isfahan station, for the GPR model, the fifth scenario has performed better than the other scenarios due to having fewer inputs. The comparison of M5Rules model scenarios also showed that the eighth scenario with RMSE=1.85 (mm day-1), had higher accuracy than other scenarios. The seventh scenario of the M5P model has performed better than other scenarios due to its RMSE=1.86 (mm day-1). Finally, the evaluation of SVR model scenarios showed that the eighth scenario with RMSE=1.88 (mm day-1) had a better performance than other scenarios.
Conclusion: The comparison of the models used to predict daily reference evapotranspiration in Astara station showed that the fifth scenario of M5P and M5Rules models having evaluation criteria of R2=0.76, RMSE=1.42 (mm day-1), NS=0.7 and WI=0.89 had the highest accuracy compared to other models and showed the best performance. Also, the evaluation of the results of the models in Isfahan station showed that the eighth scenario of the M5Rules model, having the evaluation criteria of R2=0.8, RMSE=1.85 (mm day-1), NS=0.8 and WI=0.94 had the best performance compared to other models and the M5Rules model was selected as the best model. Also, the seventh scenario of the M5P model had almost the same performance as the eighth scenario of the M5Rules model and showed a good performance. Therefore, M5P and M5Rules models successfully predicted reference evapotranspiration. One of the limitations of the present study is the lack of access to dew point temperature and solar radiation data. Therefore, the use of these parameters is suggested for further studies.