Modeling of pan evaporation using Gene Expression Programming and time series in Khuzestan

Evaporation from water levels is one of the most important processes in meteorology and hydrology. Optimum use of available water resources is necessary due to the high costs of water storage in the dams. Every year, it is evaporate millions of cubic meters of fresh water from the dam’s water. On the other hand, evaporation from the pan helps to estimate the amount of the plant water requirement in areas where there is no lysimeter information. A wide variety of methods can be used to measure or estimate water use by plants. The evaporation pan method is a simple, inexpensive, and readily understandable way to estimate irrigated crop water use. It also requires little attention and can provide farmers with reliable estimates of plant water use. Pans provide a measurement of the integrated effect of radiation, wind, temperature, and humidity on the evaporation from an open water surface. The pan has proved its practical value and has been used successfully to estimate water use by observing the evaporation loss from a water surface and applying the crop coefficients to relate pan evaporation to irrigation requirement. For this reason, the study of evaporation from the pan has always been of interest to researchers. Modeling this important parameter can be very effective and helpful in accurately estimating of missing data.

In this research, by using of the Gene Expression Programming model (GEP) and some time series models, including Exponential smoothing model, Holt’s model, ARIMA, Brown’s linear trend and Winters’ model, the daily evaporation from pans in Khuzestan province was evaluated. For this purpose, daily pan evaporation for 20 years (2000 to 2020) of three synoptic stations of Ahvaz, Abadan and Dezful were used. These stations have the longest and most complete data among the stations of this province. For modeling the pan evaporation data, 80% of the data was used for the training stage and the remaining 20% was used for the model testing stage. In this research, seven patterns were defined for data modeling. These patterns include the use of data from 20 months ago (M20), 16 months ago (M16), 14 months ago (M14), 10 months ago (M10), 6 months ago (M6), 4 months ago (M4) and 2 months ago (M2). Three evaluation statistics ware also used for evaluate the results of the models. This statistics are include the Root Mean Squared Error (RMSE), Nash- Sutcliffe coefficient (N.S) and Coefficient of Determination (R2). The model with the lowest root mean squared error value and the highest Nash- Sutcliffe coefficient and coefficient of determination was selected as the best model.

The evaluation of the results based on the 3 evaluation indices, showed that the patterns M14, M16 and M20 have the highest accuracy in modeling in both training and test stages. In other words, by increasing the memory of the model, the results show more accuracy and less error. Also, based on the evaluation statistics, the amount of simulation error in the cold months (October to March) was 28% lower than in the hot months (April to September). However, in all 12 months of the year, at least one suitable patterns with acceptable accuracy was obtained for simulating the daily evaporation data. The best results in the warm months were observed for Dezful and Abadan in August and for Ahvaz in May and in the M20. The error in these stations is 0.93 mm, 0.95 mm and 0.95 mm per day, respectively. The Nash- Sutcliffe coefficient (N.S) is more than 0.80 in all stations. In the cold months of the year, the lowest error (0.70 mm per day) was observed in December of Abadan, along with the Nash- Sutcliffe coefficient of 0.82, which indicates the high efficiency of the GEP model in data simulation. Comparing the results of the Gene Expression Programming model (GEP) with the studied time series models also showed that the GEP model has lower error and higher R2 and N.S coefficient in all months in Abadan. In Dezful, the Holt model provided better results than GEP in January and September. The error rate in these two months is 61% and 71% less than GEP model, respectively. In Ahvaz, the Exponential smoothing model in October and the Holt model in November estimated the daily pan evaporation with 48% and 68% less error, respectively.