Analysis of spatial and temporal patterns of potential evapotranspiration by combining harmonic, stochastic and Monte Carlo methods (Case study: Zayandehrud basin)

Background and objectives: This research presents a method to investigate and analyze the spatial and temporal patterns of potential evapotranspiration (ETp) in Zayandehroud basin. Due to the water resources management importance, it is necessary to use efficient methods to predict evapotranspiration (ET). So far, these patterns have been studied in different ways. However, a method that can estimate ETp for dry, normal and wet periods with a daily time step during a hundred years has not yet been presented. In this study, a hybrid method for temporal and spatial analysis of ETp was developed for the Zayandehroud basin as a research area. This method considers the daily time step and a relatively dense network of points at the basin level.
Materials and methods: The proposed method involves a combination of three approaches, namely harmonic, stochastic and Monte Carlo methods, to model and predict ETp. Harmonic method helps to analyze periodic, seasonal and annual patterns of data, stochastic method simulates natural fluctuations in data and Monte Carlo method is used to analyze different weather scenarios. In the hybrid method, the harmonic function was first fitted to the maximum and minimum air temperature data of all stations in the zayandehroud basin and its surroundings over a 26-years period, from 1994 to 2019. Then, the statistical distribution of the residuals and the correlation between the air temperature parameters were determined, and the steps of random number generation were performed. Using stochastic and Monte Carlo methods, 100-years of statistics for extremum air temperature variables were produced daily, so that ETp can be calculated in the next step using the Hargreaves-Samani method. Estimation of ETp was done in a dense network of points over the basin by the inverse squared distance method to obtain spatial patterns. By using the percentile index, in which 20% was suggested for mild drought, 50% for normal and 80% for mild drought, different humidity conditions could be investigated. The validation was performed for the normal period of the hybrid model. Thereby, the model data were compared with the observed values in the agricultural areas of the basin and for the period of wheat cultivation (PWC) using correlation tests and also one-way ANOVA, rejecting the significance of the mean difference and confirming the accuracy of the model results.
Results: The increasing trend of ETp was observed in all the agricultural areas throughout the basin, so that the slope of the trend according to the Sen method was from 1.28 mm/PWC in the lands downstream of Khamiran Dam to 3.73 mm/PWC is changing in Mahyar and Jarguyeh lands. The shortest growing period for wheat is observed in Roudasht with 211 days, while Fereidunshahr has the longest growing period of 288 days. Consequently, the expected ETp values under normal conditions are about 598 millimeters for Roudasht and 795 millimeters for Fereidunshahr in PWC. Investigations at the watershed level show that the ETp value in the mountainous regions of the basin typically varies between 1299 and 1515 mm/y under normal conditions. In contrast, the flat eastern areas have ETp values between 1524 and 1609 mm/y. Under moderately dry conditions, ETp values in the higher regions vary between 1320 and 1540 mm/y, while in the flat areas, they range between 1547 and 1644 mm/y. The same changes are estimated from 1276 to 1460 mm/y in the mountainous regions and from 1491 to 1583 mm/y in the plains.
Conclusion: The results show that using a hybrid approach improves the understanding of evapotranspiration patterns in a basin, increases prediction accuracy, and facilitates the analysis of events in the basin under different climatic conditions.