Design and analysis of statistical probability distribution and non-parametric trend analysis for reference evapotranspiration

Accurate estimates of reference evapotranspiration are critical for water-resource management strategies such as irrigation scheduling and operation. Therefore, knowledge of events such as spatial and temporal reference evapotranspiration (ET(o)) and their related principle of statistical probability theory plays a vital role in amplifying sustainable irrigation planning. Spatiotemporal statistical probability distribution and its associated trends have not yet has explored in Pakistan. In this study, we have two objectives: (1) to determine the most appropriate statistical probability distribution that better describes ET(o) on mean monthly and seasons wise estimates for the design of irrigation system in Khyber Pakhtunkhwa, and (2) to check the trends in ET(o) on a monthly, seasonal, and annual basis. To check the ET(o) trends, we used the modified version of the Mann-Kendall and Sen Slope. We used Bayesian Kriging for spatial interpolation and propose a practical approach to the design and study of statistical probability distributions for the irrigation system and water supplies management. Also, the scheme preeminent explains ET(o), on a monthly and seasonal basis. The statistical distribution that showed the best fit ET(o) result occupying 58.33% and 25% performance for the design of irrigation scheme in the entire study region on the monthly level was Johnson SB and Generalized Pareto, respectively. However, according to the Anderson-Darling (AD) and Kolmogorov–Smirnov (KS) goodness of fit measure, seasonal ET(o) estimates were preferably suited to the Burr, Johnson SB & Generalized Extreme Value. More research work must be conduct to assess the significance of this study to other fields. In conclusion, these findings might be helpful for water resource management and policymaker in future operations.