Using Ensembles of Machine Learning Techniques to Predict Reference Evapotranspiration (ET₀) Using Limited Meteorological Data

To maximize crop production, reference evapotranspiration (ET₀) measurement is crucial for managing water resources and planning crop water needs. The FAO-PM56 method is recommended globally for estimating ET₀ and evaluating alternative methods due to its extensive theoretical foundation. Numerous meteorological parameters, needed for ET₀ estimation, are difficult to obtain in developing countries. Therefore, alternative ways to estimate ET₀ using fewer climatic data are of critical importance. To estimate ET₀ with alternative methods, difference climatic parameters of temperatures, relative humidity (maximum and minimum), sunshine hours, and wind speed for a period of 20 years from 1996 to 2015 were used in the study. The data were recorded by 11 meteorological observatories situated in various climatic regions of Pakistan. The significance of the climatic parameters used was evaluated using sensitivity analysis. The machine learning techniques of single decision tree (SDT), tree boost (TB) and decision tree forest (DTF) were used to perform sensitivity analysis. The outcomes indicated that DTF-based models estimated ET₀ with higher accuracy and fewer climatic variables as compared to other ML techniques used in the study. The DTF technique, with Model 15 as input, outperformed other techniques for the most part of the performance metrics (i.e., NSE = 0.93, R² = 0.96 and RMSE = 0.48 mm/month). The results indicated that the DTF with fewer climatic variables of mean relative humidity, wind speed and minimum temperature could estimate ET₀ accurately and outperformed other ML techniques. Additionally, a non-linear ensemble (NLE) of ML techniques was further used to estimate ET₀ using the best input combination (i.e., Model 15). It was seen that the applied non-linear ensemble (NLE) approach enhanced modelling accuracy as compared to a stand-alone application of ML techniques (R² Multan = 0.97, R² Skardu = 0.99, R² ISB = 0.98, R² Bahawalpur = 0.98 etc.). The study results affirmed the use of an ensemble model for ET₀ estimation and suggest applying it in other parts of the world to validate model performance.