A novel hybrid machine learning framework for spatio-temporal analysis of reference evapotranspiration in India

Abstract

Study region

The study focuses on the diverse climatic regions of India, spanning arid, semi-arid, sub-humid, and humid zones.

Study focus

This research employs a novel hybrid machine learning (ML) framework for precise spatio-temporal reference evapotranspiration (ET_o) modelling from 1970 to 2024, addressing the variability in temperature, humidity, and precipitation. Three advanced ML models—Quantile-Adjusted xLSTM Network (QAxLNet), Quantile-Score Diffusion Model (QSDM), and Attentive Deep Quantile-Aware Autoencoder Network (ADAQNet)—are proposed and applied, focusing on relative humidity and temperature as critical predictors. Model validation, conducted with EEFlux-derived ET_o data and Indian Meteorological Department (IMD) benchmarks, revealed strong alignment across diverse climatic zones.

New hydrological insights for the region

The MPI-ESM1–2-HR model under SSP3–7.0 scenarios outperformed other CMIP6 models, with a correlation coefficient of 0.975 and spatial error of 3.55 mm. The ADAQNet demonstrated superior performance, with lowest errors RMSE (Train: 0.2247, Test: 0.2499), and R² (Train: 0.96; Test: 0.9571) among the models. ET_o declined at an average rate of 1.9 mm/year, indicating the role of climate change. ET_o variability closely mirrored the spatial distribution of the National Building Code (NBC) of India. Seasonal variations were significant, with arid regions (Rajasthan, Gujarat) experiencing the highest increase (2.5–5.1 mm/year). Humid regions showed high sensitivity to RH forecasts, with up to 20 % ET_o deviation. The study emphasizes the spatial, temporal, and seasonal variations of ET_o across the region, highlighting its dependence on climatic factors.