Adapting the multivariate patch time series transformer (M-Patch-TST) for robust hydro-climatic forecasting in arid regions

Robust forecasting of hydro-climatic indicators is crucial for adaptive water resource management and environmental sustainability. This study presents a domain-specific implementation of the Multivariate Patch Time Series Transformer (M-Patch-TST), explicitly optimized for forecasting the Global Aridity Index (GAI) in data-sparse environments. While Transformer models exist, this research bridges a critical gap by tailoring the patching mechanism to handle the high-frequency noise and zero-inflated nature of hydrological time series in arid regions. Unlike traditional models that process data point-by-point, this architecture segments time series into patches for noise reduction and leverages a self-attention mechanism to identify long-range patterns. Using seasonal data from 40 synoptic stations in Iran (1967–2019), the model was validated (2020–2025) under three scenarios devised via Random Forest (RF) importance ranking and Variance Inflation Factor (VIF) multicollinearity analysis: Scenario A (univariate GAI), Scenario B (GAI + Temperature), and Scenario C (GAI + Temperature & Sunshine Hours). Contrary to multi-variable expectations, Scenario A demonstrated superior performance, highlighting the model's capability to extract robust patterns directly from the target variable. Comparative analysis based on Kling-Gupta Efficiency (KGE), Normalized Root Mean Square Error (NRMSE), and Willmott’s Index (Wi-I) revealed that M-Patch-TST significantly outperformed benchmark models, including Long Short-Term Memory (LSTM), Support Vector Regression (SVR), Autoregressive Integrated Moving Average (ARIMA), and RF. Practical application for the autumn 2025– autumn 2035 period indicated a continued trajectory of high aridity across most stations. To provide a baseline context, trend analysis using the Mann-Kendall (MK) test on the historical observed data (1967–2025) revealed a significant negative trend (intensifying aridity) in seasonal GAI across several key stations. Furthermore, Pettitt’s test identified critical abrupt change points in the historical record, predominantly occurring between 1998 and 2007. These findings establish M-Patch-TST as a superior tool for reliable long-term prediction of sustainability indicators.