Causally guided symbolic regression for basin-scale water balance change in the China–Mongolia arid region

This study focuses on the China–Mongolia Arid Region (CMAR), a vast area spanning approximately 34–48°N latitude and 78–120°E longitude in northern China and southern Mongolia. The aim of this research is to derive a transparent, causally guided empirical model of basin-scale water balance change ( ΔS ) in the CMAR through a combined causal discovery and symbolic machine learning approach. Utilizing a 43-year (1980–2022) monthly ERA5 reanalysis dataset, the study employs the Peter-Clark Momentary Conditional Independence (PCMCI) algorithm to identify robust, lagged predictors from over 200 hydro-meteorological variables. Through a reproducible screening protocol combining physical relevance, redundancy control, and causal stability testing, this pool was reduced to 15 core variables. These causally relevant predictors then inform a symbolic regression (SR) procedure, which evolves an explicit regression form for the basin's water balance anomaly, aiming to bridge the gap between statistical accuracy and mechanistic physical insight. The combined PCMCI → SR workflow reveals that the water balance in the CMAR is co-dominated by energetic forcing (short-wave radiation), zonal moisture transport tendencies, and short-term hydrological memory, particularly runoff lags, while recognising that convergence/divergence ultimately governs the full balance. Notably, the derived equation quantifies a non-additive interaction between regional vapor transport and local precipitation recycling, whereby high recycling rates can intensify water deficits under conditions of strong advection. This causally grounded empirical framework advances the understanding of dryland hydro-climatology and offers a transferable, data-driven modelling approach for data-scarce arid regions. • PCMCI guides symbolic regression for basin-scale water-balance change ΔS . • Radiation, zonal transport, and runoff memory co-dominate arid ΔS . • High moisture recycling can worsen storage balance under strong vapor transport. • SR equation explains 73% of monthly water-balance change ΔS variability.