A flexible semi-continuous time series framework for hydrological water balance analysis using multi-source data

Hydrological models simulate relationships among variables governing water processes, traditionally relying on in situ and satellite data. While ground observations suffer from spatial and temporal gaps, especially in ungauged basins, satellite datasets (e.g. PERSIANN-CDR, CHIRPS, SSEBop, GLEAM, GRACE) provide global coverage but introduce uncertainties from errors and biases. Current uncertainty reduction methods include direct evaluation against ground truth or indirect internal consistency checks. Probabilistic fusion techniques avoid dependence on ground truth but assume normal distributions, which poorly represent skewed, heavy-tailed, and zero-inflated hydrological variables such as intermittent precipitation. This study proposes a generalized framework using semi-continuous probability distributions that separate zero-value probabilities from positive values modelled with right-skewed distributions (gamma, lognormal). The model’s non-stationary extension captures temporal variations, improving statistical representation, dynamic adaptation, and scalability. Validation shows enhanced uncertainty quantification and water-balance closure, offering a robust tool for global hydrological modelling where ground data are limited.