Effectiveness of Multivariate Bias Correction in Hydrology and Agriculture: A Systematic Review

Abstract. Climate impact assessments in hydrology and agriculture often rely heavily on outputs from Global Climate Models (GCMs). However, a fundamental scale mismatch exists between the coarse resolution of GCMs and the fine-scale, multivariate data required by impact models. While Multivariate Bias Correction (MBC) methods have emerged as a solution to restore inter-variable dependencies (e.g., the correlation between precipitation and temperature), it remains unclear whether statistical improvements in climate data translate into more accurate impact projections. This study presents a systematic review of 39 peer-reviewed articles to evaluate the added value of MBC across hydrological and agricultural domains. Our synthesis reveals a critical "validation gap" where superior statistical performance does not consistently yield improved impact simulations. We identify a divergence in added value dictated by the characteristic response time scales of the receiving systems. Agricultural models, which are often sensitive to immediate, daily compounded extremes (e.g., heat stress during low soil moisture), demonstrate a clear benefit from MBC. In contrast, general rainfall-runoff models often function as spatiotemporal integrators, acting as low-pass filters that dampen high-frequency incoherence; consequently, simpler univariate methods frequently perform equally well for bulk streamflow simulation. Furthermore, we highlight the risks of non-stationarity, where methods calibrated to historical correlations may fail under future climate regimes. We conclude that future method development must pivot from purely statistical refinement to more process-aware, regime-dependent frameworks. The ultimate goal is to produce methods capable of addressing non-stationarity and determining when – or if – multivariate correction adds value over simpler univariate approaches.