A physically constrained multivariate bias correction framework for projecting compound drought and heatwave risk in the Yangtze River Basin

Compound drought and heatwave (CDHW) events pose growing threats to water security and ecosystems in the Yangtze River Basin. Reliable projections require an accurate representation of the joint behavior of precipitation and temperature. However, biases in CMIP6 simulations and conventional univariate correction may distort this dependence, increasing projection uncertainty. This study developed a physically constrained, dependence-preserving multivariate bias-correction framework integrating CycleGAN, BiLSTM, and quantile delta mapping (QDM) to jointly correct daily precipitation, maximum temperature (Tmax), and minimum temperature (Tmin) from 13 CMIP6 models. The framework improved CDHW-relevant hot-dry dependence and reproduced the observed spatial pattern of historical normalized cumulative CDHW intensity with a correlation of 0.64. QDM compensation improved preservation of the raw CMIP6-projected Tmax warming signal, while CycleGAN–BiLSTM reduced Tmax–precipitation dependence errors relative to QDM alone. Under a fixed historical-reference heatwave threshold, projected CDHW occurrence increased, particularly under SSP5-8.5, mainly because more days exceeded the historical heat threshold. In contrast, under period-adaptive thresholds, CDHW occurrence conditional on concurrent heatwave and drought did not increase relative to the historical period. Sensitivity analyses showed that the magnitude and interpretation of projected CDHW changes depended on the heatwave-threshold definition and potential evapotranspiration formulation.