Ensuring spatiotemporal consistency in multivariate bias correction for climate projections using hierarchical vine copulas and GAMs

Univariate bias-correction methods adjust systematic errors in climate model outputs for individual variables but often fail to preserve inter-variable dependence, resulting in physically inconsistent multivariate projections. Multivariate bias-correction (MBC) methods address this limitation but are commonly applied independently at each location, thereby neglecting spatial dependence. Moreover, temporal dependencies are rarely modeled explicitly. Preserving spatiotemporal consistency is, however, essential for realistic climate dynamics and reliable regional impact assessments.

We propose a novel MBC framework that jointly accounts for inter-variable, spatial, and temporal dependence. The spatiotemporal structure is addressed by decomposing each time series using generalized additive models (GAMs) to remove deterministic components such as seasonality and spatial gradients. The resulting stochastic components are transformed via probability integral transforms into approximately independent and identically distributed variables, suitable for dependence modeling with vine copulas.

To construct a joint distribution across multiple variables and locations, we introduce CUVEE (Copulas Under Vine Extending Environment), a hierarchical vine-based merging strategy. CUVEE combines two dependence levels: (i) spatial dependence across locations modeled separately for each variable, and (ii) inter-variable dependence modeled at a selected reference location, which links the spatial models into a coherent multivariate and spatial structure. This approach enables flexible dependence modeling while remaining computationally tractable for regional applications.

We apply the proposed method to EURO-CORDEX simulations over the Swiss canton of Vaud, using gridded MeteoSwiss observations and ERA5 reanalysis data as reference. Results show substantial improvements in preserving inter-variable, temporal, and spatial dependence compared to standard quantile mapping and conventional MBC approaches, highlighting the potential of the method for physically consistent multivariate bias correction.