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Spatiotemporally Consistent Multivariate Bias Correction for Climate Projections via Nested Vine Copulas

Theresa Meier, Erwan Koch, Valérie Chavez-Demoulin, Thibault Vatter

Abstract

Climate models are essential for understanding large-scale climate dynamics and long-term climate change, yet they exhibit systematic biases when compared with historical observations. Existing multivariate bias correction (MBC) approaches do not explicitly handel spatiotemporal dependence. However, preserving both spatiotemporal and inter-variable consistency is essential for realistic climate dynamics and reliable regional impact assessments. To address this gap, we propose a novel MBC method called GN-VBC that uses generalized additive models (GAMs) to disentangle spatiotemporal deterministic effects from stochastic residuals. To model joint distributions and dependencies across variables and locations, we introduce nsted vine copulas (NVCs), a hierarchical vine merging strategy. NVC in the context of MBC 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. An application to Switzerland shows improvements in preserving inter-variable, spatial and temporal dependence across a wide range of evaluation metrics.

Spatiotemporally Consistent Multivariate Bias Correction for Climate Projections via Nested Vine Copulas

Abstract

Climate models are essential for understanding large-scale climate dynamics and long-term climate change, yet they exhibit systematic biases when compared with historical observations. Existing multivariate bias correction (MBC) approaches do not explicitly handel spatiotemporal dependence. However, preserving both spatiotemporal and inter-variable consistency is essential for realistic climate dynamics and reliable regional impact assessments. To address this gap, we propose a novel MBC method called GN-VBC that uses generalized additive models (GAMs) to disentangle spatiotemporal deterministic effects from stochastic residuals. To model joint distributions and dependencies across variables and locations, we introduce nsted vine copulas (NVCs), a hierarchical vine merging strategy. NVC in the context of MBC 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. An application to Switzerland shows improvements in preserving inter-variable, spatial and temporal dependence across a wide range of evaluation metrics.
Paper Structure (29 sections, 2 theorems, 23 equations, 16 figures, 7 tables, 4 algorithms)

This paper contains 29 sections, 2 theorems, 23 equations, 16 figures, 7 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Generalized Additive Models for Bias Correction
  3. Nested Vine Copulas
  4. Vine Copulas
  5. Nested Vine Copulas
  6. Spatiotemporal Multivariate Bias Correction
  7. Modeling Step
  8. Alignment Step
  9. Adjustment Step
  10. Application
  11. Data
  12. Inter-variable Dependencies
  13. Spatial Consistency
  14. Temporal Consistency
  15. Discussion
  16. ...and 14 more sections

Key Result

Theorem A.1

If $E_j^{(b)}$ satisfies assumption:tree and assumption:proximity for every $j \geq 1$, then the merged sequence $\mathcal{V} = (\mathcal{T}_1, \dots, \mathcal{T}_{d_1+d_2-1})$ with node and edge sets is an R-vine tree sequence on $d_1 + d_2$ elements.

Figures (16)

  • Figure 1: Panel (a) highlights the canton of Vaud in Switzerland. Panel (b) shows the 22 grid points in the study, with the black cell serving as the bridging location in \ref{['sec:application']}.
  • Figure 2: Mean reference temperature per grid point for the calibration (1980--2009) and projection (2010--2022) periods (left), and corresponding model-reference differences (right).
  • Figure 3: A 3d vine.
  • Figure 4:
  • Figure 5:
  • ...and 11 more figures

Theorems & Definitions (3)

  • Definition 3.1: czado2019analyzing
  • Theorem A.1
  • Lemma A.1