Climate Downscaling with Stochastic Interpolants (CDSI)

Global climate projections rely on computationally demanding Earth System Models (ESMs), which are typically limited to coarse spatial resolutions due to their high cost. To obtain high-resolution projections for regions of interest, it is common to use Regional Climate Models (RCMs), which are driven by data produced by ESMs as boundary conditions. While more efficient than running ESMs at fine resolution, RCMs remain expensive and restrict the size of ensemble simulations. Inspired by recent advances in probabilistic machine learning for weather and climate, we introduce a data-driven climate downscaling method based on stochastic interpolants. Our approach efficiently transforms coarse ESM output into high-resolution regional climate projections at a fraction of the computational cost of traditional RCMs. Through extensive validation, we demonstrate that our method generates accurate regional ensembles, enabling both improved uncertainty quantification and broader use of high-resolution climate information.

💡 Research Summary

The paper introduces Climate Downscaling with Stochastic Interpolants (CDSI), a data‑driven framework that transforms coarse‑resolution Earth System Model (ESM) outputs into high‑resolution regional climate fields at a fraction of the computational cost of traditional Regional Climate Models (RCMs). The authors begin by motivating the need for fine‑scale climate information for impact assessments, noting that existing ESMs operate at ~100 km resolution, which cannot resolve mesoscale processes crucial for extremes. While RCMs (e.g., HCLIM) can provide physically consistent 12 km fields, they are prohibitively expensive for large ensembles or long‑term projections.

CDSI builds on the stochastic interpolants concept (Albergo et al., 2023; Chen et al., 2024). Given paired low‑resolution (x₀) and high‑resolution (x₁) samples, a continuous interpolant xₜ = α(t)x₀ + β(t)x₁ + σ(t)Wₜ is defined with α(t)=1‑t, β(t)=t², σ(t)=1‑t. The goal is to learn the drift b(t, xₜ, x₀) that governs the stochastic differential equation (SDE) dXₜ = b(t, Xₜ, x₀)dt + σ(t)dWₜ, such that the marginal distribution of Xₜ matches the conditional distribution of the interpolant. The drift is approximated by a neural network ˆb(t, Xₜ, x₀, C), where C contains static and dynamic conditioning fields (latitude/longitude, land‑sea mask, orography, etc.). Training minimizes the L₂ loss between the network output and the analytically derived drift Rₜ.

The network architecture is a UNet with 128 top‑level channels, expanded to 256 in deeper layers. Time t is encoded via Fourier embeddings (128 frequencies, base period 16) passed through a two‑layer SiLU‑activated MLP, yielding a 512‑dimensional vector injected via conditional layer‑norm and group‑norm. Because the low‑resolution ESM input must share the high‑resolution grid, it is first upsampled with bilinear interpolation; this upsampled field serves as x₀.

Sampling proceeds by numerically solving the learned SDE from t=0 to t=1 using an Euler‑Maruyama or second‑order ODE solver with 20 steps (39 function evaluations). Each ensemble member draws an independent Brownian motion, producing diverse high‑resolution realizations that capture unresolved variability.

Experiments focus on the EUR‑CORDEX domain. The reference high‑resolution dataset is HCLIM‑ALADIN at 12 km, while low‑resolution inputs are CMIP6 ESM fields at ~100 km. The authors evaluate CDSI against state‑of‑the‑art diffusion‑based baselines (EDM, CorrDiff) using metrics such as mean absolute error, spatial correlation, and extreme‑value statistics (e.g., 95th‑percentile precipitation). Results show that CDSI matches or outperforms diffusion models across all metrics while requiring roughly one‑tenth of the compute time. Importantly, CDSI generalizes to unseen future scenarios (RCP8.5) and to ESMs not seen during training, indicating robustness to distribution shift.

The paper highlights three key advantages: (1) Direct conditioning on physically meaningful low‑resolution states keeps the generative trajectory close to the data manifold, simplifying learning and improving realism; (2) The multivariate conditioning preserves cross‑variable physical relationships, a critical requirement that distinguishes climate downscaling from generic image super‑resolution; (3) Computational efficiency enables the generation of large ensembles for uncertainty quantification, something infeasible with conventional RCMs.

In conclusion, CDSI offers a principled, efficient, and physically aware approach to climate downscaling, opening the door to widespread use of high‑resolution climate information in impact studies, policy making, and risk assessment. Future work will explore global‑scale deployment, incorporation of additional prognostic variables (soil moisture, atmospheric chemistry), and application to extreme event modeling.