Data-Efficient Generative Modeling of Non-Gaussian Global Climate Fields via Scalable Composite Transformations

Quantifying uncertainty in climate-model output requires characterizing internal variability, often through large ensembles of physical climate-model runs. Since each additional ensemble member is computationally expensive, only limited numbers of replicated fields are typically available under a fixed model configuration and forcing scenario. We propose a data-efficient stochastic generator for the internal variability of global climate fields, specifically designed to overcome these sample-size constraints. The framework targets the distribution of climate-model output under fixed forcing and model physics. Inspired by copula modeling, our approach constructs a highly expressive joint distribution via a composite transformation to a multivariate standard normal space. We combine a nonparametric Bayesian transport map for spatial dependence modeling with flexible, spatially varying marginal models, essential for capturing non-Gaussian behavior and heavy-tailed extremes. These marginals are defined by a parametric model followed by a semi-parametric B-spline correction to capture complex distributional features. The marginal parameters are spatially smoothed using Gaussian-process priors with low-rank approximations, rendering the computational cost linear in the spatial dimension. When applied to global log-precipitation-rate fields under fixed forcing at more than 50,000 grid locations, our stochastic surrogate achieves high fidelity, accurately quantifying the climate distribution's spatial dependence and marginal characteristics, including the tails. Using only 10 training fields, it outperforms a state-of-the-art competitor trained on 80 fields, effectively octupling the computational budget for climate research. We provide a Python implementation at https://github.com/jobrachem/ppptm .