Quantifying uncertainty in future climate projections is hindered by the prohibitive computational cost of running physical climate models, which severely limits the availability of training data. We propose a data-efficient framework for emulating the internal variability of global climate fields, specifically designed to overcome these sample-size constraints. 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 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 samples, it outperforms a state-of-the-art competitor trained on 80 samples, effectively octupling the computational budget for climate research. We provide a Python implementation at https://github.com/jobrachem/ppptm .

翻译：量化未来气候预测的不确定性受到物理气候模型计算成本过高的阻碍，这严重限制了训练数据的可用性。我们提出了一种数据高效框架，用于模拟全球气候场的内部变异性，专门设计以克服这些样本量限制。受连接函数建模的启发，我们的方法通过复合变换构建高度表达性的联合分布，将其映射到多元标准正态空间。我们将用于空间依赖性建模的非参数贝叶斯传输映射与灵活的、空间变化的边缘模型相结合，这对于捕捉非高斯行为和重尾极值至关重要。这些边缘模型由参数化模型定义，后接半参数B样条校正以捕捉复杂的分布特征。边缘参数通过采用低秩近似的高斯过程先验进行空间平滑处理，使计算成本在空间维度上呈线性增长。当应用于超过50,000个网格位置的全球对数降水率场时，我们的随机代理模型实现了高保真度，准确量化了气候分布的空间依赖性和边缘特征（包括尾部特性）。仅使用10个训练样本，其性能就超越了基于80个样本训练的最先进对比模型，相当于将气候研究的计算预算有效提升了八倍。我们在https://github.com/jobrachem/ppptm 提供了Python实现。