The coarse spatial resolution of gridded climate models, such as general circulation models, limits their direct use in projecting socially relevant variables like extreme precipitation. Most downscaling methods estimate the conditional distributions of extremes by generating large ensembles, complicating the assessment of robustness under distributional transformations, such as those induced by climate change. To better understand and potentially improve robustness, we propose super-resolving the parameters of the target variable's probability distribution directly using analytically tractable mappings. Within a perfect-model framework over Switzerland, we demonstrate that vector generalized linear and additive models can super-resolve the generalized extreme value distribution of summer hourly precipitation extremes from coarse precipitation fields and topography. We introduce the notion of a "robustness gap", defined as the difference in predictive error between present-trained and future-trained models, and use it to diagnose how model structure affects the generalization of each quantile to a pseudo-global warming scenario. By evaluating multiple model configurations, we also identify an upper limit on the super-resolution factor based on the spatial auto- and cross-correlation of precipitation and elevation, beyond which coarse precipitation loses predictive value. Our framework is broadly applicable to variables governed by parametric distributions and offers a model-agnostic diagnostic for understanding when and why empirical downscaling generalizes to climate change and extremes.

翻译：网格化气候模型（如大气环流模型）的空间分辨率较低，这限制了其直接用于预测极端降水等具有社会相关性的变量。大多数降尺度方法通过生成大量集合来估计极端值的条件分布，这使得在分布变换（如气候变化引起的变换）下评估鲁棒性变得复杂。为了更好地理解并可能提高鲁棒性，我们提出直接使用解析可处理的映射来超分辨率目标变量概率分布的参数。在瑞士的完美模型框架内，我们证明了向量广义线性模型和可加模型可以从粗分辨率降水场和地形数据中，对夏季小时极端降水的广义极值分布进行超分辨率。我们引入了“鲁棒性差距”的概念，其定义为当前气候训练模型与未来气候训练模型之间预测误差的差异，并利用它来诊断模型结构如何影响各分位数在伪全球变暖情景下的泛化能力。通过评估多种模型配置，我们还基于降水与高程的空间自相关和互相关性，确定了超分辨率因子的上限，超过该上限后粗分辨率降水将失去预测价值。我们的框架广泛适用于由参数化分布控制的变量，并提供了一种模型无关的诊断方法，用于理解经验降尺度何时以及为何能泛化至气候变化和极端事件。