Probabilistic Spatial Interpolation of Sparse Data Using Diffusion Models

Climate models today depend critically on confident initial conditions, a reasonably plausible snapshot of Earth from which all future predictions emerge. However, given the inherently chaotic nature of our system, this constraint is complicated by sensitivity dependence, where small uncertainties can lead to exponentially diverging outcomes over time. This challenge is particularly salient at global spatial scales and over centennial time scales, where data gaps are not just common but expected. The source of uncertainty is twofold: 1) sparse, noisy observations from satellites and ground stations; and 2) variability stemming from simplifying approximations within the models themselves. In practice, data assimilation methods are used to reconcile this missing information by conditioning model states on available observations. Our work builds on this idea but operates at the extreme end of sparsity. We propose a conditional data imputation framework that reconstructs full temperature fields from as little as 1% observational coverage. The method leverages a diffusion model guided by a prekriged mask, effectively inferring the full-state fields from minimal data points. We validate our framework over the southern Great Plains, focusing on afternoon–night (1200–0000 LT) temperature fields during the summer months of 2018–21. Across varying observational densities—from swath data to isolated in situ sensors—our model achieves strong reconstruction accuracy, highlighting its potential to fill in critical data gaps in both historical reanalysis and real-time forecasting pipelines.

Duke Scholars

Author Manolis Veveakis Civil and Environmental Engineering