Steering Diffusion Priors with Sparse Observations for 1-km, 1-hour Temperature Reconstruction

Local heatwave hazard depends on fine-scale air temperature, but ground stations are sparse and reanalysis products such as ERA5 cannot resolve terrain and land- surface contrasts. We adapt score-based data assimilation (SDA) to a conditional diffusion emulator for 2-m temperature reconstruction at approximately 1-km spatial and 1-hour temporal resolution: a differentiable Gaussian observation likelihood steers the diffusion score toward revealed temperature observations without retraining. On a 32-case synthetic-grid validation over AORC, SDA improves hidden-cell reconstruction over both ERA5 and a strong nearest-neighbor baseline at 1% observation density, approximately 655 revealed cells per 256×256 patch, or roughly one per 64 km2—reducing RMSE from 0.431 to 0.318 K and winning all 32 cases. At sparser densities (0.01% and 0.1%), direct interpolation remains superior, delineating the method’s current operating regime. The present evidence is a controlled synthetic-grid validation; station-network and held-out-year evaluations are the next steps toward deployment.