MUNDO: Temporal Downscaling by Recursive Conditional Sampling

Numerical models of the atmosphere advance in steps of minutes and are archived hours or days apart, so the sub-daily record exists while the model runs and is discarded at storage. Temporal downscaling recovers it, and splits into two subproblems: interpolation between stored states, and disaggregation of an aggregate such as a daily mean. Each is the ill-posed inversion of its own linear observation operator. We present MUNDO (Multiresolution UNified DOwnscaling), which samples the conditional law of the fine record given the coarse observation. The coarsening is factored into a ladder of small steps, each level generating only the degrees of freedom its own step removed, so the observation is reproduced exactly by construction rather than through penalties or projections. Levels are fitted with a strictly proper scoring rule and a variogram term correcting the fine-scale increment statistics the score alone does not constrain. On ERA5 over Europe, disaggregating daily means into hourly fields and interpolating between the daily states a twenty-four-hour forecast leaves behind, MUNDO matches or exceeds every method compared on accuracy and calibration, while producing realistic hourly variability, within and across windows.