Variational Downscaling, Fusion and Assimilation of Hydrometeorological States via Regularized Estimation

TL;DR

This paper presents a unified regularized inverse problem framework for hydrometeorological state estimation, improving accuracy and stability in downscaling, data fusion, and assimilation tasks by incorporating prior knowledge and probabilistic structures.

Contribution

It introduces a novel framework that integrates regularization into hydrometeorological state estimation problems, extending classic methods with derivative space regularization techniques.

Findings

Regularization improves state estimation accuracy.

Tikhonov and Huber regularization enhance stability.

Framework effective in synthetic and numerical experiments.

Abstract

Improved estimation of hydrometeorological states from down-sampled observations and background model forecasts in a noisy environment, has been a subject of growing research in the past decades. Here, we introduce a unified framework that ties together the problems of downscaling, data fusion and data assimilation as ill-posed inverse problems. This framework seeks solutions beyond the classic least squares estimation paradigms by imposing proper regularization, which are constraints consistent with the degree of smoothness and probabilistic structure of the underlying state. We review relevant regularization methods in derivative space and extend classic formulations of the aforementioned problems with particular emphasis on hydrologic and atmospheric applications. Informed by the statistical characteristics of the state variable of interest, the central results of the paper suggest that proper regularization can lead to a more accurate and stable recovery of the true state and hence more skillful forecasts. In particular, using the Tikhonov and Huber regularization in the derivative space, the promise of the proposed framework is demonstrated in static downscaling and fusion of synthetic multi-sensor precipitation data, while a data assimilation numerical experiment is presented using the heat equation in a variational setting.