Can ensemble‐based parameter estimation aid parameterization design?

• Published in: Quarterly journal of the Royal Meteorological Society
• Main Authors: Serafin, Stefano, Weissmann, Martin
• Format: Journal Article
• Language: English
• Published: 26.06.2025
• ISSN: 0035-9009; 1477-870X
• DOI: 10.1002/qj.5031

Ensemble‐based data assimilation algorithms can be exploited to estimate uncertain parameters in parameterization schemes by means of state augmentation. Parameters are appended to the model state vector and, just like state variables, they are optimized objectively on the basis of flow‐dependent ensemble covariances with observable quantities. Ensemble‐based parameter estimation (PE) is a well‐established methodology and has been used recently to account for model errors in the assimilation process. In this study, we discuss if and how it can be a useful tool for parameterization design. With simple experiments tailored to turbulence modelling, we demonstrate that quickly converged and physically interpretable empirical parameters can be obtained only under restrictive conditions. The error variance of the assimilated observations needs to be as low as that of the state perturbations induced by the parameter to be estimated, and parametric uncertainty must be the dominant contributor to the uncertainty of the assimilation ensemble. Based on these results, we outline a possible strategy for offline PE targeted at parameterization development. The strategy relies on ensemble‐based PE experiments that ingest synthetic observations from high‐resolution nature runs, in which the parameterized process is fully resolved; it is thus potentially well suited to refine the design of, for example, boundary‐layer turbulence, convection, or orographic drag parameterizations. We also demonstrate that optimally converged parameters can, to some extent, compensate for structural errors in parameterizations, and suggest exploiting this property to extend the flexibility of parameterization schemes. This can be achieved by replacing fixed parameters with adaptive parameters, drawn from lookup tables compiled from parameter estimation results.