Matrix-Free Covariance-Response Approach for Data Assimilation-Ready Weather Ensembles

We propose a lightweight, matrix-free covariance-response evaluation to assess data assimilation (DA) readiness before expensive complete cycling. Given ensemble perturbations and a localized observation-like probe, we compute covariance actions without forming dense covariance matrices. On NOAA/NCEP Global Ensemble Forecast System (GEFS) 500 hPa geopotential height (HGT500) data, a query-conditioned, analog-style historical response improves localized agreement with the query-time covariance response while preserving matrix-free scalability.