Ensemble Kalman Filtering Based on Potential Vorticity for Atmospheric Multi-scale Data Assimilation

Abstract

A multi-scale data assimilation method for the ensemble Kalman filter (EnKF) is proposed for atmospheric models in cases with insufficient observations of fast variables. This method is based on the conservation and invertibility of potential vorticity (PV). The dynamical state variables in the free atmosphere of forecast ensemble members are decomposed into balanced and unbalanced parts by applying PV inversion to the PV anomalies computed from spatially smoothed state variables. The mass variables of the two parts are adjusted to remove additional sampling errors introduced by the decomposition. The forecast error covariances between those parts are ignored in the Kalman gain to suppress spurious error correlations. This approximation makes it possible to apply different covariance localizations to each part. The Kalman gain thus obtained is used to assimilate observations. The performance of the proposed method is demonstrated with a shallow water model through twin experiments in a perfect model scenario. The results using the same localization radius for the two parts reveal that the proposed EnKF is superior in the accuracy of the analysis to a conventional EnKF unless the ensemble size is sufficiently large. It is found that the adjustment of mass variables is necessary to outperform the conventional EnKF. The benefits of the PV inversion using the Bolin-Charney balance over the quasi-geostrophic inversion are marginal in the experiments.

Machine Learning Enables Real‐Time Proactive Quality Control: A Proof‐Of‐Concept Study

“…By using these trained ML models, the proposed method could be implemented into the operational NWP systems that routinely diagnose observation impacts. Another interesting research direction is to use ML not only for PQC but also for other components in DA (e.g., Penny et al, 2022;Tsuyuki & Tamura, 2022;Yasuda & Onishi, 2023). Although we have used ML only for obtaining a reference state for PQC, it would be technically possible to replace ensemble and extended forecasts by a physics-based model with those by ML.…”

“…By using these trained ML models, the proposed method could be implemented into the operational NWP systems that routinely diagnose observation impacts. Another interesting research direction is to use ML not only for PQC but also for other components in DA (e.g., Penny et al., 2022; Tsuyuki & Tamura, 2022; Yasuda & Onishi, 2023).…”

Nonlinear Data Assimilation by Deep Learning Embedded in an Ensemble Kalman Filter

“…In Exp-IB, the two-scale Lorenz 96 model is used to assimilate observations of largescale variables. As noted by Tsuyuki (2019), when the ensemble size is relatively small, forecast correlations between large-and small-scale variables are not reliable. Hence, these forecast correlations are neglected in the EnKF, and the analysis ensemble of small-scale variables is left unchanged from the forecast ensemble at each analysis time.…”