Toward reliable ensemble Kalman filter estimates of CO₂ fluxes

The use of ensemble filters for estimating sources and sinks of carbon dioxide (CO₂) is becoming increasingly common, because they provide a relatively computationally efficient framework for assimilating high-density observations of CO₂. Their applicability for estimating fluxes at high-resolutions and the equivalence of their estimates to those from more traditional "batch" inversion methods have not been demonstrated, however. In this study, we introduce a Geostatistical Ensemble Square Root Filter (GEnSRF) as a prototypical filter and examine its performance using a synthetic data study over North America at a high spatial (1° × 1°) and temporal (3-hourly) resolution. The ensemble performance, both in terms of estimates and associated uncertainties, is benchmarked against a batch inverse modeling setup in order to isolate and quantify the degradation in the estimates due to the numerical approximations and parameter choices in the ensemble filter. The examined case studies demonstrate that adopting state-of-the-art covariance inflation and localization schemes is a necessary but not sufficient condition for ensuring good filter performance, as defined by its ability to yield reliable flux estimates and uncertainties across a range of resolutions. Observational density is found to be another critical factor for stabilizing the ensemble performance, which is attributed to the lack of a dynamical model for evolving the ensemble between assimilation times. This and other results point to key differences between the applicability of ensemble approaches to carbon cycle science relative to its use in meteorological applications where these tools were originally developed.