Improving the joint estimation of CO2 and surface carbon fluxes using a constrained ensemble Kalman filter in COLA (v1.0)

Atmospheric inversion of carbon dioxide (CO2) measurements to better understand carbon sources and sinks has made great progress over the last 2 decades. However, most of the studies, including a four-dimensional variational ensemble Kalman filter and Bayesian synthesis approaches, directly obtain only fluxes, while CO2 concentration is derived with the forward model as part of a post-analysis. Kang et al. (2012) used the local ensemble transform Kalman filter (LETKF), which updates the CO2, surface carbon flux (SCF), and meteorology fields simultaneously. Following this track, a system with a short assimilation window and a long observation window was developed (Liu et al., 2019). However, this data assimilation system faces the challenge of maintaining carbon mass conservation. To overcome this shortcoming, here we apply a constrained ensemble Kalman filter (CEnKF) approach to ensure the conservation of global CO2 mass. After a standard LETKF procedure, an additional assimilation is used to adjust CO2 at each model grid point and to ensure the consistency between the analysis and the first guess of the global CO2 mass. Compared to an observing system simulation experiment without mass conservation, the CEnKF significantly reduces the annual global SCF bias from similar to 0.2 to less than 0.06 Gt and slightly improves the seasonal and annual performance over tropical and southern extratropical regions. We show that this system can accurately track the spatial distribution of annual mean SCF. And the system reduces the seasonal flux root mean square error from a priori to analysis by 48 %-90 %, depending on the continental region. Moreover, the 2015-2016 El Nino impact is well captured with anomalies mainly in the tropics.