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

Abstract

Abstract. 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 ∼ 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 Niño impact is well captured with anomalies mainly in the tropics.

Assimilating the dynamic spatial gradient of a bottom-up carbon flux estimation as a unique observation in COLA (v2.0)

“…Another unique feature of COLA is that it applies a constrained ensemble Kalman filter (CEnKF) to retain the global mass conservation of the system (Liu et al, 2022). The standard LETKF step updates the model state based on statistical information, which could lead to model dynamic imbalance and loss of mass (Pan and Wood, 2006;Zeng et al, 2017;Janjić and Zeng, 2021).…”

“…Following Kang et al (2012), we apply an additive inflation method to the SCFs to overcome this problem. This inflation method adds to each ensemble member with an anomalous SCF field chosen randomly from the bottom-up estimation of CASA within 30 days centered at the analysis time (Kang et al, 2012;Liu et al, 2019Liu et al, , 2022.…”

“…This system accurately estimated SCF at model grid resolution for the first time without directly applying a priori information by assimilating meteorology observations and CO2 concentration observations simultaneously with a short assimilation window in observing system simulation experiments (OSSEs). Following this track, we developed the Carbon in Ocean-Land-Atmosphere (COLA) system (Liu et al, 2019;Liu et al, 2022), which maintains the LETKF with a short assimilation window and long observation window setting but replaces the general circulation model with an atmospheric transport model, GEOS-Chem (Nassar et al, 2013). The COLA system also applies a constrained ensemble Kalman filter (CEnKF) technique to retain global mass conservation (Liu et al, 2022).…”

“…Following this track, we developed the Carbon in Ocean-Land-Atmosphere (COLA) system (Liu et al, 2019;Liu et al, 2022), which maintains the LETKF with a short assimilation window and long observation window setting but replaces the general circulation model with an atmospheric transport model, GEOS-Chem (Nassar et al, 2013). The COLA system also applies a constrained ensemble Kalman filter (CEnKF) technique to retain global mass conservation (Liu et al, 2022). As a result, COLA can provide good estimates of SCFs at model grid resolution along with atmospheric CO2 concentration analyses.…”

“…The purpose of this paper is to introduce the development of the COLA (v2.0) system with a novel a priori regularization for SCF estimation, where a priori information is treated as a unique observation to be assimilated. This new approach is inspired by the CEnKF applied in COLA (Liu et al, 2022). With the comprehensive assimilation regularization, we are able to apply the spatial gradient of bottom-up SCF estimations as a priori information to improve SCF estimation.…”