Improving the joint estimation of CO2 and surface carbon fluxes using local ensemble transform Kalman filter together with constrained ensemble Kalman filter and relexed prior regularization

Estimating the global surface carbon fluxes (SCF) using ensemble Kalman filter (EnKF) has gained lots of success. Most of the studies treat carbon dioxide (CO2) as a by-product of assimilation. Kang et al. (2012), introduced a combined state and parameter method that persistently forecasts the SCF without the guidance of prior. Using a short assimilation window (AW) together with a long observation window (OW), the mean seasonal cycle and annual SCF pattern are efficiently estimated (Liu et al., 2019). But the mass conservation was failed since the state CO2 is updated together with SCF. To overcome this mass imbalance, we introduced a Constrained Ensemble Kalman Filter (CEnKF) that conserved the global total CO2 mass. It distributes the global mass imbalance to each grid by taking advantage of the analysis CO2 ensembles given by the Local Ensemble Transform Kalman Filter (LETKF). The observing system simulation experiments (OSSE) show that our system can accurately track regional annual SCF without given prior annual mean source and sink information. Comparing the results between LETKF only and LETKF with CEnKF experiments, the CEnKF not only improves the global total SCF estimation naturally but also improves the estimation of spatial and temporal SCF variation. To reduce the spatial and temporal high-frequency noise without being over-dependent on the prior, we added 20% of the combined smoothed and prior regularization term to the persistent model every 5 AW. The OSSE show that the regularization of every 5 AW excels the regularization of every 1 AW at the regional scale. At the data-sparse region, the regularization of every 1 AW leads the results overconfident on the prior and rejects the observation information. As transport errors are one of the largest error sources, instead of using a multi-model comparison approach, our method could potentially be used in the online general circulation model to jointly quantify the uncertainty of SCF and transport model with mass balance constrain.