Estimation of CH₄ emission based on advanced 4D-LETKF assimilation system

Abstract. Methane (CH₄) is the second major greenhouse gas after carbon dioxide (CO₂) which is substantially increased during last decades in the atmosphere, raising serious sustainability and climate change issues. Here, we develop a data assimilation system for in situ and column averaged concentrations using Local ensemble transform Kalman filter (LETKF) to estimate surface emissions of CH₄. The data assimilation performance is tested and optimized based on idealized settings using Observation System Simulation Experiments (OSSEs) where a known surface emission distribution (the truth) is retrieved from synthetic observations. We tested three covariance inflation methods to avoid covariance underestimation in the emission estimates, namely; fixed multiplicative (FM), relaxation to prior spread (RTPS) and adaptive multiplicative. First, we assimilate the synthetic observations at every grid point at the surface level. In such a case of dense observational network, the normalized Root Mean Square Error (RMSE) in the analyses over global land regions are smaller by 10–15 % in case of RTPS covariance inflation method compared to FM. We have shown that integrated estimated flux seasonal cycles over 15 regions using RTPS inflation are in reasonable agreement between true and estimated flux with 0.04 global absolute normalized annual mean bias. We have then assimilated the column averaged CH₄ concentration by sampling the model simulations at GOSAT observation locations and time for another OSSE experiment. Similar to the case of dense observational network, RTPS covariance inflation method performs better than FM for GOSAT synthetic observation in terms of normalized RMSE (2–3 %) and integrated flux estimation comparison with the true flux. The annual mean averaged normalized RMSE (normalized absolute mean bias) in LETKF CH₄ flux estimation in case of RTPS and FM covariance inflation is found to be 0.59 (0.18) and 0.61 (0.23) respectively. The chi-square test performed for GOSAT synthetic observations assimilation suggests high underestimation of background error covariance in both RTPS and FM covariance inflation methods, however, the underestimation is much high (>100 % always) for FM compared to RTPS covariance inflation method.