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

Abstract. Atmospheric inversion of high spatiotemporal surface CO₂ flux without dynamic constraints and sufficient observations is an ill-posed problem, and a priori flux from a "bottom-up" estimation is commonly used in "top-down" inversion systems for regularization purposes. Ensemble Kalman filter-based inversion algorithms usually weigh a priori flux to the background or directly replace the background with the a priori flux. However, the "bottom-up" flux estimations, especially the simulated terrestrial-atmosphere CO₂ exchange, are usually systematically biased at different spatiotemporal scales because of the deficiencies in understanding of some underlying processes. Here, we introduced a novel regularization algorithm into the Carbon in Ocean‒Land‒Atmosphere (COLA) data assimilation system, which assimilates a priori information as a unique observation (AAPO). The a priori information is not limited to "bottom-up" flux estimation. With the comprehensive assimilation regularization approach, COLA can apply the spatial gradient of the "bottom-up" flux estimation as a priori information to reduce the bias impact and enhance the dynamic information concerning the a priori "bottom-up" flux estimation. Benefiting from the enhanced signal-to-noise ratio in the spatial gradient, the global, regional, and grided flux estimations using the AAPO algorithm are significantly better than those obtained by the traditional regularization approach, especially over highly uncertain tropical regions in the context of observing simulation system experiments (OSSEs). We suggest that the AAPO algorithm can be applied to other greenhouse gas (e.g., CH₄, NO₂) and pollutant data assimilation studies.