A comparison of different inverse carbon flux estimation approaches for application on a regional domain

We have implemented six different inverse carbon flux estimation methods in a regional carbon dioxide (CO2) flux modeling system for the Netherlands. The system consists of the Regional Atmospheric Mesoscale Modeling System (RAMS) coupled to a simple carbon flux scheme which is run in a coupled fashion on relatively high resolution (10 km). Using an Ensemble Kalman filter approach we try to estimate spatiotemporal carbon exchange patterns from atmospheric CO2 mole fractions over the Netherlands for a two week period in spring 2008. The focus of this work is the different strategies that can be employed to turn first-guess fluxes into optimal ones, which is known as a fundamental design choice that can affect the outcome of an inversion significantly. Different state-of-the-art approaches with respect to the estimation of net ecosystem exchange (NEE) are compared quantitatively: (1) where NEE is scaled by one linear multiplication factor per land-use type, (2) where the same is done for photosynthesis (GPP) and respiration (R) separately with varying assumptions for the correlation structure, (3) where we solve for those same multiplication factors but now for each grid box, and (4) where we optimize physical parameters of the underlying biosphere model for each land-use type. The pattern to be retrieved in this pseudo-data experiment is different in nearly all aspects from the first-guess fluxes, including the structure of the underlying flux model, reflecting the difference between the modeled fluxes and the fluxes in the real world. This makes our study a stringent test of the performance of these methods, which are currently widely used in carbon cycle inverse studies. Our results show that all methods struggle to retrieve the spatiotemporal NEE distribution, and none of them succeeds in finding accurate domain averaged NEE with correct spatial and temporal behavior. The main cause is the difference between the structures of the first-guess and true CO2 flux models used. Most methods display overconfidence in their estimate as a result. A commonly used daytime-only sampling scheme in the transport model leads to compensating biases in separate GPP and R scaling factors that are readily visible in the nighttime mixing ratio predictions of these systems. Overall, we recommend that the estimate of NEE scaling factors should not be used in this regional setup, while estimating bias factors for GPP and R for every grid box works relatively well. The biosphere parameter inversion performs good compared to the other inversions at simultaneously producing space and time patterns of fluxes and CO2 mixing ratios, but non-linearity may significantly reduce the information content in the inversion if true parameter values are far from the prior estimate. Our results suggest that a carefully designed biosphere model parameter inversion or a pixel inversion of the respiration and GPP multiplication factors are from the tested inversions the most promising tools to optimize spatiotemporal patterns of NEE.