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Data assimilation (DA) approaches, including variational and the ensembleKalman filter methods, provide a computationally efficient framework forsolving the CO2 source–sink estimation problem. Unlike DA applications forweather prediction and constituent assimilation, however, the advantages anddisadvantages of DA approaches for CO2 flux estimation have not beenextensively explored. In this study, we compare and assess estimates from twoadvanced DA approaches (an ensemble square root filter and a variationaltechnique) using a batch inverse modeling setup as a benchmark, within thecontext of a simple one-dimensional advection–diffusion prototypical inverseproblem that has been designed to capture the nuances of a real CO2 fluxestimation problem. Experiments are designed to identify the impact of theobservational density, heterogeneity, and uncertainty, as well as operationalconstraints (i.e., ensemble size, number of descent iterations) on the DAestimates relative to the estimates from a batch inverse modeling scheme. Nodynamical model is explicitly specified for the DA approaches to keep theproblem setup analogous to a typical real CO2 flux estimation problem.Results demonstrate that the performance of the DA approaches depends on acomplex interplay between the measurement network and the operationalconstraints. Overall, the variational approach (contingent on theavailability of an adjoint transport model) more reliably captures thelarge-scale source–sink patterns. Conversely, the ensemble square root filterprovides more realistic uncertainty estimates. Selection of one approach overthe other must therefore be guided by the carbon science questions beingasked and the operational constraints under which the approaches are beingapplied

Technical Note: Comparison of ensemble Kalman filter and variational approaches for CO&lt;sub&gt;2&lt;/sub&gt; data assimilation

Technical Note: Comparison of ensemble Kalman filter and variational approaches for CO<sub>2</sub> data assimilation