Technical Note: Comparison of ensemble Kalman filter and variational approaches for CO₂ data assimilation

Unlike DA applications for weather prediction and constituent assimilation, however, the advantages and disadvantages of DA approaches for CO₂ flux estimation have not been extensively explored. In this study, we compare and assess estimates from two advanced DA approaches (an ensemble square root filter and a variational technique) using a batch inverse modeling setup as a benchmark, within the context of a simple one-dimensional advection-diffusion prototypical inverse problem that has been designed to capture the nuances of a real CO₂ flux estimation problem.

Experiments are designed to identify the impact of the observational density, heterogeneity, and uncertainty, as well as operational constraints (i.e., ensemble size, number of descent iterations) on the DA estimates relative to the estimates from a batch inverse modeling scheme. No dynamical model is explicitly specified for the DA approaches to keep the problem setup analogous to a typical real CO₂ flux estimation problem.