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

A. Chatterjee and A. M. Michalak


Data assimilation (DA) approaches, which use a combination of numerical approximations and time-stepping schemes, are gaining in popularity for estimating CO2 fluxes. This study compares two state-of-the-art DA approaches (a variational and an ensemble filter approach), and finds that the variational approach is slightly more robust for obtaining CO2 flux estimates while the ensemble filter approach provides more reliable estimates of analysis error. The performance of the two DA approaches is highly sensitive to the complex interplay between the underlying numerical approximations and the observational characteristics (i.e., observational density, heterogeneity, and uncertainty), which has potential implications with the emerging focus on assimilation of denser but more inaccurate satellite CO2 observations.

Figure: Performance of the BIM, the EnSRF, and the 4D-VAR appoaches for the different experiments. For each experiment, statistics are calculated between the estimates and the true fluxes across all locations and all 30 time periods and are represented on a Taylor diagram. For each Taylor diagram, the true flux is represented by a point along the abscissa corresponding to the stanfard deviation of the true fluexes ("Truth"). All other points ("BIM", "EnSRF", "4D-VAR"), which represent the estimated fluxes, are positioned such thta their standard deviation is the radial distance from the origin, the correlation coefficient between the estimates and the truth is the cosine of the azimuthal angle, and the root-mean-square difference (RMSD) between the estimates and the truth is the distance to the observed point. In the limit of perfect agreement, these other points would coincide with "Truth" (i.e., RMSD=0, CC=1, and SD of the estimates would be the same as that of the truth).


Data assimilation (DA) approaches, including variational and the ensemble Kalman filter methods, provide a computationally efficient framework for solving the CO2 source–sink estimation problem. 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. Results demonstrate that the performance of the DA approaches depends on a complex interplay between the measurement network and the operational constraints. Overall, the variational approach (contingent on the availability of an adjoint transport model) more reliably captures the large-scale source–sink patterns. Conversely, the ensemble square root filter provides more realistic uncertainty estimates. Selection of one approach over the other must therefore be guided by the carbon science questions being asked and the operational constraints under which the approaches are being applied.

Chatterjee, A., A.M. Michalak (2013), “Technical Note: Comparison of ensemble Kalman filter and variational approaches for CO2 data assimilation”, Atmospheric Chemistry and Physics, 13, 11643-11660, doi:10.5194/acp-13-11643-2013.