Abstract
Abstract. Both ensemble filtering and variational data assimilation methods have proven useful in the joint estimation of state variables and parameters of geophysical models. Yet, their respective benefits and drawbacks in this task are distinct. An ensemble variational method, known as the iterative ensemble Kalman smoother (IEnKS) has recently been introduced. It is based on an adjoint model-free variational, but flow-dependent, scheme. As such, the IEnKS is a candidate tool for joint state and parameter estimation that may inherit the benefits from both the ensemble filtering and variational approaches. In this study, an augmented state IEnKS is tested on its estimation of the forcing parameter of the Lorenz-95 model. Since joint state and parameter estimation is especially useful in applications where the forcings are uncertain but nevertheless determining, typically in atmospheric chemistry, the augmented state IEnKS is tested on a new low-order model that takes its meteorological part from the Lorenz-95 model, and its chemical part from the advection diffusion of a tracer. In these experiments, the IEnKS is compared to the ensemble Kalman filter, the ensemble Kalman smoother, and a 4D-Var, which are considered the methods of choice to solve these joint estimation problems. In this low-order model context, the IEnKS is shown to significantly outperform the other methods regardless of the length of the data assimilation window, and for present time analysis as well as retrospective analysis. Besides which, the performance of the IEnKS is even more striking on parameter estimation; getting close to the same performance with 4D-Var is likely to require both a long data assimilation window and a complex modeling of the background statistics.
Highlights
Data assimilation in geophysics is often concerned with the estimation of the state of the system
Because the iterative ensemble Kalman smoother (IEnKS) offers the advantages of both filtering and variational methods, and because it is capable of operating on long data assimilation window (DAW), it has considerable potential as an efficient parameter estimation method
As opposed to the ensemble Kalman filters (EnKFs) and ensemble Kalman smoother (EnKS), the objective of the joint state and parameter IEnKS is not to build covariances to help estimate hidden parameters, but instead to minimize a cost function that depends on the full augmented state
Summary
Data assimilation in geophysics is often concerned with the estimation of the state of the system (e.g. atmosphere, ocean). Non-observed parameters of the model can be seen as control variables. They can indirectly be estimated through the assimilation of observations. In such context, data assimilation can be a powerful inverse modeling tool. Parameter estimation is useful because it can account for model error through a parametric representation of the uncertain processes, and could serve as a tool to enhance the system state estimation. It is accepted that air quality forecasting can benefit considerably from the online estimation of forcing parameters. Again regarding air quality, data assimilation can help assess effective kinetic rates of interest to chemists, or it can help assess regulated pollutant emissions of interest to policy makers
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