A toy DA system that uses a (forced) 1D linear diffusion/advection model to compare the following ensemble DA schemes:
- Ensemble Kalman Filter: EnKF
- Ensemble Optimal Interpolation: EnOI
- Ensemble Smoother: ES
- Ensemble Kalman Smoother: EnKS
The update scheme considers the observations all at once (i.e., batch style) and uses the transformation matrix (X5; Evensen, 2003). I also provided an EnKS function that assimilates the observations serially and uses DART's style (2-step update, Anderson, 2003).
This a mere educational package. The coding style (in MATLAB) is not top-notch. The intent is to familiarize the user with different ensemble schemes, their implementation and performance.
To start, you can run DA_EnKF_EnOI_ES_EnKS.m to compare the different schemes in an OSSE framework. You can choose the model (advection or diffusion)) ensemble size and the smoother lag
DA_EnKF_EnOI_ES_EnKS.m calls the separate functions: EnKF.m, EnOI.m, ES.m and EnKS.m To simulate a realistic scenario, 2 model parameters are perturbed. Thus, the forecast model is different than the one used to generate the truth.
To study the effect of the length of the lag, you can run compare_enkf_enks_lags.m and see a comparison between the EnKF and EnKS. You will get results similar to those in the figures below.
The script run_models_offline.m shows the evolution of the truth in time.
