Atmospheric Radar Research Center (ARRC)

The EnKF method appears to be more attractive for convective scale applications due to high degrees of nonlinearity in both model physics and observation operators at such scales.
An EnKF system has been developed by our group for the assimilation of Doppler radar data as well as other sources of data (Tong and Xue, 2005; Xue et al., 2005a). In Xue et al. (2005a), an Observing System Simulation Experiment (OSSE) framework based on a more effective ensemble square-root Kalman filter (EnSRF) algorithm (Whitaker and Hamill, 2002) is used to study the effectiveness and impact of data from future CASA radar networks.

In this proposed project, the EnKF-based OSSE framework of Xue et al. (2005a) for radar data will be extended

1. to use much more realistic yet efficient forward observation operators that will be derived from the full-scale PAR emulator
2. to handle PAR data collected in various non-conventional manner including those used in the SPY-1/TEP
3. to assimilate cross-beam winds potentially available through Spaced Antenna method
4. to effectively account for model errors

The availability of an accurate and realistic radar emulator will allow us to evaluate the impact of various simplifications (needed for efficient) in the observation operator on the quality of analysis and the subsequent forecast. The varying PAR scanning strategies will require much greater flexibility in the filter code design. Concerted efforts will also be made to parallelize the filter code for distributed memory processors because of the potentially large volume of radar data to assimilate.

Our experience has shown that the model error is one of the most important issues in EnKF when assimilating real data. We use data sampled from “truth” runs of much higher resolutions than the data assimilation and prediction are performed at means that the model will be imperfect, as is the case with real data. The planned use of a different model for “truth” simulations will also introduce effective model errors. This practice will avoid the identical twin problem.

When model errors are present, the ensemble spread will underestimate the error of the background. Ineffective handling of the model error can lead to filter divergence, to the point that new observations no longer have any effect. Several methods can be used individually or in combination, to account for the model error. The background covariance inflation is a common approach for dealing with model error as well as the error underestimation problem owing to the typically small ensemble size. Several variations with covariance inflation also exist. Adding estimated model errors to the analysis background or to the analyses themselves can also be performed, but the errors should contain proper spatial and/or temporary correlations representative of the true model errors. Errors sampled from the conventional 3DVAR background error covariance have been used for large-scale EnKF analysis with certain degree of success (e.g., Houtekamer et al., 2005).

In our recent real data study, adding spatially correlated errors to the ensemble analyses appears to be more effective. This is partly because for radar data assimilation, cross covariance information is very important for retrieving unobserved variables. Additional approaches include adding to the model prediction equations stochastic terms that simulates the model errors. For this approach, a good error model is often hard to obtain, however. Otherwise, it should work the best. Within this project, we will experiment with various methods for accounting for model error. Within the OSSE framework, this problem will be simplified and the solutions found should be helpful when dealing with real data.