Handout (11.1 MB)

The National Center for Atmospheric Research (NCAR) Mesoscale and Microscale Meteorology Division Data Assimilation Group (MMM/DA) has been collaborating with the United States Air Force Weather Agency (AFWA) and the National Oceanic and Atmospheric Administration (NOAA) National Center for Environment Prediction (NCEP) to develop a regional hybrid version of NCEP's Gridpoint Statistical Interpolation (GSI) data assimilation system. NCEP in collaboration with the University of Oklahoma developed a GSI global hybrid assimilation system. MMM/DA modified that global system for regional application using the Advanced Research Weather Research and Forecast modeling system (WRF ARW). This paper presents results from that work and application of a localized ensemble transform Kalman filter (LETKF) and a quality control strategy for observations entering the ETKF.

II. OVERVIEW OF THE GSI REGIONAL HYBRID SYSTEM

The GSI Regional Hybrid follows the scheme proposed by Hamill and Snyder (2000) as implemented by Wang et al. (2008). In summary, given an initial analysis, a perturbation generation strategy such as perturbed observations, singular vectors, or an ETKF is used to generate an ensemble of initial analyses. That ensemble is used to generate an ensemble of initial forecasts, which are used to begin the assimilation cycling experiment. Cycling proceeds as follows: (i) compute the ensemble mean and variance for the ensemble of forecasts, (ii) apply the GSI Regional Hybrid to update the ensemble mean analyses, (iii) use a modified version of the ETKF described by Wang et al., (2007) to update the ensemble perturbations, (iv) combine the updated mean and perturbations to obtain an ensemble of updated analyses/initial conditions, (v) update the boundary conditions, (vi) generate an ensemble of forecasts to begin the next cycle, and (vii) repeat steps (i) through (vii) for the duration of the cycling experiment.

The quality of forecasts produced by such a cycling experiment depends on factors that include the characteristics of the GSI Regional Hybrid and the ETKF perturbation generation strategy. The characteristics of the GSI Regional Hybrid are discussed in a separate paper: Mizzi, A. P., Z. Liu, and X. Y. Huang, 2011: Cycling experiment results for a GSI regional hybrid ETKF data assimilation scheme for the WRF model. In this paper, we study the ETKF perturbation generation strategy.

III. ETKF OBSERVATION QUALITY CONTROL

The ETKF proposed by Bishop et al., (2001) solves the computational limitations of an ensemble Kalman Filter by transforming the ensemble perturbations into orthonormal vectors and attaching variance to each of the direction vectors to enable one to use the ensemble to describe the error covariance within the vector subspace of the ensemble perturbations. See Bishop et al. (2001). Generally, when applying the ensemble Kalman Filter, the number of observations greatly exceeds the number of ensemble members. Consequently, the number of ensemble perturbations is much smaller than the number of directions onto which the forecast error variance projects. Wang and Bishop (2003). To address that problem, the ETKF generally requires an inflation factor. Id. Following Wang and Bishop (2003), the inflation factor is defined as the norm of the innovation vector divided by the observation error covariance minus the number of observations divided by the sum of the eigenvalues of the domain ensemble covariance matrix. Experience shows that the inflation factor and ETKF results are sensitivity to the accuracy of the data used to calculate the normalized norm of the innovation vector. In this section, we present the results of filtering the observations/innovations entering the ETKF.

IV. LOCALIZED ETKF

We also study an LETKF which is similar to that proposed by Hunt, et al., (2007). For any particular model grid point (Localization Center}, we calculate the domain ensemble covariance matrix by first applying a localization function centered on the Localization Center to the observation operator prior to calculation of the domain ensemble covariance. The resulting transform vectors, i.e., the eigenvectors of the domain ensemble covariance matrix are localized for the Localization Center. The updated perturbations are obtained by applying the localized transform vectors to the rows of state matrix associated with the Localization Center. That procedure is applied to each grid point in the state matrix. In this section, we present resutls from a comparison of the LETKF with the Wang et al., (2007) ETKF and a modified version of the Wang et al., (2007) ETKF.

V. REFERENCES

Bishop C. H., B. J. Etherton, and S. J. Majumdar, 2001: Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon. Wea. Rev., 129, 420-436.

Hamill, T. M., and C. Snyder, 2000: A hybrid ensemble Kalman filter-3D variational analysis scheme. Mon. Wea. Rev., 128, 2905-2919.

Hunt, B. R., E. J. Kostelich, and I Szunyogh, 2007: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Physica D, 230, 112-126.

Wang, X. and C. H. Bishop, 2003: A comparison of breeding and ensemble transform Kalman filter ensemble forecast schemes. J. Atmos. Sci., 60, 1140-1158.

Wang, X., T. M. Hamill J. S. Whitaker, and C. H. Bishop, 2007: A comparison of hybrid ensemble transform Kalman filter-OI and ensemble square-root filter analysis schemes. Mon. Wea. Rev., 135, 1055-1076.

Wang, X., D. M. Barker, C. Snyder, and T. M. Hamill, 2008: A hybrid ETKF-3DVAR data assimilation scheme for the WRF model. Part I: Observing system simulation experiment. Mon. Wea. Rev., 136, 5116-5131.