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A hybrid 3DVAR-EnKF data assimilation algorithm is developed based on 3DVAR and ensemble Kalman filter (EnKF) programs within the Advanced Regional Prediction System (ARPS). The hybrid algorithm uses the extended alpha control variable approach to combine the static and ensemble-derived flow-dependent forecast error covariances. The hybrid variational analysis is performed using an equal weighting of static and flow-dependent error covariance as derived from ensemble forecasts. The method is first applied to the assimilation of simulated radar data for a supercell storm. Results obtained using 3DVAR (with static covariance entirely), hybrid 3DVAR-EnKF, and the EnKF are compared. When data from a single radar are used, the EnKF method provides the best results for the model dynamic variables, while the hybrid method provides the best results for hydrometeor related variables in term of rms errors. Although storm structures can be established reasonably well using 3DVAR, the rms errors are generally worse than seen from the other two methods. With two radars, the results from 3DVAR are closer to those from EnKF. Our tests indicate that the hybrid scheme can reduce the storm spin-up time because it fits the observations, especially the reflectivity observations, better than the EnKF and the 3DVAR at the beginning of the assimilation cycles.

The effective assimilation of radar data into a numerical weather prediction (NWP) model requires advanced data assimilation (DA) techniques, such as variational and ensemble Kalman filter methods. A three-dimensional variational (3DVAR) system, which includes a mass continuity equation and other appropriate model equations as weak constraints, has been developed in recent years [

Compared to 3DVAR, the more advanced 4DVAR technique incorporates the full prediction model into the assimilation system and implicitly includes the effects of flow-dependent error covariances through the use of both the forward and backward models. In recent years, the 4DVAR technique has helped improve global forecasts at several operational NWP centers, including the European Centre for Medium-Range Weather Forecasts, Meteo-France, Meteorological Service of Canada, and Japan Meteorological Agency (JMA) [

The ensemble Kalman filter (EnKF) is an advanced data assimilation method that shares many of the advantages of 4DVAR. It has gained considerable popularity in recent years in meteorology and oceanography since first proposed by Evensen [

As discussed above, the 3DVAR method is attractive for convective scale assimilation because of its computational efficiency and the ease by which weak constraints can be added. However, the major shortcoming is that the background error covariances are stationary and isotropic and error covariances related to the model equations cannot be simply defined. In addition, for convective-scale radar data assimilation, only observations of radial velocity and reflectivity are typically measured, while all other state variables have to be “retrieved”; in this case, the flow-dependent background error covariances, such as that derived from a forecast ensemble, are especially important. One way to blend the advanced features of both variational and EnKF methods and to overcome their respective shortcomings is to employ a hybrid ensemble 3DVAR framework. In such a framework, a combination of the static background error covariance and the flow-dependent error covariance derived from an ensemble is used within the variational analysis. For large-scale data assimilation, such an approach was initially demonstrated for a quasigeostrophic system by Hamill and Snyder [

Wang et al. [

The rest of this paper is organized as follows. In Section

In the implementation of the hybrid method for convective scale, the ensemble covariance is incorporated in the variational framework using the extended control variable method [

In (

In the current study, the hybrid system will assimilate both radar reflectivity and radial velocity data. Within this system, flow-dependent background-error covariances, in particular cross covariances between microphysical and dynamic variables, will be derived and utilized. The single-resolution version of the EnKF system of Gao and Xue [

Different from other hybrid systems [

Illustration of cycle used in a hybrid EnKF-3DVAR analysis scheme.

We test our hybrid EnKF-3DVAR algorithm and compare its results with those of 3DVAR and EnKF schemes, using simulated data from a classic supercell storm of May 20, 1977, near Del City, Oklahoma [

For our experiments, the model domain is 57 × 57 × 16 km^{3}. The horizontal grid spacing is 1 km, and the mean vertical grid spacing is 500 m. The truth simulation run is initialized from a modified real sounding plus a 4 K ellipsoidal thermal bubble centered at ^{−1} and ^{−1} is subtracted from the observed sounding to keep the primary storm cell near the center of model grid. The evolution of the simulated storms is similar to those documented in Xue et al. [^{−1} at 90 min. The initial cloud starts to form at about 10 min, and rainwater forms at about 15 min. Ice phase fields appear at about 20 min. A similar truth simulation was also used in Gao et al. [

The simulated radial velocity observations are assumed to be available on the grid points. The simulated radial velocity, ^{−1} are added to the simulated data. Since

We start the initial ensemble forecast at 20 min of the model integration time when the storm cell is well developed. To initialize the ensemble members, random noise is first added to the initially horizontally homogeneous first guess defined using the environmental sounding. A 2D five-point smoother is applied to the resultant fields, similar to a method used by Zupanski et al. [^{−1} for

We perform two set of experiments. The first group of experiments is performed to compare the performance of three different schemes when observations from a single Doppler radar are used. The second group of experiments will be performed when observations from two Doppler radars are used. For comparison purposes, all three methods (3DVAR, EnKF, and Hybrid EnKF-3DVAR) are performed with 16 data assimilation cycles where each cycle has a 5 min analysis-prediction interval. The total assimilation period is 75 min.

Figure

Wind vectors:

As stated above, the first group of experiments is performed with radial velocity and reflectivity data from a single radar. Figure

Horizontal winds (vectors; ms^{−1}), perturbation potential temperature (contours at 1-K intervals), and simulated reflectivity (shaded contours; dBZ) at 250 m AGL for (a) the truth simulation; (b) the 3DVAR analysis; (c) the EnKF analysis; and (d) the hybrid EnKF-3DVAR analysis for the single radar experiment. The time shown is at 100 min (the end of data assimilation cycles). Wind vectors are shown every 2 km.

The rms errors of the analyzed fields with data from a single radar are shown in Figure ^{−1} at 100 min for 3DVAR method, while that in EnKF and hybrid EnKF-3DVAR is close to 1.3 ms^{−1}. The rms errors of

The rms errors of the analysis and forecast for the 3DVAR, (red) EnKF, (green) hybrid EnKF-3DVAR, (blue) methods averaged over points at which the reflectivity is greater than 10 dBZ for (a)

The second group of experiments is performed with radar data from two simulated Doppler radars. Figure

The same as Figure

The same as Figure

A hybrid EnKF-3DVAR data assimilation system has been developed based on existing 3DVAR and ensemble Kalman filter (EnKF) programs within the ARPS model. The algorithm uses the extended control variable approach to combine the static and ensemble-derived flow-dependent forecast error covariances [

The method is applied to the assimilation of radar data from a simulated supercell storm. Two groups of experiments are performed using different amounts of radar data. Results obtained using 3DVAR (with static covariances entirely), hybrid EnKF-3DVAR, and EnKF are compared. When data from a single radar are used, results show that after 16 cycles of data assimilation, the EnKF and hybrid schemes provide similar results. When evaluated in term of rms errors, the EnKF provides slightly better results for the model dynamic variables, while the hybrid provides slightly better results for the hydrometeor related variables. Though the storm structures can be established reasonably well using 3DVAR, its rms errors are generally worse than those from the other two methods. When data from two radars are used, the rms errors for the hybrid method are smallest for most of the model variables. With two radars, the results from 3DVAR are close to those from EnKF. These tests also indicate that the hybrid scheme can reduce the storm spin-up time because it fits the observations, especially the reflectivity observations, better than the EnKF and the 3DVAR at the beginning of the assimilation cycles. Thus, precipitation exists from the beginning of the model integration.

Our future studies will try to answer a number of key questions within the hybrid EnKF-3DVAR framework just described. They include the following. (1) What is the optimal choice for the relative weight of the static and flow-dependent covariances for storm scale radar data assimilation? (2) What is the optimal combination of ensemble size and grid spacing for a specific computational cost? (3) How does the overall performance of the proposed method compare with 3DVAR and EnKF methods when model error is present? More sensitivity experiments will be performed to answer these questions in the near future, and results will likely help us to solve the challenges of applying this method to real-world scenarios. Even if these questions are successfully answered, the high computational cost of this method is still likely to be a big hurdle. For this, we will apply the dual-resolution strategy as developed for the EnKF scheme in Gao and Xue [

This research was funded by the NOAA Warn-on-Forecast project. The first two authors were partially supported by NSF Grants EEC-0313747, ATM-0738370, ATM-0331594, and AGS-0802888.