Studies On ERDVar And Its Application With A Global Spectral Model T106

ERDVar (Ensemble-based reduced dimension Variational assimilation method) , a new and promising data assimilation method, which was initially proposed by Qiu and Chou, has continuously developed and completed. The method tries to seek a solution in the attractor of model atmosphere to reduce the under-determination of the data assimilation. In this method, the SVD was used to extract the leading singular vectors from an ensemble of 4D perturbation fields produced by the model and the analysis is obtained by projecting actual observation data into a space spanned by the base vectors, as getting the best expanding coefficients through minimizing a cost function. As 4DVar does, the ERDVar is able to assimilate the observations at multi-time levels in an analysis cycle but avoid the heavy labor on coding the tangent and adjoint model in 4DVAR. As conventional EnKF does, the ERDVar estimates the forecast error covariance matrix from the forecast ensemble but it is belong to a variational assimilation method. The method is especially more suitable than conventional EnKF for assimilating various remote sense data by considering additional physical restricts in the cost function. Besides, the ERDVar requests to produce the forecast ensemble by integrating model from a set of initial disturbed fields in every analysis cycle, which is different from EnKF. The "flow- dependent" characteristic of the background error covariance estimated by such ensemble is intermediate between EnKF and 3DVar, which maybe is a problem but also can be a advantage for the weak dependent on model overcoming the systematic errors as the model with it. Based on the previous studies on ERDVar method, we find that there are still at least two questions must be solved before its application for real operation: the first one is the technique of producing initial perturbation, which is the common headache for ensemble based method, the other one is making a balance between improving the analysis accuracy of the assimilation and the computational efficiency by reducing the frequency of perturbation updating. In this dissertation we make a research on the above problems first. Then we put ERDVar into an application with the global spectral model T106, absorbing the simulative radiosonde data and satellite data. Until recently it is unusual in assimilating satellite data in global models with ensemble method. We develop a regional assimilation method of ERDVar to resolve the localization of background error covariance in global assimilation.The first part in this dissertation is about the perturbation research: (1) A series of experiments on ERDVar were performed with a shallow water model with three different perturbation methods (A. Monte Carlo method, B. Monte Carlo method improved by Shao, C. Evensen perturbation method). Perturbations produced by A and C are statistically uniform and isotropic with a gauss probability distribution function, while perturbation produced by B just appear approximately to that. The result of assimilation analysis shows the C method as the best one. (2) Then we make assimilation analysis using perturbation C with different de-correlation length. It is shown that the analysis accuracy is sensitive to de-correlation length when the observation types is incomplete (only height and wind), which is opposite with the complete observation types. It is benefit for assimilation by choosing proper de-correlation length of perturbation which is similar to that of forecast errors; (3) A conclusion based on the model forecast errors time-series shows that the forecast error covariance changes as location or the initial de-correlation length varies, the variance of h (or u, v) is similar to gauss function distribution (or the correlation structure derived from the geostrophic relationship). And the correlation of different variables fit the correlation structure derived from the geostrophic relationship. But the correlation structure of the perturbation forecast samples is quite different from that of forecast time series, and greatly varies with respect to different location and different initial perturbation. (4) We discover that from experiments the bad assimilation analysis comes with too small de-correlation length of the initial perturbation compared with that of the real forecast errors, also without an easily developing perturbation. The probable reason is the filter effect of the model on the high-frequency noise.Secondly, we make a research on the possibility of reducing the updating frequency of perturbation. (1) In every assimilation cycle of ERDVar, forecast perturbation sample need to be produced from integrating model. Usually an ensemble with too small size cause a bad analysis, maybe because the unreliable forecast error covariance or the truncation errors when the observation innovations are expand on the base vectors with too small size. We verify the truncation error as the leading reason through the experiments. (2) We verify that the error covariance based on forecast ensemble in ERDVar, changing slowly as time varies, shows less 'flow-dependent' than that of conventional EnKF methods, which makes it possible to reduce the updating frequency of perturbation. (3) Based on the research above, we propose several methods to improve the computational efficiency. The main idea is using forecast ensemble with large size as possible as we can, but reducing the updating frequency, or using fixed ensemble mixed with dynamic ensemble. The results of these experiments are effective on both reducing computational cost greatly and improving the analysis accuracy, which is very meaningful to apply ERDVar to real operation. Thirdly, a frame of ERDVar global assimilation with T106, the global medium-range numerical weather prediction spectral model, is set up and applied to absorb radiosonde data and satellite data. We also make a research on ensemble perturbation methods, here for Fourier random perturbation and NMC perturbation in global assimilation. The first leading singular vector of the Fourier random perturbation forecast ensemble can cover the 99% cumulative variance contribution; but is terribly filtered especially for high-order perturbation. While the NMC ensemble perturbation forecast is quite consisitent with the model dynamics, and there is no filter attenuation by the model in forecast process. Then we perform ERDVar Observing System Simulation Experiments (OSSE) with these perturbation methods, to make clear the impact of ensemble size, truncated order, observation interval, observation error on the assimilation analysis. Then in order to realize the covariance localization in ERDVar global assimilation, we develop a regional ERDVar method, and the preliminary study of OSSE with radiosonde data shows its advantage over full-area ERDVar. Then we design the OSSE with satellite data and radiosonde data, the result shows that assimilation of both the two types of data is better than that of satellite data alone.