Study On The Ensemble-based Variational Data Assimilation And Its Parallel Implementation

The atmosphere system is a nonlinear and chaos system which evolves over timeand its numerical prediction model is sensitive to the initial condition, therefore, ahigh-quality initial condition is needed for an accurate prediction. Recently, how toobtain a good-enough initial state is a bottleneck problem in Numerical WeatherPrediction (NWP), thus, the data assimilation (DA) technique which supplies the initialcondition for NWP becomes a key tool.DA is an important component of NWP, since it provides the initial values for theforecast system as accurately as possible. The idea of DA is to combine the informationfrom past observations (as encapsulated in a short term model forecasts) along withcurrent observations in an optimal way. Since the1950-1960s, data assimilation hasexperienced several stages, such as the method of successive corrections, the optimalinterpolation, three-dimensional variational data assimilation (3D-Var), etc. Nowadays,four-dimensional variational data assimilation (4D-Var) and ensemble filtering havebeen already implemented in some operational NWP centers.There are two major methods for current data assimilation techniques, such asvariational data assimilation and ensemble filtering. One of the merits of the variationaldata assimilation is that additional constraints can be introduced easily, while theensemble filtering has the advantages of dynamically generating the background errorcovariance and naturally obtaining the uncertainty of the analysis. Thus, combiningthese two methods is an important research direction of data assimilation at present andin the future.In this paper, hybrid data assimilation methods are explored and studied, accordingto their respective advantages and disadvantages. The main work in this paper is shownas follows.In the first part, an improved particle filter DA method is proposed. Particle filter isone kind of the ensemble filtering methods. Without assumptions of Gaussiandistribution and linearity, particle filtering can approximate the features of the realweather system better than other filtering methods. It is significant to study particlefiltering methods for the next generation of data assimilation techniques. Consideringthe situation that observations are obtained after several model integrations, this methoddivided the data assimilation process into two stages, data assimilation atnon-observation times and data assimilation at observation times. By introducing―pseudo‖observations at non-observation times and resampling in advance atobservation times, this method can solve the initial value problem of nonlinear systemswell. After being applied to a low-dimension system and a high-dimension system, theresults demonstrates that the system state can be well traced by using only a few particles, and the range for the model error and the observation error where the methodis credible is wider than the standard particle filter and the standard Kalman filter.For the respective merits of the3D-Var and the particle filtering, a hybridthree-dimensional variational particle filtering was presented. By solving a minimumcost function iteratively, this method can obtain a good posterior distribution. Theparticle ensemble is divided into several sub-ensembles, and an expected analysis andits weight are computed for each sub-ensemble. Afterwards, the global analysis and itserror covariance are obtained by using a weighted average. A deterministic resamplingstrategy was proposed, which can void the problem of lack of diversity resulting fromstochastically resampling. Simulation results show that the new hybrid method performsbetter than the standard ensemble Kalman filtering and the standard particle filtering,especially applied to highly nonlinear systems.Another important ensemble filtering method is the so-called ensemble Kalmanfiltering (EnKF), which attracts much attention in recent years. The3D-Var seeks theanalysis of the control variables in an iterative way, and can introduce extra nonlinearconstraints expediently. Ensemble Kalman filtering can supply a flow-dependentforecast error covariance for the3D-Var; therefore, combining the3D-Var and theEnKF is one of the significant research directions. This paper compared a fewensemble-based3D-Var methods, and proved that they are all theoretically equivalent tothe ensemble transform Kalman filtering (ETKF). Furthermore, a new method calledensemble physical space analysis system (EnPSAS) was proposed, where the Hessianmatrix of the cost function has a small condition number and the space localization canbe introduced easily.There is a common disadvantage among the ensemble filters that limited ensemblesize will introduce extra sampling errors. However, through applying spatial localizationor introducing an inflation factor, the spurious correlations in the error covarianceproduced from samples can be reduced. Therefore, a new hybrid4D-Var and EnKFmethod was presented, which applied the spatial localization directly into the forecastensemble anomalies, not the full forecast error covariance. In this way, the generatingspace of the analysis increment is expanded; meanwhile, the severe degeneration of theensemble-based forecast error covariance matrix can be avoided. Moreover, adeterministic strategy was designed, which can obtain a better posterior distribution thanthe stochastic perturbation way.The previous hybrid method (called4DETLKF) was applied to the Lorenz96system, and its performance was investigated in comparison of the standard EnKF. Thesensitivity to different parameters was investigated, such as ensemble size, inflationfactor, correlation length scale, observation error variance, observation time interval,and observation number, etc. The experimental results demonstrate that, this newmethod is robust, and performs significantly better than the standard EnKF, especially with a relatively small ensemble size, a large correlation length scale or a smallobservation number.The3DETLKF, the reduced version of the4DETLKF, is applied to the ShallowWater model, its parallel characteristics are studied and the associated parallel algorithmis presented. Since the3DETLKF is ensemble-based, it can be parallelized easier thanthe primal variational methods. Each ensemble member can correspond to an individualcomputing node, and a good load balancing can be achieved through dividing theextended ensemble perturbation matrix into a number of sub-matrices and dealing withthem on the individual computing nodes. The most work is focused on theparallelization of the forecast ensemble perturbation matrix, the observation ensembleperturbation matrix, the analysis ensemble perturbation matrix and the minimization ofthe cost function. By applying the parallelized3DETLKF method to a parallel computerwith48independent CPUs, the result shows that a high parallel speedup ratio and agood parallel efficiency can be achieved.