Ensemble Transform Kalman Filtering Method For Preliminary Applications In Ensemble Forecasting And Adaptive Observations

Recently strategies were developed that use forecast-system information to identifylocations where additional observations would provide maximal improvements in the expectedskill of forecast. We refer to these as adaptive observation, or targeted observation, commonlycalled targeting. Targeting identifies localized areas, referred to as sensitive region, in whichthe quality of the analysis has the greatest expected influence on the subsequent skill of theforecast. Now the adaptive observation becomes a sub-program of THORPEX. The EnsembleTransform Kalman filter is initially proposed as an adaptive observation method, than it is usedinto the ensemble forecast. The ETKF is a sub-optimal Kalman filter scheme. Like otherKalman filter, it provides a framework for assimilating observations and also for estimating theeffect of observations on the forecast error covariance. It differs from other ensemble Kalmanfilter in that it uses ensemble transformation and a normalization to rapidly obtain theprediction error covariance matrix associated with a particular deployment of observationresources. This rapidity enables it to quickly assess the ability of a large number of futurefeasible sequences of observational networks to reduce forecast error variance. All the resultsindicate that the ETKF could be put into operational environment. It can be used into theadaptive observation, and also can be used as an ensemble forecast method. Now the domesticscientists do not pay much attention to the ETKF method.So it is necessary to implement themethod on this field.This paper is based on the ETKF theory established by Bishop and Wang Xu guang et al.The characteristics of ETKF are studied in this paper by virtue of the model GRAPES. Themajor results and conclusions are summarized as follows:(1) In a system with fixed and perfect linear dynamics and fixed observation distributionand error statistics, provided that the initial ensemble perturbation span the vector subspace ofthe linear dynamics operator, the ETKF ensemble would eventually maintain error variance inall amplifying normal modes. And the experiment results indicate that the spectrum of theETKF eigenvalues is flat in the experiment setup.(2) When the number of ensemble perturbations is much smaller than the number ofdirections to which the forecast error variance projects, the ETKF ensembles wouldunderestimate total analysis error variance because it lacks contribution from important parts ofthe error space. To avoid this problem, we introduce the inflation factor. In the paper I use twomethods to calculate the inflation factor. One is the method introduced by Wang and Bishop(2003), and the other one is similar to the simple Breeding method. The results indicate that theWB method enlarges the ensembles at the beginning, and then it resizes them. The ensemblesin the simple Breeding method grow up slowly. But in the end the two methods nearly get thesame size.(3) The inflation factor's size depends on the ensemble number. The results show that theinflation factor will decrease to the half of the original one if you increased the ensemblenumber from 15 to 30. It indicates that as the ensemble number increases the inflation factorwill have less effect on ensembles.(4) The ETKF method can quickly assess the ability of a large number of future feasiblesequences of observational networks to reduce forecast error variance. In this paper the ETKFand the Deep layer mean wind variance (DLM) method is compared. Results indicate that thesignal variance calculated by the ETKF method is reasonable.