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. We previously performed local ensemble transform Kalman filter (LETKF)experiments with up to 10 240 ensemble members using an intermediateatmospheric general circulation model (AGCM). While the previous studyfocused on the impact of localization on the analysis accuracy, the presentstudy focuses on the probability density functions (PDFs) represented by the10 240-member ensemble. The 10 240-member ensemble can resolve the detailedstructures of the PDFs and indicates that non-Gaussianity is caused in thosePDFs by multimodality and outliers. The results show that the spatialpatterns of the analysis errors are similar to those of non-Gaussianity.While the outliers appear randomly, large multimodality corresponds wellwith large analysis error, mainly in the tropical regions and storm trackregions where highly nonlinear processes appear frequently. Therefore, wefurther investigate the life cycle of multimodal PDFs, and show that theyare mainly generated by the on–off switch of convectiveparameterization in the tropical regions and by the instability associatedwith advection in the storm track regions. Sensitivity to the ensemble sizesuggests that approximately 1000 ensemble members are necessary in theintermediate AGCM-LETKF system to represent the detailed structures ofnon-Gaussian PDFs such as skewness and kurtosis; the higher-ordernon-Gaussian statistics are more vulnerable to the sampling errors due to asmaller ensemble size.

nonlinear processes in geophysics

Non-Gaussian statistics in global atmospheric dynamics: a study with a 10 240-member ensemble Kalman filter using an intermediate atmospheric general circulation model