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An ensemble Kalman filter-variational hybrid data assimilation system based on the gridpoint statistical interpolation (GSI) three-dimensional variational data assimilation (3DVar) system was developed. The performance of the system was investigated using the National Centers for Environmental Prediction (NCEP) Global Forecast System model. Experiments covered a 6-week Northern Hemisphere winter period. Both the control and ensemble forecasts were run at the same, reduced resolution. Operational conventional and satellite observations along with an 80-member ensemble were used. Various configurations of the system including oneor two-way couplings, with zero or nonzero weights on the static covariance, were intercompared and compared with the GSI 3DVar system. It was found that the hybrid system produced more skillful forecasts than the GSI 3DVar system. The inclusion of a static component in the background-error covariance and recentering the analysis ensemble around the variational analysis did not improve the forecast skill beyond the one-way coupled system with zero weights on the static covariance. The one-way coupled system with zero static covariances produced more skillful wind forecasts averaged over the globe than the EnKF at the 1-5-day lead times and more skillful temperature forecasts than the EnKF at the 5-day lead time. Sensitivity tests indicated that the difference may be due to the use of the tangent linear normal mode constraint in the variational system. For the first outer loop, the hybrid system showed a slightly slower (faster) convergence rate at early (later) iterations than the GSI 3DVar system. For the second outer loop, the hybrid system showed a faster convergence.

New methods to center the initial ensemble perturbations on the analysis are introduced and compared with the commonly used centering method of positive-negative paired perturbations. In the new method, one linearly dependent perturbation is added to a set of linearly independent initial perturbations to ensure that the sum of the new initial perturbations equals zero; the covariance calculated from the new initial perturbations is equal to the analysis error covariance estimated by the independent initial perturbations, and all of the new initial perturbations are equally likely. The new method is illustrated by applying it to the ensemble transform Kalman filter (ETKF) ensemble forecast scheme, and the resulting ensemble is called the spherical simplex ETKF ensemble. It is shown from a multidimensional Taylor expansion that the symmetric positive-negative paired centering would yield a more accurate forecast ensemble mean and covariance than the spherical simplex centering if the ensemble were large enough to span all initial uncertain directions and thus the analysis error covariance was modeled precisely. However, when the number of uncertain directions is larger than the ensemble size, the spherical simplex centering has the advantage of allowing almost twice as many uncertain directions to be spanned as the symmetric positive-negative paired centering. The performances of the spherical simplex ETKF and symmetric positive-negative paired ETKF ensembles are compared by using the Community Climate Model Version 3 (CCM3). Each ensemble contains 1 control forecast and 16 perturbed forecasts. The NCEP-NCAR reanalysis data for the boreal summer in 2000 are used for the initialization of the control forecast and the verifications of the ensemble forecasts. The accuracy of the ensemble means, the accuracy of predictions of forecast error variance, and the ability of the ETKF ensembles to resolve inhomogeneities in the observation distribution were all tested. In all of these test categories, the spherical simplex ETKF ensemble was found to be superior to the symmetric positive-negative paired ETKF ensemble. The computational expense for generating spherical simplex ETKF initial perturbations is about as small as that for the symmetric positive-negative paired ETKF. Also shown is that the seemingly straightforward centering method, in which centered perturbations are obtained by subtracting the average of the perturbations from each individual perturbation, is unsatisfactory because the covariance estimated by the uncentered perturbations is not necessarily conserved after centering.

The PECAN field campaign assembled a rich array of observations from lower-tropospheric profiling systems, mobile radars and mesonets, and aircraft over the Great Plains during June-July 2015 to better understand nocturnal mesoscale convective systems and their relationship with the stable boundary layer, the low-level jet, and atmospheric bores.

A hybrid ensemble transform Kalman filter-three-dimensional variational data assimilation (ETKF-3DVAR) system for the Weather Research and Forecasting (WRF) Model is introduced. The system is based on the existing WRF 3DVAR. Unlike WRF 3DVAR, which utilizes a simple, static covariance model to estimate the forecast-error statistics, the hybrid system combines ensemble covariances with the static covariances to estimate the complex, flow-dependent forecast-error statistics. Ensemble covariances are incorporated by using the extended control variable method during the variational minimization. The ensemble perturbations are maintained by the computationally efficient ETKF. As an initial attempt to test and understand the newly developed system, both an observing system simulation experiment under the perfect model assumption (Part I) and the real observation experiment (Part II) were conducted. In these pilot studies, the WRF was run over the North America domain at a coarse grid spacing (200 km) to emphasize synoptic scales, owing to limited computational resources and the large number of experiments conducted. In Part I, simulated radiosonde wind and temperature observations were assimilated. The results demonstrated that the hybrid data assimilation method provided more accurate analyses than the 3DVAR. The horizontal distributions of the errors demonstrated the hybrid analyses had larger improvements over datasparse regions than over data-dense regions. It was also found that the ETKF ensemble spread in general agreed with the root-mean-square background forecast error for both the first-and second-order measures. Given the coarse resolution, relatively sparse observation network, and perfect model assumption adopted in this part of the study, caution is warranted when extrapolating the results to operational applications.