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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.

A hybrid ensemble transform Kalman filter (ETKF)-optimum interpolation (OI) analysis scheme is described and compared with an ensemble square root filter (EnSRF) analysis scheme. A two-layer primitive equation model was used under perfect-model assumptions. A simplified observation network was used, and the OI method utilized a static background error covariance constructed from a large inventory of historical forecast errors. The hybrid scheme updated the ensemble mean using a hybridized ensemble and static background-error covariance. The ensemble perturbations in the hybrid scheme were updated by the ETKF scheme. The EnSRF ran parallel data assimilation cycles for each member and serially assimilated the observations. The EnSRF background-error covariance was estimated fully from the ensemble.For 50-member ensembles, the analyses from the hybrid scheme were as accurate or nearly as accurate as those from the EnSRF, depending on the norm. For 20-member ensembles, the analyses from the hybrid scheme were more accurate than analyses from the EnSRF under certain norms. Both hybrid and EnSRF analyses were more accurate than the analyses from the OI. Further reducing the ensemble size to five members, the EnSRF exhibited filter divergence, whereas the analyses from the hybrid scheme were still better than those updated by the OI. Additionally, the hybrid scheme was less prone to spurious gravity wave activity than the EnSRF, especially when the ensemble size was small. Maximal growth in the ETKF ensemble perturbation space exceeded that in the EnSRF ensemble perturbation space. The relationship of the ETKF ensemble variance to the analysis error variance, a measure of a spread-skill relationship, was similar to that of the EnSRF ensemble. The hybrid scheme can be implemented in a reasonably straightforward manner in the operational variational frameworks, and the computational cost of the hybrid is expected to be much less than the EnSRF in the operational settings.

A GSI-based EnVar data assimilation system is extended to directly assimilate radar reflectivity to initialize convective-scale forecasts. When hydrometeor mixing ratios are used as state variables (method mixing ratio), large differences of the cost function gradients with respect to the small hydrometeor mixing ratios and wind prevent efficient convergence. Using logarithmic mixing ratios as state variables (method logarithm) fixes this problem, but generates spuriously large hydrometeor increments partly due to the transform to and from the logarithmic space. The tangent linear of the reflectivity operators further contributes to spuriously small and large hydrometeor increments in method mixing ratio and method logarithm, respectively. A new method is proposed by directly adding the reflectivity as a state variable (method dBZ). Without the tangent linear and adjoint of the nonlinear operator, the new method therefore avoids the aforementioned problems. The newly proposed method is examined on the analysis and prediction of the 8 May 2003 Oklahoma City tornadic supercell storm. Both the probabilistic forecast of strong low-level vorticity and maintenance of strong updraft and vorticity in method dBZ are more consistent with reality than in method logarithm and method mixing ratio. Detailed diagnostics suggest that a more realistic cold pool due to the better analyzed hydrometeors in method dBZ than in other methods leads to constructive interaction between the surface gust front and the updraft aloft associated with the midlevel mesocyclone. Similar low-level vorticity forecast and maintenance of the storm are produced by the WSM6 and Thompson microphysics schemes in method dBZ. The Thompson scheme matches the reflectivity distribution with the observations better for all lead times, but shows more southeastward track bias compared to the WSM6 scheme.

Neural machine translation (NMT) aims at solving machine translation (MT) problems using neural networks and has exhibited promising results in recent years. However, most of the existing NMT models are shallow and there is still a performance gap between a single NMT model and the best conventional MT system. In this work, we introduce a new type of linear connections, named fastforward connections, based on deep Long Short-Term Memory (LSTM) networks, and an interleaved bi-directional architecture for stacking the LSTM layers. Fast-forward connections play an essential role in propagating the gradients and building a deep topology of depth 16. On the WMT'14 Englishto-French task, we achieve BLEU=37.7 with a single attention model, which outperforms the corresponding single shallow model by 6.2 BLEU points. This is the first time that a single NMT model achieves state-of-the-art performance and outperforms the best conventional model by 0.7 BLEU points. We can still achieve BLEU=36.3 even without using an attention mechanism. After special handling of unknown words and model ensembling, we obtain the best score reported to date on this task with BLEU=40.4. Our models are also validated on the more difficult WMT'14 English-to-German task.