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Robert E. Kistler and David F. Parrish

Abstract

The evolution of the NMC global data assimilation system in the period 1978–81 is presented. The improvements include revisions to the analysis programs and the replacement of the initialization and the prediction model. Data are analyzed over a finer analysis grid, are scrutinized by a more thorough “buddy cheek,” and are subject to a multivariate wind relationship. The impact of the changes upon the wind analysis is examined with respect to the case of 1200 GMT, 21 October 1979. The system changes concurrent with the addition of the spectral prediction model are noted. Experimental evidence demonstrates the superiority of the spectral system with respect to the gridpoint system previously in use.

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Stephen E. Cohn and David F. Parrish

Abstract

A Kalman filter algorithm is implemented for a linearized shallow-water model over the continental United States. It is used to assimilate simulated data from the existing radiosonde network, from the demonstration network of 31 Doppler wind profilers in the central United States, and from hypothetical radiometers located at five of the profiler sites. We provide some theoretical justification of Phillips' hypothesis, and we use the hypothesis, with some modification, to formulate the model error covariance matrix required by the Kalman filter.

Our results show that assimilating the profiler wind data leads to a large reduction of forecast/analysis error in heights as well as in winds, over the profiler region and also downstream, when compared with the results of assimilating the radiosonde data alone. The forecast error covariance matrices that the Kalman filter calculates to obtain this error reduction, however, differ considerably from those prescribed by the optimal interpolation schemes that are employed for data assimilation at operational centers. Height-height forecast error correlation functions spread out broadly over the profiler region. Height-wind correlation functions for a base point near the boundary of the profiler region are not antisymmetric with respect to the line of zero correlation, nor does the zero-line pass through the base point.

We explain why these effects on forecast error correlations are to be expected for wind profilers, which provide abundant wind information but no height information. Our explanation is supported by further experiments in which height observations assimilated from radiometers at just a few profiler sites reduce these effects.

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David F. Parrish and John C. Derber

Abstract

At the National Meteorological Center (NMC), a new analysis system is being extensively tested for possible use in the operational global data assimilation system. This analysis system is called the spectral statistical- interpolation (SSI) analysis system because the spectral coefficients used in the NMC spectral model are analyzed directly using the same basic equations as statistical (optimal) interpolation. Results from several months of parallel testing with the NMC spectral model have been very encouraging. Favorable features include smoother analysis increments, greatly reduced changes from initialization, and significant improvement of 1-5-day forecasts. Although the analysis is formulated as a variational problem, the objective function being minimized is formally the same one that forms the basis of all existing optimal interpolation schemes. This objective function is a combination of forecast and observation deviations from the desired analysis, weighted by the invent of the corresponding forecast- and observation-error covariance matrices. There are two principal differences in how the SSI implements the minimization of this functional as compared to the current OI used at NMC. First, the analysis variables are spectral coefficients instead of gridpoint values. Second, all observations are used at once to solve a single global problem. No local approximations are made, and there is no special data selection. Because of these differences, it is straightforward to include unconventional data, such as radiances, in the analysis. Currently temperature, wind, surface pressure, mixing, ratio, and Special Sensor Microwave/lmager (SSM/I) total precipitable water can be used as the observation variables. Soon to be added are the scatterometer surface winds. This paper provides a detailed description of the SSI and presents a few results.

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Haixia Liu, Ming Xue, R. James Purser, and David F. Parrish

Abstract

Anisotropic recursive filters are implemented within a three-dimensional variational data assimilation (3DVAR) framework to efficiently model the effect of flow-dependent background error covariance. The background error covariance is based on an estimated error field and on the idea of Riishøjgaard. In the anisotropic case, the background error pattern can be stretched or flattened in directions oblique to the alignment of the grid coordinates and is constructed by applying, at each point, six recursive filters along six directions corresponding, in general, to a special configuration of oblique lines of the grid. The recursive filters are much more efficient than corresponding explicit filters used in an earlier study and are therefore more suitable for real-time numerical weather prediction. A set of analysis experiments are conducted at a mesoscale resolution to examine the effectiveness of the 3DVAR system in analyzing simulated global positioning system (GPS) slant-path water vapor observations from ground-based GPS receivers and observations from collocated surface stations. It is shown that the analyses produced with recursive filters are at least as good as those with corresponding explicit filters. In some cases, the recursive filters actually perform better. The impact of flow-dependent background errors modeled using the anisotropic recursive filters is also examined. The use of anisotropic filters improves the analysis, especially in terms of finescale structures. The analysis system is found to be effective in the presence of typical observational errors. The sensitivity of isotropic and anisotropic recursive-filter analyses to the decorrelation scales is also examined systematically.

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Xuguang Wang, David Parrish, Daryl Kleist, and Jeffrey Whitaker

Abstract

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 one- or 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.

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Wan-Shu Wu, David F. Parrish, Eric Rogers, and Ying Lin

Abstract

At the National Centers for Environmental Prediction, the global ensemble forecasts from the ensemble Kalman filter scheme in the Global Forecast System are applied in a regional three-dimensional (3D) and a four dimensional (4D) ensemble–variational (EnVar) data assimilation system. The application is a one-way variational method using hybrid static and ensemble error covariances. To enhance impact, three new features have been added to the existing EnVar system in the Gridpoint Statistical Interpolation (GSI). First, the constant coefficients that assign relative weight between the ensemble and static background error are now allowed to vary in the vertical. Second, a new formulation is introduced for the ensemble contribution to the analysis surface pressure. Finally, in order to make use of the information in the ensemble mean that is disregarded in the existing EnVar in GSI, the trajectory correction, a novel approach, is introduced. Relative to the application of a 3D variational data assimilation algorithm, a clear positive impact on 1–3-day forecasts is realized when applying 3DEnVar analyses in the North American Mesoscale Forecast System (NAM). The 3DEnVar DA system was operationally implemented in the NAM Data Assimilation System in August 2014. Application of a 4DEnVar algorithm is shown to further improve forecast accuracy relative to the 3DEnVar. The approach described in this paper effectively combines contributions from both the regional and the global forecast systems to produce the initial conditions for the regional NAM system.

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Wan-Shu Wu, R. James Purser, and David F. Parrish

Abstract

In this study, a global three-dimensional variational analysis system is formulated in model grid space. This formulation allows greater flexibility (e.g., inhomogeneity and anisotropy) for background error statistics. A simpler formulation, inhomogeneous only in the latitude direction, was chosen for these initial tests. The background error statistics are defined as functions of the latitudinal grid and are estimated with the National Meteorological Center (NMC) method. The horizontal scales of the variables are obtained through the variances of the variables and of their Laplacian. The vertical scales are estimated through the statistics of the vertical correlation of each variable and are applied locally using recursive filters. For the multivariate correlation between wind and mass fields, a statistical linear relationship between the streamfunction and the balanced part of temperature and surface pressure is assumed. A localized correlation between the velocity potential and the streamfunction is also used to account for the positive correlation between the vorticity and divergence in the planetary boundary layer.

Horizontally, the global domain is divided into three pieces so that efficient spatial recursive filters can be used to spread out the information from the observation locations. This analysis system is tested against the operational Spectral Statistical-Interpolation analysis system used at the National Centers for Environmental Prediction. The results indicate that 3DVAR in physical space is as effective as 3DVAR in spectral space in the extratropics and yields superior results in the Tropics as a result of the latitude dependence of the background error statistics.

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John C. Derber, David F. Parrish, and Stephen J. Lord

Abstract

At the National Meteorological Center (NMC), a new analysis system was implemented into the operational Global Data Assimilation System on 25 June 1991. This analysis system is referred to as Spectral Statistical Interpolation (SSI) because the spectral coefficients used in the NMC spectral model are analyzed directly using the same basic equations as statistical (optimum) interpolation. The major differences between the SSI analysis system and the conventional optimum interpolation (OI) analysis system previously used operationally at NMC are:

  • –The analysis variables are closely related to the coefficients of the NMC spectral model.

  • –Temperature observations are used, not heights as in the previous procedure. As a result, aircraft temperatures are being used for the first time at NMC.

  • –Nonstandard observations, such as satellite estimates of total precipitable water and ocean-surface wind speeds, can be easily included.

  • –No data selection is necessary. All observations are used simultaneously.

  • –The dynamical constraint between the wind and mass fields is more realistic and applied globally.

  • –Model initialization has been eliminated. The analysis is used directly as the forecast model initial condition.

Extensive pre-implementation testing demonstrated that the SSI consistently produced superior analyses and forecasts when compared to the previous OI system. Improvement in skill is shown not only for the 3–5-day forecasts, but also in one-day aviation forecasts.

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Daryl T. Kleist, David F. Parrish, John C. Derber, Russ Treadon, Wan-Shu Wu, and Stephen Lord

Abstract

At the National Centers for Environmental Prediction (NCEP), a new three-dimensional variational data assimilation (3DVAR) analysis system was implemented into the operational Global Data Assimilation System (GDAS) on 1 May 2007. The new analysis system, the Gridpoint Statistical Interpolation (GSI), replaced the Spectral Statistical Interpolation (SSI) 3DVAR system, which had been operational since 1991. The GSI was developed at the Environmental Modeling Center at NCEP as part of an effort to create a more unified, robust, and efficient analysis scheme. The key aspect of the GSI is that it formulates the analysis in model grid space, which allows for more flexibility in the application of the background error covariances and makes it straightforward for a single analysis system to be used across a broad range of applications, including both global and regional modeling systems and domains.

Due to the constraints of working with an operational system, the final GDAS package included many changes other than just a simple replacing of the SSI with the new GSI. The new GDAS package contained an upgrade to the Global Forecast System model, including a new vertical coordinate, as well as new features in the GSI that were never developed for the SSI. Some of these new features included changes to the observation selection, quality control, minimization algorithm, dynamic balance constraint, and assimilation of new observation types. The evaluation of the new system relative to the SSI-based system was performed for nearly an entire year of analyses and forecasts. The objective and subjective evaluations showed that the new package exhibited superior forecast performance relative to the old SSI-based system. The new system has been shown to improve forecast skill in the tropics and substantially reduce the short-term forecast error in the extratropics. This implementation has laid the groundwork for future scientific advancements in data assimilation at NCEP.

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R. James Purser, Wan-Shu Wu, David F. Parrish, and Nigel M. Roberts

Abstract

The construction and application of efficient numerical recursive filters for the task of convolving a spatial distribution of “forcing” terms with a quasi-Gaussian self-adjoint smoothing kernel in two or three dimensions are described. In the context of variational analysis, this smoothing operation may be interpreted as the convolution of a covariance function of background error with the given forcing terms, which constitutes one of the most computationally intensive components of the iterative solution of a variational analysis problem.

Among the technical aspects of the recursive filters, the problems of achieving acceptable approximations to horizontal isotropy and the implementation of both periodic and nonperiodic boundary conditions that avoid the appearance of spurious numerical artifacts are treated herein. A multigrid approach that helps to minimize numerical noise at filtering scales greatly in excess of the grid step is also discussed. It is emphasized that the methods are not inherently limited to the construction of purely Gaussian shapes, although the detailed elaboration of methods by which a more general set of possible covariance profiles may be synthesized is deferred to the companion paper ().

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