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.

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.

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.

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.

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.

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.

Abstract

Four-dimensional variational (4DVAR) data assimilation experiments for the East Coast winter storm of 25 January 2000 (i.e., “blizzard of 2000”) were performed. This storm has received wide attention in the United States, because it was one of the major failures of the operational forecast system. All operational models of the U.S. National Weather Service (NWS) failed to produce heavy precipitation over the Carolina–New Jersey corridor, especially during the early stage of the storm development. The considered analysis cycle of this study is that of 0000 to 1200 UTC 24 January. This period was chosen because the forecast from 1200 UTC 24 January had the most damaging guidance for the forecasters at the National Weather Service offices and elsewhere.

In the first set of experiments, the assimilation and forecast results between the 4DVAR and the operational three-dimensional variational (3DVAR) data assimilation method are compared. The most striking difference is in the accumulated precipitation amounts. The 4DVAR experiment produced almost perfect 24-h accumulated precipitation during the first 24 h of the forecast (after data assimilation), with accurate heavy precipitation over North and South Carolina. The operational 3DVAR-based forecast badly underforecast precipitation. The reason for the difference is traced back to the initial conditions. Apparently, the 4DVAR data assimilation was able to create strong surface convergence and an excess of precipitable water over Georgia. This initial convection was strengthened by a low-level jet in the next 6–12 h, finally resulting in a deep convection throughout the troposphere.

In the second set of experiments, the impact of model error adjustment and precipitation assimilation is examined by comparing the forecasts initiated from various 4DVAR experiments. The results strongly indicate the need for the model error adjustment in the 4DVAR algorithm, as well as the clear benefit of assimilation of the hourly accumulated precipitation.

Abstract

The errors in the first-guess (forecast field) of an analysis system vary from day to day, but, as in all current operational data assimilation systems, forecast error covariances are assumed to be constant in time in the NCEP operational three-dimensional variational analysis system (known as a spectral statistical interpolation or SSI). This study focuses on the impact of modifying the error statistics by including effects of the “errors of the day” on the analysis system. An estimate of forecast uncertainty, as defined from the bred growing vectors of the NCEP operational global ensemble forecast, is applied in the NCEP operational SSI analysis system. The growing vectors are used to estimate the spatially and temporally varying degree of uncertainty in the first-guess forecasts used in the analysis. The measure of uncertainty is defined by a ratio of the local amplitude of the growing vectors, relative to a background amplitude measure over a large area. This ratio is used in the SSI system for adjusting the observational error term (giving more weight to observations in regions of larger forecast errors). Preliminary experiments with the low-resolution global system show positive impact of this virtually cost-free method on the quality of the analysis and medium-range weather forecasts, encouraging further tests for operational use. The results of a 45-day parallel run, and a discussion of other methods to take advantage of the knowledge of the day-to-day variation in forecast uncertainties provided by the NCEP ensemble forecast system, are also presented in the paper.

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.

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.