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

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 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 ().

Abstract

In this second part of a two-part study of recursive filter techniques applied to the synthesis of covariances in a variational analysis, methods by which non-Gaussian shapes and spatial inhomogeneities and anisotropies for the covariances may be introduced in a well-controlled way are examined. These methods permit an analysis scheme to possess covariance structures with adaptive variations of amplitude, scale, profile shape, and degrees of local anisotropy, all as functions of geographical location and altitude.

First, it is shown how a wider and more useful variety of covariance shapes than just the Gaussian may be obtained by the positive superposition of Gaussian components of different scales, or by further combinations of these operators with the application of Laplacian operators in order for the products to possess negative sidelobes in their radial profiles.

Then it is shown how the techniques of recursive filters may be generalized to admit the construction of covariances whose characteristic scales relative to the grid become adaptive to geographical location, while preserving the necessary properties of self-adjointness and positivity. Special attention is paid to the problems of amplitude control for these spatially inhomogeneous filters and an estimate for the kernel amplitude is proposed based upon an asymptotic analysis of the problem.

Finally, a further generalization of the filters that enables fully anisotropic and geographically adaptive covariances to be constructed in a computationally efficient way is discussed.

Abstract

The gridpoint statistical interpolation (GSI) analysis system is a unified global/regional three-dimensional variational data assimilation (3DVAR) analysis code that has been under development for several years at the National Centers for Environmental Prediction (NCEP)/Environmental Modeling Center. It has recently been implemented into operations at NCEP in both the global and North American data assimilation systems (GDAS and NDAS, respectively). An important aspect of this development has been improving the balance of the analysis produced by GSI. The improved balance between variables has been achieved through the inclusion of a tangent-linear normal-mode constraint (TLNMC). The TLNMC method has proven to be very robust and effective. The TLNMC as part of the global GSI system has resulted in substantial improvement in data assimilation at NCEP.

Abstract

Experimental observations from coastal and island wind profilers, aircraft, and other sensors deployed during the California Land-falling Jets Experiment of 1997/98 and the Pacific Land-falling Jets Experiment of 2000/01–2003/04 were combined with observations from operational networks to document the regular occurrence and characteristic structure of shallow (∼400–500 m deep), cold airstreams flowing westward through California’s Petaluma Gap from the Central Valley to the coast during the winter months. The Petaluma Gap, which is the only major air shed outlet from the Central Valley, is ∼35–50 km wide and has walls extending, at most, a modest 600–900 m above the valley floor. Based on this geometry, together with winter meteorological conditions typical of the region (e.g., cold air pooled in the Central Valley and approaching extratropical cyclones), this gap is predisposed to generating westward-directed ageostrophic flows driven by along-gap pressure differences. Two case studies and a five-winter composite analysis of 62 gap-flow cases are presented here to show that flows through the Petaluma Gap significantly impact local distributions of wind, temperature, precipitation, and atmospheric pollutants. These gap flows preferentially occur in pre-cold-frontal conditions, largely because sea level pressure decreases westward along the gap in a stably stratified atmosphere in advance of approaching cold-frontal pressure troughs. Airstreams exiting the Petaluma Gap are only several hundred meters deep and characterized by relatively cold, easterly flow capped by a layer of enhanced static stability and directional vertical wind shear. Airborne air-chemistry observations collected offshore by the NOAA P-3 aircraft illustrate the fact that gap-flow events can transport pollutants from inland to the coast, and that they can contribute to coastally blocked airstreams. The strongest gap-flow cases occur when comparatively deep midtropospheric troughs approach the coast, while the weak cases are tied to anticyclonic conditions aloft. Low-level cold-frontal pressure troughs approaching the coast are stronger and possess a greater along-gap pressure gradient for the strong gap-flow cases. These synoptic characteristics are dynamically consistent with coastal wind profiler observations of stronger low-level gap flow and winds aloft, and greater rainfall, during the strong gap-flow events. However, gap flow, on average, inhibits rainfall at the coast.