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Zhao-Xia Pu, Eugenia Kalnay, David Parrish, Wanshu Wu, and Zoltan Toth

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.

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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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Qin Xu, Kang Nai, Li Wei, Pengfei Zhang, Shun Liu, and David Parrish

Abstract

This paper describes a new velocity–azimuth display (VAD)-based dealiasing method developed for automated radar radial velocity data quality control to satisfy the high-quality standard and efficiency required by operational radar data assimilation. The method is built on an alias-robust velocity–azimuth display (AR-VAD) analysis. It upgrades and simplifies the previous three-step dealiasing method in three major aspects. First, the AR-VAD is used with sufficiently stringent threshold conditions in place of the original modified VAD for the preliminary reference check to produce alias-free seed data in the first step. Second, the AR-VAD is more accurate than the traditional VAD for the refined reference check in the original second step, so the original second step becomes unnecessary and is removed. Third, a block-to-point continuity check procedure is developed, in place of the point-to-point continuity check in the original third step, which serves to enhance the use of the available seed data in a properly enlarged block area around each flagged data point that is being checked with multiple threshold conditions to avoid false dealiasing. The new method has been tested extensively with aliased radial velocity data collected under various weather conditions, including hurricane high-wind conditions. The robustness of the new method is exemplified by the results tested with three cases. The limitations of the new method and possible improvements are discussed.

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Daryl T. Kleist, David F. Parrish, John C. Derber, Russ Treadon, Ronald M. Errico, and Runhua Yang

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.

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Milija Zupanski, Dusanka Zupanski, David F. Parrish, Eric Rogers, and Geoffrey DiMego

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.

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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

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.

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Paul J. Neiman, F. Martin Ralph, Allen B. White, David D. Parrish, John S. Holloway, and Diana L. Bartels

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.

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Tom H. Zapotocny, Steven J. Nieman, W. Paul Menzel, James P. Nelson III, James A. Jung, Eric Rogers, David F. Parrish, Geoffrey J. DiMego, Michael Baldwin, and Timothy J. Schmit

Abstract

A case study is utilized to determine the sensitivity of the Eta Data Assimilation System (EDAS) to all operational observational data types used within it. The work described in this paper should be of interest to Eta Model users trying to identify the impact of each data type and could benefit other modelers trying to use EDAS analyses and forecasts as initial conditions for other models.

The case study chosen is one characterized by strong Atlantic and Pacific maritime cyclogenesis, and is shortly after the EDAS began using three-dimensional variational analysis. The control run of the EDAS utilizes all 34 of the operational data types. One of these data types is then denied for each of the subsequent experimental runs. Differences between the experimental and control runs are analyzed to demonstrate the sensitivity of the EDAS system to each data type for the analysis and subsequent 48-h forecasts. Results show the necessity of various nonconventional observation types, such as aircraft data, satellite precipitable water, and cloud drift winds. These data types are demonstrated to have a significant impact, especially observations in maritime regions.

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Steven E. Koch, Brian D. Jamison, Chungu Lu, Tracy L. Smith, Edward I. Tollerud, Cecilia Girz, Ning Wang, Todd P. Lane, Melvyn A. Shapiro, David D. Parrish, and Owen R. Cooper

Abstract

High-resolution dropwindsonde and in-flight measurements collected by a research aircraft during the Severe Clear-Air Turbulence Colliding with Aircraft Traffic (SCATCAT) experiment and simulations from numerical models are analyzed for a clear-air turbulence event associated with an intense upper-level jet/frontal system. Spectral, wavelet, and structure function analyses performed with the 25-Hz in situ data are used to investigate the relationship between gravity waves and turbulence. Mesoscale dynamics are analyzed with the 20-km hydrostatic Rapid Update Cycle (RUC) model and a nested 1-km simulation with the nonhydrostatic Clark–Hall (CH) cloud-scale model.

Turbulence occurred in association with a wide spectrum of upward propagating gravity waves above the jet core. Inertia–gravity waves were generated within a region of unbalanced frontogenesis in the vicinity of a complex tropopause fold. Turbulent kinetic energy fields forecast by the RUC and CH models displayed a strongly banded appearance associated with these mesoscale gravity waves (horizontal wavelengths of ∼120–216 km). Smaller-scale gravity wave packets (horizontal wavelengths of 1–20 km) within the mesoscale wave field perturbed the background wind shear and stability, promoting the development of bands of reduced Richardson number conducive to the generation of turbulence. The wavelet analysis revealed that brief episodes of high turbulent energy were closely associated with gravity wave occurrences. Structure function analysis provided evidence that turbulence was most strongly forced at a horizontal scale of 700 m.

Fluctuations in ozone measured by the aircraft correlated highly with potential temperature fluctuations and the occurrence of turbulent patches at altitudes just above the jet core, but not at higher flight levels, even though the ozone fluctuations were much larger aloft. These results suggest the existence of remnant “fossil turbulence” from earlier events at higher levels, and that ozone cannot be used as a substitute for more direct measures of turbulence. The findings here do suggest that automated turbulence forecasting algorithms should include some reliable measure of gravity wave activity.

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