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S. Lakshmivarahan, Michael E. Baldwin, and Tao Zheng

Abstract

The goal of this paper is to provide a complete picture of the long-term behavior of Lorenz’s maximum simplification equations along with the corresponding meteorological interpretation for all initial conditions and all values of the parameter.

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Benjamin R. J. Schwedler and Michael E. Baldwin

Abstract

While the use of binary distance measures has a substantial history in the field of image processing, these techniques have only recently been applied in the area of forecast verification. Designed to quantify the distance between two images, these measures can easily be extended for use with paired forecast and observation fields. The behavior of traditional forecast verification metrics based on the dichotomous contingency table continues to be an area of active study, but the sensitivity of image metrics has not yet been analyzed within the framework of forecast verification. Four binary distance measures are presented and the response of each to changes in event frequency, bias, and displacement error is documented. The Hausdorff distance and its derivatives, the modified and partial Hausdorff distances, are shown only to be sensitive to changes in base rate, bias, and displacement between the forecast and observation. In addition to its sensitivity to these three parameters, the Baddeley image metric is also sensitive to additional aspects of the forecast situation. It is shown that the Baddeley metric is dependent not only on the spatial relationship between a forecast and observation but also the location of the events within the domain. This behavior may have considerable impact on the results obtained when using this measure for forecast verification. For ease of comparison, a hypothetical forecast event is presented to quantitatively analyze the various sensitivities of these distance measures.

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Michael E. Baldwin and John S. Kain

Abstract

The sensitivity of various accuracy measures to displacement error, bias, and event frequency is analyzed for a simple hypothetical forecasting situation. Each measure is found to be sensitive to displacement error and bias, but probability of detection and threat score do not change as a function of event frequency. On the other hand, equitable threat score, true skill statistic, and odds ratio skill score behaved differently with changing event frequency. A newly devised measure, here called the bias-adjusted threat score, does not change with varying event frequency and is relatively insensitive to bias. Numerous plots are presented to allow users of these accuracy measures to make quantitative estimates of sensitivities that are relevant to their particular application.

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Michael E. Baldwin, John S. Kain, and Michael P. Kay

Abstract

The impact of parameterized convection on Eta Model forecast soundings is examined. The Betts–Miller–Janjić parameterization used in the National Centers for Environmental Prediction Eta Model introduces characteristic profiles of temperature and moisture in model soundings. These specified profiles can provide misleading representations of various vertical structures and can strongly affect model predictions of parameters that are used to forecast deep convection, such as convective available potential energy and convective inhibition. The specific procedures and tendencies of this parameterization are discussed, and guidelines for interpreting Eta Model soundings are presented.

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Kimberly L. Elmore, David M. Schultz, and Michael E. Baldwin

Abstract

A previous study of the mean spatial bias errors associated with operational forecast models motivated an examination of the mechanisms responsible for these biases. One hypothesis for the cause of these errors is that mobile synoptic-scale phenomena are partially responsible. This paper explores this hypothesis using 24-h forecasts from the operational Eta Model and an experimental version of the Eta run with Kain–Fritsch convection (EtaKF).

For a sample of 44 well-defined upper-level short-wave troughs arriving on the west coast of the United States, 70% were underforecast (as measured by the 500-hPa geopotential height), a likely result of being undersampled by the observational network. For a different sample of 45 troughs that could be tracked easily across the country, consecutive model runs showed that the height errors associated with 44% of the troughs generally decreased in time, 11% increased in time, 18% had relatively steady errors, 2% were uninitialized entering the West Coast, and 24% exhibited some other kind of behavior. Thus, landfalling short-wave troughs were typically underforecast (positive errors, heights too high), but these errors tended to decrease as they moved across the United States, likely a result of being better initialized as the troughs became influenced by more upper-air data. Nevertheless, some errors in short-wave troughs were not corrected as they fell under the influence of supposedly increased data amount and quality. These results indirectly show the effect that the amount and quality of observational data has on the synoptic-scale errors in the models. On the other hand, long-wave ridges tended to be underforecast (negative errors, heights too low) over a much larger horizontal extent.

These results are confirmed in a more systematic manner over the entire dataset by segregating the model output at each grid point by the sign of the 500-hPa relative vorticity. Although errors at grid points with positive relative vorticity are small but positive in the western United States, the errors become large and negative farther east. Errors at grid points with negative relative vorticity, on the other hand, are generally negative across the United States. A large negative bias observed in the Eta and EtaKF over the southeast United States is believed to be due to an error in the longwave radiation scheme interacting with water vapor and clouds. This study shows that model errors may be related to the synoptic-scale flow, and even large-scale features such as long-wave troughs can be associated with significant large-scale height errors.

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Elizabeth E. Ebert, Ulrich Damrath, Werner Wergen, and Michael E. Baldwin

Twenty-four-hour and 48-h quantitative precipitation forecasts (QPFs) from 11 operational numerical weather prediction models have been verified for a 4-yr period against rain gauge observations over the United States, Germany, and Australia to assess their skill in predicting the occurrence and amount of daily precipitation.

Model QPFs had greater skill in winter than in summer, and greater skill in midlatitudes than in Tropics, where they performed only marginally better than “persistence.” The best agreement among models, as well as the best ability to discriminate raining areas, occurred for a low rain threshold of 1–2 mm d−1. In contrast, the skill for forecasts of rain greater than 20 mm d−1 was generally quite low, reflecting the difficulty in predicting precisely when and where heavy rain will fall. The location errors for rain systems, determined using pattern matching with the observations, were typically about 100 km for 24-h forecasts, with smaller errors occurring for the heaviest rain systems.

It does not appear that model QPFs improved significantly during the four years examined. As new model versions were introduced their performance changed, not always for the better. The process of improving model numerics and physics is a complicated juggling act, and unless the accurate prediction of rainfall is made a top priority then improvements in model QPF will continue to come only slowly.

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Melissa S. Bukovsky, John S. Kain, and Michael E. Baldwin

Abstract

Bowing, propagating precipitation features that sometimes appear in NCEP's North American Mesoscale model (NAM; formerly called the Eta Model) forecasts are examined. These features are shown to be associated with an unusual convective heating profile generated by the Betts–Miller–Janjić convective parameterization in certain environments. A key component of this profile is a deep layer of cooling in the lower to middle troposphere. This strong cooling tendency induces circulations that favor expansion of parameterized convective activity into nearby grid columns, which can lead to growing, self-perpetuating mesoscale systems under certain conditions. The propagation characteristics of these systems are examined and three contributing mechanisms of propagation are identified. These include a mesoscale downdraft induced by the deep lower-to-middle tropospheric cooling, a convectively induced buoyancy bore, and a boundary layer cold pool that is indirectly produced by the convective scheme in this environment. Each of these mechanisms destabilizes the adjacent atmosphere and decreases convective inhibition in nearby grid columns, promoting new convective development, expansion, and propagation of the larger system. These systems appear to show a poor correspondence with observations of bow echoes on time and space scales that are relevant for regional weather prediction, but they may provide important clues about the propagation mechanisms of real convective systems.

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Kimberly L. Elmore, Michael E. Baldwin, and David M. Schultz

Abstract

The spatial structure of bias errors in numerical model output is valuable to both model developers and operational forecasters, especially if the field containing the structure itself has statistical significance in the face of naturally occurring spatial correlation. A semiparametric Monte Carlo method, along with a moving blocks bootstrap method is used to determine the field significance of spatial bias errors within spatially correlated error fields. This process can be completely automated, making it an attractive addition to the verification tools already in use. The process demonstrated here results in statistically significant spatial bias error fields at any arbitrary significance level.

To demonstrate the technique, 0000 and 1200 UTC runs of the operational Eta Model and the operational Eta Model using the Kain–Fritsch convective parameterization scheme are examined. The resulting fields for forecast errors for geopotential heights and winds at 850, 700, 500, and 250 hPa over a period of 14 months (26 January 2001–31 March 2002) are examined and compared using the verifying initial analysis. Specific examples are shown, and some plausible causes for the resulting significant bias errors are proposed.

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Nathan M. Hitchens, Michael E. Baldwin, and Robert J. Trapp

Abstract

Extreme precipitation was identified in the midwestern United States using an object-oriented approach applied to the NCEP stage-II hourly precipitation dataset. This approach groups contiguous areas that exceed a user-defined threshold into “objects,” which then allows object attributes to be diagnosed. Those objects with precipitation maxima in the 99th percentile (>55 mm) were considered extreme, and there were 3484 such objects identified in the midwestern United States between 1996 and 2010. Precipitation objects ranged in size from hundreds to over 100 000 km2, and the maximum precipitation within each object varied between 55 and 104 mm. The majority of occurrences of extreme precipitation were in the summer (June, July, and August), and peaked in the afternoon into night (1900–0200 UTC) in the diurnal cycle. Consistent with the previous work by the authors, this study shows that the systems that produce extreme precipitation in the midwestern United States vary widely across the convective-storm spectrum.

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William A. Gallus Jr., Michael E. Baldwin, and Kimberly L. Elmore

Abstract

This note examines the connection between the probability of precipitation and forecasted amounts from the NCEP Eta (now known as the North American Mesoscale model) and Aviation (AVN; now known as the Global Forecast System) models run over a 2-yr period on a contiguous U.S. domain. Specifically, the quantitative precipitation forecast (QPF)–probability relationship found recently by Gallus and Segal in 10-km grid spacing model runs for 20 warm season mesoscale convective systems is tested over this much larger temporal and spatial dataset. A 1-yr period was used to investigate the QPF–probability relationship, and the predictive capability of this relationship was then tested on an independent 1-yr sample of data. The same relationship of a substantial increase in the likelihood of observed rainfall exceeding a specified threshold in areas where model runs forecasted higher rainfall amounts is found to hold over all seasons. Rainfall is less likely to occur in those areas where the models indicate none than it is elsewhere in the domain; it is more likely to occur in those regions where rainfall is predicted, especially where the predicted rainfall amounts are largest. The probability of rainfall forecasts based on this relationship are found to possess skill as measured by relative operating characteristic curves, reliability diagrams, and Brier skill scores. Skillful forecasts from the technique exist throughout the 48-h periods for which Eta and AVN output were available. The results suggest that this forecasting tool might assist forecasters throughout the year in a wide variety of weather events and not only in areas of difficult-to-forecast convective systems.

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