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Kimberly L. Elmore

Abstract

Rank histograms are a commonly used tool for evaluating an ensemble forecasting system’s performance. Because the sample size is finite, the rank histogram is subject to statistical fluctuations, so a goodness-of-fit (GOF) test is employed to determine if the rank histogram is uniform to within some statistical certainty. Most often, the χ 2 test is used to test whether the rank histogram is indistinguishable from a discrete uniform distribution. However, the χ 2 test is insensitive to order and so suffers from troubling deficiencies that may render it unsuitable for rank histogram evaluation. As shown by examples in this paper, more powerful tests, suitable for small sample sizes, and very sensitive to the particular deficiencies that appear in rank histograms are available from the order-dependent Cramér–von Mises family of statistics, in particular, the Watson and Anderson–Darling statistics.

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Kimberly L. Elmore

Abstract

The National Severe Storms Laboratory (NSSL) has developed a hydrometeor classification algorithm (HCA) for use with the polarimetric upgrade of the current Weather Surveillance Radar-1988 Doppler (WSR-88D) network. The algorithm was developed specifically for warm-season convection, but it will run regardless of season, and so its performance on surface precipitation type during winter events is examined here. The HCA output is compared with collocated (in time and space) observations of precipitation type provided by the public. The Peirce skill score (PSS) shows that the NSSL HCA applied to winter surface precipitation displays little skill, with a PSS of only 0.115. Further analysis indicates that HCA failures are strongly linked to the inability of HCA to accommodate refreezing below the first freezing level and to errors in the melting-level detection algorithm. Entrants in the 2009 American Meteorological Society second annual artificial intelligence competition developed classification methods that yield a PSS of 0.35 using a subset of available radar data merged with limited environmental data. Thus, when polarimetric radar data and environmental data are appropriately combined, more information about winter surface precipitation type is available than from either data source alone.

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Kimberly L. Elmore
and
Michael B. Richman

Abstract

Eigentechniques, in particular principal component analysis (PCA), have been widely used in meteorological analyses since the early 1950s. Traditionally, choices for the parent similarity matrix, which are diagonalized, have been limited to correlation, covariance, or, rarely, cross products. Whereas each matrix has unique characteristic benefits, all essentially identify parameters that vary together. Depending on what underlying structure the analyst wishes to reveal, similarity matrices can be employed, other than the aforementioned, to yield different results. In this work, a similarity matrix based upon Euclidean distance, commonly used in cluster analysis, is developed as a viable alternative. For PCA, Euclidean distance is converted into Euclidean similarity. Unlike the variance-based similarity matrices, a PCA performed using Euclidean similarity identifies parameters that are close to each other in a Euclidean distance sense. Rather than identifying parameters that change together, the resulting Euclidean similarity–based PCA identifies parameters that are close to each other, thereby providing a new similarity matrix choice. The concept used to create Euclidean similarity extends the utility of PCA by opening a wide range of similarity measures available to investigators, to be chosen based on what characteristic they wish to identify.

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William P. Mahoney III
and
Kimberly L. Elmore

Abstract

The structure and evolution of a microburst-producing cell were studied using dual-Doppler data collected in eastern Colorado during the summer of 1987. Eight volumes of multiple-Doppler data with a temporal resolution of 2.5 min were analyzed. The radar data were interpolated onto a Cartesian grid with horizontal and vertical spacing of 250 m and 200 m, respectively. The analysis of this dataset revealed that the 56 dBZ, storm produced two adjacent microbursts with different kinematic structures. The first microburst, which de-veloped a maximum velocity differential of 16 m s−1 over 2.5 km, was associated with a strong horizontal vortex (rotor) that developed new the surface at the precipitation edge. The second stronger micreburst obtained a velocity dilterential of 22 m s−1 over 3.2 km and was associated with a strengthening downdraft and collapse of the cell. Both microbursts developed ∼14 min after precipitation reached the surface.

Trajectory and equivalent potential temperature (θ e ) analyses were used to determine the history of the microburst-producing cell. These analyses indicate that the source region of air for the rotor-associated microburst was below cloud base and upwind of the precipitation shaft. Air entered the cell from the west at low levels, ascended over the horizontal rotor, and descended rapidly to the ground on the east side of the rotor. The source height of the air within the second microburst was well above cloud base. As the cell collapsed and the microburst developed, air accelerated into the downdraft at midlevels and descended to the surface. Features associated with this microburst included a descending reflectivity echo, convergence above cloud base, and the development and descent of strong vertical vorticity.

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Kimberly L. Elmore
,
Pamela L. Heinselman
, and
David J. Stensrud

Abstract

Prior work shows that Weather Surveillance Radar-1988 Doppler (WSR-88D) clear-air reflectivity can be used to determine convective boundary layer (CBL) depth. Based on that work, two simple linear regressions are developed that provide CBL depth. One requires only clear-air radar reflectivity from a single 4.5° elevation scan, whereas the other additionally requires the total, clear-sky insolation at the radar site, derived from the radar location and local time. Because only the most recent radar scan is used, the CBL depth can, in principle, be computed for every scan. The “true” CBL depth used to develop the models is based on human interpretation of the 915-MHz profiler data. The regressions presented in this work are developed using 17 summer days near Norman, Oklahoma, that have been previously investigated. The resulting equations and algorithms are applied to a testing dataset consisting of 7 days not previously analyzed. Though the regression using insolation estimates performs best, errors from both models are on the order of the expected error of the profiler-estimated CBL depth values. Of the two regressions, the one that uses insolation yields CBL depth estimates with an RMSE of 208 m, while the regression with only clear-air radar reflectivity yields CBL depth estimates with an RMSE of 330 m.

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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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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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Corey K. Potvin
,
Kimberly L. Elmore
, and
Steven J. Weiss

Abstract

Proximity sounding studies typically seek to optimize several trade-offs that involve somewhat arbitrary definitions of how to define a “proximity sounding.” More restrictive proximity criteria, which presumably produce results that are more characteristic of the near-storm environment, typically result in smaller sample sizes that can reduce the statistical significance of the results. Conversely, the use of broad proximity criteria will typically increase the sample size and the apparent robustness of the statistical analysis, but the sounding data may not necessarily be representative of near-storm environments, given the presence of mesoscale variability in the atmosphere. Previous investigations have used a wide range of spatial and temporal proximity criteria to analyze severe storm environments. However, the sensitivity of storm environment climatologies to the proximity definition has not yet been rigorously examined.

In this study, a very large set (∼1200) of proximity soundings associated with significant tornado reports is used to generate distributions of several parameters typically used to characterize severe weather environments. Statistical tests are used to assess the sensitivity of the parameter distributions to the proximity criteria. The results indicate that while soundings collected too far in space and time from significant tornadoes tend to be more representative of the larger-scale environment than of the storm environment, soundings collected too close to the tornado also tend to be less representative due to the convective feedback process. The storm environment itself is thus optimally sampled at an intermediate spatiotemporal range referred to here as the Goldilocks zone. Implications of these results for future proximity sounding studies are discussed.

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Kimberly L. Elmore
,
David J. Stensrud
, and
Kenneth C. Crawford

Abstract

A cloud model ensemble forecasting approach is developed to create forecasts that describe the range and distribution of thunderstorm lifetimes that may be expected to occur on a particular day. Such forecasts are crucial for anticipating severe weather, because long-lasting storms tend to produce more significant weather and have a greater impact on public safety than do storms with brief lifetimes. Eighteen days distributed over two warm seasons with 1481 observed thunderstorms are used to assess the ensemble approach. Forecast soundings valid at 1800, 2100, and 0000 UTC provided by the 0300 UTC run of the operational Meso Eta Model from the National Centers for Environmental Prediction are used to provide horizontally homogeneous initial conditions for a cloud model ensemble made up from separate runs of the fully three-dimensional Collaborative Model for Mesoscale Atmospheric Simulation. These soundings are acquired from a 160 km × 160 km square centered over the location of interest; they are shown to represent a likely, albeit biased, range of atmospheric states. A minimum threshold value for maximum vertical velocity of 8 m s−1 within the cloud model domain is used to estimate storm lifetime. Forecast storm lifetimes are verified against observed storm lifetimes, as derived from the Storm Cell Identification and Tracking algorithm applied to Weather Surveillance Radar—1988 Doppler (WSR-88D) data from the National Weather Service (reflectivity exceeding 40 dBZ e ). Probability density functions (pdfs) are estimated from the storm lifetimes that result from the ensemble. When results from all 18 days are pooled, a vertical velocity threshold of 8 m s−1 is found to generate a forecast pdf of storm lifetime that most closely resembles the pdf that describes the collection of observed storm lifetimes. Standard 2 × 2 contingency statistics reveal that, on identifiable occasions, the ensemble model displays skill in comparison with the climatologic mean in locating where convection is most likely to occur. Contingency statistics also show that when storm lifetimes of at least 60 min are used as a proxy for severe weather, the ensemble shows considerable skill at identifying days that are likely to produce severe weather. Because the ensemble model has skill in predicting the range and distribution of storm lifetimes on a daily basis, the forecast pdf of storm lifetime is used directly to create probabilistic forecasts of storm lifetime, given the current age of a storm.

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Kimberly L. Elmore
,
F. Wesley Wilson Jr.
, and
Michael J. Carpenter

Abstract

On occasion, digital data gathered during field projects suffers damage due to hardware problems. If no more than half the data are damaged and if the damaged data are randomly distributed in space or time, there is a high probability that the damage can be isolated and repaired using the algorithm described in this paper. During subsequent analysis, some data from the NCAR CP4 Doppler radar were found to be damaged and initially seemed to be lost. Later, the nature of the problem was found and a general algorithm was developed that identifies outliers, which can then be corrected. This algorithm uses the fact that the second derivative of the damaged data with respect to (in this case) radial distance is relatively small. The algorithm can be applied to any similar data. Such data can be closely approximated by a first order, least-squares regression line if the regression line is not applied over too long an interval. This algorithm is especially robust because the length of the regression fit is adaptively chosen, determined by the residuals, such that the slope of the regression line approximates the first radial derivative. The outliers are then marked as candidates for correction, allowing data recovery. This method is not limited to radar data; it may be applied to any data with damage as outlined above. Examples of damaged and corrected data sets are shown and the limitations of this method are discussed as are general applications to other data.

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