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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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Abstract
The problem of predicting the onset of damaging downburst winds from high-reflectivity storm cells that develop in an environment of weak vertical shear with Weather Surveillance Radar-1988 Doppler (WSR-88D) is examined. Ninety-one storm cells that produced damaging outflows are analyzed with data from the WSR- 88D network, along with 1247 nonsevere storm cells that developed in the same environments. Twenty-six reflectivity and radial velocity–based parameters are calculated for each cell, and a linear discriminant analysis was performed on 65% of the dataset in order to develop prediction equations that would discriminate between severe downburst-producing cells and cells that did not produce a strong outflow. These prediction equations are evaluated on the remaining 35% of the dataset. The datasets were resampled 100 times to determine the range of possible results. The resulting automated algorithm has a median Heidke skill score (HSS) of 0.40 in the 20–45-km range with a median lead time of 5.5 min, and a median HSS of 0.17 in the 45–80-km range with a median lead time of 0 min. As these lead times are medians of the mean lead times calculated from a large, resampled dataset, many of the storm cells in the dataset had longer lead times than the reported median lead times.
Abstract
The problem of predicting the onset of damaging downburst winds from high-reflectivity storm cells that develop in an environment of weak vertical shear with Weather Surveillance Radar-1988 Doppler (WSR-88D) is examined. Ninety-one storm cells that produced damaging outflows are analyzed with data from the WSR- 88D network, along with 1247 nonsevere storm cells that developed in the same environments. Twenty-six reflectivity and radial velocity–based parameters are calculated for each cell, and a linear discriminant analysis was performed on 65% of the dataset in order to develop prediction equations that would discriminate between severe downburst-producing cells and cells that did not produce a strong outflow. These prediction equations are evaluated on the remaining 35% of the dataset. The datasets were resampled 100 times to determine the range of possible results. The resulting automated algorithm has a median Heidke skill score (HSS) of 0.40 in the 20–45-km range with a median lead time of 5.5 min, and a median HSS of 0.17 in the 45–80-km range with a median lead time of 0 min. As these lead times are medians of the mean lead times calculated from a large, resampled dataset, many of the storm cells in the dataset had longer lead times than the reported median lead times.
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.
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.
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.
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.
No Abstract available.
No Abstract available.
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.
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.
