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Abstract
This work investigates the inconsistency between forecasts issued at different times but valid for the same time, and shows that ensemble-mean forecasts are less inconsistent than corresponding control forecasts. The “jumpiness” index, the concepts of different forecast jumps—the “flip,” “flip-flop,” and “flip-flop-flip”—and the inconsistency correlation between time series of inconsistency indices are introduced to measure the consistency/inconsistency of consecutive forecasts. These new measures are used to compare the behavior of the ECMWF and the Met Office control and ensemble-mean forecasts for an 18-month period over Europe. Results indicate that for both the ECMWF and the Met Office ensembles, the ensemble-mean forecast is less inconsistent than the control forecast. However, they also indicate that the ensemble mean follows its corresponding control forecast more closely than the controls (or the ensemble means) of the two ensemble systems following each other, thus suggesting weaknesses in both ensemble systems in the simulation of forecast uncertainty due to model or analysis error. Results also show that there is only a weak link between forecast jumpiness and forecast error (i.e., forecasts with lower inconsistency do not necessarily have, on average, lower error).
Abstract
This work investigates the inconsistency between forecasts issued at different times but valid for the same time, and shows that ensemble-mean forecasts are less inconsistent than corresponding control forecasts. The “jumpiness” index, the concepts of different forecast jumps—the “flip,” “flip-flop,” and “flip-flop-flip”—and the inconsistency correlation between time series of inconsistency indices are introduced to measure the consistency/inconsistency of consecutive forecasts. These new measures are used to compare the behavior of the ECMWF and the Met Office control and ensemble-mean forecasts for an 18-month period over Europe. Results indicate that for both the ECMWF and the Met Office ensembles, the ensemble-mean forecast is less inconsistent than the control forecast. However, they also indicate that the ensemble mean follows its corresponding control forecast more closely than the controls (or the ensemble means) of the two ensemble systems following each other, thus suggesting weaknesses in both ensemble systems in the simulation of forecast uncertainty due to model or analysis error. Results also show that there is only a weak link between forecast jumpiness and forecast error (i.e., forecasts with lower inconsistency do not necessarily have, on average, lower error).
Abstract
Dual-Doppler wind synthesis and ensemble Kalman filter analyses produced by assimilating Doppler-on-Wheels velocity data collected in four tornadic supercells are examined in order to further understand the maintenance of tornadoes. Although tornado-scale features are not resolved in these analyses, larger-scale processes involved with tornado maintenance are well represented.
The longest-lived tornado is maintained underneath the midlevel updraft within a zone of low-level horizontal convergence along a rear-flank gust front for a considerable time, and dissipates when horizontally displaced from the midlevel updraft. The shortest-lived tornado resides in a similar zone of low-level convergence briefly, but dissipates underneath the location of the midlevel updraft when the updraft becomes tilted and low-level convergence is displaced several kilometers from the tornado. This suggests that a location beneath the midlevel updraft is not always a sufficient condition for tornado maintenance, particularly in the presence of strongly surging outflow. Tornadoes in two other storms persist within a band of low-level convergence in the outflow air (a possible secondary rear-flank gust front), suggesting that tornado maintenance can occur away from the main boundary separating the outflow air and the ambient environment.
In at least one case, tilting of horizontal vorticity occurs near the tornado along the secondary gust front, as evidenced by three-dimensional vortex line arching. This observation suggests that a relatively cold secondary rear-flank downdraft may assist with tornado maintenance through the baroclinic generation and tilting of horizontal vorticity, despite the fact that parcels composing them would be more negatively buoyant than the preceding outflow air.
Abstract
Dual-Doppler wind synthesis and ensemble Kalman filter analyses produced by assimilating Doppler-on-Wheels velocity data collected in four tornadic supercells are examined in order to further understand the maintenance of tornadoes. Although tornado-scale features are not resolved in these analyses, larger-scale processes involved with tornado maintenance are well represented.
The longest-lived tornado is maintained underneath the midlevel updraft within a zone of low-level horizontal convergence along a rear-flank gust front for a considerable time, and dissipates when horizontally displaced from the midlevel updraft. The shortest-lived tornado resides in a similar zone of low-level convergence briefly, but dissipates underneath the location of the midlevel updraft when the updraft becomes tilted and low-level convergence is displaced several kilometers from the tornado. This suggests that a location beneath the midlevel updraft is not always a sufficient condition for tornado maintenance, particularly in the presence of strongly surging outflow. Tornadoes in two other storms persist within a band of low-level convergence in the outflow air (a possible secondary rear-flank gust front), suggesting that tornado maintenance can occur away from the main boundary separating the outflow air and the ambient environment.
In at least one case, tilting of horizontal vorticity occurs near the tornado along the secondary gust front, as evidenced by three-dimensional vortex line arching. This observation suggests that a relatively cold secondary rear-flank downdraft may assist with tornado maintenance through the baroclinic generation and tilting of horizontal vorticity, despite the fact that parcels composing them would be more negatively buoyant than the preceding outflow air.
Abstract
The effects of observation errors on rank histograms and reliability diagrams are investigated using a perfect model approach. The three-variable Lorenz-63 model was used to simulate an idealized ensemble prediction system (EPS) with 50 perturbed ensemble members and one control forecast. Observation errors at verification time were introduced by adding normally distributed noise to the true state at verification time. Besides these simulations, a theoretical analysis was also performed. One of the major findings was that rank histograms are very sensitive to the presence of observation errors, leading to overpopulated upper- and lowermost ranks. This sensitivity was shown to grow for larger ensemble sizes. Reliability diagrams were far less sensitive in this respect. The resulting u-shaped rank histograms can easily be misinterpreted as indicating too little spread in the ensemble prediction system. To account for this effect when real observations are used to assess an ensemble prediction system, normally distributed noise based on the verifying observation error can be added to the ensemble members before the statistics are calculated. The method has been tested for the ECMWF ensemble forecasts of ocean waves and forecasts of the geopotential at 500 hPa. The EPS waves were compared with buoy observations from the Global Telecommunication System (GTS) for a period of almost 3 yr. When the buoy observations were taken as the true value, more than 25% of the observations appeared in the two extreme ranks for the day 3 forecast range. This number was reduced to less than 10% when observation errors were added to the ensemble members. Ensemble forecasts of the 500-hPa geopotential were verified against the ECMWF analysis. When analysis errors were neglected, the maximum number of outliers was more than 10% for most areas except for Europe, where the analysis errors are relatively smaller. Introducing noise to the ensemble members, based on estimates of analysis errors, reduced the number of outliers, particularly in the short range, where a peak around day 1 more or less vanished.
Abstract
The effects of observation errors on rank histograms and reliability diagrams are investigated using a perfect model approach. The three-variable Lorenz-63 model was used to simulate an idealized ensemble prediction system (EPS) with 50 perturbed ensemble members and one control forecast. Observation errors at verification time were introduced by adding normally distributed noise to the true state at verification time. Besides these simulations, a theoretical analysis was also performed. One of the major findings was that rank histograms are very sensitive to the presence of observation errors, leading to overpopulated upper- and lowermost ranks. This sensitivity was shown to grow for larger ensemble sizes. Reliability diagrams were far less sensitive in this respect. The resulting u-shaped rank histograms can easily be misinterpreted as indicating too little spread in the ensemble prediction system. To account for this effect when real observations are used to assess an ensemble prediction system, normally distributed noise based on the verifying observation error can be added to the ensemble members before the statistics are calculated. The method has been tested for the ECMWF ensemble forecasts of ocean waves and forecasts of the geopotential at 500 hPa. The EPS waves were compared with buoy observations from the Global Telecommunication System (GTS) for a period of almost 3 yr. When the buoy observations were taken as the true value, more than 25% of the observations appeared in the two extreme ranks for the day 3 forecast range. This number was reduced to less than 10% when observation errors were added to the ensemble members. Ensemble forecasts of the 500-hPa geopotential were verified against the ECMWF analysis. When analysis errors were neglected, the maximum number of outliers was more than 10% for most areas except for Europe, where the analysis errors are relatively smaller. Introducing noise to the ensemble members, based on estimates of analysis errors, reduced the number of outliers, particularly in the short range, where a peak around day 1 more or less vanished.
Abstract
Precipitation forecasts from five global numerical weather prediction (NWP) models are verified against rain gauge observations using the new stable equitable error in probability space (SEEPS) score. It is based on a 3 × 3 contingency table and measures the ability of a forecast to discriminate between “dry,” “light precipitation,” and “heavy precipitation.” In SEEPS, the threshold defining the boundary between the light and heavy categories varies systematically with precipitation climate. Results obtained for SEEPS are compared to those of more well-known scores, and are broken down with regard to individual contributions from the contingency table. It is found that differences in skill between the models are consistent for different scores, but are small compared to seasonal and geographical variations, which themselves can be largely ascribed to the varying prevalence of deep convection. Differences between the tropics and extratropics are quite pronounced. SEEPS scores at forecast day 1 in the tropics are similar to those at day 6 in the extratropics. It is found that the model ranking is robust with respect to choices in the score computation. The issue of observation representativeness is addressed using a “quasi-perfect model” approach. Results suggest that just under one-half of the current forecast error at day 1 in the extratropics can be attributed to the fact that gridbox values are verified against point observations.
Abstract
Precipitation forecasts from five global numerical weather prediction (NWP) models are verified against rain gauge observations using the new stable equitable error in probability space (SEEPS) score. It is based on a 3 × 3 contingency table and measures the ability of a forecast to discriminate between “dry,” “light precipitation,” and “heavy precipitation.” In SEEPS, the threshold defining the boundary between the light and heavy categories varies systematically with precipitation climate. Results obtained for SEEPS are compared to those of more well-known scores, and are broken down with regard to individual contributions from the contingency table. It is found that differences in skill between the models are consistent for different scores, but are small compared to seasonal and geographical variations, which themselves can be largely ascribed to the varying prevalence of deep convection. Differences between the tropics and extratropics are quite pronounced. SEEPS scores at forecast day 1 in the tropics are similar to those at day 6 in the extratropics. It is found that the model ranking is robust with respect to choices in the score computation. The issue of observation representativeness is addressed using a “quasi-perfect model” approach. Results suggest that just under one-half of the current forecast error at day 1 in the extratropics can be attributed to the fact that gridbox values are verified against point observations.
Abstract
Finescale single- and dual-Doppler observations are used to diagnose the three-dimensional structure of the wind field surrounding a tornado that occurred near the town of Orleans, Nebraska, on 22 May 2004. The evolution of the vorticity and divergence fields and other structures near the tornado are documented in the lowest kilometer. Changes in tornado intensity are compared to the position of the tornado relative to primary and secondary gust fronts. Circulation on scales of a few kilometers surrounding the tornado remains relatively constant during the analysis period, which spans the intensifying and mature periods of the tornado’s life cycle. Stretching of vertical vorticity and tilting of horizontal vorticity are diagnosed, but the latter is near or below the threshold of detectability in this analysis during the observation period in the analyzed domain. Low-level circulation within 500 m of the tornado increased several minutes before vortex-relative and ground-relative near-surface wind speeds in the tornado increased, raising the possibility that such trends in circulation may be useful in forecasting tornado intensification.
Abstract
Finescale single- and dual-Doppler observations are used to diagnose the three-dimensional structure of the wind field surrounding a tornado that occurred near the town of Orleans, Nebraska, on 22 May 2004. The evolution of the vorticity and divergence fields and other structures near the tornado are documented in the lowest kilometer. Changes in tornado intensity are compared to the position of the tornado relative to primary and secondary gust fronts. Circulation on scales of a few kilometers surrounding the tornado remains relatively constant during the analysis period, which spans the intensifying and mature periods of the tornado’s life cycle. Stretching of vertical vorticity and tilting of horizontal vorticity are diagnosed, but the latter is near or below the threshold of detectability in this analysis during the observation period in the analyzed domain. Low-level circulation within 500 m of the tornado increased several minutes before vortex-relative and ground-relative near-surface wind speeds in the tornado increased, raising the possibility that such trends in circulation may be useful in forecasting tornado intensification.
Abstract
High-resolution Doppler radar velocities and in situ surface observations collected in a tornadic supercell on 5 June 2009 during the second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2) are assimilated into a simulated convective storm using an ensemble Kalman filter (EnKF). A series of EnKF experiments using a 1-km horizontal model grid spacing demonstrates the sensitivity of the cold pool and kinematic structure of the storm to the assimilation of these observations and to different model microphysics parameterizations. An experiment is performed using a finer grid spacing (500 m) and the most optimal data assimilation and model configurations from the sensitivity tests to produce a realistically evolving storm. Analyses from this experiment are verified against dual-Doppler and in situ observations and are evaluated for their potential to confidently evaluate mesocyclone-scale processes in the storm using trajectory analysis and calculations of Lagrangian vorticity budgets. In Part II of this study, these analyses will be further evaluated to learn the roles that mesocyclone-scale processes play in tornado formation, maintenance, and decay. The coldness of the simulated low-level outflow is generally insensitive to the choice of certain microphysical parameterizations, likely owing to the vast quantity of kinematic and in situ thermodynamic observations assimilated. The three-dimensional EnKF wind fields and parcel trajectories resemble those retrieved from dual-Doppler observations within the storm, suggesting that realistic four-dimensional mesocyclone-scale processes are captured. However, potential errors are found in trajectories and Lagrangian three-dimensional vorticity budget calculations performed within the mesocyclone that may be due to the coarse (2 min) temporal resolution of the analyses. Therefore, caution must be exercised when interpreting trajectories in this area of the storm.
Abstract
High-resolution Doppler radar velocities and in situ surface observations collected in a tornadic supercell on 5 June 2009 during the second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2) are assimilated into a simulated convective storm using an ensemble Kalman filter (EnKF). A series of EnKF experiments using a 1-km horizontal model grid spacing demonstrates the sensitivity of the cold pool and kinematic structure of the storm to the assimilation of these observations and to different model microphysics parameterizations. An experiment is performed using a finer grid spacing (500 m) and the most optimal data assimilation and model configurations from the sensitivity tests to produce a realistically evolving storm. Analyses from this experiment are verified against dual-Doppler and in situ observations and are evaluated for their potential to confidently evaluate mesocyclone-scale processes in the storm using trajectory analysis and calculations of Lagrangian vorticity budgets. In Part II of this study, these analyses will be further evaluated to learn the roles that mesocyclone-scale processes play in tornado formation, maintenance, and decay. The coldness of the simulated low-level outflow is generally insensitive to the choice of certain microphysical parameterizations, likely owing to the vast quantity of kinematic and in situ thermodynamic observations assimilated. The three-dimensional EnKF wind fields and parcel trajectories resemble those retrieved from dual-Doppler observations within the storm, suggesting that realistic four-dimensional mesocyclone-scale processes are captured. However, potential errors are found in trajectories and Lagrangian three-dimensional vorticity budget calculations performed within the mesocyclone that may be due to the coarse (2 min) temporal resolution of the analyses. Therefore, caution must be exercised when interpreting trajectories in this area of the storm.
Abstract
On 2 June 1995, the large-scale environment of eastern New Mexico and western Texas was generally favorable for the occurrence of supercells because of the presence of strong deep shear and storm-relative helicity, as well as sufficient convective available potential energy (CAPE). Indeed, many supercells occurred, but the only storms to produce tornadoes were those supercells that crossed, or developed and persisted on the immediate cool side of a particular outflow boundary generated by earlier convection. Surface conditions, vertical vorticity, and horizontal vorticity near this boundary are documented using conventional and special observations from the VORTEX field program. It is shown that the boundary was locally rich in horizontal vorticity, had somewhat enhanced vertical vorticity, and enhanced CAPE. Theoretical arguments indicate that the observed horizontal vorticity (around 1 × 10−2 s−1), largely parallel to the boundary, can be readily produced with the type of buoyancy contrast observed. It is hypothesized that such local enhancement of horizontal vorticity often is required for the occurrence of significant (e.g., F2 or stronger) tornadoes, even in large-scale environments that appear conducive to tornado occurrence without the aid of local influences.
Abstract
On 2 June 1995, the large-scale environment of eastern New Mexico and western Texas was generally favorable for the occurrence of supercells because of the presence of strong deep shear and storm-relative helicity, as well as sufficient convective available potential energy (CAPE). Indeed, many supercells occurred, but the only storms to produce tornadoes were those supercells that crossed, or developed and persisted on the immediate cool side of a particular outflow boundary generated by earlier convection. Surface conditions, vertical vorticity, and horizontal vorticity near this boundary are documented using conventional and special observations from the VORTEX field program. It is shown that the boundary was locally rich in horizontal vorticity, had somewhat enhanced vertical vorticity, and enhanced CAPE. Theoretical arguments indicate that the observed horizontal vorticity (around 1 × 10−2 s−1), largely parallel to the boundary, can be readily produced with the type of buoyancy contrast observed. It is hypothesized that such local enhancement of horizontal vorticity often is required for the occurrence of significant (e.g., F2 or stronger) tornadoes, even in large-scale environments that appear conducive to tornado occurrence without the aid of local influences.
Abstract
Spatial variability of precipitation is analyzed to characterize to what extent precipitation observed at a single location is representative of precipitation over a larger area. Characterization of precipitation representativeness is made in probabilistic terms using a parametric approach, namely, by fitting a censored shifted gamma distribution to observation measurements. Parameters are estimated and analyzed for independent precipitation datasets, among which one is based on high-density gauge measurements. The results of this analysis serve as a basis for accounting for representativeness error in an ensemble verification process. Uncertainty associated with the scale mismatch between forecast and observation is accounted for by applying a perturbed-ensemble approach before the computation of scores. Verification results reveal a large impact of representativeness error on precipitation forecast reliability and skill estimates. The parametric model and estimated coefficients presented in this study could be used directly for forecast postprocessing to partly compensate for the limitation of any modeling system in terms of precipitation subgrid-scale variability.
Abstract
Spatial variability of precipitation is analyzed to characterize to what extent precipitation observed at a single location is representative of precipitation over a larger area. Characterization of precipitation representativeness is made in probabilistic terms using a parametric approach, namely, by fitting a censored shifted gamma distribution to observation measurements. Parameters are estimated and analyzed for independent precipitation datasets, among which one is based on high-density gauge measurements. The results of this analysis serve as a basis for accounting for representativeness error in an ensemble verification process. Uncertainty associated with the scale mismatch between forecast and observation is accounted for by applying a perturbed-ensemble approach before the computation of scores. Verification results reveal a large impact of representativeness error on precipitation forecast reliability and skill estimates. The parametric model and estimated coefficients presented in this study could be used directly for forecast postprocessing to partly compensate for the limitation of any modeling system in terms of precipitation subgrid-scale variability.
Abstract
Numerical weather prediction models often perform poorly for weakly forced, highly variable winds in nocturnal stable boundary layers (SBLs). When used as input to air-quality and dispersion models, these wind errors can lead to large errors in subsequent plume forecasts. Finer grid resolution and improved model numerics and physics can help reduce these errors. The Advanced Research Weather Research and Forecasting model (ARW-WRF) has higher-order numerics that may improve predictions of finescale winds (scales <~20 km) in nocturnal SBLs. However, better understanding of the physics controlling SBL flow is needed to take optimal advantage of advanced modeling capabilities.
To facilitate ARW-WRF evaluations, a small network of instrumented towers was deployed in the ridge-and-valley topography of central Pennsylvania (PA). Time series of local observations and model forecasts on 1.333- and 0.444-km grids were filtered to isolate deterministic lower-frequency wind components. The time-filtered SBL winds have substantially reduced root-mean-square errors and biases, compared to raw data. Subkilometer horizontal and very fine vertical resolutions are found to be important for reducing model speed and direction errors. Nonturbulent fluctuations in unfiltered, very finescale winds, parts of which may be resolvable by ARW-WRF, are shown to generate horizontal meandering in stable weakly forced conditions. These submesoscale motions include gravity waves, primarily horizontal 2D motions, and other complex signatures. Vertical structure and low-level biases of SBL variables are shown to be sensitive to parameter settings defining minimum “background” mixing in very stable conditions in two representative turbulence schemes.
Abstract
Numerical weather prediction models often perform poorly for weakly forced, highly variable winds in nocturnal stable boundary layers (SBLs). When used as input to air-quality and dispersion models, these wind errors can lead to large errors in subsequent plume forecasts. Finer grid resolution and improved model numerics and physics can help reduce these errors. The Advanced Research Weather Research and Forecasting model (ARW-WRF) has higher-order numerics that may improve predictions of finescale winds (scales <~20 km) in nocturnal SBLs. However, better understanding of the physics controlling SBL flow is needed to take optimal advantage of advanced modeling capabilities.
To facilitate ARW-WRF evaluations, a small network of instrumented towers was deployed in the ridge-and-valley topography of central Pennsylvania (PA). Time series of local observations and model forecasts on 1.333- and 0.444-km grids were filtered to isolate deterministic lower-frequency wind components. The time-filtered SBL winds have substantially reduced root-mean-square errors and biases, compared to raw data. Subkilometer horizontal and very fine vertical resolutions are found to be important for reducing model speed and direction errors. Nonturbulent fluctuations in unfiltered, very finescale winds, parts of which may be resolvable by ARW-WRF, are shown to generate horizontal meandering in stable weakly forced conditions. These submesoscale motions include gravity waves, primarily horizontal 2D motions, and other complex signatures. Vertical structure and low-level biases of SBL variables are shown to be sensitive to parameter settings defining minimum “background” mixing in very stable conditions in two representative turbulence schemes.
Abstract
The authors analyze the pretornadic phase (2100–2148 UTC; tornadogenesis began at 2152 UTC) of the Goshen County, Wyoming, supercell of 5 June 2009 intercepted by the second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2). The analysis relies on radar data from the Weather Surveillance Radar-1988 Doppler (WSR-88D) in Cheyenne, Wyoming (KCYS), and a pair of Doppler-on-Wheels (DOW) radars, mobile mesonet observations, and mobile sounding observations.
The storm resembles supercells that have been observed in the past. For example, it develops a couplet of counter-rotating vortices that straddle the hook echo within the rear-flank outflow and are joined by arching vortex lines, with the cyclonic vortex becoming increasingly dominant in the time leading up to tornadogenesis. The outflow in the hook echo region, where sampled, has relatively small virtual potential temperature θυ deficits during this stage of evolution. A few kilometers upstream (north) of the location of maximum vertical vorticity, θυ is no more than 3 K colder than the warmest θυ readings in the inflow of the storm. Forward trajectories originating in the outflow within and around the low-level mesocyclone rise rapidly, implying that the upward-directed perturbation pressure gradient force exceeds the negative buoyancy.
Low-level rotation intensifies in the 2142–2148 UTC period. The intensification is preceded by the formation of a descending reflectivity core (DRC), similar to others that have been documented in some supercells recently. The DRC is associated with a rapid increase in the vertical vorticity and circulation of the low-level mesocyclone.
Abstract
The authors analyze the pretornadic phase (2100–2148 UTC; tornadogenesis began at 2152 UTC) of the Goshen County, Wyoming, supercell of 5 June 2009 intercepted by the second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2). The analysis relies on radar data from the Weather Surveillance Radar-1988 Doppler (WSR-88D) in Cheyenne, Wyoming (KCYS), and a pair of Doppler-on-Wheels (DOW) radars, mobile mesonet observations, and mobile sounding observations.
The storm resembles supercells that have been observed in the past. For example, it develops a couplet of counter-rotating vortices that straddle the hook echo within the rear-flank outflow and are joined by arching vortex lines, with the cyclonic vortex becoming increasingly dominant in the time leading up to tornadogenesis. The outflow in the hook echo region, where sampled, has relatively small virtual potential temperature θυ deficits during this stage of evolution. A few kilometers upstream (north) of the location of maximum vertical vorticity, θυ is no more than 3 K colder than the warmest θυ readings in the inflow of the storm. Forward trajectories originating in the outflow within and around the low-level mesocyclone rise rapidly, implying that the upward-directed perturbation pressure gradient force exceeds the negative buoyancy.
Low-level rotation intensifies in the 2142–2148 UTC period. The intensification is preceded by the formation of a descending reflectivity core (DRC), similar to others that have been documented in some supercells recently. The DRC is associated with a rapid increase in the vertical vorticity and circulation of the low-level mesocyclone.
