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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
Two neutrally buoyant SOFAR floats vigorously looped and meandered at depths of 950–1150 m in the eastern tropical Atlantic Ocean. The float trajectories illustrate a poleward flow along the tropical eastern boundary and significant intermediate-depth mesoscale variability in the low-latitude eastern basin. One float, caught within an energetic cyclonic eddy near the eastern boundary, looped cyclonically 14 times while translating 600 km northward parallel to the African coastline. A second float, launched near the Mid-Atlantic Ridge, meandered eastward with a Lagrangian zonal wavelength of 400 km and meridional amplitude exceeding 200 km. Satellite infrared imagery indicates that horizontal shear associated with the system of near-surface zonal equatorial currents may contribute to the observed intermediate-depth variability.
Abstract
Two neutrally buoyant SOFAR floats vigorously looped and meandered at depths of 950–1150 m in the eastern tropical Atlantic Ocean. The float trajectories illustrate a poleward flow along the tropical eastern boundary and significant intermediate-depth mesoscale variability in the low-latitude eastern basin. One float, caught within an energetic cyclonic eddy near the eastern boundary, looped cyclonically 14 times while translating 600 km northward parallel to the African coastline. A second float, launched near the Mid-Atlantic Ridge, meandered eastward with a Lagrangian zonal wavelength of 400 km and meridional amplitude exceeding 200 km. Satellite infrared imagery indicates that horizontal shear associated with the system of near-surface zonal equatorial currents may contribute to the observed intermediate-depth variability.
Abstract
Subsurface float and surface drifter observations illustrate the structure, evolution, and eventual demise of 10 North Brazil Current (NBC) rings as they approached and collided with the Lesser Antilles in the western tropical Atlantic Ocean. Upon encountering the shoaling topography east of the Lesser Antilles, most of the rings were deflected abruptly northward and several were observed to completely engulf the island of Barbados. The near-surface and subthermocline layers of two rings were observed to cleave or separate upon encountering shoaling bathymetry between Tobago and Barbados, with the resulting portions each retaining an independent and coherent ringlike vortical circulation. Surface drifters and shallow (250 m) subsurface floats that looped within NBC rings were more likely to enter the Caribbean through the passages of the Lesser Antilles than were deeper (500 or 900 m) floats, indicating that the regional bathymetry preferentially inhibits transport of intermediate-depth ring components. No evidence was found for the wholesale passage of rings through the island chain.
Abstract
Subsurface float and surface drifter observations illustrate the structure, evolution, and eventual demise of 10 North Brazil Current (NBC) rings as they approached and collided with the Lesser Antilles in the western tropical Atlantic Ocean. Upon encountering the shoaling topography east of the Lesser Antilles, most of the rings were deflected abruptly northward and several were observed to completely engulf the island of Barbados. The near-surface and subthermocline layers of two rings were observed to cleave or separate upon encountering shoaling bathymetry between Tobago and Barbados, with the resulting portions each retaining an independent and coherent ringlike vortical circulation. Surface drifters and shallow (250 m) subsurface floats that looped within NBC rings were more likely to enter the Caribbean through the passages of the Lesser Antilles than were deeper (500 or 900 m) floats, indicating that the regional bathymetry preferentially inhibits transport of intermediate-depth ring components. No evidence was found for the wholesale passage of rings through the island chain.
Abstract
The relative operating characteristic (ROC) curve is a popular diagnostic tool in forecast verification, with the area under the ROC curve (AUC) used as a verification metric measuring the discrimination ability of a forecast. Along with calibration, discrimination is deemed as a fundamental probabilistic forecast attribute. In particular, in ensemble forecast verification, AUC provides a basis for the comparison of potential predictive skill of competing forecasts. While this approach is straightforward when dealing with forecasts of common events (e.g., probability of precipitation), the AUC interpretation can turn out to be oversimplistic or misleading when focusing on rare events (e.g., precipitation exceeding some warning criterion). How should we interpret AUC of ensemble forecasts when focusing on rare events? How can changes in the way probability forecasts are derived from the ensemble forecast affect AUC results? How can we detect a genuine improvement in terms of predictive skill? Based on verification experiments, a critical eye is cast on the AUC interpretation to answer these questions. As well as the traditional trapezoidal approximation and the well-known binormal fitting model, we discuss a new approach that embraces the concept of imprecise probabilities and relies on the subdivision of the lowest ensemble probability category.
Abstract
The relative operating characteristic (ROC) curve is a popular diagnostic tool in forecast verification, with the area under the ROC curve (AUC) used as a verification metric measuring the discrimination ability of a forecast. Along with calibration, discrimination is deemed as a fundamental probabilistic forecast attribute. In particular, in ensemble forecast verification, AUC provides a basis for the comparison of potential predictive skill of competing forecasts. While this approach is straightforward when dealing with forecasts of common events (e.g., probability of precipitation), the AUC interpretation can turn out to be oversimplistic or misleading when focusing on rare events (e.g., precipitation exceeding some warning criterion). How should we interpret AUC of ensemble forecasts when focusing on rare events? How can changes in the way probability forecasts are derived from the ensemble forecast affect AUC results? How can we detect a genuine improvement in terms of predictive skill? Based on verification experiments, a critical eye is cast on the AUC interpretation to answer these questions. As well as the traditional trapezoidal approximation and the well-known binormal fitting model, we discuss a new approach that embraces the concept of imprecise probabilities and relies on the subdivision of the lowest ensemble probability category.
Abstract
The distribution, number and movement of cyclonic Gulf Stream rings were estimated from an analysis of 50 000 temperature records obtained from the National Oceanographic Data Center and Fleet Numerical Weather Central. The data were taken from 1970 through September 1976 in the region bounded by 20–40°N and 50–80°W. Additional ring observations from other sources were also used. Twenty-five ring time series, together with 26 single ring observations were obtained; approximately 11 rings were found to exist at one time. Rings typically moved westward, turned southwest when close to the Gulf Stream and appeared to coalesce with the Stream near Florida. On the average, two rings per year moved down this path with a mean speed of 3 km day−1 and an estimated life span of 2–3 years. Although ring observations were concentrated in the northwestern Sargasso Sea, several were documented east of 60°W. In addition to cold core rings several warm eddies were found south of the Stream; they consisted of at least a 150 m deepening of the main thermocline. The movement of anticyclonic rings north of the Stream was also determined; approximately three exist at a single time and they move westward with a mean speed of 5 km day−1.
Abstract
The distribution, number and movement of cyclonic Gulf Stream rings were estimated from an analysis of 50 000 temperature records obtained from the National Oceanographic Data Center and Fleet Numerical Weather Central. The data were taken from 1970 through September 1976 in the region bounded by 20–40°N and 50–80°W. Additional ring observations from other sources were also used. Twenty-five ring time series, together with 26 single ring observations were obtained; approximately 11 rings were found to exist at one time. Rings typically moved westward, turned southwest when close to the Gulf Stream and appeared to coalesce with the Stream near Florida. On the average, two rings per year moved down this path with a mean speed of 3 km day−1 and an estimated life span of 2–3 years. Although ring observations were concentrated in the northwestern Sargasso Sea, several were documented east of 60°W. In addition to cold core rings several warm eddies were found south of the Stream; they consisted of at least a 150 m deepening of the main thermocline. The movement of anticyclonic rings north of the Stream was also determined; approximately three exist at a single time and they move westward with a mean speed of 5 km day−1.
Abstract
SOFAR floats at different depths within two Mediterranean Water eddies (meddies) reveal that the meddy rotation axes tilt transversely with respect to the meddy translation direction. The rotation axis of one of the meddies (Meddy 1) was displaced by about 6 km over a depth of roughly 100 m; the axis of the second meddy (Meddy 2) was displaced by about 0.4 km over 100-m depth. These results are compared to a simple theoretical model that predicts the deformation and translation of a lens-shaped eddy embedded in large-scale external shear. Observed lateral deformations of the meddles are in good agreement with model predictions. The observed tilt of Meddy 1 is attributed to a combination of depth-varying rotation rate beneath the meddy core and the horizontal translation of the meddy; the tilt of Meddy 2 is attributed to a deformation of the meddy core by vertically sheared flow outside the meddy. The observed translation speed of the meddies with respect to nearby floats outside of the meddies is significantly larger than that predicted by the model.
Abstract
SOFAR floats at different depths within two Mediterranean Water eddies (meddies) reveal that the meddy rotation axes tilt transversely with respect to the meddy translation direction. The rotation axis of one of the meddies (Meddy 1) was displaced by about 6 km over a depth of roughly 100 m; the axis of the second meddy (Meddy 2) was displaced by about 0.4 km over 100-m depth. These results are compared to a simple theoretical model that predicts the deformation and translation of a lens-shaped eddy embedded in large-scale external shear. Observed lateral deformations of the meddles are in good agreement with model predictions. The observed tilt of Meddy 1 is attributed to a combination of depth-varying rotation rate beneath the meddy core and the horizontal translation of the meddy; the tilt of Meddy 2 is attributed to a deformation of the meddy core by vertically sheared flow outside the meddy. The observed translation speed of the meddies with respect to nearby floats outside of the meddies is significantly larger than that predicted by the model.
Abstract
Early awareness of extreme precipitation can provide the time necessary to make adequate event preparations. At the European Centre for Medium-Range Weather Forecasts (ECMWF), one tool that condenses the forecast information from the Integrated Forecasting System ensemble (ENS) is the extreme forecast index (EFI), an index that highlights regions that are forecast to have potentially anomalous weather conditions compared to the local climate. This paper builds on previous findings by undertaking a global verification throughout the medium-range forecast horizon (out to 15 days) on the ability of the EFI for water vapor transport [integrated vapor transport (IVT)] and precipitation to capture extreme observed precipitation. Using the ECMWF ENS for winters 2015/16 and 2016/17 and daily surface precipitation observations, the relative operating characteristic is used to show that the IVT EFI is more skillful than the precipitation EFI in forecast week 2 over Europe and western North America. It is the large-scale nature of the IVT, its higher predictability, and its relationship with extreme precipitation that result in its potential usefulness in these regions, which, in turn, could provide earlier awareness of extreme precipitation. Conversely, at shorter lead times the precipitation EFI is more useful, although the IVT EFI can provide synoptic-scale understanding. For the whole globe, the extratropical Northern Hemisphere, the tropics, and North America, the precipitation EFI is more useful throughout the medium range, suggesting that precipitation processes not captured in the IVT are important (e.g., tropical convection). Following these results, the operational implementation of the IVT EFI is currently being planned.
Abstract
Early awareness of extreme precipitation can provide the time necessary to make adequate event preparations. At the European Centre for Medium-Range Weather Forecasts (ECMWF), one tool that condenses the forecast information from the Integrated Forecasting System ensemble (ENS) is the extreme forecast index (EFI), an index that highlights regions that are forecast to have potentially anomalous weather conditions compared to the local climate. This paper builds on previous findings by undertaking a global verification throughout the medium-range forecast horizon (out to 15 days) on the ability of the EFI for water vapor transport [integrated vapor transport (IVT)] and precipitation to capture extreme observed precipitation. Using the ECMWF ENS for winters 2015/16 and 2016/17 and daily surface precipitation observations, the relative operating characteristic is used to show that the IVT EFI is more skillful than the precipitation EFI in forecast week 2 over Europe and western North America. It is the large-scale nature of the IVT, its higher predictability, and its relationship with extreme precipitation that result in its potential usefulness in these regions, which, in turn, could provide earlier awareness of extreme precipitation. Conversely, at shorter lead times the precipitation EFI is more useful, although the IVT EFI can provide synoptic-scale understanding. For the whole globe, the extratropical Northern Hemisphere, the tropics, and North America, the precipitation EFI is more useful throughout the medium range, suggesting that precipitation processes not captured in the IVT are important (e.g., tropical convection). Following these results, the operational implementation of the IVT EFI is currently being planned.
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.
The potential economic benefit associated with the use of an ensemble of forecasts versus an equivalent or higher-resolution control forecast is discussed. Neither forecast systems are postprocessed, except a simple calibration that is applied to make them reliable. A simple decision-making model is used where all potential users of weather forecasts are characterized by the ratio between the cost of their action to prevent weather-related damages, and the loss that they incur in case they do not protect their operations. It is shown that the ensemble forecast system can be used by a much wider range of users. Furthermore, for many, and for beyond 4-day lead time for all users, the ensemble provides greater potential economic benefit than a control forecast, even if the latter is run at higher horizontal resolution. It is argued that the added benefits derive from 1) the fact that the ensemble provides a more detailed forecast probability distribution, allowing the users to tailor their weather forecast–related actions to their particular cost–loss situation, and 2) the ensemble's ability to differentiate between high-and low-predictability cases. While single forecasts can statistically be supplemented by more detailed probability distributions, it is not clear whether with more sophisticated postprocessing they can identify more and less predictable forecast cases as successfully as ensembles do.
The potential economic benefit associated with the use of an ensemble of forecasts versus an equivalent or higher-resolution control forecast is discussed. Neither forecast systems are postprocessed, except a simple calibration that is applied to make them reliable. A simple decision-making model is used where all potential users of weather forecasts are characterized by the ratio between the cost of their action to prevent weather-related damages, and the loss that they incur in case they do not protect their operations. It is shown that the ensemble forecast system can be used by a much wider range of users. Furthermore, for many, and for beyond 4-day lead time for all users, the ensemble provides greater potential economic benefit than a control forecast, even if the latter is run at higher horizontal resolution. It is argued that the added benefits derive from 1) the fact that the ensemble provides a more detailed forecast probability distribution, allowing the users to tailor their weather forecast–related actions to their particular cost–loss situation, and 2) the ensemble's ability to differentiate between high-and low-predictability cases. While single forecasts can statistically be supplemented by more detailed probability distributions, it is not clear whether with more sophisticated postprocessing they can identify more and less predictable forecast cases as successfully as ensembles do.
