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Abstract
Observations of hurricane position, which in practice might be available from satellite or radar imagery, can be easily assimilated with an ensemble Kalman filter (EnKF) given an operator that computes the position of the vortex in the background forecast. The simple linear updating scheme used in the EnKF is effective for small displacements of forecasted vortices from the true position; this situation is operationally relevant since hurricane position is often available frequently in time. When displacements of the forecasted vortices are comparable to the vortex size, non-Gaussian effects become significant and the EnKF’s linear update begins to degrade. Simulations using a simple two-dimensional barotropic model demonstrate the potential of the technique and show that the track forecast initialized with the EnKF analysis is improved. The assimilation of observations of the vortex shape and intensity, along with position, extends the technique’s effectiveness to larger displacements of the forecasted vortices than when assimilating position alone.
Abstract
Observations of hurricane position, which in practice might be available from satellite or radar imagery, can be easily assimilated with an ensemble Kalman filter (EnKF) given an operator that computes the position of the vortex in the background forecast. The simple linear updating scheme used in the EnKF is effective for small displacements of forecasted vortices from the true position; this situation is operationally relevant since hurricane position is often available frequently in time. When displacements of the forecasted vortices are comparable to the vortex size, non-Gaussian effects become significant and the EnKF’s linear update begins to degrade. Simulations using a simple two-dimensional barotropic model demonstrate the potential of the technique and show that the track forecast initialized with the EnKF analysis is improved. The assimilation of observations of the vortex shape and intensity, along with position, extends the technique’s effectiveness to larger displacements of the forecasted vortices than when assimilating position alone.
Abstract
Assimilation of Doppler radar data into cloud models is an important obstacle to routine numerical weather prediction for convective-scale motions; the difficulty lies in initializing fields of wind, temperature, moisture, and condensate given only observations of radial velocity and reflectivity from the radar. This paper investigates the potential of the ensemble Kalman filter (EnKF), which estimates the covariances between observed variables and the state through an ensemble of forecasts, to assimilate radar observations at convective scales. In the basic experiment, simulated observations are extracted from a reference simulation of a splitting supercell and assimilated using the EnKF and the same numerical model that produced the reference simulation. The EnKF produces accurate analyses, including the unobserved variables, after roughly 30 min (or six scans) of radial velocity observations. Additional experiments, in which forecasts are made from the ensemble-mean analysis, reveal that forecast errors grow significantly in this simple system, so that the ability of the EnKF to track the reference solution is not simply because of stable system dynamics. It is also found that the covariances between radial velocity and temperature, moisture, and condensate are important to the quality of the analyses, as is the initialization chosen for the ensemble members prior to assimilating the first observations. These results are promising, especially given the ease of implementing the EnKF. A number of important issues remain, however, including the initialization of the ensemble prior to the first observation, the treatment of uncertainty in the environmental sounding, the role of error in the forecast model (particularly the microphysical parameterizations), and the treatment of lateral boundary conditions.
Abstract
Assimilation of Doppler radar data into cloud models is an important obstacle to routine numerical weather prediction for convective-scale motions; the difficulty lies in initializing fields of wind, temperature, moisture, and condensate given only observations of radial velocity and reflectivity from the radar. This paper investigates the potential of the ensemble Kalman filter (EnKF), which estimates the covariances between observed variables and the state through an ensemble of forecasts, to assimilate radar observations at convective scales. In the basic experiment, simulated observations are extracted from a reference simulation of a splitting supercell and assimilated using the EnKF and the same numerical model that produced the reference simulation. The EnKF produces accurate analyses, including the unobserved variables, after roughly 30 min (or six scans) of radial velocity observations. Additional experiments, in which forecasts are made from the ensemble-mean analysis, reveal that forecast errors grow significantly in this simple system, so that the ability of the EnKF to track the reference solution is not simply because of stable system dynamics. It is also found that the covariances between radial velocity and temperature, moisture, and condensate are important to the quality of the analyses, as is the initialization chosen for the ensemble members prior to assimilating the first observations. These results are promising, especially given the ease of implementing the EnKF. A number of important issues remain, however, including the initialization of the ensemble prior to the first observation, the treatment of uncertainty in the environmental sounding, the role of error in the forecast model (particularly the microphysical parameterizations), and the treatment of lateral boundary conditions.
Abstract
Particle filtering methods for data assimilation may suffer from the “curse of dimensionality,” where the required ensemble size grows rapidly as the dimension increases. It would, therefore, be useful to know a priori whether a particle filter is feasible to implement in a given system. Previous work provides an asymptotic relation between the necessary ensemble size and an exponential function of 
Abstract
Particle filtering methods for data assimilation may suffer from the “curse of dimensionality,” where the required ensemble size grows rapidly as the dimension increases. It would, therefore, be useful to know a priori whether a particle filter is feasible to implement in a given system. Previous work provides an asymptotic relation between the necessary ensemble size and an exponential function of
Abstract
The spontaneous generation of inertia–gravity waves in idealized life cycles of baroclinic instability is investigated using the Weather Research and Forecasting Model. Two substantially different life cycles of baroclinic instability are obtained by varying the initial zonal jet. The wave generation depends strongly on the details of the baroclinic wave’s development. In the life cycle dominated by cyclonic behavior, the most conspicuous gravity waves are excited by the upper-level jet and are broadly consistent with previous simulations of O’Sullivan and Dunkerton. In the life cycle that is dominated by anticyclonic behavior, the most conspicuous gravity waves even in the stratosphere are excited by the surface fronts, although the fronts are no stronger than in the cyclonic life cycle. The anticyclonic life cycle also reveals waves in the lower stratosphere above the upper-level trough of the baroclinic wave; these waves have not been previously identified in idealized simulations. The sensitivities of the different waves to both resolution and dissipation are discussed.
Abstract
The spontaneous generation of inertia–gravity waves in idealized life cycles of baroclinic instability is investigated using the Weather Research and Forecasting Model. Two substantially different life cycles of baroclinic instability are obtained by varying the initial zonal jet. The wave generation depends strongly on the details of the baroclinic wave’s development. In the life cycle dominated by cyclonic behavior, the most conspicuous gravity waves are excited by the upper-level jet and are broadly consistent with previous simulations of O’Sullivan and Dunkerton. In the life cycle that is dominated by anticyclonic behavior, the most conspicuous gravity waves even in the stratosphere are excited by the surface fronts, although the fronts are no stronger than in the cyclonic life cycle. The anticyclonic life cycle also reveals waves in the lower stratosphere above the upper-level trough of the baroclinic wave; these waves have not been previously identified in idealized simulations. The sensitivities of the different waves to both resolution and dissipation are discussed.
Abstract
Deficiencies in forecast models commonly stem from inadequate representation of physical processes; yet, improvement to any single physics component within a model may lead to degradations in other physics components or the model as a whole. In this study, a systematic investigation of physics tendencies is demonstrated to help identify and correct compensating sources of model biases. The model improvement process is illustrated by addressing a commonly known issue in warm-season rainfall forecasts from parameterized convection models: the misrepresentation of the diurnal precipitation cycle over land, especially in its timing. Recent advances in closure assumptions in mass-flux cumulus schemes have made remarkable improvements in this respect. Here, we investigate these improvements in the representation of the diurnal precipitation cycle for a spring period over the United States, and how changes to the cumulus scheme impact the model climate and the behavior of other physics schemes. The modified cumulus scheme improves both the timing of the diurnal precipitation cycle and reduces midtropospheric temperature and moisture biases. However, larger temperature and moisture biases are found in the boundary layer as compared to a predecessor scheme, along with an overamplification of the diurnal precipitation cycle, relative to observations. Guided by a tendency analysis, we find that biases in the diurnal amplitude of the precipitation cycle in our simulations, along with temperature and moisture biases in the boundary layer, originate from the land surface model.
Abstract
Deficiencies in forecast models commonly stem from inadequate representation of physical processes; yet, improvement to any single physics component within a model may lead to degradations in other physics components or the model as a whole. In this study, a systematic investigation of physics tendencies is demonstrated to help identify and correct compensating sources of model biases. The model improvement process is illustrated by addressing a commonly known issue in warm-season rainfall forecasts from parameterized convection models: the misrepresentation of the diurnal precipitation cycle over land, especially in its timing. Recent advances in closure assumptions in mass-flux cumulus schemes have made remarkable improvements in this respect. Here, we investigate these improvements in the representation of the diurnal precipitation cycle for a spring period over the United States, and how changes to the cumulus scheme impact the model climate and the behavior of other physics schemes. The modified cumulus scheme improves both the timing of the diurnal precipitation cycle and reduces midtropospheric temperature and moisture biases. However, larger temperature and moisture biases are found in the boundary layer as compared to a predecessor scheme, along with an overamplification of the diurnal precipitation cycle, relative to observations. Guided by a tendency analysis, we find that biases in the diurnal amplitude of the precipitation cycle in our simulations, along with temperature and moisture biases in the boundary layer, originate from the land surface model.
Abstract
The ensemble Kalman filter (EnKF) uses an ensemble of short-range forecasts to estimate the flow-dependent background error covariances required in data assimilation. The feasibility of the EnKF for convective-scale data assimilation has been previously demonstrated in perfect-model experiments using simulated observations of radial velocity from a supercell storm. The present study further explores the potential and behavior of the EnKF at convective scales by considering more realistic initial analyses and variations in the availability and quality of the radar observations. Assimilation of simulated radial-velocity observations every 5 min where there is significant reflectivity using 20 ensemble members proves to be successful in most realistic observational scenarios for simulated supercell thunderstorms, although the same degree of success may not be readily expected with real observations and an imperfect model, at least with the present EnKF implementation. Even though the filter converges toward the truth simulation faster from a better initial estimate, an experiment with the initial estimate of the supercell displaced by 10 km still yields an accurate estimate of the storm for both observed and unobserved variables within 40 min. Similarly, radial-velocity observations below 2 km are certainly beneficial to capturing the storm (especially the detailed cold pool structure), but in their absence the assimilation scheme can still achieve a comparably accurate estimate of the state of the storm given a slightly longer assimilation period. An experiment with radar observations only above 4 km fails to assimilate the storm properly, but, with the addition of a hypothetical surface mesonet taking wind and temperature observations, the EnKF can again provide a good estimate of the storm. The supercell can also be successfully assimilated in the case of radar observations only below 4 km (such as those from the ground-based mobile radars). More frequent observations can help the storm assimilation initially, but the benefit diminishes after half an hour. Results presented here indicate that the vertical resolution and the uncertainty of observations, for the typical range of most of the observational radars, would have little impact on the overall performance of the EnKF in assimilating the storm.
Abstract
The ensemble Kalman filter (EnKF) uses an ensemble of short-range forecasts to estimate the flow-dependent background error covariances required in data assimilation. The feasibility of the EnKF for convective-scale data assimilation has been previously demonstrated in perfect-model experiments using simulated observations of radial velocity from a supercell storm. The present study further explores the potential and behavior of the EnKF at convective scales by considering more realistic initial analyses and variations in the availability and quality of the radar observations. Assimilation of simulated radial-velocity observations every 5 min where there is significant reflectivity using 20 ensemble members proves to be successful in most realistic observational scenarios for simulated supercell thunderstorms, although the same degree of success may not be readily expected with real observations and an imperfect model, at least with the present EnKF implementation. Even though the filter converges toward the truth simulation faster from a better initial estimate, an experiment with the initial estimate of the supercell displaced by 10 km still yields an accurate estimate of the storm for both observed and unobserved variables within 40 min. Similarly, radial-velocity observations below 2 km are certainly beneficial to capturing the storm (especially the detailed cold pool structure), but in their absence the assimilation scheme can still achieve a comparably accurate estimate of the state of the storm given a slightly longer assimilation period. An experiment with radar observations only above 4 km fails to assimilate the storm properly, but, with the addition of a hypothetical surface mesonet taking wind and temperature observations, the EnKF can again provide a good estimate of the storm. The supercell can also be successfully assimilated in the case of radar observations only below 4 km (such as those from the ground-based mobile radars). More frequent observations can help the storm assimilation initially, but the benefit diminishes after half an hour. Results presented here indicate that the vertical resolution and the uncertainty of observations, for the typical range of most of the observational radars, would have little impact on the overall performance of the EnKF in assimilating the storm.
Abstract
A method for determining adaptive observation locations is demonstrated. This method is based on optimal estimation (Kalman filter) theory; it determines the observation location that will maximize the expected improvement, which can be measured in terms of the expected reduction in analysis or forecast variance. This technique requires an accurate model for background error statistics that vary both in space and in time. Here, these covariances are generated using an ensemble Kalman filter assimilation scheme. A variant is also developed that can estimate the analysis improvement in data assimilation schemes where background error statistics are less accurate.
This approach is demonstrated using a quasigeostrophic channel model under perfect-model assumptions. The algorithm is applied here to find the supplemental rawinsonde location to add to a regular network of rawinsondes that will reduce analysis errors the most. The observation network is configured in this experiment so there is a data void in the western third of the domain. One-hundred-member ensembles from three data assimilation schemes are tested as input to the target selection procedure, two variants of the standard ensemble Kalman filter and a third perturbed observation (3DVAR) ensemble. The algorithm is shown to find large differences in the expected variance reduction depending on the observation location, the flow of the day, and the ensemble used in the adaptive observation algorithm. When using the two variants of the ensemble Kalman filter, the algorithm defined consistently similar adaptive locations to each other, and assimilation of the adaptive observation typically reduced analysis errors significantly. When the 3DVAR ensemble was used, the algorithm picked very different observation locations and the analyses were not improved as much.
The amount of improvement from assimilating a supplemental adaptive observation instead of a fixed observation in the middle of the void depended on whether the observation was assimilated sporadically or during every analysis cycle. For sporadic assimilation, the adaptive observation provided a dramatic improvement relative to the supplemental fixed observation. When an adaptive observation was regularly assimilated every cycle, the improvement was smaller.
For the sporadic assimilation of an adaptive observation, targeting based simply on the maximum spread in background forecasts provided similar target locations and similar analysis improvements to those generated with the full algorithm. The improvement from the regular assimilation of an adaptive observation based on the spread algorithm was no larger than when observations from a fixed target in the middle of the void were regularly assimilated.
Abstract
A method for determining adaptive observation locations is demonstrated. This method is based on optimal estimation (Kalman filter) theory; it determines the observation location that will maximize the expected improvement, which can be measured in terms of the expected reduction in analysis or forecast variance. This technique requires an accurate model for background error statistics that vary both in space and in time. Here, these covariances are generated using an ensemble Kalman filter assimilation scheme. A variant is also developed that can estimate the analysis improvement in data assimilation schemes where background error statistics are less accurate.
This approach is demonstrated using a quasigeostrophic channel model under perfect-model assumptions. The algorithm is applied here to find the supplemental rawinsonde location to add to a regular network of rawinsondes that will reduce analysis errors the most. The observation network is configured in this experiment so there is a data void in the western third of the domain. One-hundred-member ensembles from three data assimilation schemes are tested as input to the target selection procedure, two variants of the standard ensemble Kalman filter and a third perturbed observation (3DVAR) ensemble. The algorithm is shown to find large differences in the expected variance reduction depending on the observation location, the flow of the day, and the ensemble used in the adaptive observation algorithm. When using the two variants of the ensemble Kalman filter, the algorithm defined consistently similar adaptive locations to each other, and assimilation of the adaptive observation typically reduced analysis errors significantly. When the 3DVAR ensemble was used, the algorithm picked very different observation locations and the analyses were not improved as much.
The amount of improvement from assimilating a supplemental adaptive observation instead of a fixed observation in the middle of the void depended on whether the observation was assimilated sporadically or during every analysis cycle. For sporadic assimilation, the adaptive observation provided a dramatic improvement relative to the supplemental fixed observation. When an adaptive observation was regularly assimilated every cycle, the improvement was smaller.
For the sporadic assimilation of an adaptive observation, targeting based simply on the maximum spread in background forecasts provided similar target locations and similar analysis improvements to those generated with the full algorithm. The improvement from the regular assimilation of an adaptive observation based on the spread algorithm was no larger than when observations from a fixed target in the middle of the void were regularly assimilated.
Abstract
A mesoscale model is used here to investigate the possible sources of forecast error for the 24–25 January 2000 snowstorm along the east coast of the United States. The primary focus is the quantitative precipitation forecast out to lead times of 36 h. The success of the present high-resolution control forecast shows that the storm could have been well forecasted with conventional data in real time. Various experiments suggest that insufficient model grid resolution and errors in the initial conditions both contributed significantly to problems in the forecast. Other experiments, motivated by the possibility that the forecast errors arose from the operational analysis poorly fitting one or two key soundings, test the effects of withholding single soundings from the control initial conditions. While no single sounding results in forecast changes that are more than a small fraction of the error in the operational forecast, these experiments do reveal that the detailed mesoscale distribution of precipitation in the 24- or 36-h forecast can be significantly altered even by such small changes in the initial conditions. The experiments also reveal that the forecast changes arise from the rapid growth of error at scales below 500 km in association with moist processes. The results presented emphasize the difficulty of forecasting precipitation relative to, say, surface pressure and suggest that the predictability of mesoscale precipitation features in cases of the type studied here may be limited to less than 2–3 days.
Abstract
A mesoscale model is used here to investigate the possible sources of forecast error for the 24–25 January 2000 snowstorm along the east coast of the United States. The primary focus is the quantitative precipitation forecast out to lead times of 36 h. The success of the present high-resolution control forecast shows that the storm could have been well forecasted with conventional data in real time. Various experiments suggest that insufficient model grid resolution and errors in the initial conditions both contributed significantly to problems in the forecast. Other experiments, motivated by the possibility that the forecast errors arose from the operational analysis poorly fitting one or two key soundings, test the effects of withholding single soundings from the control initial conditions. While no single sounding results in forecast changes that are more than a small fraction of the error in the operational forecast, these experiments do reveal that the detailed mesoscale distribution of precipitation in the 24- or 36-h forecast can be significantly altered even by such small changes in the initial conditions. The experiments also reveal that the forecast changes arise from the rapid growth of error at scales below 500 km in association with moist processes. The results presented emphasize the difficulty of forecasting precipitation relative to, say, surface pressure and suggest that the predictability of mesoscale precipitation features in cases of the type studied here may be limited to less than 2–3 days.
