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Abstract
Suppose that one has the freedom to adapt the observational network by choosing the times and locations of observations. Which choices would yield the best analysis of the atmospheric state or the best subsequent forecast? Here, this problem of “adaptive observations” is formulated as a problem in statistical design. The statistical framework provides a rigorous mathematical statement of the adaptive observations problem and indicates where the uncertainty of the current analysis, the dynamics of error evolution, the form and errors of observations, and data assimilation each enter the calculation. The statistical formulation of the problem also makes clear the importance of the optimality criteria (for instance, one might choose to minimize the total error variance in a given forecast) and identifies approximations that make calculation of optimal solutions feasible in principle. Optimal solutions are discussed and interpreted for a variety of cases. Selected approaches to the adaptive observations problem found in the literature are reviewed and interpreted from the optimal statistical design viewpoint. In addition, a numerical example, using the 40-variable model of Lorenz and Emanuel, suggests that some other proposed approaches may often be close to the optimal solution, at least in this highly idealized model.
Abstract
Suppose that one has the freedom to adapt the observational network by choosing the times and locations of observations. Which choices would yield the best analysis of the atmospheric state or the best subsequent forecast? Here, this problem of “adaptive observations” is formulated as a problem in statistical design. The statistical framework provides a rigorous mathematical statement of the adaptive observations problem and indicates where the uncertainty of the current analysis, the dynamics of error evolution, the form and errors of observations, and data assimilation each enter the calculation. The statistical formulation of the problem also makes clear the importance of the optimality criteria (for instance, one might choose to minimize the total error variance in a given forecast) and identifies approximations that make calculation of optimal solutions feasible in principle. Optimal solutions are discussed and interpreted for a variety of cases. Selected approaches to the adaptive observations problem found in the literature are reviewed and interpreted from the optimal statistical design viewpoint. In addition, a numerical example, using the 40-variable model of Lorenz and Emanuel, suggests that some other proposed approaches may often be close to the optimal solution, at least in this highly idealized model.
Abstract
During the spring 2011 season, a real-time continuously cycled ensemble data assimilation system using the Advanced Research version of the Weather Research and Forecasting Model (WRF) coupled with the Data Assimilation Research Testbed toolkit provided initial and boundary conditions for deterministic convection-permitting forecasts, also using WRF, over the eastern two-thirds of the conterminous United States (CONUS). In this study the authors evaluate the mesoscale assimilation system and the convection-permitting forecasts, at 15- and 3-km grid spacing, respectively. Experiments employing different physics options within the continuously cycled ensemble data assimilation system are shown to lead to differences in the mean mesoscale analysis characteristics. Convection-permitting forecasts with a fixed model configuration are initialized from these physics-varied analyses, as well as control runs from 0.5° Global Forecast System (GFS) analysis. Systematic bias in the analysis background influences the analysis fit to observations, and when this analysis initializes convection-permitting forecasts, the forecast skill is degraded as bias in the analysis background increases. Moreover, differences in mean error characteristics associated with each physical parameterization suite lead to unique errors of spatial, temporal, and intensity aspects of convection-permitting rainfall forecasts. Observation bias by platform type is also shown to impact the analysis quality.
Abstract
During the spring 2011 season, a real-time continuously cycled ensemble data assimilation system using the Advanced Research version of the Weather Research and Forecasting Model (WRF) coupled with the Data Assimilation Research Testbed toolkit provided initial and boundary conditions for deterministic convection-permitting forecasts, also using WRF, over the eastern two-thirds of the conterminous United States (CONUS). In this study the authors evaluate the mesoscale assimilation system and the convection-permitting forecasts, at 15- and 3-km grid spacing, respectively. Experiments employing different physics options within the continuously cycled ensemble data assimilation system are shown to lead to differences in the mean mesoscale analysis characteristics. Convection-permitting forecasts with a fixed model configuration are initialized from these physics-varied analyses, as well as control runs from 0.5° Global Forecast System (GFS) analysis. Systematic bias in the analysis background influences the analysis fit to observations, and when this analysis initializes convection-permitting forecasts, the forecast skill is degraded as bias in the analysis background increases. Moreover, differences in mean error characteristics associated with each physical parameterization suite lead to unique errors of spatial, temporal, and intensity aspects of convection-permitting rainfall forecasts. Observation bias by platform type is also shown to impact the analysis quality.
Abstract
Real-time analyses and forecasts using an ensemble Kalman filter (EnKF) and the Advanced Hurricane Weather Research and Forecasting Model (AHW) are evaluated from the 2009 North Atlantic hurricane season. This data assimilation system involved cycling observations that included conventional in situ data, tropical cyclone (TC) position, and minimum SLP and synoptic dropsondes each 6 h using a 96-member ensemble on a 36-km domain for three months. Similar to past studies, observation assimilation systematically reduces the TC position and minimum SLP errors, except for strong TCs, which are characterized by large biases due to grid resolution. At 48 different initialization times, an AHW forecast on 12-, 4-, and 1.33-km grids is produced with initial conditions drawn from a single analysis member. Whereas TC track analyses and forecasts exhibit a pronounced northward bias, intensity forecast errors are similar to (lower than) the NWS Hurricane Weather Research Model (HWRF) and GFDL forecasts for forecast lead times ≤60 h (>60 h), with the largest track errors associated with the weakest systems, such as Tropical Storm (TS) Erika. Several shortcomings of the data assimilation system are addressed through postseason sensitivity tests, including using the maximum 800-hPa circulation to identify the TC position during assimilation and turning off the quality control for the TC minimum SLP observation when the initial intensity is far too weak. In addition, the improved forecast of TS Erika relative to HWRF is shown to be related to having initial conditions that are more representative of a sheared TC and not using a cumulus parameterization.
Abstract
Real-time analyses and forecasts using an ensemble Kalman filter (EnKF) and the Advanced Hurricane Weather Research and Forecasting Model (AHW) are evaluated from the 2009 North Atlantic hurricane season. This data assimilation system involved cycling observations that included conventional in situ data, tropical cyclone (TC) position, and minimum SLP and synoptic dropsondes each 6 h using a 96-member ensemble on a 36-km domain for three months. Similar to past studies, observation assimilation systematically reduces the TC position and minimum SLP errors, except for strong TCs, which are characterized by large biases due to grid resolution. At 48 different initialization times, an AHW forecast on 12-, 4-, and 1.33-km grids is produced with initial conditions drawn from a single analysis member. Whereas TC track analyses and forecasts exhibit a pronounced northward bias, intensity forecast errors are similar to (lower than) the NWS Hurricane Weather Research Model (HWRF) and GFDL forecasts for forecast lead times ≤60 h (>60 h), with the largest track errors associated with the weakest systems, such as Tropical Storm (TS) Erika. Several shortcomings of the data assimilation system are addressed through postseason sensitivity tests, including using the maximum 800-hPa circulation to identify the TC position during assimilation and turning off the quality control for the TC minimum SLP observation when the initial intensity is far too weak. In addition, the improved forecast of TS Erika relative to HWRF is shown to be related to having initial conditions that are more representative of a sheared TC and not using a cumulus parameterization.
Abstract
The feasibility of using an ensemble Kalman filter (EnKF) to retrieve the wind and temperature fields in an isolated convective storm has been tested by applying the technique to observations of the 17 May 1981 Arcadia, Oklahoma, tornadic supercell. Radial-velocity and reflectivity observations from a single radar were assimilated into a nonhydrostatic, anelastic numerical model initialized with an idealized (horizontally homogeneous) base state. The assimilation results were compared to observations from another Doppler radar, the results of dual-Doppler wind syntheses, and in situ measurements from an instrumented tower. Observation errors make it more difficult to assess EnKF performance than in previous storm-scale EnKF experiments that employed synthetic observations and a perfect model; nevertheless, the comparisons in this case indicate that the locations of the main updraft and mesocyclone in the Arcadia storm were determined rather accurately, especially at midlevels. The magnitudes of vertical velocity and vertical vorticity in these features are similar to those in the dual-Doppler analyses, except that the low-level updraft is stronger in the EnKF analyses than in the dual-Doppler analyses.
Several assimilation-scheme parameters are adjustable, including the method of initializing the ensemble, the inflation factor applied to perturbations, the magnitude of the assumed observation-error variance, and the degree of localization of the filter. In the Arcadia storm experiments, in which observations of a mature storm were assimilated over a relatively short (47 min) period, the results depended most on the ensemble-initialization method.
In the data assimilation experiments, too much northerly storm-relative outflow along the south side of the low-level cold pool eventually developed during the assimilation period. Assimilation of Doppler observations did little to correct temperature errors near the surface in the cold pool. Both observational limitations (poor spatial resolution in the radar data near the ground) and model errors (coarse resolution and uncertainties in the parameterizations of moist processes) probably contributed to poor low-level temperature analyses in these experiments.
Abstract
The feasibility of using an ensemble Kalman filter (EnKF) to retrieve the wind and temperature fields in an isolated convective storm has been tested by applying the technique to observations of the 17 May 1981 Arcadia, Oklahoma, tornadic supercell. Radial-velocity and reflectivity observations from a single radar were assimilated into a nonhydrostatic, anelastic numerical model initialized with an idealized (horizontally homogeneous) base state. The assimilation results were compared to observations from another Doppler radar, the results of dual-Doppler wind syntheses, and in situ measurements from an instrumented tower. Observation errors make it more difficult to assess EnKF performance than in previous storm-scale EnKF experiments that employed synthetic observations and a perfect model; nevertheless, the comparisons in this case indicate that the locations of the main updraft and mesocyclone in the Arcadia storm were determined rather accurately, especially at midlevels. The magnitudes of vertical velocity and vertical vorticity in these features are similar to those in the dual-Doppler analyses, except that the low-level updraft is stronger in the EnKF analyses than in the dual-Doppler analyses.
Several assimilation-scheme parameters are adjustable, including the method of initializing the ensemble, the inflation factor applied to perturbations, the magnitude of the assumed observation-error variance, and the degree of localization of the filter. In the Arcadia storm experiments, in which observations of a mature storm were assimilated over a relatively short (47 min) period, the results depended most on the ensemble-initialization method.
In the data assimilation experiments, too much northerly storm-relative outflow along the south side of the low-level cold pool eventually developed during the assimilation period. Assimilation of Doppler observations did little to correct temperature errors near the surface in the cold pool. Both observational limitations (poor spatial resolution in the radar data near the ground) and model errors (coarse resolution and uncertainties in the parameterizations of moist processes) probably contributed to poor low-level temperature analyses in these experiments.
Abstract
Kinetic energy (KE) spectra derived from global high-resolution atmospheric simulations from the Model for Prediction Across Scales (MPAS) are presented. The simulations are produced using quasi-uniform global Voronoi horizontal meshes with 3-, 7.5-, and 15-km mean cell spacings. KE spectra from the MPAS simulations compare well with observations and other simulations in the literature and possess the canonical KE spectra structure including a very-well-resolved shallow-sloped mesoscale region in the 3-km simulation. There is a peak in the vertical velocity variance at the model filter scale for all simulations, indicating the underresolved nature of updrafts even with the 3-km mesh. The KE spectra reveal that the MPAS configuration produces an effective model resolution (filter scale) of approximately 6Δx. Comparison with other published model KE spectra highlight model filtering issues, specifically insufficient filtering that can lead to spectral blocking and the production of erroneous shallow-sloped mesoscale tails in the KE spectra. The mesoscale regions in the MPAS KE spectra are produced without use of kinetic energy backscatter, in contrast to other results reported in the literature. No substantive difference is found in KE spectra computed on constant height or constant pressure surfaces. Stratified turbulence is not resolved with the vertical resolution used in this study; hence, the results do not support recent conjecture that stratified turbulence explains the mesoscale portion of the KE spectrum.
Abstract
Kinetic energy (KE) spectra derived from global high-resolution atmospheric simulations from the Model for Prediction Across Scales (MPAS) are presented. The simulations are produced using quasi-uniform global Voronoi horizontal meshes with 3-, 7.5-, and 15-km mean cell spacings. KE spectra from the MPAS simulations compare well with observations and other simulations in the literature and possess the canonical KE spectra structure including a very-well-resolved shallow-sloped mesoscale region in the 3-km simulation. There is a peak in the vertical velocity variance at the model filter scale for all simulations, indicating the underresolved nature of updrafts even with the 3-km mesh. The KE spectra reveal that the MPAS configuration produces an effective model resolution (filter scale) of approximately 6Δx. Comparison with other published model KE spectra highlight model filtering issues, specifically insufficient filtering that can lead to spectral blocking and the production of erroneous shallow-sloped mesoscale tails in the KE spectra. The mesoscale regions in the MPAS KE spectra are produced without use of kinetic energy backscatter, in contrast to other results reported in the literature. No substantive difference is found in KE spectra computed on constant height or constant pressure surfaces. Stratified turbulence is not resolved with the vertical resolution used in this study; hence, the results do not support recent conjecture that stratified turbulence explains the mesoscale portion of the KE spectrum.
Abstract
The role of vertical mesh spacing in the convergence of full-physics global atmospheric model solutions is examined for synoptic, mesoscale, and convective-scale horizontal resolutions. Using the MPAS-Atmosphere model, convergence is evaluated for three solution metrics: the horizontal kinetic energy spectrum, the Richardson number probability density function, and resolved flow features. All three metrics exhibit convergence in the free atmosphere for a 15-km horizontal mesh when the vertical grid spacing is less than or equal to 200 m. Nonconvergence is accompanied by noise, spurious structures, reduced levels of mesoscale kinetic energy, and reduced Richardson number peak frequencies. Coarser horizontal mesh solutions converge in a similar manner but contain much less noise than the 15-km solutions for coarse vertical resolution. For convective-scale resolution simulations with 3-km cell spacing on a variable-resolution mesh, solution convergence is almost attained with a vertical mesh spacing of 200 m. The boundary layer scheme is the dominant source of vertical filtering in the free atmosphere. Although the increased vertical mixing at coarser vertical mesh spacing depresses the kinetic energy spectra and Richardson number convergence, it does not produce sufficient dissipation to effectively halt scale collapse. These results confirm and extend the results from a number of previous studies, and further emphasize the sensitivity of the energetics to the vertical mixing formulations in the model.
Abstract
The role of vertical mesh spacing in the convergence of full-physics global atmospheric model solutions is examined for synoptic, mesoscale, and convective-scale horizontal resolutions. Using the MPAS-Atmosphere model, convergence is evaluated for three solution metrics: the horizontal kinetic energy spectrum, the Richardson number probability density function, and resolved flow features. All three metrics exhibit convergence in the free atmosphere for a 15-km horizontal mesh when the vertical grid spacing is less than or equal to 200 m. Nonconvergence is accompanied by noise, spurious structures, reduced levels of mesoscale kinetic energy, and reduced Richardson number peak frequencies. Coarser horizontal mesh solutions converge in a similar manner but contain much less noise than the 15-km solutions for coarse vertical resolution. For convective-scale resolution simulations with 3-km cell spacing on a variable-resolution mesh, solution convergence is almost attained with a vertical mesh spacing of 200 m. The boundary layer scheme is the dominant source of vertical filtering in the free atmosphere. Although the increased vertical mixing at coarser vertical mesh spacing depresses the kinetic energy spectra and Richardson number convergence, it does not produce sufficient dissipation to effectively halt scale collapse. These results confirm and extend the results from a number of previous studies, and further emphasize the sensitivity of the energetics to the vertical mixing formulations in the model.
Abstract
Ensembles provide an opportunity to greatly improve short-term prediction of local weather hazards, yet generating reliable predictions remain a significant challenge. In particular, convection-permitting ensemble forecast systems (CPEFSs) have persistent problems with underdispersion. Representing initial and or lateral boundary condition uncertainty along with forecast model error provides a foundation for building a more dependable CPEFS, but the best practice for ensemble system design is not well established.
Several configurations of CPEFSs are examined where ensemble forecasts are nested within a larger domain, drawing initial conditions from a downscaled, continuously cycled, ensemble data assimilation system that provides state-dependent initial condition uncertainty. The control ensemble forecast, with initial condition uncertainty only, is skillful but underdispersive. To improve the reliability of the ensemble forecasts, the control ensemble is supplemented with 1) perturbed lateral boundary conditions; or, model error representation using either 2) stochastic kinetic energy backscatter or 3) stochastically perturbed parameterization tendencies. Forecasts are evaluated against stage IV accumulated precipitation analyses and radiosonde observations. Perturbed ensemble forecasts are also compared to the control forecast to assess the relative impact from adding forecast perturbations. For precipitation forecasts, all perturbation approaches improve ensemble reliability relative to the control CPEFS. Deterministic ensemble member forecast skill, verified against radiosonde observations, decreases when forecast perturbations are added, while ensemble mean forecasts remain similarly skillful to the control.
Abstract
Ensembles provide an opportunity to greatly improve short-term prediction of local weather hazards, yet generating reliable predictions remain a significant challenge. In particular, convection-permitting ensemble forecast systems (CPEFSs) have persistent problems with underdispersion. Representing initial and or lateral boundary condition uncertainty along with forecast model error provides a foundation for building a more dependable CPEFS, but the best practice for ensemble system design is not well established.
Several configurations of CPEFSs are examined where ensemble forecasts are nested within a larger domain, drawing initial conditions from a downscaled, continuously cycled, ensemble data assimilation system that provides state-dependent initial condition uncertainty. The control ensemble forecast, with initial condition uncertainty only, is skillful but underdispersive. To improve the reliability of the ensemble forecasts, the control ensemble is supplemented with 1) perturbed lateral boundary conditions; or, model error representation using either 2) stochastic kinetic energy backscatter or 3) stochastically perturbed parameterization tendencies. Forecasts are evaluated against stage IV accumulated precipitation analyses and radiosonde observations. Perturbed ensemble forecasts are also compared to the control forecast to assess the relative impact from adding forecast perturbations. For precipitation forecasts, all perturbation approaches improve ensemble reliability relative to the control CPEFS. Deterministic ensemble member forecast skill, verified against radiosonde observations, decreases when forecast perturbations are added, while ensemble mean forecasts remain similarly skillful to the control.
Abstract
Real-time forecasts of five landfalling Atlantic hurricanes during 2005 using the Advanced Research Weather Research and Forecasting (WRF) (ARW) Model at grid spacings of 12 and 4 km revealed performance generally competitive with, and occasionally superior to, other operational forecasts for storm position and intensity. Recurring errors include 1) excessive intensification prior to landfall, 2) insufficient momentum exchange with the surface, and 3) inability to capture rapid intensification when observed. To address these errors several augmentations of the basic community model have been designed and tested as part of what is termed the Advanced Hurricane WRF (AHW) model. Based on sensitivity simulations of Katrina, the inner-core structure, particularly the size of the eye, was found to be sensitive to model resolution and surface momentum exchange. The forecast of rapid intensification and the structure of convective bands in Katrina were not significantly improved until the grid spacing approached 1 km. Coupling the atmospheric model to a columnar, mixed layer ocean model eliminated much of the erroneous intensification of Katrina prior to landfall noted in the real-time forecast.
Abstract
Real-time forecasts of five landfalling Atlantic hurricanes during 2005 using the Advanced Research Weather Research and Forecasting (WRF) (ARW) Model at grid spacings of 12 and 4 km revealed performance generally competitive with, and occasionally superior to, other operational forecasts for storm position and intensity. Recurring errors include 1) excessive intensification prior to landfall, 2) insufficient momentum exchange with the surface, and 3) inability to capture rapid intensification when observed. To address these errors several augmentations of the basic community model have been designed and tested as part of what is termed the Advanced Hurricane WRF (AHW) model. Based on sensitivity simulations of Katrina, the inner-core structure, particularly the size of the eye, was found to be sensitive to model resolution and surface momentum exchange. The forecast of rapid intensification and the structure of convective bands in Katrina were not significantly improved until the grid spacing approached 1 km. Coupling the atmospheric model to a columnar, mixed layer ocean model eliminated much of the erroneous intensification of Katrina prior to landfall noted in the real-time forecast.
