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Abstract
The assimilation of operational Doppler radar observations into convection-resolving numerical weather prediction models for very short-range forecasting represents a significant scientific and technological challenge. Numerical experiments over the past few years indicate that convective-scale forecasts are sensitive to the details of the data assimilation methodology, the quality of the radar data, the parameterized microphysics, and the storm environment. In this study, the importance of horizontal environmental variability to very short-range (0–1 h) convective-scale ensemble forecasts initialized using Doppler radar observations is investigated for the 4–5 May 2007 Greensburg, Kansas, tornadic thunderstorm event. Radar observations of reflectivity and radial velocity from the operational Doppler radar network at 0230 UTC 5 May 2007, during the time of the first large tornado, are assimilated into each ensemble member using a three-dimensional variational data assimilation system (3DVAR) developed at the Center for Analysis and Prediction of Storms (CAPS). Very short-range forecasts are made using the nonhydrostatic Advanced Regional Prediction System (ARPS) model from each ensemble member and the results are compared with the observations. Explicit three-dimensional environmental variability information is provided to the convective-scale ensemble using analyses from a 30-km mesoscale ensemble data assimilation system. Comparisons between convective-scale ensembles with initial conditions produced by 3DVAR using 1) background fields that are horizontally homogeneous but vertically inhomogeneous (i.e., have different vertical environmental profiles) and 2) background fields that are horizontally and vertically inhomogeneous are undertaken. Results show that the ensemble with horizontally and vertically inhomogeneous background fields provides improved predictions of thunderstorm structure, mesocyclone track, and low-level circulation track than the ensemble with horizontally homogeneous background fields. This suggests that knowledge of horizontal environmental variability is important to successful convective-scale ensemble predictions and needs to be included in real-data experiments.
Abstract
The assimilation of operational Doppler radar observations into convection-resolving numerical weather prediction models for very short-range forecasting represents a significant scientific and technological challenge. Numerical experiments over the past few years indicate that convective-scale forecasts are sensitive to the details of the data assimilation methodology, the quality of the radar data, the parameterized microphysics, and the storm environment. In this study, the importance of horizontal environmental variability to very short-range (0–1 h) convective-scale ensemble forecasts initialized using Doppler radar observations is investigated for the 4–5 May 2007 Greensburg, Kansas, tornadic thunderstorm event. Radar observations of reflectivity and radial velocity from the operational Doppler radar network at 0230 UTC 5 May 2007, during the time of the first large tornado, are assimilated into each ensemble member using a three-dimensional variational data assimilation system (3DVAR) developed at the Center for Analysis and Prediction of Storms (CAPS). Very short-range forecasts are made using the nonhydrostatic Advanced Regional Prediction System (ARPS) model from each ensemble member and the results are compared with the observations. Explicit three-dimensional environmental variability information is provided to the convective-scale ensemble using analyses from a 30-km mesoscale ensemble data assimilation system. Comparisons between convective-scale ensembles with initial conditions produced by 3DVAR using 1) background fields that are horizontally homogeneous but vertically inhomogeneous (i.e., have different vertical environmental profiles) and 2) background fields that are horizontally and vertically inhomogeneous are undertaken. Results show that the ensemble with horizontally and vertically inhomogeneous background fields provides improved predictions of thunderstorm structure, mesocyclone track, and low-level circulation track than the ensemble with horizontally homogeneous background fields. This suggests that knowledge of horizontal environmental variability is important to successful convective-scale ensemble predictions and needs to be included in real-data experiments.
Abstract
In this two-part paper, the impact of level-II Weather Surveillance Radar-1988 Doppler (WSR-88D) radar reflectivity and radial velocity data on the prediction of a cluster of tornadic thunderstorms in the Advanced Regional Prediction System (ARPS) model is studied. Radar reflectivity data are used primarily in a cloud analysis procedure that retrieves the amount of hydrometeors and adjusts in-cloud temperature, moisture, and cloud fields, while radial velocity data are analyzed through a three-dimensional variational (3DVAR) data assimilation scheme that contains a 3D mass divergence constraint in the cost function. In Part I, the impact of the cloud analysis and modifications to the scheme are discussed. In this part, the impact of radial velocity data and the mass divergence constraint in the 3DVAR cost function are studied.
The case studied is that of the 28 March 2000 Fort Worth tornadoes. The addition of the radial velocity improves the forecasts beyond that experienced with the cloud analysis alone. The prediction is able to forecast the morphology of individual storm cells on the 3-km grid up to 2 h; the rotating supercell characteristics of the storm that spawned two tornadoes are well captured; timing errors in the forecast are less than 15 min and location errors are less than 10 km at the time of the tornadoes.
When forecasts were made with radial velocity assimilation but not reflectivity, they failed to predict nearly all storm cells. Using the current 3DVAR and cloud analysis procedure with 10-min intermittent assimilation cycles, reflectivity data are found to have a greater positive impact than radial velocity. The use of radial velocity does improve the storm forecast when combined with reflectivity assimilation, by, for example, improving the forecasting of the strong low-level vorticity centers associated with the tornadoes. Positive effects of including a mass divergence constraint in the 3DVAR cost function are also documented.
Abstract
In this two-part paper, the impact of level-II Weather Surveillance Radar-1988 Doppler (WSR-88D) radar reflectivity and radial velocity data on the prediction of a cluster of tornadic thunderstorms in the Advanced Regional Prediction System (ARPS) model is studied. Radar reflectivity data are used primarily in a cloud analysis procedure that retrieves the amount of hydrometeors and adjusts in-cloud temperature, moisture, and cloud fields, while radial velocity data are analyzed through a three-dimensional variational (3DVAR) data assimilation scheme that contains a 3D mass divergence constraint in the cost function. In Part I, the impact of the cloud analysis and modifications to the scheme are discussed. In this part, the impact of radial velocity data and the mass divergence constraint in the 3DVAR cost function are studied.
The case studied is that of the 28 March 2000 Fort Worth tornadoes. The addition of the radial velocity improves the forecasts beyond that experienced with the cloud analysis alone. The prediction is able to forecast the morphology of individual storm cells on the 3-km grid up to 2 h; the rotating supercell characteristics of the storm that spawned two tornadoes are well captured; timing errors in the forecast are less than 15 min and location errors are less than 10 km at the time of the tornadoes.
When forecasts were made with radial velocity assimilation but not reflectivity, they failed to predict nearly all storm cells. Using the current 3DVAR and cloud analysis procedure with 10-min intermittent assimilation cycles, reflectivity data are found to have a greater positive impact than radial velocity. The use of radial velocity does improve the storm forecast when combined with reflectivity assimilation, by, for example, improving the forecasting of the strong low-level vorticity centers associated with the tornadoes. Positive effects of including a mass divergence constraint in the 3DVAR cost function are also documented.
Abstract
The utility of the anelastic vertical vorticity equation in a weak-constraint (least squares error) variational dual-Doppler wind analysis procedure is explored. The analysis winds are obtained by minimizing a cost function accounting for the discrepancies between observed and analyzed radial winds, errors in the mass conservation equation, errors in the anelastic vertical vorticity equation, and spatial smoothness constraints. By using Taylor’s frozen-turbulence hypothesis to shift analysis winds to observation points, discrepancies between radially projected analysis winds and radial wind observations can be calculated at the actual times and locations the data are acquired. The frozen-turbulence hypothesis is also used to evaluate the local derivative term in the vorticity equation. Tests of the analysis procedure are performed with analytical pseudo-observations of an array of translating and temporally decaying counterrotating updrafts and downdrafts generated from a Beltrami flow solution of the Navier–Stokes equations. The experiments explore the value added to the analysis by the vorticity equation constraint in the common scenario of substantial missing low-level data (radial wind observations at heights beneath 1.5 km are withheld from the analysis). Experiments focus on the sensitivity of the most sensitive analysis variable—the vertical velocity component—to values of the weighting coefficients, volume scan period, number of volume scans, and errors in the estimated frozen-turbulence pattern-translation components. Although the vorticity equation constraint is found to add value to many of these analyses, the analysis can become significantly degraded if estimates of the pattern-translation components are largely in error or if the frozen-turbulence hypothesis itself breaks down. However, tests also suggest that these negative impacts can be mitigated if data are available in a rapid-scan mode.
Abstract
The utility of the anelastic vertical vorticity equation in a weak-constraint (least squares error) variational dual-Doppler wind analysis procedure is explored. The analysis winds are obtained by minimizing a cost function accounting for the discrepancies between observed and analyzed radial winds, errors in the mass conservation equation, errors in the anelastic vertical vorticity equation, and spatial smoothness constraints. By using Taylor’s frozen-turbulence hypothesis to shift analysis winds to observation points, discrepancies between radially projected analysis winds and radial wind observations can be calculated at the actual times and locations the data are acquired. The frozen-turbulence hypothesis is also used to evaluate the local derivative term in the vorticity equation. Tests of the analysis procedure are performed with analytical pseudo-observations of an array of translating and temporally decaying counterrotating updrafts and downdrafts generated from a Beltrami flow solution of the Navier–Stokes equations. The experiments explore the value added to the analysis by the vorticity equation constraint in the common scenario of substantial missing low-level data (radial wind observations at heights beneath 1.5 km are withheld from the analysis). Experiments focus on the sensitivity of the most sensitive analysis variable—the vertical velocity component—to values of the weighting coefficients, volume scan period, number of volume scans, and errors in the estimated frozen-turbulence pattern-translation components. Although the vorticity equation constraint is found to add value to many of these analyses, the analysis can become significantly degraded if estimates of the pattern-translation components are largely in error or if the frozen-turbulence hypothesis itself breaks down. However, tests also suggest that these negative impacts can be mitigated if data are available in a rapid-scan mode.
Abstract
An approximate (rapid scan) dynamical model for single-Doppler retrieval of the vector wind field is investigated. This approximate model is based on the Lagrangian form of the radial component of the equation of motion and is valid for retrieval time windows that are smaller than the effective timescale of the flow but larger than the product of the effective timescale and (nondimensional) relative error in the radial wind observations. The retrieval was tested with data gathered by two Doppler-on-Wheels mobile Doppler research radars of a cold front on 16 June 2000 near Grandfield, Oklahoma. Experiments focused on the impact of time resolution and the utility of a background constraint obtained from a volume velocity processing (VVP)-like estimate of the wind field. Retrieval error statistics were substantially improved as the volume scan intervals decreased from 5 min [characterizing the current Weather Surveillance Radar-1988 Doppler (WSR-88D) scan rates] down to 1 min. Use of the background constraint also improved the results, with superior results obtained in the high temporal resolution experiments when the background constraint was selectively imposed.
Abstract
An approximate (rapid scan) dynamical model for single-Doppler retrieval of the vector wind field is investigated. This approximate model is based on the Lagrangian form of the radial component of the equation of motion and is valid for retrieval time windows that are smaller than the effective timescale of the flow but larger than the product of the effective timescale and (nondimensional) relative error in the radial wind observations. The retrieval was tested with data gathered by two Doppler-on-Wheels mobile Doppler research radars of a cold front on 16 June 2000 near Grandfield, Oklahoma. Experiments focused on the impact of time resolution and the utility of a background constraint obtained from a volume velocity processing (VVP)-like estimate of the wind field. Retrieval error statistics were substantially improved as the volume scan intervals decreased from 5 min [characterizing the current Weather Surveillance Radar-1988 Doppler (WSR-88D) scan rates] down to 1 min. Use of the background constraint also improved the results, with superior results obtained in the high temporal resolution experiments when the background constraint was selectively imposed.
Abstract
The radar ray path and beam broadening equations are important for assimilation of radar data into numerical weather prediction (NWP) models. They can be used to determine the physical location of each radar measurement and to properly map the atmospheric state variables from the model grid to the radar measurement space as part of the forward observation operators. Historically, different degrees of approximations have been made with these equations; however, no systematic evaluation of their impact exists, at least in the context of variational data assimilation. This study examines the effects of simplifying ray path and ray broadening calculations on the radar data assimilation in a 3D variational data assimilation (3DVAR) system. Several groups of Observational System Simulation Experiments (OSSEs) are performed to test the impact of these equations to radar data assimilation with an idealized tornadic thunderstorm case. This study shows that the errors caused by simplifications vary with the distance between the analyzed storm and the radar. For single time level wind analysis, as the surface range increases, the impact of beam broadening on analyzed wind field becomes evident and can cause relatively large error for distances beyond 150 km. The impact of the earth’s curvature is more significant, even for distances beyond 60 km, because it places the data at the wrong vertical location. The impact of refractive index gradient is also tested. It is shown that the variations of refractive index gradient have a very small impact on the wind analysis results.
Two time series of 1-h-long data assimilation experiments are further conducted to illustrate the impact of the beam broadening and earth curvature on all retrieved model variables. It is shown that all model variables can be retrieved to some degrees in all data assimilation experiments. Similar to the wind analysis experiments, the impacts of both factors are not obvious when radars are relatively close to the storm. When the radars are far from the storm (especially beyond 150 km), overlooking beam broadening degrades the accuracy of assimilation results slightly, whereas ignoring the earth’s curvature leads to significant errors.
Abstract
The radar ray path and beam broadening equations are important for assimilation of radar data into numerical weather prediction (NWP) models. They can be used to determine the physical location of each radar measurement and to properly map the atmospheric state variables from the model grid to the radar measurement space as part of the forward observation operators. Historically, different degrees of approximations have been made with these equations; however, no systematic evaluation of their impact exists, at least in the context of variational data assimilation. This study examines the effects of simplifying ray path and ray broadening calculations on the radar data assimilation in a 3D variational data assimilation (3DVAR) system. Several groups of Observational System Simulation Experiments (OSSEs) are performed to test the impact of these equations to radar data assimilation with an idealized tornadic thunderstorm case. This study shows that the errors caused by simplifications vary with the distance between the analyzed storm and the radar. For single time level wind analysis, as the surface range increases, the impact of beam broadening on analyzed wind field becomes evident and can cause relatively large error for distances beyond 150 km. The impact of the earth’s curvature is more significant, even for distances beyond 60 km, because it places the data at the wrong vertical location. The impact of refractive index gradient is also tested. It is shown that the variations of refractive index gradient have a very small impact on the wind analysis results.
Two time series of 1-h-long data assimilation experiments are further conducted to illustrate the impact of the beam broadening and earth curvature on all retrieved model variables. It is shown that all model variables can be retrieved to some degrees in all data assimilation experiments. Similar to the wind analysis experiments, the impacts of both factors are not obvious when radars are relatively close to the storm. When the radars are far from the storm (especially beyond 150 km), overlooking beam broadening degrades the accuracy of assimilation results slightly, whereas ignoring the earth’s curvature leads to significant errors.
Abstract
This paper proposes a new method of dual-Doppler radar analysis based on a variational approach. In it, a cost function, defined as the distance between the analysis and the observations at the data points, is minimized through a limited memory, quasi-Newton conjugate gradient algorithm with the mass continuity equation imposed as a weak constraint. The analysis is performed in Cartesian space.
Compared with traditional methods, the variational method offers much more flexibility in its use of observational data and various constraints. Using the radar data directly at observation locations avoids an interpolation step, which is often a source of error, especially in the presence of data voids. In addition, using the mass continuity equation as a weak instead of strong constraint avoids the error accumulation and the subsequent somewhat arbitrary adjustment associated with the explicit vertical integration of the continuity equation.
The current method is tested on both model-simulated and observed datasets of supercell storms. It is shown that the circulation inside and around the storms, including the strong updraft and associated downdraft, is well analyzed in both cases. Furthermore, the authors found that the analysis is not very sensitive to the specification of boundary conditions and to data contamination. The method also has the potential for retrieving, with reasonable accuracy, the wind in regions of single-Doppler radar coverage.
Abstract
This paper proposes a new method of dual-Doppler radar analysis based on a variational approach. In it, a cost function, defined as the distance between the analysis and the observations at the data points, is minimized through a limited memory, quasi-Newton conjugate gradient algorithm with the mass continuity equation imposed as a weak constraint. The analysis is performed in Cartesian space.
Compared with traditional methods, the variational method offers much more flexibility in its use of observational data and various constraints. Using the radar data directly at observation locations avoids an interpolation step, which is often a source of error, especially in the presence of data voids. In addition, using the mass continuity equation as a weak instead of strong constraint avoids the error accumulation and the subsequent somewhat arbitrary adjustment associated with the explicit vertical integration of the continuity equation.
The current method is tested on both model-simulated and observed datasets of supercell storms. It is shown that the circulation inside and around the storms, including the strong updraft and associated downdraft, is well analyzed in both cases. Furthermore, the authors found that the analysis is not very sensitive to the specification of boundary conditions and to data contamination. The method also has the potential for retrieving, with reasonable accuracy, the wind in regions of single-Doppler radar coverage.
Abstract
The Advanced Regional Prediction System (ARPS) model is employed to perform high-resolution numerical simulations of a mesoscale convective system and associated cyclonic line-end vortex (LEV) that spawned several tornadoes in central Oklahoma on 8–9 May 2007. The simulation uses a 1000 km × 1000 km domain with 2-km horizontal grid spacing. The ARPS three-dimensional variational data assimilation (3DVAR) is used to assimilate a variety of data types. All experiments assimilate routine surface and upper-air observations as well as wind profiler and Oklahoma Mesonet data over a 1-h assimilation window. A subset of experiments assimilates radar data. Cloud and hydrometeor fields as well as in-cloud temperature are adjusted based on radar reflectivity data through the ARPS complex cloud analysis procedure. Radar data are assimilated from the Weather Surveillance Radar-1988 Doppler (WSR-88D) network as well as from the Engineering Research Center for Collaborative and Adaptive Sensing of the Atmosphere (CASA) network of four X-band Doppler radars. Three-hour forecasts are launched at the end of the assimilation window. The structure and evolution of the forecast MCS and LEV are markedly better throughout the forecast period in experiments in which radar data are assimilated. The assimilation of CASA radar data in addition to WSR-88D data increases the structural detail of the modeled squall line and MCS at the end of the assimilation window, which appears to yield a slightly better forecast track of the LEV.
Abstract
The Advanced Regional Prediction System (ARPS) model is employed to perform high-resolution numerical simulations of a mesoscale convective system and associated cyclonic line-end vortex (LEV) that spawned several tornadoes in central Oklahoma on 8–9 May 2007. The simulation uses a 1000 km × 1000 km domain with 2-km horizontal grid spacing. The ARPS three-dimensional variational data assimilation (3DVAR) is used to assimilate a variety of data types. All experiments assimilate routine surface and upper-air observations as well as wind profiler and Oklahoma Mesonet data over a 1-h assimilation window. A subset of experiments assimilates radar data. Cloud and hydrometeor fields as well as in-cloud temperature are adjusted based on radar reflectivity data through the ARPS complex cloud analysis procedure. Radar data are assimilated from the Weather Surveillance Radar-1988 Doppler (WSR-88D) network as well as from the Engineering Research Center for Collaborative and Adaptive Sensing of the Atmosphere (CASA) network of four X-band Doppler radars. Three-hour forecasts are launched at the end of the assimilation window. The structure and evolution of the forecast MCS and LEV are markedly better throughout the forecast period in experiments in which radar data are assimilated. The assimilation of CASA radar data in addition to WSR-88D data increases the structural detail of the modeled squall line and MCS at the end of the assimilation window, which appears to yield a slightly better forecast track of the LEV.
Abstract
Four-dimensional variational data assimilation (4D-Var) seeks to find an optimal initial field that minimizes a cost function defined as the squared distance between model solutions and observations within an assimilation window. For a perfect linear model, Lorenc showed that the 4D-Var forecast at the end of the window coincides with a Kalman filter analysis if two conditions are fulfilled: (a) addition to the cost function of a term that measures the distance to the background at the beginning of the assimilation window, and (b) use of the Kalman filter background error covariance in this term. The standard 4D-Var requires minimization algorithms along with adjoint models to compute gradient information needed for the minimization. In this study, an alternative method is suggested based on the use of the quasi-inverse model that, for certain applications, may help accelerate the solution of problems close to 4D-Var.
The quasi-inverse approach for the forecast sensitivity problem is introduced, and then a closely related variational assimilation problem using the quasi-inverse model is formulated (i.e., the model is integrated backward but changing the sign of the dissipation terms). It is shown that if the cost function has no background term, and has a complete set of observations (as assumed in many classical 4D-Var papers), the new method solves the 4D-Var-minimization problem efficiently, and is in fact equivalent to the Newton algorithm but without having to compute a Hessian. If the background term is included but computed at the end of the interval, allowing the use of observations that are not complete, the minimization can still be carried out very efficiently. In this case, however, the method is much closer to a 3D-Var formulation in which the analysis is attained through a model integration. For this reason, the method is called “inverse 3D-Var” (I3D-Var).
The I3D-Var method was applied to simple models (viscous Burgers’ equation and Lorenz model), and it was found that when the background term is ignored and complete fields of noisy observations are available at multiple times, the inverse 3D-Var method minimizes the same cost function as 4D-Var but converges much faster. Tests with the Advanced Regional Prediction System (ARPS) indicate that I3D-Var is about twice as fast as the adjoint Newton method and many times faster than the quasi-Newton LBFGS algorithm, which uses the adjoint model. Potential problems (including the growth of random errors during the integration back in time) and possible applications to preconditioning, and to problems such as storm-scale data assimilation and reanalysis are also discussed.
Abstract
Four-dimensional variational data assimilation (4D-Var) seeks to find an optimal initial field that minimizes a cost function defined as the squared distance between model solutions and observations within an assimilation window. For a perfect linear model, Lorenc showed that the 4D-Var forecast at the end of the window coincides with a Kalman filter analysis if two conditions are fulfilled: (a) addition to the cost function of a term that measures the distance to the background at the beginning of the assimilation window, and (b) use of the Kalman filter background error covariance in this term. The standard 4D-Var requires minimization algorithms along with adjoint models to compute gradient information needed for the minimization. In this study, an alternative method is suggested based on the use of the quasi-inverse model that, for certain applications, may help accelerate the solution of problems close to 4D-Var.
The quasi-inverse approach for the forecast sensitivity problem is introduced, and then a closely related variational assimilation problem using the quasi-inverse model is formulated (i.e., the model is integrated backward but changing the sign of the dissipation terms). It is shown that if the cost function has no background term, and has a complete set of observations (as assumed in many classical 4D-Var papers), the new method solves the 4D-Var-minimization problem efficiently, and is in fact equivalent to the Newton algorithm but without having to compute a Hessian. If the background term is included but computed at the end of the interval, allowing the use of observations that are not complete, the minimization can still be carried out very efficiently. In this case, however, the method is much closer to a 3D-Var formulation in which the analysis is attained through a model integration. For this reason, the method is called “inverse 3D-Var” (I3D-Var).
The I3D-Var method was applied to simple models (viscous Burgers’ equation and Lorenz model), and it was found that when the background term is ignored and complete fields of noisy observations are available at multiple times, the inverse 3D-Var method minimizes the same cost function as 4D-Var but converges much faster. Tests with the Advanced Regional Prediction System (ARPS) indicate that I3D-Var is about twice as fast as the adjoint Newton method and many times faster than the quasi-Newton LBFGS algorithm, which uses the adjoint model. Potential problems (including the growth of random errors during the integration back in time) and possible applications to preconditioning, and to problems such as storm-scale data assimilation and reanalysis are also discussed.
Abstract
The Advanced Regional Prediction System (ARPS) three-dimensional variational (3DVAR) system is enhanced to include the analysis of radar-derived refractivity measurements. These refractivity data are most sensitive to atmospheric moisture content and provide high-resolution information on near-surface moisture that is important to convective initiation (CI) and precipitation forecasting. Observing system simulation experiments (OSSEs) are performed using simulated refractivity data. The impacts of refractivity on CI and subsequent forecasts are investigated in the presence of varying observation error, radar location, data coverage, and different uncertainties in the background field. Cycled refractivity assimilation and forecasts are performed and the results compared to the truth. In addition to the perfect model experiments, imperfect model experiments are performed where the forecasts use the Weather Research and Forecasting (WRF) model instead of the ARPS. A simulation for the 19 May 2010 central plain convection case is used for the OSSEs. It involves a large storm system, large convective available potential energy, and little convective inhibition, allowing for CI along a warm front in northern Oklahoma and ahead of a dryline later to the southwest. Emphasis is placed on the quality of moisture analyses and the subsequent forecasts of CI. Results show the ability of refractivity assimilation to correct low-level moisture errors, leading to improved CI forecasts. Equitable threat scores for reflectivity are generally higher when refractivity data are assimilated. Tests show small sensitivity to increased observational error or ground clutter coverage, and greater sensitivity to the limited data coverage of a single radar.
Abstract
The Advanced Regional Prediction System (ARPS) three-dimensional variational (3DVAR) system is enhanced to include the analysis of radar-derived refractivity measurements. These refractivity data are most sensitive to atmospheric moisture content and provide high-resolution information on near-surface moisture that is important to convective initiation (CI) and precipitation forecasting. Observing system simulation experiments (OSSEs) are performed using simulated refractivity data. The impacts of refractivity on CI and subsequent forecasts are investigated in the presence of varying observation error, radar location, data coverage, and different uncertainties in the background field. Cycled refractivity assimilation and forecasts are performed and the results compared to the truth. In addition to the perfect model experiments, imperfect model experiments are performed where the forecasts use the Weather Research and Forecasting (WRF) model instead of the ARPS. A simulation for the 19 May 2010 central plain convection case is used for the OSSEs. It involves a large storm system, large convective available potential energy, and little convective inhibition, allowing for CI along a warm front in northern Oklahoma and ahead of a dryline later to the southwest. Emphasis is placed on the quality of moisture analyses and the subsequent forecasts of CI. Results show the ability of refractivity assimilation to correct low-level moisture errors, leading to improved CI forecasts. Equitable threat scores for reflectivity are generally higher when refractivity data are assimilated. Tests show small sensitivity to increased observational error or ground clutter coverage, and greater sensitivity to the limited data coverage of a single radar.
Abstract
In this paper, a new method of dual-Doppler radar wind analysis based on a three-dimensional variational data assimilation (3DVAR) approach is proposed. In it, a cost function, including background term and radial observation term, is minimized through a limited memory, quasi-Newton conjugate-gradient algorithm with the mass continuity equation imposed as a weak constraint. In the method, the background error covariance matrix, though simple in this case, is modeled by a recursive filter. Furthermore, the square root of this matrix is used to precondition the minimization problem.
The current method is applied to Doppler radar observation of a supercell storm, and the analysis results are compared to a conceptual model and previous research. It is shown that the horizontal circulations, both within and around the storms, as well as the strong updraft and the associated downdraft, are well analyzed. Because no explicit integration of the anelastic mass continuity equation is involved, error accumulation associated with such integration is avoided. As a result, the method is less sensitive to the vertical boundary uncertainties.
Abstract
In this paper, a new method of dual-Doppler radar wind analysis based on a three-dimensional variational data assimilation (3DVAR) approach is proposed. In it, a cost function, including background term and radial observation term, is minimized through a limited memory, quasi-Newton conjugate-gradient algorithm with the mass continuity equation imposed as a weak constraint. In the method, the background error covariance matrix, though simple in this case, is modeled by a recursive filter. Furthermore, the square root of this matrix is used to precondition the minimization problem.
The current method is applied to Doppler radar observation of a supercell storm, and the analysis results are compared to a conceptual model and previous research. It is shown that the horizontal circulations, both within and around the storms, as well as the strong updraft and the associated downdraft, are well analyzed. Because no explicit integration of the anelastic mass continuity equation is involved, error accumulation associated with such integration is avoided. As a result, the method is less sensitive to the vertical boundary uncertainties.
