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## Abstract

Observation experiments are performed on a set of high-resolution large-eddy simulations of translating tornado-like vortices. Near-surface Doppler wind measurements are taken by emulating a mobile radar positioned from 1 to 10 km south of each vortex track and conducting single-level scans every 2 s. The departure of each observed gust (wind measurement averaged over two successive scans) from the corresponding true maximum 3-s gust at 10 m AGL (“S10–3s”) is partitioned into error sources associated with resolution volume size, wind direction relative to the radar beam, beam elevation, and temporal sampling. The distributions of each error type are diagrammed as functions of range, observed wind speed, and predicted deviation between the wind direction and the radar beam. The results indicate that the deviation between the wind direction and the radar beam is the predominant source of error in these rapid scan scenarios, although range is also a substantial factor. The median total error is ~10% for small deviation at close range, but it approximately doubles if the range is increased from 1 to 10 km; a more pronounced increase in both the median value and the variance of the total error is seen as the deviation becomes large. Because of this, the underestimate of the global maximum S10–3s approaches 30–40 m s^{−1} at a longer range, although the global maximum of the time-averaged observed wind speed gives a reasonable approximation of the time-mean maximum S10–3s in many cases. Because of simplifying assumptions and the limited number of cases examined, these results are intended as a baseline for further research.

## Abstract

Observation experiments are performed on a set of high-resolution large-eddy simulations of translating tornado-like vortices. Near-surface Doppler wind measurements are taken by emulating a mobile radar positioned from 1 to 10 km south of each vortex track and conducting single-level scans every 2 s. The departure of each observed gust (wind measurement averaged over two successive scans) from the corresponding true maximum 3-s gust at 10 m AGL (“S10–3s”) is partitioned into error sources associated with resolution volume size, wind direction relative to the radar beam, beam elevation, and temporal sampling. The distributions of each error type are diagrammed as functions of range, observed wind speed, and predicted deviation between the wind direction and the radar beam. The results indicate that the deviation between the wind direction and the radar beam is the predominant source of error in these rapid scan scenarios, although range is also a substantial factor. The median total error is ~10% for small deviation at close range, but it approximately doubles if the range is increased from 1 to 10 km; a more pronounced increase in both the median value and the variance of the total error is seen as the deviation becomes large. Because of this, the underestimate of the global maximum S10–3s approaches 30–40 m s^{−1} at a longer range, although the global maximum of the time-averaged observed wind speed gives a reasonable approximation of the time-mean maximum S10–3s in many cases. Because of simplifying assumptions and the limited number of cases examined, these results are intended as a baseline for further research.

## Abstract

This study is the first in a series that investigates the effects of turbulence in the boundary layer of a tornado vortex. In this part, axisymmetric simulations with constant viscosity are used to explore the relationships between vortex structure, intensity, and unsteadiness as functions of diffusion (measured by a Reynolds number Re_{
r
}) and rotation (measured by a swirl ratio *S*
_{
r
}). A deep upper-level damping zone is used to prevent upper-level disturbances from affecting the low-level vortex. The damping zone is most effective when it overlaps with the specified convective forcing, causing a reduction to the effective convective velocity scale *W*
_{
e
}. With this damping in place, the tornado-vortex boundary layer shows no sign of unsteadiness for a wide range of parameters, suggesting that turbulence in the tornado boundary layer is inherently a three-dimensional phenomenon. For high Re_{
r
}, the most intense vortices have maximum mean tangential winds well in excess of *W*
_{
e
}, and maximum mean vertical velocity exceeds 3 times *W*
_{
e
}. In parameter space, the most intense vortices fall along a line that follows

## Abstract

This study is the first in a series that investigates the effects of turbulence in the boundary layer of a tornado vortex. In this part, axisymmetric simulations with constant viscosity are used to explore the relationships between vortex structure, intensity, and unsteadiness as functions of diffusion (measured by a Reynolds number Re_{
r
}) and rotation (measured by a swirl ratio *S*
_{
r
}). A deep upper-level damping zone is used to prevent upper-level disturbances from affecting the low-level vortex. The damping zone is most effective when it overlaps with the specified convective forcing, causing a reduction to the effective convective velocity scale *W*
_{
e
}. With this damping in place, the tornado-vortex boundary layer shows no sign of unsteadiness for a wide range of parameters, suggesting that turbulence in the tornado boundary layer is inherently a three-dimensional phenomenon. For high Re_{
r
}, the most intense vortices have maximum mean tangential winds well in excess of *W*
_{
e
}, and maximum mean vertical velocity exceeds 3 times *W*
_{
e
}. In parameter space, the most intense vortices fall along a line that follows

## Abstract

A large-eddy simulation (LES) framework with an “eddy injection” technique has been developed that ensures a majority of turbulent kinetic energy in numerically simulated tornado-like vortices is represented by resolved eddies. This framework is used to explore the relationships between environmental forcing mechanisms, surface boundary conditions, and tornado vortex structure, intensity, and wind gusts. Similar to previous LES studies, results show that the maximum time- and azimuthal-mean tangential winds {*V*}_{max} can be well in excess of the “thermodynamic speed limit,” which is 66 m s^{−1} for most of the simulations. Specifically, {*V*}_{max} exceeds this speed by values ranging from 21% for a large, high-swirl vortex to 59% for a small, low-swirl vortex. Budgets of mean and eddy angular and radial momentum are used to show that resolved eddies in the tornado core act to reduce the wind speed at the location of {*V*}_{max}, although they do transport angular momentum downward into the lowest levels of the boundary layer, increasing low-level swirl.

Three measures of tornado intensity are introduced: maximum time–azimuthal-mean surface (10 m) horizontal wind speed ({S10}_{max}), maximum 3-s gusts of S10 (S10-3s), and maximum vertical 3-s gusts at 10 m (W10-3s). While {S10}_{max} is considerably less than {*V*}_{max}, transient features in the boundary layer can generate S10-3s in excess of 150 m s^{−1}, and W10-3s in excess of 100 m s^{−1}. For high-swirl vortices, the extreme gusts are confined closer to the center, well inside the radius of maximum azimuthal-mean surface winds. For the low-swirl vortex, both the strongest mean winds and the extreme gusts are restricted to a very narrow core.

## Abstract

A large-eddy simulation (LES) framework with an “eddy injection” technique has been developed that ensures a majority of turbulent kinetic energy in numerically simulated tornado-like vortices is represented by resolved eddies. This framework is used to explore the relationships between environmental forcing mechanisms, surface boundary conditions, and tornado vortex structure, intensity, and wind gusts. Similar to previous LES studies, results show that the maximum time- and azimuthal-mean tangential winds {*V*}_{max} can be well in excess of the “thermodynamic speed limit,” which is 66 m s^{−1} for most of the simulations. Specifically, {*V*}_{max} exceeds this speed by values ranging from 21% for a large, high-swirl vortex to 59% for a small, low-swirl vortex. Budgets of mean and eddy angular and radial momentum are used to show that resolved eddies in the tornado core act to reduce the wind speed at the location of {*V*}_{max}, although they do transport angular momentum downward into the lowest levels of the boundary layer, increasing low-level swirl.

Three measures of tornado intensity are introduced: maximum time–azimuthal-mean surface (10 m) horizontal wind speed ({S10}_{max}), maximum 3-s gusts of S10 (S10-3s), and maximum vertical 3-s gusts at 10 m (W10-3s). While {S10}_{max} is considerably less than {*V*}_{max}, transient features in the boundary layer can generate S10-3s in excess of 150 m s^{−1}, and W10-3s in excess of 100 m s^{−1}. For high-swirl vortices, the extreme gusts are confined closer to the center, well inside the radius of maximum azimuthal-mean surface winds. For the low-swirl vortex, both the strongest mean winds and the extreme gusts are restricted to a very narrow core.

## Abstract

The structure and intensity of tornado-like vortices are examined using large-eddy simulations (LES) in an idealized framework. The analysis focuses on whether the simulated boundary layer contains resolved turbulent eddies, and whether most of the vertical component of turbulent momentum flux is resolved rather than parameterized. Initial conditions are first generated numerically using a “precursor simulation” with an axisymmetric model. A three-dimensional “baseline” LES is then integrated using these initial conditions plus random perturbations. With this baseline approach, the inner core of the simulated vortex clearly contains resolved turbulent eddies (as expected); however, the boundary layer inflow has very weak resolved turbulent eddies, and the subgrid model accounts for most of the vertical turbulent momentum flux (contrary to the design of these simulations). To overcome this problem, a second precursor simulation is conducted in which resolved turbulent fluctuations develop within a smaller, doubly periodic LES domain. Perturbation flow fields from this precursor LES are then “injected” into the large-domain LES at a specified radius. With this approach, the boundary layer inflow clearly contains resolved turbulent fluctuations, often organized as quasi-2D rolls, which persist into the inner core of the simulation; thus, the simulated tornado-like vortex *and* its inflowing boundary layer can be characterized as LES. When turbulence is injected, the inner-core vortex structure is always substantially different, the boundary layer inflow is typically deeper, and in most cases the maximum wind speeds are reduced compared to the baseline simulation.

## Abstract

The structure and intensity of tornado-like vortices are examined using large-eddy simulations (LES) in an idealized framework. The analysis focuses on whether the simulated boundary layer contains resolved turbulent eddies, and whether most of the vertical component of turbulent momentum flux is resolved rather than parameterized. Initial conditions are first generated numerically using a “precursor simulation” with an axisymmetric model. A three-dimensional “baseline” LES is then integrated using these initial conditions plus random perturbations. With this baseline approach, the inner core of the simulated vortex clearly contains resolved turbulent eddies (as expected); however, the boundary layer inflow has very weak resolved turbulent eddies, and the subgrid model accounts for most of the vertical turbulent momentum flux (contrary to the design of these simulations). To overcome this problem, a second precursor simulation is conducted in which resolved turbulent fluctuations develop within a smaller, doubly periodic LES domain. Perturbation flow fields from this precursor LES are then “injected” into the large-domain LES at a specified radius. With this approach, the boundary layer inflow clearly contains resolved turbulent fluctuations, often organized as quasi-2D rolls, which persist into the inner core of the simulation; thus, the simulated tornado-like vortex *and* its inflowing boundary layer can be characterized as LES. When turbulence is injected, the inner-core vortex structure is always substantially different, the boundary layer inflow is typically deeper, and in most cases the maximum wind speeds are reduced compared to the baseline simulation.

## Abstract

Large-eddy simulations are used to produce realistic, high-resolution depictions of near-surface winds in translating tornadoes. The translation speed, swirl ratio, and vertical forcing are varied to provide a range of vortex intensities and structural types. Observation experiments are then performed in which the tornadoes are passed over groups of simulated sensors. Some of the experiments use indestructible, error-free anemometers while others limit the range of observable wind speeds to mimic the characteristics of damage indicators specified in the enhanced Fujita (EF) scale. Also, in some of the experiments the sensors are randomly placed while in others they are positioned in regularly spaced columns perpendicular to the vortex tracks to mimic field project deployments.

Statistical analysis of the results provides quantitative insight into the limitations of tornado intensity estimates based on damage surveys or in situ measurements in rural or semirural areas. The mean negative bias relative to the “true” global maximum 3-s gust at 10 m AGL (the standard for EF ratings) exceeds 10 m s^{−1} in all cases and 45 m s^{−1} in some cases. A small number of sensors are generally sufficient to provide a good approximation of the running time-mean maximum during the period of observation, although the required spatial resolution of the sensor group is still substantially higher than that previously attained by any field program. Because of model limitations and simplifying assumptions, these results are regarded as a lower bound for tornado intensity underestimates in rural and semirural areas and provide a baseline for further inquiry.

## Abstract

Large-eddy simulations are used to produce realistic, high-resolution depictions of near-surface winds in translating tornadoes. The translation speed, swirl ratio, and vertical forcing are varied to provide a range of vortex intensities and structural types. Observation experiments are then performed in which the tornadoes are passed over groups of simulated sensors. Some of the experiments use indestructible, error-free anemometers while others limit the range of observable wind speeds to mimic the characteristics of damage indicators specified in the enhanced Fujita (EF) scale. Also, in some of the experiments the sensors are randomly placed while in others they are positioned in regularly spaced columns perpendicular to the vortex tracks to mimic field project deployments.

Statistical analysis of the results provides quantitative insight into the limitations of tornado intensity estimates based on damage surveys or in situ measurements in rural or semirural areas. The mean negative bias relative to the “true” global maximum 3-s gust at 10 m AGL (the standard for EF ratings) exceeds 10 m s^{−1} in all cases and 45 m s^{−1} in some cases. A small number of sensors are generally sufficient to provide a good approximation of the running time-mean maximum during the period of observation, although the required spatial resolution of the sensor group is still substantially higher than that previously attained by any field program. Because of model limitations and simplifying assumptions, these results are regarded as a lower bound for tornado intensity underestimates in rural and semirural areas and provide a baseline for further inquiry.

## Abstract

Accurate vertical velocity retrieval from dual-Doppler analysis (DDA) is a long-standing problem of radar meteorology. Typical radar scanning strategies poorly observe the vertical component of motion, leading to large uncertainty in vertical velocity estimates. Using a vertical vorticity equation constraint in addition to a mass conservation constraint in DDA has shown promise in improving vertical velocity retrievals. However, observation system simulation experiments (OSSEs) suggest this technique requires rapid radar volume scans to realize the improvements due to the vorticity tendency term in the vertical vorticity constraint. Here, the vertical vorticity constraint DDA is tested with real, rapid-scan radar data to validate prior OSSEs results. Generally, the vertical vorticity constraint DDA produced more accurate vertical velocities from DDAs than those that did not use the constraint. When the time between volume scans was greater than 30 s, the vertical velocity accuracy was significantly affected by the vorticity tendency estimation method. A technique that uses advection correction on provisional DDA wind fields to shorten the discretization interval for the vorticity tendency calculation improved the vertical velocity retrievals for longer times between volume scans. The skill of these DDAs was similar to those using a shorter time between volume scans. These improvements were due to increased accuracy of the vertical vorticity tendency using the advection correction technique. The real radar data tests also revealed that the vertical vorticity constraint DDAs are more forgiving to radar data errors. These results suggest that vertical vorticity constraint DDA with rapid-scan radars should be prioritized for kinematic analyses.

## Abstract

Accurate vertical velocity retrieval from dual-Doppler analysis (DDA) is a long-standing problem of radar meteorology. Typical radar scanning strategies poorly observe the vertical component of motion, leading to large uncertainty in vertical velocity estimates. Using a vertical vorticity equation constraint in addition to a mass conservation constraint in DDA has shown promise in improving vertical velocity retrievals. However, observation system simulation experiments (OSSEs) suggest this technique requires rapid radar volume scans to realize the improvements due to the vorticity tendency term in the vertical vorticity constraint. Here, the vertical vorticity constraint DDA is tested with real, rapid-scan radar data to validate prior OSSEs results. Generally, the vertical vorticity constraint DDA produced more accurate vertical velocities from DDAs than those that did not use the constraint. When the time between volume scans was greater than 30 s, the vertical velocity accuracy was significantly affected by the vorticity tendency estimation method. A technique that uses advection correction on provisional DDA wind fields to shorten the discretization interval for the vorticity tendency calculation improved the vertical velocity retrievals for longer times between volume scans. The skill of these DDAs was similar to those using a shorter time between volume scans. These improvements were due to increased accuracy of the vertical vorticity tendency using the advection correction technique. The real radar data tests also revealed that the vertical vorticity constraint DDAs are more forgiving to radar data errors. These results suggest that vertical vorticity constraint DDA with rapid-scan radars should be prioritized for kinematic analyses.

## Abstract

Observation system simulation experiments are used to evaluate different dual-Doppler analysis (DDA) methods for retrieving vertical velocity *w* at grid spacings on the order of 100 m within a simulated tornadic supercell. Variational approaches with and without a vertical vorticity equation constraint are tested, along with a typical (traditional) method involving vertical integration of the mass conservation equation. The analyses employ emulated radar data from dual-Doppler placements 15, 30, and 45 km east of the mesocyclone, with volume scan intervals ranging from 10 to 150 s. The effect of near-surface data loss is examined by denying observations below 1 km in some of the analyses. At the longer radar ranges and when no data denial is imposed, the “traditional” method produces results similar to those of the variational method and is much less expensive to implement. However, at close range and/or with data denial, the variational method is much more accurate, confirming results from previous studies. The vorticity constraint shows the potential to improve the variational analysis substantially, reducing errors in the *w* retrieval by up to 30% for rapid-scan observations (≤30 s) at close range when the local vorticity tendency is estimated using spatially variable advection correction. However, the vorticity constraint also degrades the analysis for longer scan intervals, and the impact diminishes with increased range. Furthermore, analyses using 30-s data also frequently outperform analyses using 10-s data, suggesting a limit to the benefit of increasing the radar scan rate for variational DDA employing the vorticity constraint.

## Abstract

Observation system simulation experiments are used to evaluate different dual-Doppler analysis (DDA) methods for retrieving vertical velocity *w* at grid spacings on the order of 100 m within a simulated tornadic supercell. Variational approaches with and without a vertical vorticity equation constraint are tested, along with a typical (traditional) method involving vertical integration of the mass conservation equation. The analyses employ emulated radar data from dual-Doppler placements 15, 30, and 45 km east of the mesocyclone, with volume scan intervals ranging from 10 to 150 s. The effect of near-surface data loss is examined by denying observations below 1 km in some of the analyses. At the longer radar ranges and when no data denial is imposed, the “traditional” method produces results similar to those of the variational method and is much less expensive to implement. However, at close range and/or with data denial, the variational method is much more accurate, confirming results from previous studies. The vorticity constraint shows the potential to improve the variational analysis substantially, reducing errors in the *w* retrieval by up to 30% for rapid-scan observations (≤30 s) at close range when the local vorticity tendency is estimated using spatially variable advection correction. However, the vorticity constraint also degrades the analysis for longer scan intervals, and the impact diminishes with increased range. Furthermore, analyses using 30-s data also frequently outperform analyses using 10-s data, suggesting a limit to the benefit of increasing the radar scan rate for variational DDA employing the vorticity constraint.

## Abstract

Techniques to mitigate analysis errors arising from the nonsimultaneity of data collections typically use advection-correction procedures based on the hypothesis (frozen turbulence) that the analyzed field can be represented as a pattern of unchanging form in horizontal translation. It is more difficult to advection correct the radial velocity than the reflectivity because even if the vector velocity field satisfies this hypothesis, its radial component does not—but that component does satisfy a second-derivative condition. We treat the advection correction of the radial velocity (*υ*
_{
r
}) as a variational problem in which errors in that second-derivative condition are minimized subject to smoothness constraints on spatially variable pattern-translation components (*U*, *V*). The Euler–Lagrange equations are derived, and an iterative trajectory-based solution is developed in which *U*, *V*, and *υ*
_{
r
} are analyzed together. The analysis code is first verified using analytical data, and then tested using Atmospheric Imaging Radar (AIR) data from a band of heavy rainfall on 4 September 2018 near El Reno, Oklahoma, and a decaying tornado on 27 May 2015 near Canadian, Texas. In both cases, the analyzed *υ*
_{
r
} field has smaller root-mean-square errors and larger correlation coefficients than in analyses based on persistence, linear time interpolation, or advection correction using constant *U* and *V*. As some experimentation is needed to obtain appropriate parameter values, the procedure is more suitable for non-real-time applications than use in an operational setting. In particular, the degree of spatial variability in *U* and *V*, and the associated errors in the analyzed *υ*
_{
r
} field are strongly dependent on a smoothness parameter.

## Abstract

Techniques to mitigate analysis errors arising from the nonsimultaneity of data collections typically use advection-correction procedures based on the hypothesis (frozen turbulence) that the analyzed field can be represented as a pattern of unchanging form in horizontal translation. It is more difficult to advection correct the radial velocity than the reflectivity because even if the vector velocity field satisfies this hypothesis, its radial component does not—but that component does satisfy a second-derivative condition. We treat the advection correction of the radial velocity (*υ*
_{
r
}) as a variational problem in which errors in that second-derivative condition are minimized subject to smoothness constraints on spatially variable pattern-translation components (*U*, *V*). The Euler–Lagrange equations are derived, and an iterative trajectory-based solution is developed in which *U*, *V*, and *υ*
_{
r
} are analyzed together. The analysis code is first verified using analytical data, and then tested using Atmospheric Imaging Radar (AIR) data from a band of heavy rainfall on 4 September 2018 near El Reno, Oklahoma, and a decaying tornado on 27 May 2015 near Canadian, Texas. In both cases, the analyzed *υ*
_{
r
} field has smaller root-mean-square errors and larger correlation coefficients than in analyses based on persistence, linear time interpolation, or advection correction using constant *U* and *V*. As some experimentation is needed to obtain appropriate parameter values, the procedure is more suitable for non-real-time applications than use in an operational setting. In particular, the degree of spatial variability in *U* and *V*, and the associated errors in the analyzed *υ*
_{
r
} field are strongly dependent on a smoothness parameter.