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Abstract
Horizontal homogeneity is typically assumed in the design of planetary boundary layer (PBL) parameterizations in weather prediction models. Consistent with this assumption, PBL schemes with predictive equations for subgrid turbulence kinetic energy (TKE) typically neglect advection of TKE. However, tropical cyclone (TC) boundary layers are inhomogeneous, particularly in the eyewall. To gain further insight, this study examines the effect of advection of TKE using the Mellor–Yamada–Nakanishi–Niino (MYNN) PBL scheme in idealized TC simulations. The analysis focuses on two simulations, one that includes TKE advection (CTL) and one that does not (NoADV). Results show that relatively large TKE in the eyewall above 2 km is predominantly attributable to vertical advection of TKE in CTL. Interestingly, buoyancy production of TKE is negative in this region in both simulations; thus, buoyancy effects cannot explain observed columns of TKE in TC eyewalls. Both horizontal and vertical advection of TKE tends to reduce TKE and vertical viscosity in the near-surface inflow layer, particularly in the eyewall of TCs. Results also show that the simulated TC in CTL has slightly stronger maximum winds, slightly smaller radius of maximum wind, and ~5% smaller radius of gale-force wind than in NoADV. These differences are consistent with absolute angular momentum being advected to smaller radii in CTL. Sensitivity simulations further reveal that the differences between CTL and NoADV are more attributable to vertical advection (rather than horizontal advection) of TKE. Recommendations for improvements of PBL schemes that use predictive equations for TKE are also discussed.
Abstract
Horizontal homogeneity is typically assumed in the design of planetary boundary layer (PBL) parameterizations in weather prediction models. Consistent with this assumption, PBL schemes with predictive equations for subgrid turbulence kinetic energy (TKE) typically neglect advection of TKE. However, tropical cyclone (TC) boundary layers are inhomogeneous, particularly in the eyewall. To gain further insight, this study examines the effect of advection of TKE using the Mellor–Yamada–Nakanishi–Niino (MYNN) PBL scheme in idealized TC simulations. The analysis focuses on two simulations, one that includes TKE advection (CTL) and one that does not (NoADV). Results show that relatively large TKE in the eyewall above 2 km is predominantly attributable to vertical advection of TKE in CTL. Interestingly, buoyancy production of TKE is negative in this region in both simulations; thus, buoyancy effects cannot explain observed columns of TKE in TC eyewalls. Both horizontal and vertical advection of TKE tends to reduce TKE and vertical viscosity in the near-surface inflow layer, particularly in the eyewall of TCs. Results also show that the simulated TC in CTL has slightly stronger maximum winds, slightly smaller radius of maximum wind, and ~5% smaller radius of gale-force wind than in NoADV. These differences are consistent with absolute angular momentum being advected to smaller radii in CTL. Sensitivity simulations further reveal that the differences between CTL and NoADV are more attributable to vertical advection (rather than horizontal advection) of TKE. Recommendations for improvements of PBL schemes that use predictive equations for TKE are also discussed.
Abstract
This study considers a two-layer fluid with constant density in each layer connected by a layer of continuously varying density for flows past topography in which hydraulic jumps with lee vortices are expected based on shallow-water theory. Numerical integrations of the Navier–Stokes equations at a Reynolds number high enough for a direct numerical simulation of turbulent flow allow an examination of the internal mechanics of the turbulent leeside hydraulic jump and how this mechanics is related to lee vortices. Analysis of the statistically steady state shows that the original source of lee-vortex vertical vorticity is through the leeside descent of baroclinically produced spanwise vorticity associated with the hydraulic jump. This spanwise vorticity is tilted to the vertical at the spanwise extremities of the leeside hydraulic jump. Turbulent energy dissipation in flow through the hydraulic jump allows this leeside vertical vorticity to diffuse and extend downstream. The present simulations also suggest a geometrical interpretation of lee-vortex potential-vorticity creation, a concept central to interpretations of lee vortices based on the shallow-water equations.
Abstract
This study considers a two-layer fluid with constant density in each layer connected by a layer of continuously varying density for flows past topography in which hydraulic jumps with lee vortices are expected based on shallow-water theory. Numerical integrations of the Navier–Stokes equations at a Reynolds number high enough for a direct numerical simulation of turbulent flow allow an examination of the internal mechanics of the turbulent leeside hydraulic jump and how this mechanics is related to lee vortices. Analysis of the statistically steady state shows that the original source of lee-vortex vertical vorticity is through the leeside descent of baroclinically produced spanwise vorticity associated with the hydraulic jump. This spanwise vorticity is tilted to the vertical at the spanwise extremities of the leeside hydraulic jump. Turbulent energy dissipation in flow through the hydraulic jump allows this leeside vertical vorticity to diffuse and extend downstream. The present simulations also suggest a geometrical interpretation of lee-vortex potential-vorticity creation, a concept central to interpretations of lee vortices based on the shallow-water equations.
Abstract
Extreme updrafts (≥10 m s−1) and wind gusts (≥90 m s−1) are ubiquitous within the low-level eyewall of intense tropical cyclones (TCs). Previous studies suggest that both of these features are associated with coherent subkilometer-scale vortices. Here, over 100 000 “virtual” dropsonde trajectories are examined within a large-eddy simulation (31.25-m horizontal grid spacing) of a category 5 hurricane in order to gain insight into the nature of these features and to better understand and interpret dropsonde observations. At such a high resolution, profiles of wind speed and vertical velocity from the virtual sondes are difficult to distinguish from those of real dropsondes. PDFs of the strength of updrafts and wind gusts compare well between the simulated and observed dropsondes, as do the respective range of heights over which these features are found. Individual simulated updrafts can be tracked for periods of up to several minutes, revealing structures that are both coherent and rapidly evolving. It appears that the updrafts are closely associated with vortices and wind speed maxima, consistent with previous studies. The peak instantaneous wind gusts in the simulations (up to 150 m s−1) are substantially stronger than have ever been observed. Using the virtual sondes, it is demonstrated that the probability of sampling such extremes is vanishingly small, and it is argued that actual intense TCs might also be characterized by gusts of these magnitudes.
Abstract
Extreme updrafts (≥10 m s−1) and wind gusts (≥90 m s−1) are ubiquitous within the low-level eyewall of intense tropical cyclones (TCs). Previous studies suggest that both of these features are associated with coherent subkilometer-scale vortices. Here, over 100 000 “virtual” dropsonde trajectories are examined within a large-eddy simulation (31.25-m horizontal grid spacing) of a category 5 hurricane in order to gain insight into the nature of these features and to better understand and interpret dropsonde observations. At such a high resolution, profiles of wind speed and vertical velocity from the virtual sondes are difficult to distinguish from those of real dropsondes. PDFs of the strength of updrafts and wind gusts compare well between the simulated and observed dropsondes, as do the respective range of heights over which these features are found. Individual simulated updrafts can be tracked for periods of up to several minutes, revealing structures that are both coherent and rapidly evolving. It appears that the updrafts are closely associated with vortices and wind speed maxima, consistent with previous studies. The peak instantaneous wind gusts in the simulations (up to 150 m s−1) are substantially stronger than have ever been observed. Using the virtual sondes, it is demonstrated that the probability of sampling such extremes is vanishingly small, and it is argued that actual intense TCs might also be characterized by gusts of these magnitudes.
Abstract
Axisymmetric and three-dimensional simulations are used to evaluate the theory of tropical cyclone (TC) intensification proposed by K. A. Emanuel, which is based on gradient wind balance and moist-neutral ascent along angular momentum (M) surfaces. According to the numerical model results, the intensification of the TC can be divided into two periods, phase I and phase II. During phase I, the TC intensifies while the M and saturation entropy (s*) surfaces evolve from nearly orthogonal to almost congruent. During phase II, the M and s* surfaces in the eyewall and outflow are congruent as the TC intensifies, which is consistent with Emanuel’s study. Therefore, the condition of moist slantwise neutrality in Emanuel’s study is sufficiently satisfied throughout the intensification in phase II. It is also found that the sensitivity of the intensification rates to the surface exchange coefficient for entropy C k matches Emanuel’s theoretical result, which is that the intensification rate is proportional to C k . However, the intensification rate varies in proportion to the surface exchange coefficient for momentum C d , while the Emanuel model growth rate is insensitive to C d . Furthermore, although the tendency diagnosed by Emanuel is qualitatively similar to the numerical model result during phase II, it is not quantitatively similar. The present analysis finds the inclusion of non–gradient wind effects in the theoretical framework of Emanuel’s study produces an intensification rate that is quantitatively similar to the numerical model results. The neglect of non–gradient wind effects in Emanuel’s study may be the reason for the different dependence of its intensification rate on C d compared to that of the numerical model. Other aspects of Emanuel’s study in the context of recent research on TC intensification are discussed.
Abstract
Axisymmetric and three-dimensional simulations are used to evaluate the theory of tropical cyclone (TC) intensification proposed by K. A. Emanuel, which is based on gradient wind balance and moist-neutral ascent along angular momentum (M) surfaces. According to the numerical model results, the intensification of the TC can be divided into two periods, phase I and phase II. During phase I, the TC intensifies while the M and saturation entropy (s*) surfaces evolve from nearly orthogonal to almost congruent. During phase II, the M and s* surfaces in the eyewall and outflow are congruent as the TC intensifies, which is consistent with Emanuel’s study. Therefore, the condition of moist slantwise neutrality in Emanuel’s study is sufficiently satisfied throughout the intensification in phase II. It is also found that the sensitivity of the intensification rates to the surface exchange coefficient for entropy C k matches Emanuel’s theoretical result, which is that the intensification rate is proportional to C k . However, the intensification rate varies in proportion to the surface exchange coefficient for momentum C d , while the Emanuel model growth rate is insensitive to C d . Furthermore, although the tendency diagnosed by Emanuel is qualitatively similar to the numerical model result during phase II, it is not quantitatively similar. The present analysis finds the inclusion of non–gradient wind effects in the theoretical framework of Emanuel’s study produces an intensification rate that is quantitatively similar to the numerical model results. The neglect of non–gradient wind effects in Emanuel’s study may be the reason for the different dependence of its intensification rate on C d compared to that of the numerical model. Other aspects of Emanuel’s study in the context of recent research on TC intensification are discussed.
Abstract
Tropical cyclones that intensify abruptly experience “rapid intensification.” Rapid intensification remains a formidable forecast challenge, in part because the underlying science has not been settled. One way to reconcile the debates and inconsistencies in the literature is to presume that different forms (or modes) of rapid intensification exist. The present study provides evidence in support of this hypothesis by documenting two modes of rapid intensification in a global convection-permitting simulation and the HURDAT2 database. The “marathon mode” is characterized by a moderately paced and long-lived intensification period, whereas the “sprint mode” is characterized by explosive and short-lived intensification bursts. Differences between the modes were also found in initial vortex structure (well defined versus poorly defined), nature of intensification (symmetric versus asymmetric), and environmental conditions (weak shear versus strong shear). Collectively, these differences indicate that the two modes involve distinct intensification mechanisms. Recognizing the existence of multiple intensification modes may help to better understand and predict rapid intensification by, for example, explaining the lack of consensus in the literature, or by raising awareness that rapid intensification in strongly sheared cyclones is not just an exception to a rule, but a typical process.
Significance Statement
Hurricanes are serious threats to society—in particular those that suddenly and quickly intensify before striking land. Forecasting these “rapid intensification” events is a challenge, in part because we do not fully understand the science behind rapid intensification. This study furthers our understanding of hurricane rapid intensification by documenting that rapid intensification comes in different types. Specifically, we show that one type of rapid intensification happens under conditions that meteorologists have thought would lessen the chances of intensification. Awareness of such a type of rapid intensification could lead to better predictions of hurricane intensity because forecasters are more cognizant of this type of event and the conditions in which they occur.
Abstract
Tropical cyclones that intensify abruptly experience “rapid intensification.” Rapid intensification remains a formidable forecast challenge, in part because the underlying science has not been settled. One way to reconcile the debates and inconsistencies in the literature is to presume that different forms (or modes) of rapid intensification exist. The present study provides evidence in support of this hypothesis by documenting two modes of rapid intensification in a global convection-permitting simulation and the HURDAT2 database. The “marathon mode” is characterized by a moderately paced and long-lived intensification period, whereas the “sprint mode” is characterized by explosive and short-lived intensification bursts. Differences between the modes were also found in initial vortex structure (well defined versus poorly defined), nature of intensification (symmetric versus asymmetric), and environmental conditions (weak shear versus strong shear). Collectively, these differences indicate that the two modes involve distinct intensification mechanisms. Recognizing the existence of multiple intensification modes may help to better understand and predict rapid intensification by, for example, explaining the lack of consensus in the literature, or by raising awareness that rapid intensification in strongly sheared cyclones is not just an exception to a rule, but a typical process.
Significance Statement
Hurricanes are serious threats to society—in particular those that suddenly and quickly intensify before striking land. Forecasting these “rapid intensification” events is a challenge, in part because we do not fully understand the science behind rapid intensification. This study furthers our understanding of hurricane rapid intensification by documenting that rapid intensification comes in different types. Specifically, we show that one type of rapid intensification happens under conditions that meteorologists have thought would lessen the chances of intensification. Awareness of such a type of rapid intensification could lead to better predictions of hurricane intensity because forecasters are more cognizant of this type of event and the conditions in which they occur.
Abstract
The authors evaluate whether the structure and intensity of simulated squall lines can be explained by “RKW theory,” which most specifically addresses how density currents evolve in sheared environments. In contrast to earlier studies, this study compares output from four numerical models, rather than from just one. All of the authors’ simulations support the qualitative application of RKW theory, whereby squall-line structure is primarily governed by two effects: the intensity of the squall line’s surface-based cold pool, and the low- to midlevel environmental vertical wind shear. The simulations using newly developed models generally support the theory’s quantitative application, whereby an optimal state for system structure also optimizes system intensity. However, there are significant systematic differences between the newer numerical models and the older model that was originally used to develop RKW theory. Two systematic differences are analyzed in detail, and causes for these differences are proposed.
Abstract
The authors evaluate whether the structure and intensity of simulated squall lines can be explained by “RKW theory,” which most specifically addresses how density currents evolve in sheared environments. In contrast to earlier studies, this study compares output from four numerical models, rather than from just one. All of the authors’ simulations support the qualitative application of RKW theory, whereby squall-line structure is primarily governed by two effects: the intensity of the squall line’s surface-based cold pool, and the low- to midlevel environmental vertical wind shear. The simulations using newly developed models generally support the theory’s quantitative application, whereby an optimal state for system structure also optimizes system intensity. However, there are significant systematic differences between the newer numerical models and the older model that was originally used to develop RKW theory. Two systematic differences are analyzed in detail, and causes for these differences are proposed.
Abstract
Diffusion that is implicit in the odd-ordered advection schemes in early versions of the Advanced Research core of the Weather Research and Forecasting (WRF) model is sometimes insufficient to remove noise from kinematical fields. The problem is worst when grid-relative wind speeds are low and when stratification is nearly neutral or unstable, such as in weakly forced daytime boundary layers, where noise can grow until it competes with the physical phenomena being simulated. One solution to this problem is an explicit, sixth-order numerical diffusion scheme that preserves the WRF model’s high effective resolution and uses a flux limiter to ensure monotonicity. The scheme, and how it was added to the WRF model, are explained. The scheme is then demonstrated in an idealized framework and in simulations of salt breezes and lake breezes in northwestern Utah.
Abstract
Diffusion that is implicit in the odd-ordered advection schemes in early versions of the Advanced Research core of the Weather Research and Forecasting (WRF) model is sometimes insufficient to remove noise from kinematical fields. The problem is worst when grid-relative wind speeds are low and when stratification is nearly neutral or unstable, such as in weakly forced daytime boundary layers, where noise can grow until it competes with the physical phenomena being simulated. One solution to this problem is an explicit, sixth-order numerical diffusion scheme that preserves the WRF model’s high effective resolution and uses a flux limiter to ensure monotonicity. The scheme, and how it was added to the WRF model, are explained. The scheme is then demonstrated in an idealized framework and in simulations of salt breezes and lake breezes in northwestern Utah.
Abstract
Previous studies have found surprisingly strong vertical motions in low levels of some tropical cyclones. In this study, all available dropsondes (
Abstract
Previous studies have found surprisingly strong vertical motions in low levels of some tropical cyclones. In this study, all available dropsondes (
Abstract
The spatial resolution appropriate for the simulation of deep moist convection is addressed from a turbulence perspective. To provide a clear theoretical framework for the problem, techniques for simulating turbulent flows are reviewed, and the source of the subgrid terms in the Navier–Stokes equation is clarified.
For decades, cloud-resolving models have used large-eddy simulation (LES) techniques to parameterize the subgrid terms. A literature review suggests that the appropriateness of using traditional LES closures for this purpose has never been established. Furthermore, examination of the assumptions inherent in these closures suggests that grid spacing on the order of 100 m may be required for the performance of cloud models to be consistent with their design.
Based on these arguments, numerical simulations of squall lines were conducted with grid spacings between 1 km and 125 m. The results reveal that simulations with 1-km grid spacing do not produce equivalent squall-line structure and evolution as compared to the higher-resolution simulations. Details of the simulated squall lines that change as resolution is increased include precipitation amount, system phase speed, cloud depth, static stability values, the size of thunderstorm cells, and the organizational mode of convective overturning (e.g., upright towers versus sloped plumes). It is argued that the ability of the higher-resolution runs to become turbulent leads directly to the differences in evolution.
There appear to be no systematic trends in specific fields as resolution is increased. For example, mean vertical velocity and rainwater values increase in magnitude with increasing resolution in some environments, but decrease with increasing resolution in other environments. The statistical properties of the simulated squall lines are still not converged between the 250- and 125-m runs. Several possible explanations for the lack of convergence are offered. Nevertheless, it is clear that simulations with O(1 km) grid spacing should not be used as benchmark or control solutions for resolution sensitivity studies.
The simulations also support the contention that a minimum grid spacing of O(100 m) is required for traditional LES closures to perform appropriately for their design. Specifically, only simulations with 250- and 125-m grid spacing resolve an inertial subrange. In contrast, the 1-km simulations do not even reproduce the correct magnitude or scale of the spectral kinetic energy maximum. Furthermore, the 1-km simulations contain an unacceptably large amount of subgrid turbulence kinetic energy, and do not adequately resolve turbulent fluxes of total water.
A guide to resolution requirements for the operational and research communities is proposed. The proposal is based primarily on the intended use of the model output. Even though simulations with O(1 km) grid spacing display behavior that is unacceptable for the model design, it is argued that these simulations can still provide valuable information to operational forecasters. For the research community, O(100 m) grid spacing is recommended for most applications, because a modeling system that is well founded should be desired for most purposes.
Abstract
The spatial resolution appropriate for the simulation of deep moist convection is addressed from a turbulence perspective. To provide a clear theoretical framework for the problem, techniques for simulating turbulent flows are reviewed, and the source of the subgrid terms in the Navier–Stokes equation is clarified.
For decades, cloud-resolving models have used large-eddy simulation (LES) techniques to parameterize the subgrid terms. A literature review suggests that the appropriateness of using traditional LES closures for this purpose has never been established. Furthermore, examination of the assumptions inherent in these closures suggests that grid spacing on the order of 100 m may be required for the performance of cloud models to be consistent with their design.
Based on these arguments, numerical simulations of squall lines were conducted with grid spacings between 1 km and 125 m. The results reveal that simulations with 1-km grid spacing do not produce equivalent squall-line structure and evolution as compared to the higher-resolution simulations. Details of the simulated squall lines that change as resolution is increased include precipitation amount, system phase speed, cloud depth, static stability values, the size of thunderstorm cells, and the organizational mode of convective overturning (e.g., upright towers versus sloped plumes). It is argued that the ability of the higher-resolution runs to become turbulent leads directly to the differences in evolution.
There appear to be no systematic trends in specific fields as resolution is increased. For example, mean vertical velocity and rainwater values increase in magnitude with increasing resolution in some environments, but decrease with increasing resolution in other environments. The statistical properties of the simulated squall lines are still not converged between the 250- and 125-m runs. Several possible explanations for the lack of convergence are offered. Nevertheless, it is clear that simulations with O(1 km) grid spacing should not be used as benchmark or control solutions for resolution sensitivity studies.
The simulations also support the contention that a minimum grid spacing of O(100 m) is required for traditional LES closures to perform appropriately for their design. Specifically, only simulations with 250- and 125-m grid spacing resolve an inertial subrange. In contrast, the 1-km simulations do not even reproduce the correct magnitude or scale of the spectral kinetic energy maximum. Furthermore, the 1-km simulations contain an unacceptably large amount of subgrid turbulence kinetic energy, and do not adequately resolve turbulent fluxes of total water.
A guide to resolution requirements for the operational and research communities is proposed. The proposal is based primarily on the intended use of the model output. Even though simulations with O(1 km) grid spacing display behavior that is unacceptable for the model design, it is argued that these simulations can still provide valuable information to operational forecasters. For the research community, O(100 m) grid spacing is recommended for most applications, because a modeling system that is well founded should be desired for most purposes.
Abstract
Idealized supercell thunderstorms are simulated with the Weather Research and Forecasting (WRF) Model at 15 cloud condensation nuclei (CCN) concentrations (100–10 000 cm−3) using four environmental soundings with different low-level relative humidity (RH) and vertical wind shear values. The Morrison microphysics scheme is used with explicit prediction of cloud droplet number concentration and a variable shape parameter for the raindrop size distribution (results from simulations with a fixed shape parameter are also presented). Changes in the microphysical process rates with CCN concentration are negligible beyond CCN ≈ 3000 cm−3. Changes in cold pool characteristics with CCN concentration are nonmonotonic and highly dependent on the environmental conditions. In moist conditions with moderate vertical wind shear, the cold pool area is nearly constant with respect to CCN concentration, while the area is reduced by 84% and 22% in the soundings with dry RH and large vertical wind shear, respectively. With the exception of the dry RH sounding, domain-averaged precipitation peaks between 500 and 5000 cm−3, after which it remains constant or slowly decreases. For the dry RH sounding, the domain-averaged precipitation monotonically decreases with CCN concentration. Accumulated precipitation is enhanced (by up to 25 mm) in the most polluted cases near the updrafts, except for the dry RH sounding. The different responses for moist and dry soundings are mostly due to increased (decreased) low-level latent cooling from melting hail (evaporating rain) with increasing CCN concentration in the moist soundings. This compensating effect does not exist when the low-level RH is dry.
Abstract
Idealized supercell thunderstorms are simulated with the Weather Research and Forecasting (WRF) Model at 15 cloud condensation nuclei (CCN) concentrations (100–10 000 cm−3) using four environmental soundings with different low-level relative humidity (RH) and vertical wind shear values. The Morrison microphysics scheme is used with explicit prediction of cloud droplet number concentration and a variable shape parameter for the raindrop size distribution (results from simulations with a fixed shape parameter are also presented). Changes in the microphysical process rates with CCN concentration are negligible beyond CCN ≈ 3000 cm−3. Changes in cold pool characteristics with CCN concentration are nonmonotonic and highly dependent on the environmental conditions. In moist conditions with moderate vertical wind shear, the cold pool area is nearly constant with respect to CCN concentration, while the area is reduced by 84% and 22% in the soundings with dry RH and large vertical wind shear, respectively. With the exception of the dry RH sounding, domain-averaged precipitation peaks between 500 and 5000 cm−3, after which it remains constant or slowly decreases. For the dry RH sounding, the domain-averaged precipitation monotonically decreases with CCN concentration. Accumulated precipitation is enhanced (by up to 25 mm) in the most polluted cases near the updrafts, except for the dry RH sounding. The different responses for moist and dry soundings are mostly due to increased (decreased) low-level latent cooling from melting hail (evaporating rain) with increasing CCN concentration in the moist soundings. This compensating effect does not exist when the low-level RH is dry.
