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Daniel R. Chavas

Abstract

In a recent study, a theory was presented for the dependence of tropical cyclone intensity on the ventilation of dry air by environmental vertical wind shear. This theory was found to successfully capture the statistics of intensity dynamics in the historical record. This theory is rederived here from a simple three-term power budget and extended to analytical solutions for the complete phase space, including the change in storm intensity itself. The derivation is then generalized to the case of a capped surface entropy flux wind speed, including analytical solutions defined relative to both the traditional potential intensity and the capped-flux potential intensity. The results demonstrate that a cap on the surface entropy flux wind speed reduces the potential intensity of the system and effectively amplifies the detrimental effect of ventilation on the tropical cyclone heat engine. However, such a cap does not alter the qualitative structure of the phase-space solution for intensity change phrased relative to the capped-flux potential intensity. Thus, the wind speed dependence of surface entropy fluxes is important for intensity change in real-world storms, though it is not a necessary condition for intensification in general. Indeed, a residual power surplus may remain available to intensify a storm even in the presence of a cap, though intensification may be fully suppressed for sufficiently strong ventilation. This work complements a recent numerical simulation study and provides further evidence that there is no disconnect between extant tropical cyclone theory and the finding in numerical simulations that a storm may intensify in the presence of capped surface entropy fluxes.

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Daniel R. Chavas and Kerry Emanuel

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Tropical cyclone size remains an unsolved problem in tropical meteorology, yet size plays a significant role in modulating damage. This work employs the Bryan cloud model (CM1) to systematically explore the sensitivity of the structure of an axisymmetric tropical cyclone at statistical equilibrium to the set of relevant model, initial, and environmental external parameters. The analysis is performed in a highly idealized state of radiative–convective equilibrium (RCE) governed by only four thermodynamic parameters, which are shown to modulate the storm structure primarily via modulation of the potential intensity.

Using dimensional analysis, the authors find that the equilibrium radial wind profile is primarily a function of a single nondimensional parameter given by the ratio of the storm radial length scale to the parameterized eddy radial length scale. The former is found to be the ratio of the potential intensity to the Coriolis parameter, matching the prediction for the “natural” storm length scale embedded within prevailing axisymmetric tropical cyclone theory; the Rossby deformation radius is shown not to be fundamental. Beyond this primary scaling, a second nondimensional parameter representing the nondimensional Ekman suction velocity is found to modulate the far outer wind field. Implications of the primary nondimensional parameter are discussed, including the critical role of effective turbulence in modulating inner-core structure and new insight into empirical estimates of the radial mixing length.

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Zhanxiang Hua and Daniel R. Chavas

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Recent research suggests that surface elevation variability may influence tornado activity, though separating this effect from reporting biases is difficult to do in observations. Here we employ Bayes’s law to calculate the empirical joint dependence of tornado probability on population density and elevation roughness in the vicinity of Arkansas for the period 1955–2015. This approach is based purely on data, exploits elevation and population information explicitly in the vicinity of each tornado, and enables an explicit test of the dependence of results on elevation roughness length scale. A simple log-link linear regression fit to this empirical distribution yields an 11% decrease in tornado probability per 10-m increase in elevation roughness at fixed population density for large elevation roughness length scales (15–20 km). This effect increases by at least a factor of 2 moving toward smaller length scales down to 1 km. The elevation effect exhibits no time trend, while the population bias effect decreases systematically in time, consistent with the improvement of reporting practices. Results are robust across time periods and the exclusion of EF1 tornadoes and are consistent with recent county-level and gridded analyses. This work highlights the need for a deeper physical understanding of how elevation heterogeneity affects tornadogenesis and also provides the foundation for a general Bayesian tornado probability model that integrates both meteorological and nonmeteorological parameters.

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Daniel R. Chavas and Ning Lin

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Part I of this work developed a simple physical model for the complete radial structure of the low-level azimuthal wind field in a tropical cyclone that compared well with observations. However, wind field variability in the model is tied principally to its external parameters given by the maximum wind speed and the radius of maximum wind, the latter of which lacks a credible independent physical model for its variability. Here the authors explore the modes of variability that arise from the alternative specification of the model, which takes the outer radius in lieu of the radius of maximum wind. Nondimensionalization of the model reveals two theoretical modes of structural variability in absolute angular momentum that are shown to closely match observations. These two modes correspond to three modes of wind field variability associated with variations in intensity, outer storm size, and latitude. These wind field modes are demonstrated to mirror the dominant modes of variability found in nature, in particular the intrastorm variation of inner-core structure and the interstorm variation of overall storm size. In combination, the model offers a credible physical solution for the complete time-dependent tropical cyclone wind field in conjunction with the external specification of intensity, outer size, and latitude. More broadly, the model offers theoretical and conceptual insight into the nature of the tropical cyclone wind field, including the oft-conflated terms “size” and “structure” and their distinct variabilities.

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Jie Chen and Daniel R. Chavas

Abstract

Inland tropical cyclone (TC) impacts due to high winds and rainfall-induced flooding depend strongly on the evolution of the wind field and precipitation distribution after landfall. However, research has yet to test the detailed response of a mature TC and its hazards to changes in surface forcing in idealized settings. This work tests the transient responses of an idealized hurricane to instantaneous transitions in two key surface properties associated with landfall: roughening and drying. Simplified axisymmetric numerical modeling experiments are performed in which the surface drag coefficient and evaporative fraction are each systematically modified beneath a mature hurricane. Surface drying stabilizes the eyewall and consequently weakens the overturning circulation, thereby reducing inward angular momentum transport that slowly decays the wind field only within the inner core. In contrast, surface roughening initially (~12 h) rapidly weakens the entire low-level wind field and enhances the overturning circulation dynamically despite the concurrent thermodynamic stabilization of the eyewall; thereafter the storm gradually decays, similar to drying. As a result, total precipitation temporarily increases with roughening but uniformly decreases with drying. Storm size decreases monotonically and rapidly with surface roughening, whereas the radius of maximum wind can increase with moderate surface drying. Overall, this work provides a mechanistic foundation for understanding the inland evolution of real storms in nature.

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Daniel R. Chavas and Daniel T. Dawson II

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This work develops a theoretical model for steady thermodynamic and kinematic profiles for severe convective storm environments, building off the two-layer static energy framework developed in work by Agard and Emanuel. The model is phrased in terms of static energy, and it allows for independent variation of the boundary layer and free troposphere separated by a capping inversion. An algorithm is presented to apply the model to generate a sounding for numerical simulations of severe convective storms, and the model is compared and contrasted with that of Weisman and Klemp. The model is then fit to a case-study sounding associated with the 3 May 1999 tornado outbreak, and its potential utility is demonstrated via idealized numerical simulation experiments. A long-lived supercell is successfully simulated with the historical sounding but not the analogous theoretical sounding. Two types of example experiments are then performed that do simulate a long-lived supercell: 1) a semitheoretical experiment in which a portion of the theoretical sounding is modified to match the real sounding (low-level moisture); 2) a fully theoretical experiment in which a model physical parameter is modified (free-tropospheric relative humidity). Overall, the construction of this minimal model is flexible and amenable to additional modifications as needed. The model offers a novel framework that may be useful for testing how severe convective storms depend on the vertical structure of the hydrostatic environment, as well as for linking variability in these environments to the physical processes that produce them within the climate system.

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Daniel R. Chavas, Ning Lin, and Kerry Emanuel

Abstract

Part I of this work develops a simple model for the complete radial structure of the low-level tropical cyclone wind field. The model is constructed by mathematically merging existing theoretical solutions for the radial wind structure at the top of the boundary layer in the inner ascending and outer descending regions. The model is then compared with two observational datasets. First, the outer solution is compared with a global database from the QuikSCAT satellite (1999–2009) and found to reproduce the characteristic wind structure of the broad outer region of tropical cyclones at large radii, indicating that the solution successfully captures the physics of this region. Second, the inner solution is compared with the HWind database (2004–12) for the Atlantic and eastern Pacific basins and is shown to be capable of reproducing the inner-core structure while substantially underestimating wind speeds at larger radii. The complete model is then shown to largely, though not entirely, rectify this underestimation. Limitations of the model are discussed, including the need for a formal evaluation of the physics of the inner core as well as a transition-region model at intermediate radii characterized by intermittent convection, such as spiral rainbands. Part II will characterize the model’s modes of wind field variability and their relationship to the variability observed in nature.

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Timothy W. Cronin and Daniel R. Chavas

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It is widely believed that tropical cyclones are an intrinsically moist phenomenon, requiring evaporation and latent heat release in cumulus convection. Recent numerical modeling by Mrowiec et al., however, challenged this conventional wisdom by finding the formation of axisymmetric dry tropical cyclones in dry radiative–convective equilibrium (RCE). This paper addresses ensuing questions about the stability of dry tropical cyclones in 3D, the moist–dry vortex transition, and whether existing theories for intensity, size, and structure apply to dry cyclones. A convection-permitting model is used to simulate rotating 3D RCE, with surface wetness (0–1) and surface temperature (240–300 K) smoothly varying between dry and moist states. Tropical cyclones spontaneously form and persist for tens of days in both moist and dry/cold states, as well as part of the relatively moist/warm intermediate parameter space. As the surface is dried or cooled, cyclones weaken, both in absolute terms and relative to their potential intensities. Dry and semidry cyclones have smaller outer radii but similar-sized or larger convective centers compared to moist cyclones, consistent with existing structural theory. Strikingly, spontaneous cyclogenesis fails to occur at moderately low surface wetness values and intermediate surface temperatures of 250–270 K. Simulations with time-varying surface moisture and sea surface temperatures indicate this range of parameter space is a barrier to spontaneous genesis but not cyclone existence. Dry and semidry tropical cyclones in rotating RCE provide a compelling model system to further our understanding of real moist tropical cyclones.

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Daniel R. Chavas and Kevin A. Reed

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Existing hypotheses for the dynamical dependence of tropical cyclone genesis and size on latitude depend principally on the Coriolis parameter f. These hypotheses are tested via dynamical aquaplanet experiments with uniform thermal forcing in which planetary rotation rate and planetary radius are varied relative to Earth values; the control simulation is also compared to a present-day Earth simulation. Storm genesis rate collapses to a quasi-universal dependence on f that attains its maximum at the critical latitude, where the inverse-f scale and Rhines scale are equal. Minimum genesis distance from the equator is set by the equatorial Rhines (or deformation) scale and not by a minimum value of f. Outer storm size qualitatively follows the smaller of the two length scales, including a slow increase with latitude equatorward of 45° in the control simulation, similar to the Earth simulation. The latitude of peak size scales with the critical latitude for varying planetary radius but not rotation rate, possibly because of the dependence of genesis specifically on f. The latitudes of peak size and peak packing density scale closely together. Results suggest that temporal effects and interstorm interaction may be significant for size dynamics. More generally, the critical latitude separates two regimes: 1) a mixed wave–cyclone equatorial belt, where wave effects are strong and the Rhines scale likely limits storm size, and 2) a cyclone-filled polar cap, where wave effects are weak and cyclones persist. The large-planet limit predicts a world nearly covered with long-lived storms, equivalent to the f plane. Overall, spherical geometry is likely important for understanding tropical cyclone genesis and size on Earthlike planets.

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Morgan E O’Neill and Daniel R. Chavas

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The heat engine model of tropical cyclones describes a thermally direct overturning circulation. Outflowing air slowly subsides as radiative cooling to space balances adiabatic warming, a process that does not consume any work. However, we show here that the lateral spread of the outflow is limited by the environmental deformation radius, which at high latitudes can be rather small. In such cases, the outflowing air is radially constrained, which limits how far downward it can subside via radiative cooling alone. Some literature has invoked the possibility of “mechanical subsidence” or “forced descent” in the storm outflow region in the presence of high inertial stability, which would be a thermally indirect circulation. Mechanical subsidence in the subsiding branch of a tropical cyclone has not before been observed or characterized. A series of axisymmetric tropical cyclone simulations at different latitudes and domain sizes is conducted to study the impact of environmental inertial stability on storm dynamics. In higher-latitude storms in large axisymmetric domains, the outflow acts as a wavemaker to excite an inertial wave at the environmental inertial (Coriolis) frequency. This inertial wave periodically ventilates the core of a high-latitude storm with its own low-entropy exhaust air. The wave response is in contrast to the presumed forced descent model, and we hypothesize that this is because inertial stability provides less resistance than buoyant stability, even in highly inertially stable environments.

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