Abstract

A number of studies in recent years have used wind fields derived from portable Doppler radars in combination with the ground-based velocity track display (GBVTD) technique to diagnose the primary (tangential) and secondary (radial and vertical) circulations in tornadoes. These analyses indicate very strong vertical motions in the vortex core, in some cases with updrafts and downdrafts exceeding 100 m s⁻¹. In addition, many of the analyses indicate strong radial outflow at low levels and in the vicinity of the low-level tangential wind maximum. This paper shows that strong outward motion at this location cannot be consistent with a tornado circulation that lasts more than a few minutes. In addition, using data from numerical simulations as truth, it is shown that using observed radial velocities to diagnose vertical velocities greatly overestimates the intensity of downward motion in the core for two reasons: neglect of the mass flux into the core through the swirling boundary layer, and the likely positive bias in low-level radial velocities due to the centrifuging of debris. Possible methods for accounting for these errors are briefly discussed.

Abstract

A new approach is presented for the nondimensionalization of the Navier–Stokes equations for tornado-like vortices. This scaling is based on the results of recent numerical simulations and physical reasoning. The method clarifies and unifies the results of numerous earlier studies that used numerical simulations of axisymmetric incompressible flow to study tornadoes. Some examples are presented.

Abstract

A recent study showed observational and numerical evidence for small-scale gravity waves that radiate outward from tropical cyclones. These waves are wrapped into tight spirals by the radial and vertical shears of the tangential wind field. Reexamination of the previously studied tropical cyclone simulations suggests that the dominant source for these waves are convective asymmetries rotating along the eyewall, modulated in intensity by the preferred convection region on the left side of the environmental wind shear vector. A linearized, nonhydrostatic model for perturbations to a balanced vortex is used to study the waves. Forcing the linear model with rotating and pulsing asymmetric heat sources generates radiating gravity waves with multiple vertical and horizontal structures. The pulsation of the rotating heat source generates two types of waves: fast, deep waves with larger radial wavelengths, and slower, secondary waves with shorter radial and vertical wavelengths. The deeper waves produce surface pressure oscillations that have time scales consistent with surface observations, whereas the shorter waves have little surface indication but produce oscillations in vertical velocity with shorter radial wavelengths that are consistent with aircraft observations. Convective forcing that is either not pulsing or not rotating produces gravity waves but they are not as similar to the observed or simulated waves. The effects of varying the intensity of the cyclone, the asymmetry of the forcing, and the static stability of the surrounding atmosphere are explored.

Abstract

The maximum surface wind speed is an important parameter for tropical cyclone operational analysis and forecasting, since it defines the intensity of a cyclone. Operational forecast centers typically refer the wind speed to a maximum 1- or 10-min averaged value. Aircraft reconnaissance provides measurements of surface winds; however, because of the large variation of winds in the eyewall, it remains unclear to what extent observing the maximum wind is limited by the sampling pattern. Estimating storm intensity as simply the maximum of the observed winds is generally assumed by forecasters to underestimate the true storm intensity. The work presented herein attempts to quantify this difference by applying a methodology borrowed from the observing system simulation experiment concept, in which simulated “observations” are drawn from a numerical model. These “observations” may then be compared to the actual peak wind speed of the simulation. By sampling a high-resolution numerical simulation of Hurricane Isabel (2003) with a virtual aircraft equipped with a stepped-frequency microwave radiometer flying a standard “figure-four” pattern, the authors find that the highest wind observed over a flight typically underestimates the 1-min averaged model wind speed by 8.5% ± 1.5%. In contrast, due to its corresponding larger spatial scale, the 10-min averaged maximum wind speed is far less underestimated (1.5% ± 1.7%) using the same sampling method. These results support the National Hurricane Center’s practice, which typically assumes that the peak 1-min wind is somewhat greater than the highest observed wind speed over a single reconnaissance aircraft mission.

Abstract

Statistical methods are used to develop the Prediction of Intensity Model Error (PRIME) for both the absolute error and bias of intensity forecasts of Atlantic basin tropical cyclones from 2007 to 2014. These forecasts of forecast error are formulated using a stepwise multiple linear regression framework and are applied to 12–120-h intensity forecasts for the Logistic Growth Equation Model (LGEM), Decay–Statistical Hurricane Intensity Prediction Scheme (DSHP), interpolated Hurricane Weather Research and Forecasting Model (HWFI), and interpolated Geophysical Fluid Dynamics Laboratory (GHMI) hurricane model. The predictors selected for the regression are a combination of storm-specific characteristics, synoptic features, and parameters representing initial condition error and atmospheric flow stability.

The performance of PRIME is assessed by comparing the predictions of forecast absolute error and bias to the climatology of these quantities for each of the models. Using paired t tests, the errors in PRIME are found to be significantly smaller than climatology at the 99% level for bias and at the 95% level for absolute error. These percentages vary based on the model and forecast interval, with larger improvement observed for less accurate models and long-range forecasts. A second, more accurate version of PRIME is trained using retrospective forecasts generated by applying the 2014 version of each model to the 2008–13 hurricane seasons. Considering the positive results and use of predictors available prior to the National Hurricane Center official forecast deadline, PRIME forecasts could be valuable to the hurricane forecasting community.

Abstract

The connection relating upper-ocean salinity stratification in the form of oceanic barrier layers to tropical cyclone (TC) intensification is investigated in this study. Previous works disagree on whether ocean salinity is a negligible factor on TC intensification. Relationships derived in many of these studies are based on observations, which can be sparse or incomplete, or uncoupled models, which neglect air–sea feedbacks. Here, idealized ensemble simulations of TCs performed using the Weather Research and Forecasting (WRF) Model coupled to the 3D Price–Weller–Pinkel (PWP) ocean model facilitate examination of the TC–upper-ocean system in a controlled, high-resolution, mesoscale environment. Idealized vertical ocean profiles are modeled after barrier layer profiles of the Amazon–Orinoco river plume region, where barrier layers are defined as vertical salinity gradients between the mixed and isothermal layer depths. Our results reveal that for TCs of category 1 hurricane strength or greater, thick (24–30 m) barrier layers may favor further intensification by 6%–15% when averaging across ensemble members. Conversely, weaker cyclones are hindered by thick barrier layers. Reduced sea surface temperature cooling below the TC inner core is the primary reason for additional intensification. Sensitivity tests of the results to storm translation speed, initial oceanic mixed layer temperature, and atmospheric vertical wind shear provide a more comprehensive analysis. Last, it is shown that the ensemble mean intensity results are similar when using a 3D or 1D version of PWP.

Abstract

The effects of stochastically excited asymmetric disturbances on two-dimensional vortices are investigated. These vortices are maintained by the radial inflow of fixed cylindrical deformation fields, which are chosen so that both one-celled and two-celled vortices may be studied. The linearized perturbation equations are reduced to the form of a linear dynamical system with stochastic forcing, that is, d x/dt = Ax + F ξ , where the columns of F are forcing functions and the elements of ξ are Gaussian white-noise processes. Through this formulation the stochastically maintained variance of the perturbations, the structures that dominate the response (the empirical orthogonal functions), and the forcing functions that contribute most to this response (the stochastic optimals) can be directly calculated.

For all cases the structures that most effectively induce the transfer of energy from the mean flow to the perturbation field are close approximations to the global optimals (i.e., the initial perturbations with the maximum growth in energy in finite time), and that the structures that account for most of the variance are close approximations to the global optimals evolved forward in time to when they reach their maximum energy. For azimuthal wavenumbers in each vortex where nearly neutral modes are present (k = 1 for the one-celled vortex and 1 ⩽ k ⩽ 4 for the two-celled vortex), the variance sustained by the stochastic forcing is large, and in these cases the variance may be greatly overestimated if the radial inflow that sustains the mean vortex is neglected in the dynamics of the perturbations.

Through a modification of this technique the ensemble average eddy momentum flux divergences associated with the stochastically maintained perturbation fields can be computed, and this information is used to determine the perturbation-induced mean flow tendency in the linear limit. Examination of these results shows that the net effect of the low wavenumber perturbations is to cause downgradient eddy fluxes in both vortex types, while high wavenumber perturbations cause upgradient eddy fluxes. However, to determine how these eddy fluxes actually change the mean flow, the local accelerations caused by the eddy flux divergences must be incorporated into the equation for the steady-state azimuthal velocity. From calculations of this type, it is found that the effect of the radial inflow can be crucial in determining whether or not the vortex is intensified or weakened by the perturbations: though the net eddy fluxes are most often downgradient, the radial inflow carries the transported angular momentum back into the vortex core, resulting in an increase in the maximum wind speed. In most cases for the vortex flows studied, the net effect of stochastically forced asymmetric perturbations is to intensify the mean vortex. Applications of the same analysis techniques to vortices with azimuthal velocity profiles more like those used in previous studies give similar results.

Abstract

In this paper, the first of two parts, the dynamics of linearized perturbations to hurricane-like vortices are studied. Unlike previous studies, which are essentially two-dimensional or assume that the perturbations are quasi-balanced, the perturbations are fully three-dimensional and nonhydrostatic. The vortices used as basic states are also three-dimensional (though axisymmetric), with wind fields modeled closely after observations of hurricanes and tropical storms, and are initially in hydrostatic and gradient wind balance.

The equations of motion, computational methods for solving them, and methods for generating the basic-state hurricane-like vortices are presented. In particular, three basic states are studied: a vortex modeled after an intense (category 3) hurricane, a moderate (category 1) hurricane, and a weak tropical storm. The stability of each vortex is considered. The category 3 vortex is found to be rather unstable, with its fastest growing mode occurring for azimuthal wavenumber three with an e-folding time of approximately 1 h. The category 1 vortex is less unstable, as its most unstable mode occurs for wavenumber two with an e-folding time of 5 h. In both cases, these unstable modes are found to be close analogs of their strictly two-dimensional counterparts, and essentially barotropic in nature.

The tropical storm–like vortex is found to be stable for all azimuthal wavenumbers. For this vortex, the evolution of purely thermal, unbalanced perturbations in the vortex environment are studied; such disturbances might be the result of asymmetric bursts of convection in the vicinity of the vortex, which are typical for developing storms. The evolution of these perturbations goes through two phases. First, there is substantial gravity wave radiation and rapid adjustment to quasi-gradient wind balance. In the second phase, the quasi-balanced perturbations are axisymmetrized by the shear of the basic-state vortex, and cause localized accelerations of the symmetric vortex via eddy momentum and heat fluxes. The full response of the symmetric vortex and comparisons to fully nonlinear simulations are the topics of the second part.

Abstract

The dynamics of both transient and exponentially growing disturbances in two-dimensional vortices that are maintained by the radial inflow of a fixed cylindrical deformation field are investigated. Such deformation fields are chosen so that both one-celled and two-celled vortices may be studied. The linearized evolution of asymmetric perturbations is expressed in the form of a linear dynamical system d x/dt = Ax. The shear of the mean flow results in a nonnormal dynamical operator A, allowing for the transient growth of perturbations even when all the modes of the operator are decaying. It is found that one-celled vortices are stable to asymmetric perturbations of all azimuthal wavenumbers, whereas two-celled vortices can have low-wavenumber instabilities. In all cases, generalized stability analysis of the dynamical operator identifies the perturbations that grow the fastest, both instantaneously and over a finite period of time. While the unstable modal perturbations necessarily convert mean-flow vorticity to perturbation vorticity, the perturbations with the fastest instantaneous growth rate use the deformation of the mean flow to rearrange their vorticity fields into configurations with higher kinetic energy. Also found are perturbations that use a hybrid of these two mechanisms to achieve substantial energy growth over finite time periods.

Inclusion of the dynamical effects of radial inflow—vorticity advection and vorticity stretching—is found to be extremely important in assessing the potential for transient growth and instability in these vortices. In the two-celled vortex, neglecting these terms destabilizes the vortex for azimuthal wavenumbers one and two. In the one-celled vortex, neglect of the radial inflow terms results in an overestimation of transient growth for all wavenumbers, and it is also found that for high wavenumbers the maximum transient growth decreases as the strength of the radial inflow increases.

The effects of these perturbations through eddy flux divergences on the mean flow are also examined. In the one-celled vortex it is found that for all wavenumbers greater than one the net effect of most perturbations, regardless of their initial configuration, is to increase the kinetic energy of the mean flow. As these perturbations are sheared over they cause upgradient eddy momentum fluxes, thereby transferring their kinetic energy to the mean flow and intensifying the vortex. However, for wavenumber one in the one-celled vortex, and all wavenumbers in the two-celled vortex, it was found that nearly all perturbations have the net effect of decreasing the kinetic energy of the mean flow. In these cases, the kinetic energy of the perturbations accumulates in nearly neutral or unstable modal structures, so that energy acquired from the mean flow is not returned to the mean flow but instead is lost through dissipation.

Abstract

The warm-core structure of tropical cyclones is examined in idealized simulations using the Weather Research and Forecasting (WRF) Model. The maximum perturbation temperature in a control simulation occurs in the midtroposphere (5–6 km), in contrast to the upper-tropospheric (>10 km) warm core that is widely believed to be typical. This conventional view is reassessed and found to be largely based on three case studies, and it is argued that the “typical” warm-core structure is actually not well known. In the control simulation, the height of the warm core is nearly constant over a wide range of intensities. From additional simulations in which either the size of the initial vortex or the microphysics parameterization is varied, it is shown that the warm core is generally found at 4–8 km. A secondary maximum often develops near 13–14 km but is almost always weaker than the primary warm core. It is demonstrated that microwave remote sensing instruments are of insufficient resolution to detect this midlevel warm core, and the conclusions of some studies that have utilized these instruments may not be reliable. Using simple arguments based on thermal wind balance, it is shown that the height of the warm core is not necessarily related to either the height where the vertical shear of the tangential winds is maximized or the height where the radial temperature gradient is maximized. In particular, changes in the height of the warm core need not imply changes in either the intensity of the storm or in the manner in which the winds in the eyewall decay with height.