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Jonathan Lin, Kerry Emanuel, and Jonathan L. Vigh

Abstract

This paper describes the development of a model framework for Forecasts of Hurricanes Using Large-Ensemble Outputs (FHLO). FHLO quantifies the forecast uncertainty of a tropical cyclone (TC) by generating probabilistic forecasts of track, intensity, and wind speed that incorporate the state-dependent uncertainty in the large-scale field. The main goal is to provide useful probabilistic forecasts of wind at fixed points in space, but these require large ensembles [O(1000)] to flesh out the tails of the distributions. FHLO accomplishes this by using a computationally inexpensive framework, which consists of three components: 1) a track model that generates synthetic tracks from the TC tracks of an ensemble numerical weather prediction (NWP) model, 2) an intensity model that predicts the intensity along each synthetic track, and 3) a TC wind field model that estimates the time-varying two-dimensional surface wind field. The intensity and wind field of a TC evolve as though the TC were embedded in a time-evolving environmental field, which is derived from the forecast fields of ensemble NWP models. Each component of the framework is evaluated using 1000-member ensembles and four years (2015–18) of TC forecasts in the Atlantic and eastern Pacific basins. We show that the synthetic track algorithm generates tracks that are statistically similar to those of the underlying global ensemble models. We show that FHLO produces competitive intensity forecasts, especially when considering probabilistic verification statistics. We also demonstrate the reliability and accuracy of the probabilistic wind forecasts. Limitations of the model framework are also discussed.

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Thomas Frisius, Daria Schönemann, and Jonathan Vigh

Abstract

The assumption of gradient wind balance is customarily made so as to derive the theoretical upper-bound intensity of a mature tropical cyclone. Emanuel's theory of hurricane potential intensity (E-PI) makes use of this assumption, whereas more recent studies by Bryan and Rotunno demonstrate that the effect of unbalanced flow can result in maximum winds that are well in excess of E-PI (superintensity). The existence of supergradient winds has been verified in a slab boundary layer model developed by Smith. Here, the authors apply the slab boundary layer model within the framework of classical E-PI theory to investigate the sensitivity of supergradient winds to the radius of maximum gradient wind (RMGW) and four nondimensional model parameters. The authors find that the Rossby number, the drag coefficient, and the modified Rankine decay parameter all have a considerable influence on the strength of the unbalanced flow. In contrast, the ratio of surface exchange coefficients has little noticeable effect on superintensity. The inclusion of horizontal momentum diffusion leads to a weaker superintensity, but the qualitative features of the model remain similar. To further elucidate these findings, the authors use the boundary layer model to examine the modified E-PI theory proposed by Emanuel and Rotunno. They assume a constant Richardson number for the outflow. The boundary layer model driven by the modified E-PI solution depends on just three model parameters rather than the four parameters used in the classical E-PI framework. Despite this apparent advantage, the results obtained in the framework of the modified E-PI are less realistic than those computed with the classical E-PI approach.

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Jonathan L. Vigh and Wayne H. Schubert

Abstract

This paper presents a simple theoretical argument to isolate the conditions under which a tropical cyclone can rapidly develop a warm-core thermal structure and subsequently approach a steady state. The theoretical argument is based on the balanced vortex model and, in particular, on the associated transverse circulation equation and the geopotential tendency equation. These second-order partial differential equations contain the diabatic forcing and three spatially varying coefficients: the static stability A, the baroclinity B, and the inertial stability C. Thus, the transverse circulation and the temperature tendency in a tropical vortex depend not only on the diabatic forcing but also on the spatial distributions of A, B, and C. Experience shows that the large radial variations of C are typically the most important effect. Under certain simplifying assumptions as to the vertical structure of the diabatic forcing and the spatial variability of A, B, and C, the transverse circulation equation and the geopotential tendency equation can be solved via separation of variables. The resulting radial structure equations retain the dynamically important radial variation of C and can be solved in terms of Green’s functions. These analytical solutions show that the vortex response to a delta function in the diabatic heating depends critically on whether the heating occurs in the low-inertial-stability region outside the radius of maximum wind or in the high-inertial-stability region inside the radius of maximum wind. This result suggests that rapid intensification is favored for storms that have at least some of the eyewall convection inside the radius of maximum wind. The development of an eye partially removes diabatic heating from the high-inertial-stability region of the storm center; however, rapid intensification may continue if the eyewall heating continues to become more efficient. As the warm core matures and static stability increases over the inner core, conditions there become less favorable for deep upright convection and the storm tends to approach a steady state.

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Jonathan Vigh, Scott R. Fulton, Mark DeMaria, and Wayne H. Schubert

Abstract

The performance of a multigrid barotropic tropical cyclone track model (MUDBAR) is compared to that of a current operational barotropic model (LBAR). Analysis of track forecast errors for the 2001 Atlantic hurricane season shows that MUDBAR gives accuracy similar to LBAR with substantially lower computational cost. Despite the use of a barotropic model, the MUDBAR forecasts show skill relative to climatology and persistence (CLIPER) out to 5 days.

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Jonathan L. Vigh, John A. Knaff, and Wayne H. Schubert

Abstract

This paper presents a climatology of the initial eye formations of a broad set of Atlantic tropical cyclones (TCs) during 1989–2008. A new dataset of structure and intensity parameters is synthesized from the vortex data messages transmitted by routine aircraft reconnaissance. Using these data together with satellite imagery and other established datasets, the times when each TC achieved various stages of eye development are tabulated to form the basis of the climatology. About 60% of Atlantic TCs form eyes. Most often, aircraft observe the eye structure before it appears in IR satellite imagery. Eyes tend to form in high potential intensity environments characterized by high sea surface temperatures and low-to-moderate environmental vertical wind shear. A notable discovery is that most (67%) TCs that form eyes tend to do so within 48 h of the cyclone’s reaching tropical storm strength. This suggests the existence of an opportune time window during which a TC can readily form an eye. From the lengths of time taken to reach various stages of eye development, the characteristic time scale for eye formation is estimated to be about 36 h.

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Jonathan Martinez, Michael M. Bell, Jonathan L. Vigh, and Robert F. Rogers

Abstract

A comprehensive examination of tropical cyclone (TC) kinematic and thermodynamic structure in the Atlantic basin is created from the Extended Flight Level Dataset for Tropical Cyclones (FLIGHT+, version 1.1). In situ data collected at the 700-hPa flight level by NOAA WP-3D and USAF WC-130 aircraft from 1999 to 2012 are analyzed. A total of 233 azimuthal mean profiles comprising 1498 radial legs are stratified by TC intensity and 12-h intensity change. A matrix of composite structures is created for minor (category 1 and 2) and major (category 3 and above) hurricanes that are intensifying [intensity increase ≥10 kt (12 h)−1], steady state [intensity change between ±5 kt (12 h)−1], and weakening [intensity decrease kt (12 h)−1]. Additional considerations to the impacts of age on TC structure are given as well. Axisymmetric radial composites reveal that intensifying TCs have statistically significant structural differences from TCs that are steady state or weakening, but that these differences also depend on the intensity of the TC. Intensifying TCs (both minor and major hurricanes) are characterized by steep tangential wind gradients radially inward of the radius of maximum tangential wind (RMW) that contribute to a ringlike structure of vorticity and inertial stability. Tangential wind structural differences are more pronounced in the eye of minor hurricanes compared to major hurricanes. Intensifying TCs are found to have higher inner- and outer-core moisture compared to steady-state and weakening TCs. Furthermore, intensifying major hurricanes possess drier eyes compared to steady-state and weakening major hurricanes.

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Daniel P. Stern, Jonathan L. Vigh, David S. Nolan, and Fuqing Zhang

Abstract

In the widely accepted convective ring model of tropical cyclone intensification, the intensification of the maximum winds and the contraction of the radius of maximum winds (RMW) occur simultaneously. This study shows that in idealized numerical simulations, contraction and intensification commence at the same time, but that contraction ceases long before peak intensity is achieved. The rate of contraction decreases with increasing initial size, while the rate of intensification does not vary systematically with initial size. Utilizing a diagnostic expression for the rate of contraction, it is shown that contraction is halted in association with a rapid increase in the sharpness of the tangential wind profile near the RMW and is not due to changes in the radial gradient of the tangential wind tendency. It is shown that a number of real storms exhibit a relationship between contraction and intensification that is similar to what is seen in the idealized simulations. In particular, the statistical distribution of intensifying tropical cyclones indicates that, for major hurricanes, most contraction is completed prior to most intensification.

By forcing a linearized vortex model with the diabatic heating and frictional tendencies from a simulation, it is possible to qualitatively reproduce the simulated secondary circulation and separately examine the vortex responses to heating and friction. It is shown that heating and friction both contribute substantially to boundary layer inflow. They also both contribute to the contraction of the RMW, as the positive wind tendency from heating-induced inflow is maximized inside of the RMW, while the net negative wind tendency from friction and frictionally induced inflow is maximized outside of the RMW.

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Stephanie N. Stevenson, Kristen L. Corbosiero, Mark DeMaria, and Jonathan L. Vigh

Abstract

This study seeks to reconcile discrepancies between previous studies analyzing the relationship between lightning and tropical cyclone (TC) intensity change. Inner-core lightning bursts (ICLBs) were identified from 2005 to 2014 in North Atlantic (NA) and eastern North Pacific (ENP) TCs embedded in favorable environments (e.g., vertical wind shear ≤ 10 m s−1; sea surface temperatures ≥ 26.5°C) using data from the World Wide Lightning Location Network (WWLLN) transformed onto a regular grid with 8-km grid spacing to replicate the expected nadir resolution of the Geostationary Lightning Mapper (GLM). Three hypothesized factors that could impact the 24-h intensity change after a burst were tested: 1) prior intensity change, 2) azimuthal burst location, and 3) radial burst location. Most ICLBs occurred in weak TCs (tropical depressions and tropical storms), and most TCs intensified (remained steady) 24 h after burst onset in the NA (ENP). TCs were more likely to intensify 24 h after an ICLB if they were steady or intensifying prior to burst onset. Azimuthally, 75% of the ICLBs initiated downshear, with 92% of downshear bursts occurring in TCs that remained steady or intensified. Of the ICLBs that initiated or rotated upshear, 2–3 times more were associated with TC intensification than weakening, consistent with recent studies finding more symmetric convection in intensifying TCs. The radial burst location relative to the radius of maximum wind (RMW) provided the most promising result: TCs with an ICLB inside (outside) the RMW were associated with intensification (weakening).

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Daniel P. Stern, Jonathan L. Vigh, David S. Nolan, and Fuqing Zhang

Abstract

In their comment, Kieu and Zhang critique the recent study of Stern et al. that examined the contraction of the radius of maximum wind (RMW) and its relationship to tropical cyclone intensification. Stern et al. derived a diagnostic expression for the rate of contraction and used this to show that while RMW contraction begins and accelerates as a result of an increasing negative radial gradient of tangential wind tendency inward of the RMW, contraction slows down and eventually ceases as a result of the increasing sharpness of the wind profile around the RMW during intensification. Kieu and Zhang claim that this kinematic framework does not yield useful understanding, that Stern et al. are mistaken in their favorable comparison of this framework to earlier work by Willoughby et al., and that Stern et al. are mistaken in their conclusion that an equation for the contraction of the RMW derived by Kieu is erroneous. This reply demonstrates that each of these claims by Kieu and Zhang is incorrect.

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Kerry Emanuel, Philippe Caroff, Sandy Delgado, Charles “Chip” Guard, Mark Guishard, Christopher Hennon, John Knaff, Kenneth R. Knapp, James Kossin, Carl Schreck, Christopher Velden, and Jonathan Vigh
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