Some Refinements to the Most Recent Simple Time-Dependent Theory of Tropical Cyclone Intensification and Sensitivity

Abstract

Several key issues in the simple time-dependent theories of tropical cyclone (TC) intensification developed in recent years remain, including the lacks of a closure for the pressure dependence of saturation enthalpy at sea surface temperature (SST) under the eyewall and the definition of environmental conditions, such as the boundary-layer enthalpy in TC environment and the TC outflow-layer temperature. In this study, some refinements to the most recent time-dependent theory of TC intensification have been accomplished to resolve those issues. The first is the construction of a functional relationship between the surface pressure under the eyewall and the TC intensity, which is derived using the cyclostrophic wind balance and calibrated using full-physics axisymmetric model simulations. The second is the definition of TC environment that explicitly includes the air-sea temperature difference. The third is the TC outflow-layer temperature parameterized as a linear function of SST based on global reanalysis data. With these refinements, the updated time-dependent theory becomes self-contained and can give both the intensity-dependent TC intensification rate (IR) and the maximum potential intensity (MPI) under given environmental thermodynamic conditions. It is shown that the pressure dependence of saturation enthalpy at SST can lead to an increase in the TC MPI and IR by about half of that induced by dissipative heating due to surface friction. Results also show that both MPI and IR increase with increasing SST, surface enthalpy exchange coefficient, environmental air-sea temperature difference, and decreasing environmental boundary-layer relative humidity, but the maximum IR is insensitive to surface drag coefficient.

Why Does the Initial Wind Profile Inside the Radius of Maximum Wind Matter to Tropical Cyclone Development?

“…Although limited high‐resolution observations indicate considerable differences in the wind structure inside the RMW during the development of TCs (Reasor et al., 2013), it is still unclear what the initial inner‐core wind structure is and what determines the inner‐core wind structure inside the RMW of TCs in nature, which could be another topic for a future study when more reliable observational data are available. In addition, recent time‐dependent theories of TC intensification do not include the TC structure parameters (e.g., Wang, Li, Xu, 2021; Wang, Li, Xu, Tan & Lin, 2021; Wang et al., 2022; Xu and Wang, 2022). Since the initial wind profile both inside and outside the RMW may affect the TC intensification (Xu and Wang, 2018b), results from this study also strongly suggest that future efforts in further improving the time‐dependent theory of TC intensification should be devoted to include the TC structure parameters.…”

“…The experimental design follows that in Li et al. (2020, 2021) and Wang, Li, Xu, 2021; Wang, Li, Xu, Tan and Lin, 2021 but with the initial TC vortices having different radial profiles of tangential wind given below $$$V(r,z)=\left\{\begin{array}{lr}{V}_{m}(z){\left(\frac{r}{{r}_{m}}\right)}^{A},\hfill & \hfill r\le {r}_{m}\\ \frac{{V}_{m}(z)\left(\frac{r}{{r}_{m}}\right)}{{\left\{1+\frac{1}{B}\left[{\left(\frac{r}{{r}_{m}}\right)}^{\left(\frac{B}{0.2}\right)}-1\right]\right\}}^{0.2}}\hfill & \hfill {r}_{m}< r\le 600\text{km,}\\ \frac{{V}_{m}(z)\left(\frac{r}{{r}_{m}}\right)}{{\left\{1+\frac{1}{B}\left[{\left(\frac{r}{{r}_{m}}\right)}^{\left(\frac{B}{0.2}\right)}-1\right]\right\}}^{0.2}}{e}^{-\left(\frac{r-600}{600}\right)},\hfill & \hfill r > 600\text{km}\end{array}\right.$$$ where r is radius, z is height, r m is the RMW, A and B are shape parameters, and V m ( z ) is the maximum tangential wind speed at each height, which is maximum at the surface and decreases with height to zero at 18 km height. The wind profile outside the RMW follows that given by Wood and White (2011) with the shape parameter B being 1.6 and a further exponential decay with radius as r > 600 km.…”

Effects of Sea Spray on the Simulated Tropical Cyclone Development: Dependence on Surface Drag Coefficient Parameterization

“…(2017) showed that a relatively large C D could accelerate the initial organization of deep convection in the inner core and thus shorten the initial spin‐up stage of a simulated TC. In a more recent study, Li and Wang (2021a) found that although the initial spin‐up of the simulated TC development was considerably shortened with a larger C D , the subsequent intensification rate showed little difference while a larger C D also shortened the intensification period, thus resulting a weaker steady‐state intensity (see also the recent theoretical study by Wang et al., 2023).…”

“…Surface drag coefficient (C D ) is an important parameter affecting TC development, structure, and the maximum intensity (Li & Wang, 2021a; Montgomery et al., 2010; Peng et al., 2018; Rosenthal, 1971; Thomsen et al., 2012). Most previous numerical studies (Craig & Gray, 1996; Li & Wang, 2021a; Montgomery et al., 2010; Peng et al., 2018; Thomsen et al., 2012) showed that the intensification rate of a TC simulated in state‐of‐the‐art high‐resolution numerical models is often insensitive to C D but the maximum intensity is limited by C D , as predicted by the theoretical maximum potential intensity (MPI) (Emanuel, 1986, 1995; Wang, Li, Xu, 2021; Wang, Li, Xu, Tan, et al., 2021). Montgomery et al.…”

The Effect of Initial Vortex Asymmetric Structure on Tropical Cyclone Intensity Change in Response to an Imposed Environmental Vertical Wind Shear

“…A strong tropical cyclone (TC) is often considered to be quasi‐axisymmetric with relatively weak embedded asymmetric structure, therefore, it is common to assume a TC as an axisymmetric vortex in previous theoretical and numerical modeling studies on TC intensification and maximum potential intensity (e.g., Bryan & Rotunno, 2009a, 2009b; Emanuel, 1986, 2012; Li et al., 2019, 2020, 2021, 2022; Ooyama, 1969; Rotunno & Emanuel, 1987; Wang, Li, & Xu, 2021; Wang, Li, Xu, Tan, & Lin, 2021; Wang et al., 2023). Furthermore, our current understanding on TC development has also been largely based on the axisymmetric processes, such as the conditional instability of the second kind, the wind‐induced surface heat exchange, and the balanced TC vortex dynamics (Charney & Eliassen, 1964; Emanuel et al., 2004; Ooyama, 1969; Schubert & Hack, 1982; Wang & Wu, 2004), although the asymmetric processes may play critical roles in TCs (e.g., Montgomery & Smith, 2014; Montgomery et al., 2006; Nolan et al., 2007).…”