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Abstract This study revisits the issue of why tropical cyclones (TCs) develop more rapidly at lower latitudes, using ensemble axisymmetric numerical simulations and energy diagnostics based on the isentropic analysis, with the focus on the relative importance of the outflow-layer and boundary layer inertial stabilities to TC intensification and energy cycle. Results show that although lowering the outflow-layer Coriolis parameter and thus inertial stability can slightly strengthen the outflow, it does not affect the simulated TC development, whereas lowering the boundary layer Coriolis parameter largely enhances the secondary circulation and TC intensification as in the experiment with a reduced Coriolis parameter throughout the model atmosphere. This suggests that TC outflow is more likely a passive result of the convergent inflow in the boundary layer and convective updraft in the eyewall. The boundary layer inertial stability is found to control the convergent inflow in the boundary layer and depth of convection in the eyewall and thus the temperature of the energy sink in the TC heat engine, which determines the efficiency and overall mechanical output of the heat engine and thus TC intensification. It is also shown that the hypothesized isothermal and adiabatic compression legs at the downstream end of the outflow in the classical Carnot cycle are not supported in the thermodynamic cycle of the simulated TCs, implying that the hypothesized classical TC Carnot cycle is not closed. It is the theoretical maximum work of the heat engine, not the energy expenditure following the outflow downstream, that determines the mechanical work used to intensify a TC. 

Abstract Several key issues in the simple time-dependent theories of tropical cyclone (TC) intensification developed in recent years remain, including the lack 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. Significance StatementA new advancement in the recent decade is the development of simple time-dependent theories of tropical cyclone (TC) intensification, which can provide quantitative understanding of TC intensity change. However, several key issues in these simple time-dependent theories remain, including the lack of a closure for the pressure dependence of saturation enthalpy at sea surface temperature under the eyewall and the definition of environmental conditions. These are resolved in this study with several refinements, which make the most recent time-dependent theory of TC intensification self-contained and practical. 

Abstract Previous observational studies have shown that the intensification rate (IR) of a tropical cyclone (TC) is often correlated with its real-time size. However, no any size parameter explicitly appears in the recent time-dependent theory of TC intensification, while the theory can still well capture the intensity evolution of simulated TCs. This study provides a detailed analysis to address how TC real-time size affects its intensification and why no size parameter explicitly appears in the theory based on the results from axisymmetric numerical simulations. The results show that the overall correlation between the TC IR and real-time size as reported in previous observational studies, in terms of both the radius of maximum wind (RMW) and the radius of 17 m s⁻¹wind (R17), is largely related to the correlation between the IR and intensity because the size and intensity are highly interrelated. As a result, the correlation between the TC IR and size for a given intensity is rather weak. Diagnostic analysis shows that the TC real-time size (RMW and R17) has two opposing effects on intensification. A larger TC size tends to result in a higher steady-state intensity but reduce the conversion efficiency of thermodynamic energy to inner-core kinetic energy or the degree of moist neutrality of the eyewall ascent for a given intensity. The former is favorable, while the latter is unfavorable for intensification. The two effects are implicitly included in the theory and largely offset, resulting in the weak dependence of the IR on TC size for a given intensity. 

Abstract Previous studies have demonstrated the contribution of dissipative heating (DH) to the maximum potential intensity (MPI) of tropical cyclones (TCs). Since DH is a function of near-surface wind speed and thus TC intensity, a natural question arises as to whether DH contributes to the intensity dependence of TC potential intensification rate (PIR). To address this issue, an attempt has been made to include DH in a recently developed time-dependent theory of TC intensification. With this addition, the theory predicts a shift of the maximum PIR toward the higher intensity side, which is consistent with the intensity dependence of TC intensification rate in observed strong TCs. Since the theory without DH predicts a dependence of TC PIR on the square of the MPI, the inclusion of DH results in an even higher PIR for strong TCs. Considering the projected increase in TC MPI under global warming, the theoretical work implies that as the climate continues to warm, TCs may intensify more rapidly. This may not only make the TC intensity forecasting more difficult, but also may increase the threats of TCs to the coastal populations if TCs intensify more rapidly just before they make landfall. Significance Statement Previous studies have demonstrated that dissipative heating (DH) can significantly contribute to the maximum potential intensity (MPI) that a tropical cyclone (TC) can achieve given favorable environmental thermodynamic conditions of the atmosphere and the underlying ocean. Here we show that because DH is a function of near-surface wind speed and thus TC intensity, DH can also significantly contribute to the intensity dependence of TC potential intensification rate (PIR). This has been demonstrated by introducing DH into a recently developed time-dependent theory of TC intensification. With DH the theory predicts a shift of the maximum PIR toward the higher intensity side as observed in strong TCs. Therefore, as the climate continues to warm, TCs may intensify more rapidly and become stronger. 

Abstract The phenomenon that rapid contraction (RC) of the radius of maximum wind (RMW) could precede rapid intensification (RI) in tropical cyclones (TCs) has been found in several previous studies, but it is still unclear how frequently and to what extent RC precedes RI in rapidly intensifying and contracting TCs in observations. In this study, the statistical relationship between RMW RC and TC RI is examined based on the extended best track dataset for the North Atlantic and eastern North Pacific during 1999–2019. Results show that for more than ∼65% of available TCs, the time of the peak contraction rate precedes the time of the peak intensification rate, on average, by ∼10–15 h. With the quantitatively defined RC and RI, results show that ∼50% TCs with RC experience RI, and TCs with larger intensity and smaller RMW and embedded in more favorable environmental conditions tend to experience RI more readily following an RC. Among those TCs with RC and RI, more than ∼65% involve the onset of RC preceding the onset of RI, on average, by ∼15–25 h. The preceding time tends to be longer with lower TC intensity and larger RMW and shows weak correlations with environmental conditions. The qualitative results are insensitive to the time interval for the calculation of intensification/contraction rates and the definition of RI. The results from this study can improve our understanding of TC structure and intensity changes. 

Abstract Recent study indicates that the non-instantaneous interaction of convection and circulation is essential for evolution of large-scale convective systems. It is incorporated into cumulus parameterization (CP) by relating cloud-base mass flux of shallow convection to a composite of subcloud moisture convergence in the past 6 h. Three pairs of 19-yr simulations with original and modified CP schemes are conducted in a tropical channel model to verify their ability to reproduce the Madden–Julian oscillation (MJO). More coherent tropical precipitation and improved eastward propagation signal are observed in the simulations with the modified CP schemes based on the non-instantaneous interaction. It is found that enhanced feedback between shallow convection and low-level moisture convergence results in amplified shallow convective heating, and then generates reinforced moisture convergence, which transports more moisture upward. The improved simulations of eastward propagation of the MJO are largely attributed to higher specific humidity below 600 hPa in the free troposphere to the east of maximum rainfall center, which is related to stronger boundary layer moisture convergence forced by shallow convection. Large-scale horizontal advection causes asymmetric moisture tendencies relative to rainfall center (positive to the east and negative to the west) and also gives rise to eastward propagation. The zonal advection, especially the advection of anomalous specific humidity by mean zonal wind, is found to dominate the difference of horizontal advection between each pair of simulations. The results indicate the vital importance of non-instantaneous feedback between shallow convection and moisture convergence for convection organization and the eastward MJO propagation. 

Abstract In this study, a simple energetically based dynamical system model of tropical cyclone (TC) intensification is modified to account for the observed dependence of the intensification rate (IR) on the storm intensity. According to the modified dynamical system model, the TC IR is controlled by the intensification potential (IP) and the weakening rate due to surface friction beneath the eyewall. The IP is determined primarily by the rate of change in the potential energy available for a TC to develop, which is a function of the thermodynamic conditions of the atmosphere and the underlying ocean, and the dynamical efficiency of the TC system. The latter depends strongly on the degree of convective organization within the eyewall and the inner-core inertial stability of the storm. At a relatively low TC intensity, the IP of the intensifying storm is larger than the frictional weakening rate, leading to an increase in the TC IR with TC intensity in this stage. As the storm reaches an intermediate intensity of 30-40 m s -1 , the difference between IP and frictional weakening rate reaches its maximum, concurrent with the maximum IR. Later on, the IR decreases as the TC intensifies further because the frictional dissipation increases with TC intensity at a faster rate than the IP. Finally, the storm approaches its maximum potential intensity (MPI) and the IR becomes zero. The modified dynamical system model is validated with results from idealized simulations with an axisymmetric nonhydrostatic, cloud-resolving model. 

Abstract The interaction between tropical convective heating and thermally forced circulation is investigated using a global dry primitive-equation model with the parameterization of wave-conditional instability of the second kind (CISK). It is demonstrated that deep convective heating can hardly sustain itself through the moisture convergence at low levels regardless of the fraction of immediate consumption of converged moisture. In contrast, when the fraction is large, shallow convective heating and its forced circulation exhibit preferred growth of small scales. As the “CISK catastrophe” mainly comes from the instantaneous characters of moisture–convection feedback in the conventional wave-CISK, a noninstantaneous wave-CISK is proposed, which highlights the accumulation–consumption (AC) time scale for the convective heating accumulation and/or the converged moisture consumption. In the new wave-CISK, once moisture is converged, the release of latent heat takes place gradually within an AC time scale. In this sense, convective heating is not only related to the instantaneous moisture convergence at the current time, but also to that which occurred in the past period of the AC time scale. The noninstantaneous wave-CISK could guarantee the occurrence of convective heating and/or moisture convergence at larger scales, and then favor the growth of long waves, and thus solve the problem of CISK catastrophe. With the new wave-CISK and AC time scale of 2 days, the simulated convective heating-driven system bears a large similarity to that of the observed convectively coupled Kelvin wave.