A New Model For Quantifying Tropical Cyclone Intensification Rate: Theoretical Basis And Verification

Prediction of tropical cyclone(TC)intensity has emerged as the most challenging question in TC forecasting because of our incomplete understanding of the dominant dynamics/physics in control of TC intensity changes and lack of quantitative theories.In this study,a simple quantitative dynamical system model of TC intensification is introduced,based conceptually on the viewpoint that a TC can be described energetically as a Carnot heat engine in a non-steady state framework.In this model,the TC intensification rate(IR)is controlled by the intensification potential and the weakening rate due to surface friction beneath the eyewall.The intensification potential is determined primarily by the surface potential energy available for a TC to develop.In addition,an empirical dynamical efficiency has been introduced to explain the partition of energy production to fuel the rotational component of the inner-core circulation.Based on idealized ensemble simulations with different combinations of sea surface temperature(SST)and environmental atmospheric profiles,it is found that,consistent with the assumption of our model,at relatively weak intensity,the local surface available power production is greater than the surface friction dissipation,and the friction dissipation increases much faster than the available power production as the storm intensifies.This means that the energy used to accelerate the inner core become less and less as the storm intensifies.However,our diagnostic results indicate that in the quasisteady state of the simulated TCs,the local power generation and frictional dissipation may not be balanced under the eyewall.This yields superintensity in the simulation.A new finding is that the increase in either convective activity in the TC outer region or theoretical maximum potential intensity(MPI)or both as SST increases could cause decrease of superintensity with increasing SST.In order to understand the dominant dynamics in TC intensity changes and parameterize the dynamical efficiency,a recent debate regarding the importance of unbalanced boundary layer spinup mechanism has been analyzed.The simulation results show that the emphasized process in this mechanism,i.e.,the positive upward advection of the supergradient wind from the boundary layer,is largely offset by the negative radial advection due to the outward agradient force caused by the upward advection of the supergradient wind.As a result,the upward advection of the supergradient wind contributes little(often less than 4%)to the IR,but it contributes about 10%–15% to the final intensity of the simulated TC due to the enhanced inner-core air-sea thermodynamic disequilibrium and thus MPI.Results from this study,together with several previous studies,suggest that compared with the unbalanced dynamics,the balanced dynamics dominates the TC intensification directly.However,in the later stage of intensification,in contrast to the balanced dynamics,there is an asynchrony between the simulated TC intensification and contraction of the radius of maximum wind(RMW).It is found that the increase of mixings(including the resolved eddy mixing in three dimensions),especially of horizontal component,and its radial gradient near the eyewall prohibits RMW contraction in the later stage of intensification.Based on those conclusions above,we modified our intensification model by considering the superintensity,and parameterizing the dynamical efficiency as a function of the normalized inner-core inertial stability associated with the balanced dynamics.Diagnostic results from several ensemble simulations have verified that the estimated IR from the modified model can capture well the evolution of the simulated IR,the maximum simulated IR,and the intensity dependence of the simulated IR.The simplified model gives a maximum IR around the intermediate intensity for each experiment,and both the estimated maximum IR and the intensity at the maximum IR tend to increase with increasing SST,which are in agreement with the model simulations and observations.