Dynamical system properties of an axisymmetric convective tropical cyclone model

Abstract

The dynamical system behaviour of tropical cyclones and their potential intensity with a view to sea surface temperature, tropospheric temperature stratification and tropospheric moisture content is investigated in the axisymmetric convective model HURMOD. The model results exhibit the existence of a fixed-point attractor associated with a strong tropical cyclone. Moreover, the initial vortex strength forms an amplitude threshold to cyclogenesis. Above this threshold, the size of the tropical cyclone and its intensity are independent of the initial vortex strength and its horizontal extent. Below the amplitude threshold, cyclogenesis does not occur and the system approaches an atmospheric state of rest. In case one allows for a deviation of the tropospheric stratification from moist-neutral conditions, the modelling results reveal the existence of bifurcations with the sea surface temperature representing the bifurcation parameter: As the sea surface temperature decreases and the storm weakens, the fixed-point attractor turns first into a limit cycle indicating a Hopf-bifurcation and then gives way to a steady-state of lower intensity, before the intensity oscillation becomes chaotic, and finally the tropical storm dies. The amplitude threshold and the sea surface temperature range, within which the system exhibits bifurcation points, are sensitive to the reference value of relative humidity and the reference tropospheric temperature stratification. If the reference troposphere is presumed to be moist-neutral, the dynamical behaviour of the modelled tropical cyclone does not change within the range of tropical sea surface temperature, and the tropical cyclone only slightly weakens with decreasing sea surface temperature, without any abrupt changes in intensity. Apart from the existence of Hopf-bifurcations, these findings are qualitatively similar to results gained from a low-order model presented in a precursory study.

• tropical cyclone dynamics
• potential intensity
• bifurcations
• convection-resolving model

Acknowledgements

This work was supported by the DFG within the Cluster of Excellence 177 Integrated Climate System Analysis and Prediction (CliSAP). The authors would also like to thank two anonymous reviewers for their constructive criticism on this work.

Notes

¹Emanuel, K. A. and D. S. Nolan, 2004: Tropical Cyclone Activity and the Global Climate System. The 26th Conference on Hurricanes and Tropical Meteorology.

²For reasons of simplicity, we only work with ‘warm-rain’ simulations in the present work, i.e. the ice phase is not considered in the calculation of the water budget, and the cloud–micro-physical parameterisation follows a Kessler type scheme. For possible effects of the inclusion of an ice phase in axisymmetric models, we may refer the reader to previous studies by Willoughby et al. (1984) as well as Frisius and Hasselbeck (2009).

³Note, in the low-order model, moist neutrality is either maintained by an adjustment of the boundary layer relative humidity or by a lapse rate adjustment, whereas a physically more consistent combination of both a moisture and a temperature profile adjustment, cannot be realised in the low-order model. Therefore, case N is subdivided into case N1 and N2 in the low-order model.

⁴The decay rate is chosen to be very slow in order to stay close to the respective equilibrium, which eases the detection of bifurcations.

⁵To test the robustness of the limit cycle behaviour, the simulations at 25.8°C were continued and run 2000 hours longer (not shown). The oscillation with a period of about 225 hours is sustained in both experiments.

⁶We note that this question cannot be answered with certainty here, since we have not tested whether spontaneous cyclogenesis occurs at SSTs much higher than 30°C in HURMOD or not.