CliSAP successfully finished in 2018. Climate research continues in the Cluster of Excellence "CLICCS".

Tropical cyclone system dynamics

Dynamical system properties of tropical cyclones in a box model

The dynamical system behaviour of tropical cyclones and particularly their potential intensity and sensitivity to several climatological parameters are the chief aspects we investigate in this project.

The study started with the development and analysis of a low-order model for a tropical cyclone. In this model, the tropical cyclone is made up of an eye, an eyewall and the ambient region (Figure 1). The lateral boundaries of the eyewall region are formed by angular momentum isopleths. The eyewall and the ambient region are further subdivided into a boundary layer and a free troposphere.

Making use of the gradient-wind and hydrostatic balance assumptions and some other simplifying approximations, it is possible to derive a dynamical system described by three ordinary differential equations. These are thermodynamic budget equations for the entropy.

The model exhibits multiple equilibria in a phase space spanned by different environmental thermodynamic parameters such as sea surface temperature and relative humidity (Figure 2). Both the tropical cyclone intensity (in terms of maximum wind speed) and the bifurcation points turn out to be sensitive to changes in the prescribed environmental parameters.

Participating researchers: Daria Schönemann and Thomas Frisius



Figure1: Scetch of the tropical cyclone box-model
Figure 2: Maximum tangential wind of the equilibria in the tropical cyclone box model as a function of sea surface temperature and ambient relative humidity.

Tropical cyclone dynamics in an axisymmetric convective model

To compare the dynamical properties of models of different complexity, a similar analysis is performed using the axisymmetric atmospheric convection-resolving model HURMOD (Frisius and Wacker 2007). Simulations of long-term behaviour show that a fixed-point attractor associated with a mature tropical cyclone also exists in HURMOD.

The final state is, within a certain range, independent of the initial size and strength of the disturbance, in agreement with the conceptual model. Furthermore, HURMOD has an amplitude threshold for tropical cyclogenesis, i.e. there exists a certain threshold value in the initial vortex strength, below which cyclogenesis does not take place. Bifurcations can take place in HURMOD by decreasing the sea surface temperature at a very slow rate.

At a certain sea surface temperature, the fixed point attractor gives birth to a limit cycle that settles once again, at a still lower sea surface temperature, into a new steady state. Finally, the tropical cyclone decays completely, which clearly indicates the existence of a sea surface temperature threshold to the formation of tropical cyclones in the model.

These results agree with observations, which show evidence for such thresholds in cyclogenesis. Regarding the intensity in terms of maximum wind speed, HURMOD’s results suggest that the temperature stratification plays a more important role than environmental relative humidity.

On the other hand, environmental relative humidity appears to be of higher relevance to the amplitude threshold, which suggests that this parameter is important in regard to tropical cyclones’ frequency of occurrence. This confirms results from previous modelling and observational studies.

Participating researchers: Daria Schönemann and Thomas Frisius

Figure 3: Maximum wind speed as a function of SST for reference (black curve), fixed tropopause temperature (purple curve), low relative environmental humidity (red curve) und warm tropopause (green curve).