Tom Bracegirdle: An investigation into the evolution of CAPE during the intensification phase of a model polar low

Department of Meteorology, University of Reading, Reading, RG6 6BB



The evolution of CAPE (Convective Available Potential Energy) within a developing convective polar low is investigated with a focus on the implications for the intensification mechanisms conditional instability of the second kind (CISK) and wind induced surface heat exchange (WISHE). A lack of extensive observations of polar lows means that we still have much to learn about their formation; the utilisation of a computer model provides an opportunity to develop an understanding of the mechanisms leading to development. The main aim of the work was to establish how CAPE within polar lows evolves with time. CAPE at the eye-wall was found to be strongly linked to intensification, as measured by azimuthal velocity, but less so elsewhere in the domain. The implications of the results with reference to the intensification theories CISK (Conditional Instability of the Second Kind) and WISHE (Wind Induced Surface Heat Exchange) are discussed and closer agreement with WISHE is found, but with the suggestion that CISK may play a role.


It is increasingly accepted that strongly convective Polar Lows may intensify in a similar manner to tropical cyclones, Rassmussen (1979) was one of the first Meteorologists to attempt to model Polar Lows using mechanisms of tropical cyclone development. The intensification of tropical cyclones and strongly convective Polar Lows has undergone a revolution in understanding over the last few years, an important shift in thinking has been the closure relating the convection to intensification (Rotunno and Emanuel (1987)). The rate of intensification has also been shown to have a major dependence on the radiation budget.

A paper by Craig and Gray (1996) presented results which suggest that the WISHE (as opposed to CISK) mechanism best describes hurricane and polar low intensification. Part of the evidence presented to support this was the lack of any discernible trend in CAPE during intensification. In this study a more detailed investigation into the evolution of CAPE is undertaken following suggestions any trends that do exist in the model CAPE may not have been captured by previous methods of averaging.

Key Questions

Is there a discernible trend in CAPE during intensification of the polar low?

No discernible trend was found by Craig and Gray (1996), a result consistent with WISHE.

Is there a relationship between the polar low intensity and any trends in CAPE?

Constant CAPE and low CAPE is consistent with WISHE. A decrease from high initial values is more suggestive of CISK (Craig and Gray (1996)).


The model used is a modified version of the code developed by Rotunno and Emanuel (1987) which was used to investigate tropical cyclones. It is an axisymmetric, non-hydrostatic model which explicitly represents convection and contains schemes for cloud micro-physics (altered by Craig 1994).



Figure 1:
The intensification of the vortex is well represented by both changes in the minimum central pressure and maximum azimuthal velocity. The azimuthal velocity however includes a lot of noise caused by the evolution of individual convective cells, the signal from the minimum pressure is far smoother and would appear to be a better indicator of cyclone intensity.

In figure 1 there is a rapid deepening of the minimum surface pressure that begins at around 20-25 hours. The rate of deepening during the rapid intensification phase is variable, with a reduction in the intensification rate at both 40 and 55 hours. Maturity is reached at ~ 70 hours.

The evolution of CAPE

Figure 2:This plot is a time-series diagram of changing values of CAPE along a radial section from the vortex axis to 250km. This represents the inner part of the model domain, which extends to 2500km. The magnitudes of CAPE are capped at 20 J/kg in order that a clearer picture of CAPE distribution be presented.

Figure two demonstrates clearly that there is variations in CAPE, of the order of 10 hours, at the eyewall region (~70km radius). At higher radii (125 and above) there appears to be coherent structure and organisation into bands of activity propagating inwards.

Eye-wall averaged CAPE and intensification

Figure 3: The solid red line is an average of CAPE measured across a 24km section from the inner eye-wall out (cf. figure 2). The black dashed line is an estimate of the rate of change of the deepening rate calculated from the pressure trend in figure 1. This can be thought of as the acceleration of the intensity.

By inspection of figure three it is evident that minima in values of CAPE across the eye-wall region coincide with a decreasing intensification rate, and vice versa. However the absolute values of CAPE remain very low, consistent with the maintenance of a near-neutral atmosphere.

A possible explanation for the relationship between CAPE and intensification.

During periods of rapid intensification plots of equivalent potential temperature show a rapid heating of the boundary layer at the eye-wall region. This coincides with a slight increase in values of CAPE, suggestive of a time-scale of delay between the creation of CAPE and it's consumption by convection. A cross-correlation between the time series of vertical velocity and CAPE showed a time-lag of around 1/2 an hour. Therefore, due to this time-lag, the convection maintains a nearly neutral vertical atmospheric temperature profile that exhibits residual fluctuations in CAPE. According to Emanuel et al (1994), if this short time-lag is of no consequence to the large-scale circulation then the system can be assumed to be in a state of 'statistical equilibrium'. This is consistent with the WISHE principle that variations in CAPE do not have an important feedback on the larger scale and that these fluctuations are merely a reaction to evolution on the large scale.


Strong correlation between CAPE in the eye-wall region and minimum pressure trend, not seen when CAPE was averaged over a larger radial section. The trends in CAPE are suggestive of a CISK-type mechanism, but can be better explained in terms of WISHE.


Rassmussen, E. 1979: The polar low as an extra-tropical CISK disturbance. Quart. J. R. Met. Soc. (1979), 105, pp. 531-549.

Rotunno R., and K. A. Emanuel, 1987: An Air-Sea Interaction Theory for Tropical Cyclones. Part II: Evolutionary Study Using a Non-hydrostatic Axisymmetric Numerical Model. J. Atmos, Sci., 44, 542-561.

Craig, G. C., S. L. Gray, 1996: CISK or WISHE as the mechanism for Tropical Cyclone Intensification. J. Atmos. Sci., 53, pp. 3528-3540.

Emanuel, K. A., J. D. Neelin and C. S. Bretherton, 1994: On Large-Scale Circulations in Convecting Atmospheres. Q. J. R. Met. Soc., 120, pp. 1111-1143.


Figure 1: Intensification
Figure 2: The evolution of cape
Figure 3: Eye-wall averaged CAPE and intensification