Theory for the spinup of tropical depressions

Tropical cyclogenesis is a comparatively rare event in which pre-existing synoptic scale disturbances in the tropics occasionally intensify into tropical storms. Empirically determined conditions for a disturbance to intensify include a warm underlying ocean, low wind shear, a moist troposphere, and an environment rich in cyclonic vorticity. Quantifying the relative importance of these factors in a systematic theory remains a challenge.

We propose a theory for the earliest stages of cyclogenesis, which consists of the development of tropical wave disturbances such as easterly waves into tropical depressions. The theory is based on the use of the flux form of the vorticity equation, which shows that development occurs when the spinup tendency due to low-level convergence exceeds the spindown tendency due to surface friction. Simple application of the theory yields a minimum precursor disturbance radius for spinup to occur. In addition, spinup only takes place when the initial disturbance is sufficiently intense.

Low-level convergence is intimately related to the production of precipitation, which according to recent developments can be related to atmospheric saturation fraction (precipitable water divided by saturated precipitable water) and the surface moist entropy flux. A form of the gross moist stability enters into this calculation, and we point to efforts to determine this quantity as a function of environmental conditions.

The strength of the spindown tendency depends on how surface friction is distributed vertically in the atmosphere. A possible additional factor is the downward convective transport of momentum from aloft. Observational work has shown that the simplest models for the vertical distribution of surface friction lead to too strong a spindown tendency. Resolution of this discrepancy is needed for a complete understanding of tropical cyclogenesis.