A. Langousis, and D. Veneziano, A simple theoretical model for the mean rainfall field of tropical cyclones, Eos Trans. AGU, 87(52), San Francisco, American Geophysical Union, 2006.
We develop a simple model for the mean rainfall intensity profile in tropical cyclones (TCs) before landfall. The model assumes that rainfall is caused primarily by condensation of the humid outflow at the top of the TC boundary layer. This upward-directed flux originates from convergence of the horizontal winds in the boundary layer. The model combines Holland’s (1980) representation of the tangential wind speed in the main vortex, an Ekman-type solution for the horizontal and vertical wind profiles inside the TC boundary layer, and moist air thermodynamics to estimate how the mean rainrate i depends on radial distance r from the low pressure center and azimuth θ relative to the direction of motion. We start by studying the axisymmetric component i(r), which is also the mean rainrate profile for zero translational velocity. i(r) depends on the maximum pressure deficit ΔPmax (or the maximum tangential wind speed Vmax), Holland’s B parameter, the radius of maximum winds Rwind, and the depth-averaged temperature in the boundary layer T. The mean rainrate is zero for r = 0, increases to a maximum imax at a distance Rrain somewhat larger than Rwind, and then decays to zero in an almost exponential way. More intense cyclones tend to have lower Rrain and higher imax. The difference Rrain-Rwind is higher for tangential wind profiles that are more picked around Rwind. Such wind profiles are generally associated with more intense cyclones and higher B values. When cyclones in the Northern hemisphere move, the mean rainrate intensifies in the north-east quadrant relative to the direction of motion and de-intesifies in the south-west quadrant. These azimuthal effects are stronger for faster-moving storms. For preliminary validation, we compare model estimates of i(r) under representative parameters with ensemble averages from 548 CAT12 and 212 CAT35 TCs extracted from the TRMM dataset (Lonfat et al., Mon. Wea. Rev., 132 (2004): 1645-1660). The model reproduces very well the shape and intensity of the empirical profiles, except near the TC center where the high gradient of the rainfall intensity and the limited resolution of the data make the empirical values less accurate.