Theoretical estimation of the mean rainfall intensity field in tropical cyclones: Axi-symmetric component and asymmetry due to motion

We develop a simple theoretical model for the mean rainfall intensity field in tropical cyclones (TCs). The model estimates the axi-symmetric rainfall profile Isym(r) as well as the asymmetric component due to storm motion Imot(r,θ), where r is the radial distance from the TC center and θ is the azimuth relative to the direction of the storm. Currently, the model does not include asymmetries due to wind shear, coastline geometry and topography, or fluctuations associated with rainbands and small-scale convection; hence its main use is to provide large-scale rainfall estimates. Rainfall intensity is estimated as the vertical outflow of water vapor at the top of the TC boundary layer (BL). The analysis combines Holland’s (1980) (or any other) tangential wind profile, an Ekman-type solution for the horizontal and vertical wind profiles inside the TC boundary layer, and moist air thermodynamics. The BL solution for wind is based on Smith’s (1968) formulation, which is modified and solved to account for the effects of storm motion. The axi-symmetric rainrate Isym(r) is zero for r = 0, increases to a maximum Imax at a distance Rrain, and then decays to zero in an approximately power-law way. Model results are compared to those from other studies (Shapiro, 1983; Kepert, 2001; Kepert and Wang, 2001). The three formulations are generally in good agreement for both horizontal and vertical fluxes, except for close to the storm center where nonlinear effects are dominant and Kepert’s (2001) solution is less accurate and for the far-field where both the Shapiro (1983) and Kepert and Wang (2001) approaches are affected by numerical instabilities. The present scheme is computationally very efficient and stable also for high storm translation velocities. In a parametric analysis, we study how the symmetric component and the motion-induced asymmetries of rainfall depend on TC characteristics such as the maximum tangential wind velocity Vmax, the radius of maximum winds Rmax, Holland’s B parameter, and the temperature T in the boundary layer. More intense cyclones have higher Imax and lower Rrain. The pickness of the tangential wind velocity profile, expressed through Holland’s B parameter, has insignificant effects on the Isym(r) profile. These theoretical findings are in agreement with observations. The model shows that when cyclones in the Northern hemisphere move, their mean rainrate intensifies in the north-east quadrant relative to the direction of motion and de-intensifies in the south-west quadrant. The asymmetry is concentrated near the TC center and is stronger for less intense and faster-moving storms.