Formula of spiral cloud-rain bands of a tropical cyclone

A physically substantiated equation of the spiral cloud-rain bands of a tropical cyclone (TC) is derived. The adopted hypothesis is based on the entrapment of cloud masses of TC into the systems of its streamlines. The derivation was computed utilizing the known law of the inflow angle dependence in TC as a function of its radius. As a result, a cloud-rain band's configuration can be analytically represented as an additive combination of hyperbolic and logarithmic spirals (HLS). The main feature of the HLS is the dependence of the spiral's coefficients on the physical parameters of TC and the environment. In particular the coefficient at the hyperbolic component of the HLS governs mainly the roundness of spiral shape near the core of a TC and depends on its intensity. The HLS obtained includes the known logarithmic spiral as a specific case. The HLS was applied for approximation of several spiral complexes of a TC, the ground/airborne radar and satellite optic sensor images of which are available in the literature and obtained by the author. The analysis show that the description of spiral cloud-rain bands by the HLS mainly has notable better accuracy compare with the known logarithmic approach. The illustration of the HLS application for a more exact determination of a TC center is provided as well. It might be expected that the proposed formula will be a useful tool for assessments of the TC intensity and its center location on remote sensing data in addition to the known technique based on the analysis of a qualitative shape of the cloud cover of a TC.