The method of decomposing wind field in a limited area and its application to typhoon SAOMEI

Abstract

The harmonic-cosine series expansion method (H-C method) for horizontal wind is introduced. It divides a function, such as horizontal wind, stream function and velocity potential, into two parts. One is a harmonic function which is the solution of a Laplace equation with nonzero boundary condition, and thus can be called the harmonic part. It is also been called the external part since it is independent of any values inside the limited area. The other is the difference of the original wind and the harmonic part, which is the solution of Poisson equation with homogeneous boundary condition and can be expanded into double Fourierism cosine series. It only depends on vorticity or divergence inside the limited area, so it is also called the inner part. The H-C method uses a spectrum approach in calculating derivatives, so it is more precise than the differential ones. The boundary condition given to solve the harmonic part has definite physical meaning and it is well handled in solving stream function and velocity potential in a limited area. Therefore, problems such as the instability in the calculation, the original wind field not being able to be reversed accurately, and the system deficiencies on the boundary occurring in previous methods, are successfully overcome. Using the NCEP/NCAR 1°×1° analysis data with a time resolution of 6 h, the Regional Spectrum Model (RSM) reanalysis data from Japan Meteorological Agency with a horizontal resolution of 20km and a time interval of 6 h, we decompose the horizontal wind of super-intensity Typhoo SAOMEI (0608) based on the H-C method. The two parts are called the nondivergent and the irrotational components, respectively. Analyses of the two parts indicate that the typhoon center marked by the nondivergent component at lower levels approaches more closely the observed center than the original wind did. In addition, the nondivergent wind can clearly manifest the water transporting passageway. The phenomenon that horizontal winds converge at lower levels and diverge at upper levels is more obvious in irrotational wind field than that in the original one. Convective activities at the South China Sea and in the west of Philippines confront the development of SAOMEI by blocking off its water transport after it landed. It may be a reasonable explanation for the fact that SAOMEI weakened so rapidly despite of its landing as a super-intensity typhoon. Before it landed, the nondivengent and irrotational centers in wind component fields are not always in the same location. It can only be seen by using the decomposing method for horizontal winds. The two components derived from the H-C method may provide more detailed characteristics than the original wind does. Therefore, this approach would be important in understanding the characteristics of typhoon and can be used widely in the future.