A Harmonic-Fourier Spectral Limited-Area Model with an External Wind Lateral Boundary Condition*

Abstract

In comparison to the Tatsumi's spectral method, the harmonic-Fourier spectral method has two major advantages. 1) The semi-implicit scheme is quite efficient because the solutions of the Poisson and Helmholtz equations are readily derived. 2) The lateral boundary value problem of a limited-area model is easily solved. These advantages are the same as those of the spherical harmonics used in global models if the singularity at the pole points for a globe is considered to be the counterpart of the lateral boundary condition for a limited region.If a limited-area model is nested in a global model, the prediction of the limited-area model at each time step is the sum of the inner part and the harmonic part predictions. The inner part prediction is solved by the double sine series from the inner part equations for the limited-area model. The harmonic part prediction is derived from the prediction of the global model. An external wind lateral boundary method is proposed based on the basic property of the wind separation in a limited region. The boundary values of a limited-area model in this method are not given at the closed boundary line, but always given by harmonic functions defined throughout the limited domain. The harmonic functions added to the inner parts at each time step represent the effects of the lateral boundary values on the prediction of the limited-area model, and they do not cause any discontinuity near the boundary.Tests show that predicted motion systems move smoothly in and out through the boundary, where the predicted variables are very smooth without any other boundary treatment. In addition, the boundary method can also be used in the most complicated mountainous region where the boundary intersects high mountains. The tests also show that the adiabatic dynamical part of the limited-area model very accurately predicts the rapid development of a cyclone caused by dry baroclinic instability along the east coast of North America and a lee cyclogenesis case in East Asia. The predicted changes of intensity and location of both cyclones are close to those given by the observations.

An Updated Statistical Hurricane Intensity Prediction Scheme (SHIPS) for the Atlantic and Eastern North Pacific Basins

“…The hydrostatic primitive equations on a Mercator projection with a sigma vertical coordinate are solved using the energy-conserving vertical finite difference method described by Arakawa and Lamb (1977). The spectral method described by Chen et al (1997) is used in the horizontal. This spectral method divides the dependent variables into a boundary part, which satisfies Laplace's equation on the interior of a limited area domain with inhomogeneous boundary conditions, and the residual part that satisfies homogenous boundary conditions, and is expanded in a double sine series.…”