A HARMONIC-FOURIER SPECTRAL LIMITED-AREA MODEL WITH AN EXTERNAL WIND LATERAL BOUNDARY-CONDITION

In comparison to the Tatsumi's spectral method, the harmonic-fourier s pectral method has two major advantages. 1) The semi-implicit scheme i s quite efficient because the solutions of the Poisson and Helmholtz e quations 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 singu larity at the pole points for a globe is Considered to be the counterp art of the lateral boundary condition for a limited region. If a limit ed-area model is nested in a global model, the prediction of the limit ed-area model at each time step is the sum of the inner part and the h armonic part predictions. The inner part prediction is solved by the d ouble sine series from the inner part equations for the limited-area m odel. The harmonic parr prediction is derived from the prediction off the global model. An external wind lateral boundary method is proposed based on the basic property of the wind separation in a limited regio n. The boundary values of a limited-area model in this method are not given at the closed boundary line, but always given by harmonic functi ons defined throughout the limited domain. The harmonic functions adde d to the inner parts at each time step represent the effects of the la teral boundary values on the prediction of the limited-area model, and they do nor cause any discontinuity near the boundary. Tests show tha t predicted motion systems move smoothly in and out through the bounda ry, where the predicted variables are very smooth without any other bo undary treatment. In addition, the boundary method can also be used in the most complicated mountainous region where the boundary intel:sect s high mountains. The tests also show that the adiabatic dynamical par t of the limited-area model very accurately predicts the rapid develop ment of a cyclone caused by dry baroclinic instability along the east coast of North America and a lee cyclogenesis case in East Asia; The p redicted changes of intensity and location of both cyclones are close to those given by the observations.