Qs. Chen et al., A HARMONIC-FOURIER SPECTRAL LIMITED-AREA MODEL WITH AN EXTERNAL WIND LATERAL BOUNDARY-CONDITION, Monthly weather review, 125(1), 1997, pp. 143-167
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.