L-3. A spherical coordinate version for a global nonhydrostatic model.

Development of a spherical, curvilinear orthogonal coordinate version of MRI/NPD-NHM is underway. In the new model, we introduce two map factors, m₁ and m₂, along the x- and y- (longitudinal and latitudinal) directions instead of the single map factor m in the conformal projection. The curvature terms (C1-3-15) and (C1-3-16) become

In a longitude-latitude grid, if we take

basic equations (C1-3-9)-(C1-3-11) are reduced to the following conventional momentum equations in spherical coordinates.

In the new model, we use the Cylindrical Equidistant projection,

whose map factors become unity at the standard latitude j₀, and the basic equations are rewritten into the flux form in terrain-following coordinates.

Figure L-3-2 shows an example of 18- and 36-hour forecasts of the sea-level pressure predicted by the new model nested with the global analysis data of JMA (GNANL; 1.25 x 1.25 degrees, pressure plain, 17 levels). The horizontal resolution of the nonhydrostatic model is 1.45 x 1.45 degrees. Vertically, 38 layers are employed, and vertical resolution at the lowest level is 40 m, where the horizontal wind is computed at 20 m level above the ground surface. The domain covers from 80 degrees north to 80 degrees south and from 5 degrees east to 7 degrees west, which corresponds to about 95% of the global surface. For simplicity, a dry model is used, and the lowest level temperature in GANL is used for the initial value of the ground and sea-surface temperatures. The surface pressure pattern of the model generally follows the global analysis well at the corresponding valid times (figures not shown).

Fig. L-3-2. Sea-level pressure at t = 18 and 36 hours predicted by the nonhydrostatic model. Contour interval is 4 hPa. Model initial time is 2400 UTC 1 March 1999. After Saito (2001).