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Figure 9. (a) GPCP day mean precipitation; and (b) simulated day mean precipitation during July 30—August 18, flooding spread in Manchuria, Korea, and Yangtze River Valley. The model missed the tropical depression from southern boundary due to the coarse resolution (Sun, 2002).

PRCM and the dust/chemistry module as illustrated in Fig. 11 to simulate the distribution of aerosols and the interactions between aerosols and regional climate during April 1998.

The dust module consists of: (a) a dust source function derived by Ginoux et al. (2001) based on a 1°-by-1° terrain and vegetation data set derived from Advanced Very High Resolution Radiometer (AVHRR) data (DeFries and Townshend, 1994); (b) particle sizes, which are a function of the source region's soil properties (Tegen and Fung, 1994); seven-size bins (0.10.18 ym, 0.18-0.3 ym, 0.3-0.6 ym, 0.6-1 ym, 11.8 ym, 1.8-3 ym, and 3-6 ym, with corresponding effective radii of 0.15, 0.25, 0.4, 0.8, 1.5, 2.5, and 4 ym) are applied for dust sizes (Yang, 2004a); (c) the threshold friction velocity, defined as the horizontal wind velocity required to lift dust particles from the surface, is a function of particle diameter (Marticorena and

Figure 10. The mean vorticity over South China Sea (15-20° N; 110-120° E) during May-August from 19911998, solid lines are calculated from ECMWF analysis and dashed lines are PRCM results (Yu et al., 2004a,b). Correlation coefficients between ECMWF analysis and PRCM results for individual years are also shown in each panel.

Figure 10. The mean vorticity over South China Sea (15-20° N; 110-120° E) during May-August from 19911998, solid lines are calculated from ECMWF analysis and dashed lines are PRCM results (Yu et al., 2004a,b). Correlation coefficients between ECMWF analysis and PRCM results for individual years are also shown in each panel.

dust during the 17-day continuous integration of April 1998 (not shown in the figures).

Yang (2004b) also included the chemistry mechanism of SAPRC97 (Statewide Air Pollution Research Center) (Carter et al., 1995, 1997), which is a detailed mechanism for gasphase atmospheric reactions of volatile organic compounds (VOCs) and oxides of nitrogen (NOx) in urban and regional atmospheres. Coupling SAPRC97 and PRCM dust, Yang (2004b) showed that the model can reproduce the observed ozone concentration in the sky and at the surface in the US after a spin-up period of two days.

Wu et al. (2003) and Hsu (2001) applied the PRCM to study the transport of pollutants from a point source at the northern tip of Taiwan during four seasons in 1999. Figures 12(a) and 12(b) show the observed and simulated wind (after 48-hour integration) at 12Z on 31 October 1999; while the schematic diagram of pollutant transport and the vertically integrated concentration from the PRCM for the same time are shown in Figs. 12(c) and 12(d), respectively. They indicate that the plume moves around the western coast, the eastern coast, or even the entire island, depending on the detailed wind speed and direction under northerly wind.

Bergametti, 1995) and soil wetness; (d) dust emission, which depends on source function, surface wind speed, threshold velocity, and the fraction of each size class; and (e) transport and removal processes — dust aerosols in the PRCM dust are transported by advection, dispersion, and subgrid cumulus convection, and are removed by wet and dry depositions. The dry deposition of dust aerosols is assessed through the gravitational settling for each model vertical layer and surface deposition velocity. The removal of dust aerosols by wet deposition is calculated using the model precipitation rate at all model levels, for both stratified and con-vective clouds. PRCM dust is capable of reproducing observed weather and satellite images of

3. Nonhydrostatic Models 3.1. Basic equations

In recent years, we have developed two non-hydrostatic models suited for studying a wide range of spatial scales of atmospheric systems. Both models are based on a fully compressible fluid in a terrain-following vertical coordinate. The National Taiwan University (NTU)/Purdue Nonhydrostatic Model (Hsu and Sun, 2001) is an explicit model in terms of its time integration scheme, while the other model (Chen and Sun, 2001), using a semi-implicit scheme, is an implicit model.

Figure 11. The schematic illustration of the components in the integrated PRCM-dust Model (Yang, 2004a).

Figure 11. The schematic illustration of the components in the integrated PRCM-dust Model (Yang, 2004a).

The NTU/Purdue Nonhydrostatic Model uses a double forward-backward time integration procedure for treating both sound waves and internal gravity waves. The algorithm is stable, and does not generate computational modes. Although the integration time step is very small due to the CFL criterion imposed by treating high-frequency sound waves explicitly, this shortcoming is mitigated by using a time-splitting scheme and parallel computing. The explicit integration procedure is particularly well suited for parallel computing since a minimal amount of data transfer among CPUs is required with all partial differentiations calculated through local grid points. With the help of the National Center for High-performance Computing (NCHC) in Taiwan, the of has been written in Fortran 77 and Message Passing Interface (MPI) codes so that it can work on both supercomputers and PC clusters. The efficiency of the parallel processing depends on the number of grid points used in a simulation and the characteristics of the particular atmospheric circulation simulated. In one of the simulations with no clouds, our model achieved over 95% efficiency for a 128-processor job (Hsu et al., 2000). The high efficiency allows us to apply the model in studying resource-demanding problems, such as turbulence and local circulations.

In addition to its basic dynamic framework, the NTU/Purdue Nonhydrostatic Model takes into account many physical processes, such as land/ocean processes, cloud microphysics and atmospheric turbulence. The prognostic ther-modynamic variables are the same as in the PRCM, with the addition of density in the continuity equation. The NTU/Purdue Nonhydrostatic Model is, thus, quite compatible with the PRCM. It will be possible in the future, with the improving computer technology, to nest the two models together for studying problems involving multiple-scale interactions.

Chen and Sun (2001) (CS) applied a mul-tigrid solver in the Purdue Nonhydrostatic Model, which is a semi-implicit time integration scheme and can have a much larger time interval than that used in the NTU/Purdue

Figure 12. (a) ECWMF-reanalysis wind at 850 mb at 1200 UTC 31 Oct 1999, (b) same as (a) except for PRCM simulation (after 48 h integration), (c) schematic diagram of pollutant transport under northerly, and (d) vertical integrated concentration at 1200 UTC 31 Oct 1999 (after 48-h integration) (Wu et al.., 2003, Hsu, 2001) (Div: divergence, Acc: accelerateion, Con: convergence, W: westerly wind, H: high pressure, and L: low pressure).

Figure 12. (a) ECWMF-reanalysis wind at 850 mb at 1200 UTC 31 Oct 1999, (b) same as (a) except for PRCM simulation (after 48 h integration), (c) schematic diagram of pollutant transport under northerly, and (d) vertical integrated concentration at 1200 UTC 31 Oct 1999 (after 48-h integration) (Wu et al.., 2003, Hsu, 2001) (Div: divergence, Acc: accelerateion, Con: convergence, W: westerly wind, H: high pressure, and L: low pressure).

Nonhydrostatic Model. In addition, a flexible hybrid coordinate in vertical was designed and used in that model. The two nonhydro-static models produced consistent results for mountain waves, thermal convection, etc. The complicated multigrid approach has shown great potential for future development of nonhydro-static models.

3.2. Flow over mountains

3.2.1. Linear 'mountain waves

Both (NTU/Purdue and CS) nonhydrostatic models have been validated with steady-state analytical solutions in several linear mountain wave situations, such as the two-dimensional, nonhydrostatic solution in Queney (1948); the two-layer, trapped-wave situation (Scorer, 1949); and the three-dimensional, nonhydro-static situation (Smith, 1980). The model results are very close to the analytical solution in all cases. Figure 13 shows the horizontal distribution of the potential temperature anomaly, which is inversely proportional to the vertical displacement of airflow passing over a bell-shaped mountain at a height close the ground surface. The 2-hour simulation result is in good agreement with the analytical solution.

Figure 13. Horizontal distributions of the potential temperature anomaly for airflow passing over a bell-shaped mountain at the non-dimensional height of Nz/U = n/4. Solid contour lines correspond to the model result after 2 h. The grid interval is 300 m in all three directions. The dashed contour lines represent the analytical, steady-state solution in Smith (1980). The center of the bell-shaped mountain is located at the (0, 0) coordinate. The linear mountain waves is nonhydrostatic with Na/U = 1. The vertical static stability, mean wind speed and the half-width length of the mountain are N = 0.01s"1, U = 10 m s 1 (from left to right in the figure), and a = 1km, respectively. The contour interval is 0.003 K.

Figure 13. Horizontal distributions of the potential temperature anomaly for airflow passing over a bell-shaped mountain at the non-dimensional height of Nz/U = n/4. Solid contour lines correspond to the model result after 2 h. The grid interval is 300 m in all three directions. The dashed contour lines represent the analytical, steady-state solution in Smith (1980). The center of the bell-shaped mountain is located at the (0, 0) coordinate. The linear mountain waves is nonhydrostatic with Na/U = 1. The vertical static stability, mean wind speed and the half-width length of the mountain are N = 0.01s"1, U = 10 m s 1 (from left to right in the figure), and a = 1km, respectively. The contour interval is 0.003 K.

Hsu and Sun (2001) also found an error in Queney's classic 1948 paper. The surface pressure distribution in the two-dimensional, nonhydrostatic, linear mountain wave solution is off by about 100%, and the vertical displacement plotted in the original paper is not accurate either. The erroneous diagram has been cited repeatedly in many books (Gill, 1982; Smith, 1979) and papers over half a century. Our results, which have been confirmed by Chen and Sun (2001), can serve as a basis for future nonhydrostatic model development.

3.2.2. 11 January 1972 Boulder-windstorm,

Both nonhydrostatic models have been used to simulate the famous 11 January 1972 Boulder windstorm (Lilly, 1978). The models reproduced the strong downslope wind and hydraulic jump for both free-slip surface and viscous surface simulations. With a free-slip boundary, the simulated hydraulic jump propagates downstream; however, the jump becomes stationary with a more realistic no-slip boundary condition (Fig. 14). The maximum wind also differs, depending on the lower boundary. For a viscous surface, it is around 45-50 m s_1, compared with 70 m or more for a free-slip surface (Sun and Hsu, 2005).

3.2.3. White Sands simulation

The NTU/Purdue model was applied to several well-observed real terrain cases for local circulations over the Organ Mountains in White Sands, New Mexico, USA, using 1 km grid resolution. The model successfully simulated strong winds over the valley, lee vortices, and downdrafts on the lee side for a weak prevailing wind situation (not shown in the figure). On the other hand, waves of strong-weak surface winds were simulated on the lee under a strong prevailing wind. The simulated wind patterns have been confirmed by upper air soundings and surface observations (Haines et a., 2003). Oh (2003) also

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