Figure 9. SCAT analysis of ocean surface winds (m/s) at 40 m over the southern Asia—Pacific ocean for 0000 UTC May 2, 1994.

winds retrieved from the passive microwave radiometer of SSM/I on board the DMSP satellites, and from active microwave scat-terometer measurements on board SEASAT, NSCAT, ERS-1/2 and QuikSCAT satellites were discussed.

Of special import are the summaries of pre-implementation test results on the use of these various satellite ocean surface wind data at NCEP global data assimilation systems, based on which these surface wind data have been operationally implemented at various timelines during the last two decades. It is fair to state that from gross statistics based on many cases of forecasts, the impact of the satellite ocean surface winds on NWP short range forecasts is mostly positive, small but significant because the data are of a single level nature and only available at the ocean surface. Large impacts of the satellite ocean surface winds may only occur over some special synoptic situations and over the areas of severe weather storms when conventional data are lacking. This is well demonstrated in a special case investigation over the southwestern Pacific Ocean, where ERS-1 scatterometer winds are found to be most significant in identifying the storm center intensity and circulation.

The author would like express his sincere appreciation to Dr Stephen Lord of NCEP and Dr A. Hollingsworth of ECMWF for permission to use their centers' forecast performance statistics on anomaly correlations as shown in Figs. 1 and 2 of this article. He is also grateful to the two anonymous reviewers for their constructive comments and suggestions, which improved the final version of the manuscript.

[Received 15 January 2006; Revised 3 May 2007; Accepted 2 June 2007.]

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Wen-Yih Sun*'**, Wu-Ron Hsu^**, Jiun-Dar Chern*, Shu-Hua Chen$'**, Ching-Chi Wut, Kate Jr-Shiuan Yang*, Kaosan Yeh*, Michael G. Bosilovich*, Patrick A. Haines^, Ki-Hong Min", Tae-Jin Oh*'**, B. T. MacCall*'**, Ahmet Yildirim*, Yi-Lin Chang*, Chiao-Zen Chang*

and Yi-Chiang Yut

* Purdue University, West Lafayette, Indiana, USA t National Taiwan University, Taipei, Taiwan *Goddard Space Fight Center/NASA, Greenbelt, Maryland, USA $ University of California, Davis, California, USA ^ Army Research Laboratory, White Sand, New Mexico, USA "Valparaiso University, Valparaiso, Indiana, USA **Taiwan Typhoon and Flood Research Institute, Hsin-chu, Taiwan [email protected]

This article summarizes our research related to geofluid dynamics and numerical modeling. In order to have a better understanding of the motion in the atmosphere, we have been working on various forms of the Navier-Stokes equations, including the linearized and nonlinear systems as well as turbulence parametrization, cumulus parametrization, cloud physics, soil-snow parametrization, atmospheric chemistry, etc. We have also been working on numerical methods in order to solve the equations more accurately. The results show that many weather systems in the initial/growing stage can be qualitatively described by the linearized equations; on the other hand, many developed weather phenomena can be quantitatively reproduced by the nonlinear Purdue Regional Climate Model, when the observational data or reanalysis is used as the initial and lateral boundary conditions. The model can also reveal the detailed structure and physics involved, which sometimes can be misinterpreted by meteorologists according to the incomplete observations. However, it is also noted that systematic biases/errors can exist in the simulations and become difficult to correct. Those errors can be caused by the errors in the initial and boundary conditions, model physics and parametrizations, or inadequate equations or poor numerical methods. When the regional model is coupled with a GCM, it is required that both models should be accurate so as to produce meaningful results. In addition to the Purdue Regional Climate Model, we have presented the results obtained from the nonhydrostatic models, the one-dimensional cloud model, the turbulence-pollution model, the characteristic system of the shallow water equations, etc. Although the numerical model is the most important tool for studying weather and climate, more research should be done on data assimilation, the physics, the numerical method and the mathematic formulation in order to improve the accuracy of the models and have a better understanding of the weather and climate.

The motion of the atmosphere and ocean can be represented by Navier-Stokes equations, which should be solved numerically. However, the evolution of a weather/climate system consists of motions on many different scales. At the beginning, some of the small disturbances may be described by the linearized equations. When disturbances grow, nonlinear equations become necessary. It is also noted that eigen values/vectors can be easily obtained and interpreted in a linearized system. Hence, for the past few decades, we have been working on linear instability and nonlinear numerical models to study meteorological phenomena, ranging from convection, turbulence, air pollution, cumulus clouds, cloud streets, symmetric instabilities, mountain waves, lee vortices, and land-sea breezes, to synoptic scale waves, barotropic instabilities, cyclones, fronts, and regional climate in East Asia and North America. In order to obtain accurate numerical results, we have also been developing aspects of the model such as the new diffusion equation; turbulence parametrization; snow-vegetation-soil and snow-sea ice packages; forward-backward, advection, and semi-Lagrangian schemes; the pressure gradient force; the multigrid method; the transport of dust and trace gases; and the interaction between aerosols and regional climate. The important components of our mesoscale model are shown in Fig. 1.

We developed the Purdue Regional Climate Model (PRCM). However, several mesoscale regional models exist, with varying approaches. They include the fifth-generation Penn State/ NCAR Mesoscale model (MM5; Grell et al, 1995) and the Weather Research and Forecast (WRF) model (Skamarock et al, 2005). Table 1 shows the important features that are used in the PRCM, MM5, and WRF.

A few topics will be briefly discussed here. Many of them require further study. The basic structure of the PRCM and applications will be discussed in Sec. 2, the nonhydrostatic models in Sec. 3, other topics in Sec. 4, and a summary is provided at the end.

2. Purdue Regional Climate Model

2.1. Basic equations

The PRCM is a hydrostatic primitive equation model that utilizes the terrain-following coordinate (ap) in the vertical direction. It has

Purdue Regional Climate Model

Snow-vegetation-soil Sea-ice-mixed layer ocean

( Sun and Wu 1992, Bosilovich and Sun 1995, Sun and Chern 1998,2005 )

Lin et al. (1983) Rutledge and Hobbs (1983) Chern (1994)

Kuo (1965, 1974) Anthes (1978) Molinari (1982) Sun and Haines (1996)

Purdue Regional Climate Model

Liou et al. (1988) Chou and Suarez (1994) Chouetal. (1001)

Chern (1994)

Cumulus Cloud

Dynamics

Hydrostatic Arakawa C Grid Forward-Backward scheme 4th-order advection Scheme Pressure gradient force (Sun and Hsu 1988, Sun 1993c, 1995)

Liou et al. (1988) Chou and Suarez (1994) Chouetal. (1001)

Chern (1994)

Cumulus Cloud

Dynamics

Hydrostatic Arakawa C Grid Forward-Backward scheme 4th-order advection Scheme Pressure gradient force (Sun and Hsu 1988, Sun 1993c, 1995)

Figure 1. The schematic diagram of Purdue Regional Climate Model.

Table 1. The characteristics of PRCM, WRF, and MM5. WRF has three different dynamical cores. The one that mentioned here is Advanced Research WRF (ARW).

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