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標題: 軌跡模式應用於地勢座標系統之研究
The application of trajectory model to terrain following coordinate system
作者: 林宏乾
Lin, Hong-Qiant
關鍵字: advection-diffusion equation;平流擴散方程;terrain following coordinate system;second aerosol;streak lines;地形座標系統;二次氣膠;煙線
出版社: 環境工程學系
本研究沿續2000年本實研室發展的空氣污染物垂直擴散模式,以平流擴散方程為理論的基礎,將座標系統由直角座標系統(x,y,z)改為非直角地形座標系統(x,y,z''),推導地面一層和地上十二層的偏微分方程式,來模擬原生性和二次氣膠污染物。將統御偏微分式子以數值插分法整理成對三角矩陣的型式,採L U decomposition method,在Linux工作平台上應用C++程式語言撰寫程式以作反覆的數值計算。

This research follows the vertical-diffusion model of the aerial pollutants , which was developed by our laboratory in year 2000. On the basis of the theory of the advection-diffusion equation , the reference frame is changed from rectangular coordinate system (x,y,z) into terrain following coordinate system (x,y,z''). In that case, we can derive a partial differential equation of the first and the twelfth layers above the ground and use the equation to simulate the primary and second aerosol pollutants.Utilizes finite-difference approximations to the derivatives in the equation to change the differential equation to difference equation, the governing equation can be performed as tridiagonal matrix. Then I introduce in L U decomposition method to the repeat repetitious calculation with C++ programming language on the Linux work station.
Advection term,vertical and horizontal diffusion term,pollutants emitted from stacks of each layer,dry deposition,scavenging,chemical reaction,instantaneous meteorological condition,mixing height,etc. are all taken into consideration in this model. The model is proved empirically by comparing calculated values with the observed values experimented from October 30 to September 6 in year 1999. In those simulation cases, I select two days─Oct.30 and Sep.5, the day is the PM10 episode─of back of high pressure system to make a comparison and discussion. The comparison of the two graphs, the GrADS graph of the streak lines and the contour graph of pollutants, is introduced into model to apparently show the influence hit by the fetal pollutive sources of central Taiwan.
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