相當正壓模式及其預報誤差

An Equivalent Barotropic Model and Its Forecast Errors in the Area of Taiwan and Its Vicinity

蔡清彥(Ching-Yen Tsay)

《大氣科學》 3卷1期 (1976/05) Pp. 67-86

摘要

本文扼要討論東亞地區相當正壓模式數值預報所需處理的問題，包括網格點結構，經緯度的計算，地形資料，初始資料（等壓面高值）的分析，資料修勻法，相當正壓模式的差分方程及邊界條件等。經選擇了三個個案為相當正壓模式的研究對象。Case A是預報臺灣地區寒潮爆發期間的500 mb槽脊線變化。Case B也是預報寒潮爆發期間的槽脊線變化，而此槽線則是切斷低壓開展以後開始移動的。Case C研究槽線從青康藏高原移出的情形。一般而言相當正壓模式能够準確的預報槽脊線在24小時內之移動。但幾種有規則的誤差使得36小時以後的預報圖與觀測圖有出入。最嚴重的現象是槽線由蒙古附近往東南移動時，模式預報槽線末端的渦旋度中心不合理的往南移動。因而在36小時以後造成華中華南地區不合理的滯留性切斷低區。推究原因可能是因為相當正壓模式沒有考慮青康藏高原的阻擋，偏向及摩擦效應的緣故。又預報槽線所以在中高緯略快，在低緯則略慢，可能是由於準地轉模式假設科氏參數為常數，而使模式中的地轉風在中高緯較實際風為大，在低緯則較小的結果。相當正壓模式無法預報Case B切斷低壓的開展，但能預報此低壓開展以後的移動情形。可能部份因相當正壓模式無法預報天氣系統的加強。但最主要的，可能是因為初始分裂成的三個低壓中心範圍太小（直徑約為250 km），無法正確的被模式（網格點距離為240 km）判別，而逐漸又合併成為範園大的切斷低壓。Case C期間內華中區地面氣旋生成的原因，亦經討論。可能是在大氣層共備了斜壓帶及雲區等有利環境以後，由500 mb槽線前的正渦旋度平流所引發的。氣旋形成後，1000－500 mb大氣層中的暖平流及不穩定條件促使氣旋迅速發展。

並列摘要

Numerical method for an equivalent barotropic model which includes grid structure, topography, finite difference equation, boundary conditions, data analysis and smoothing methods; are presented.Three cases have been selected for the study of the limited-area equivalent barotropic model. Case A predicts the movements of 500mb troughs and ridges related to cold-air outbreak in Taiwan. Case B also predicts the movements of troughs and ridges related to cold-air outbreak. The trough in this case moved after the cut-off low system opened up. Case C studies the movement of a trough in the eastern slope of Tibetan Plateau. Generally, movements of troughs and ridges in 24 hours were well predicted by the equivalent barotropic model. However, several systematic errors are apparently presented in the predictions after 36 hours. The most serious error is the unrealistic southward movement of a positive. vorticity center during a trough passes over the northeastern part of Tibetan Plateau. As a result, an unrealistic low system is separated from the main trough and stays in Southeast Mainland. The error is suspected as the result of the model without considering the blocking, deflecting and frictional effect of Tibetan Plateau. Another systematic error is the displacement of forecast trough being fast in the north and slow in the south. The error may comes from the beta-plane approximation in assuming the Coriolis parameter being constant. The geostrophic wind computed by this assumption is larger in the north and smaller in the south than its real value. The equivalent barotropic model did not predict the open up of cut-off low in case B but well predicted its movement after it opened up. The error is suspected partly due to the equivalent barotropic model being unable to predict the intensification, but mainly due to the scales of the initial low pressure centers being small and not able to be observed correctly by the model.In the period of case C. a surface cyclone is formed and developed in Central East China. Synoptic analysis suggests that the formation of the cyclone is initiated by the positive vorticity advection ahead of 500 mb trough, although the warm advection and moist instability in 1000-500mb layer may play important roles in the development of the cyclone.