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Title: | 地形約束下之等熵座標平衡模式 Isentropic Model of Topographically Bound Balanced Motions |
Authors: | Da-Kai Peng 彭達剴 |
Advisor: | 郭鴻基(Hung-Chi Kuo) |
Keyword: | 位渦,反演原理,無質量層,非線性平衡反演,落磯山脈,青康藏高原,台灣附近西南氣流, Potential vorticity,invertibility principle,massless layer,nonlinear balance invertibility,Rocky Mountains,Tibetan Plateau,Southwesterly near Taiwan, |
Publication Year : | 2021 |
Degree: | 碩士 |
Abstract: | 位渦蘊含平衡大氣中之熱力及動力資訊。在靜力平衡近似和水平平衡關係下,從位渦場中可以得到平衡風場及溫度場,此種特性被稱為「位渦反演」。位渦反演涉及解橢圓形偏微分方程,其反演結果是非局部的。若我們有位渦場,則可以有效的反演出平衡動力以及熱力場。本研究探討地形約束下之等熵座標平衡運動,即等熵面與地形相交如何影響平衡流場。其中「無質量層」方法幫助我們求解等熵面與地形相交需要的數學技巧。 本研究主要參考Silvers and Schubert (2012) 和Fulton et al. (2017) 對於二維線性平衡模式的工作。我們延伸建立了等熵座標之二維線性平衡模型和三維線性與非線性平衡模式。利用這些模式,我們重現了Silvers and Schubert (2012)對低層噴流的動力研究,在此之上並給予了地表加熱以及地形冷卻效應的量化分析,此外,我們也發現低層逆溫層在不同等熵座標高度下,根據逆溫層是否碰觸地形,分別有增強或削弱低層噴流的強度的效果。此外我們利用非線性平衡模式模擬類似於颱風結構的位渦場,並在中心上層設置負位渦結構。結果顯示負位渦在強渦旋中心上層產生之壓力擾動往周圍擴散,但在強渦旋中心則傾向垂直擴散。此外我們也利用2020年七月之月平均ERA5 再分析資料對於:1) 落磯山脈 2) 青康藏高原做位渦反演;利用2015年7月20日00UTC-24UTC之每小時ERA5 再分析資料對於 3) 鄰近台灣之鋒面個案做位渦反演。落磯山脈的三維位渦反演結果整體與觀測吻合,如反演場之低層噴流強度與延伸範圍皆與觀測十分吻合。青康藏高原的三維位渦反演結果則能部分捕捉如索馬利噴流和高原東側南風等特徵。此外,我們在落磯山脈的反演中分離上層與下層動力條件,其線性疊加後之結果與原反演場幾乎一致,這顯示了位渦反演可用於分離特定位渦在地形附近對整體反演平衡場之重要性。另一方面,台灣個案平衡模式中層大氣位渦反演的風速比起觀測的風速小約16%,顯示在一天的時間尺度下平衡場在觀測場中的重要性。反演的低層西南風場展現空間均勻性,風速區並往西南方向延伸,這特性和觀測一致,也顯示位渦動力的重要性。 本研究包含: 1. 建構地形約束下之線性平衡與非線性平衡等熵座標平衡模式;模式可以在等熵座標下處理地形與地表斜壓性 2. 分析地表暖心結構以及地形冷卻作用,得出兩者對於低層噴流強度影響為線性關係 3. 分析低層逆溫層對低層噴流強度之影響;在地形之上的逆溫層會增強低層噴流強度 4. 非線性平衡下類颱風位渦反演,並探討高層與低層暖心結構下壓力擾動分布 5. 以ERA5再分析資料為基礎,反演落磯山脈,青康藏高原,及台灣附近西南氣流之平衡場;反演結果與觀測場部分相似。 Potential vorticity (PV) contains information on the dynamical and thermal properties of the atmosphere. With hydrostatic balance approximation and horizontal wind balance relation, the balanced wind and the temperature information can be retrieved solely from PV field. This retrieval is often called the PV inversion or the invertibility principle of PV. The PV inversion often involved solving an elliptic partial differential equation with the nonlocal solution that is global in the domain. The PV inversion is a powerful method to recover balanced horizontal motions and vertical temperature structure. This thesis studies the topographically bound balanced motion with isentropic coordinate. Namely, we study the balanced motion in the presence of the topography with temperature intersection. We applied “massless layer approach” in our models, which can solve invertibility problems that isentropes intersect with ground or topography. Our approach mainly followed the work from the two-dimensional linear balanced modeling of Silvers and Schubert (2012) and Fulton et al. (2017). We have built both linear and nonlinear balanced models in the three-dimensional geometry with the isentropic coordinate. With such balanced model and massless layer approach, we studied idealized numerical simulations in 2-D and 3-D geometries. The dynamics of LLJs in Silvers and Schubert (2012) are reproduced and further gave a quantitative analysis of the effect from both thermal and orographic forcing. Additionally, we found that the low-level inversion layer can enhance or weaken the strength of the LLJs depending on whether the inversion layer touches the topography. For a 3-D invertibility, we found that the flow strength of the LLJs would be weaker than a 2-D case. The nonlinear balanced model is for the typhoon-like vortex invertibility. The pressure perturbations in a strong and in a small vortex structure is studied. Stronger vortex allows a stronger pressure perturbation. Finally, we performed real case PV inversions in: 1) The Rocky Mountains regions and 2) the Tibetan Plateau region. 3) southwesterly flow near Taiwan island. ERA5 Monthly averaged reanalysis data were used in 1) and 2) while ERA5 hourly reanalysis data were used in 3). The inverted fields in 3-D geometry near the Rocky Mountains highly resemble the observed fields both in the strength and the spatial distribution of the LLJs. Besides, the superposition of the upper-level and lower-level dynamics wind fields in the Rocky Mountains case implies that we can trace the influence of PV source near the topography, which manifest the importance of the PV invertibility principle. The inverted fields near Tibetan Plateau partially captured the features in observation like the occurrence of Somali jet and the southerly at the east of plateau. On the other hand, the balanced models underestimated the wind speed of southwesterly flow only about 16% near Taiwan, which reminds us that in daily time-scale balanced wind fields might be important. The low-level south-easterly near Taiwan is smooth and extend southwestwards, which is consistent with observations and reveals that PV dynamics is important. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/53850 |
DOI: | 10.6342/NTU202100565 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 大氣科學系 |
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U0001-0502202110210300.pdf Restricted Access | 9.37 MB | Adobe PDF |
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