正常高系統於臺灣地區之可應用性研究

高程系統在國家建設與科學研究中皆扮演重要角色，臺灣目前之高程基準是採用正高系統（orthometric heights），而正高系統因水準面之不平行性，故在兩觀測點間以不同水準路線，施測之高差成果會有所不同。此外要維護全國性之正高系統，其所耗費之成本亦相當高昂。本研究將探討以準大地水準面為基礎之正常高系統（normal heights）之建構方法與可應用性，並分析比較三種正常高建構之方法，分別為數學法、重力觀測法、以及全球大地位模式精化法，藉以瞭解該各方法在我國臺灣地區可達到的品質水準。根據研究成果顯示，數學法與國家法定正高系統相對高差之均方根（RMS）誤差為±15mm/√k、重力觀測法為±4mm/√k、全球大地位模式精化法為±13mm/√k。重力觀測法雖可達到最小之差異性，但其維護成本高昂。另一方面，採用全球大地位模式精化法所建立之正常高於臺灣地區已可滿足工程測量精度，且其維護成本低廉，可作為一般工程應用任務上之實務選擇。

關鍵字

高程系統；正常高；準大地起伏；全球重力場模型

並列摘要

A height reference system plays an important role in national developments as well as in scientific research. The orthometric height system is adopted as the current national height datum in Taiwan. Due to the non-parallelity of the leveling of the orthometric height system, the results of the height difference measured between the two observation points on different levels will be different. Besides, maintaining a nationalwide orthometric height system which is costly and time-consuming. This study aims to build the normal heights datum by quasi-geoid. Normal height system is constructed by using three methods in this study, and the applicability in Taiwan is analyzed. Numerical results illustrate that the relative differences to the current orthometric height system are ±15 mm / √k , ±4 mm / √k , and ±13 mm /√k for the mathematical approach, gravity observation approach, and improved global spherical harmonic model approach, respectively. According to the research results, the gravity observation method can achieve the best accuracy, it is also the most expensive than other methods. Considering both the achievable quality and maintenance cost, the improved of the global spherical harmonic model approach fulfils the needs of most engineering applications, but with less cost than that of the traditional approach for maintaining the normal height system.

並列關鍵字

height system ； normal heights ； quasi-geoid ； global earth gravity model

國際替代計量

正常高系統於臺灣地區之可應用性研究

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