臺灣大地起伏模型之發展與2025年現況

Development and 2025 Status of Taiwan Geoid Models

大地起伏模型是高程現代化、工程測量、地形製圖、災害評估及海陸空間資料整合的重要基礎。本文回顧臺灣大地起伏模型之發展脈絡，說明重力法與混合法大地起伏模型之差異，並整理截至2025年臺灣大地起伏模型之建置現況與實務應用。重力法大地起伏模型以Stokes積分法為主要理論基礎，可由重力異常推求具有物理意義的大地水準面起伏；然而，其實務精度仍受到重力資料品質、全球重力場模型、地形改正、長短波長訊號分離、資料格網化及誤差控制等因素影響。對臺灣而言，劇烈地形、山區重力資料不足、近岸與海陸交界資料銜接、離島垂直基準、不同觀測時間、坐標框架及地表變形等因素，使大地起伏模型建構更具挑戰。本文建立2025年臺灣重力法與混合法大地起伏模型，並利用GNSS／水準觀測大地起伏資料進行評估。結果顯示，重力法模型可呈現臺灣本島、離島及周邊海域連續且具物理意義的大地起伏場，但相對於GNSS／水準觀測資料仍存在約-0.22 m的平均差，反映其與TWVD2001現行高程基準之間的系統性差異。混合法模型透過GNSS／水準觀測資料建立修正面，可有效降低此差異；獨立驗證中平均差降至0.003 m，均方根為0.041 m；整體GNSS／水準資料評估中平均差為0.001 m，均方根為0.024 m。由於正高可由H=h−N（橢球高減大地起伏）求得，若使用偏小的大地起伏值，將可能使GNSS、LiDAR、UAV或衛星測量所得橢球高轉換之正高偏高，進而影響低平海岸地區之淹水與海平面上升風險評估。因此，本文建議重力法模型應作為具有物理意義之基礎模型，而混合法模型較適合作為臺灣現行高程基準下橢球高轉換為正高之實務模型。

Geoid models are fundamental to height modernization, engineering surveying, topographic mapping, hazard assessment, and the integration of land–sea spatial data. This paper reviews the development of Taiwan geoid models, explains the distinction between gravimetric and hybrid geoid models, and summarizes their status and practical applications as of 2025. A gravimetric geoid model is mainly based on Stokes’integral, which transforms gravity anomalies into geoid undulations with a clear physical meaning. In practice, however, its accuracy depends not only on the theoretical formula but also on gravity data quality, global gravity field models, terrain corrections, wavelength separation, gridding, and error control. In Taiwan, steep topography, sparse gravity data in mountainous areas, nearshore and land–sea data connection, offshore island datums, different observation times, coordinate frames, and surface deformation complicate geoid modeling. This study establishes 2025 gravimetric and hybrid geoid models for Taiwan and evaluates them using GNSS/leveling-derived geoid undulations. The results show that the gravimetric model provides a continuous and physically meaningful geoid surface over Taiwan, its offshore islands, and surrounding seas. However, it shows an average difference of about -0.22 m relative to GNSS/leveling observations, reflecting a systematic difference from the current TWVD2001 height datum. The hybrid model reduces this difference by fitting a correction surface using GNSS/leveling observations. In the independent validation, the mean difference is reduced to 0.003 m and the root mean square difference (RMSD) to 0.041 m. For the full GNSS/leveling dataset, the mean difference is 0.001 m and the RMSD is 0.024 m. Because orthometric height is obtained from H=h−N (ellipsoidal height minus geoid undulation), using an underestimated geoid undulation may lead to overestimated orthometric heights derived from GNSS, LiDAR, UAV, or satellite-based ellipsoidal heights. This could affect flood and sea-level-rise assessments in low-lying coastal areas. The gravimetric model is best regarded as a physically meaningful reference model, whereas the hybrid model is more suitable for operational ellipsoidal-to-orthometric height conversion under Taiwan’s current height datum.