台灣大地起伏模型之精進及其在DEM製作之應用

Abstract

台灣重力大地起伏模型採用去除計算回復法，其將大地起伏分成長、中及短波長三部分，此法使用全球大地位模式及台灣數值高程模型，殘餘大地起伏則以最小二乘配置法計算。新增加一改正項大幅提昇大地起伏在高山區精度。長波長部份採用最新地球重力模型GGM01、GGM02、EIGEN-CG01C，經測試最佳成果為GGM02C結合EGM96計算之台灣重力大地起伏模型，在四條一等水準線用實際觀測值導得之大地起伏檢核本文大地起伏模型，其差值的標準偏差均在10公分以內。採用1920個GPS/水準點上之大地起伏模型與實際觀測大地起伏差值，製作一諧和面修正重力大地起伏模型，經在四條水準線測試成果為標準偏差2、3公分左右。用此改善後之大地起伏模型應用在航測及光達製作DEM時之高程轉換上，首先在新竹測試區採用航測法生產橢球高再以大地起伏模型改算為正高，與以航測正高高程控制之正高成果相比，因地面控制點之選擇不同造成兩法高程差值的標準偏差有11~40公分不等之成果；在屏東測試區比較光達橢球高經大地起伏模型改算之正高DEM，與水準正高之差值獲得標準偏差15.8公分。

A gravimetric geoid model of Taiwan is computed using remove-compute-restore technique, which divides a geoid model into the long, medium and short wavelength parts. This technique requires a global geopotential model and an elevation model. The residual geoid modeling is done by least-squares collocation. An correction term accounting for the terrain effect is introduced, and it improves greatly the accuracy of modeled geoidal undulations, especially in the high mountain areas. For the long wavelength part, this research experiments with earth gravity models GGM01, GGM02 and EIGEN-CG01C. The combined GGM02C-EGM96 model yields the best result in geoid modeling. The modeled and observed geoidal undulations are compared at four first-order leveling lines, resulting in standard deviations of geoidal differences of less than 10 cm. A refined geoid model is created by applying a harmonic surface of geoidal differences between modeled and observed geoidal undulations at 1920 first-order benchmarks, where GPS-derived ellipsoidal heights are available. The refined geoid model yields standard deviations of geoidal differences of 2 to 3 cm at the same four leveling lines. The refined geoid model is used in the photogrammetry and Lidar methods to generate orthometric heights. In a testing area in Hsinchu County, ellipsoidal heights are first generated by the photogrammetry method, orthometric heights are then computed using the geoid model. Comparing the orthometric heights generated by this approach and the conventional orthometric-height-controlled photogrammetry approach, the standard deviations of height differences range from 11 to 40 cm, depending on the scenarios of the ground control points for the aerial triangulation adjustment. At a testing line in Pintung County, the standard deviation of the differences between Lidar-geoid-derived orthometric height and levelling-derived orthometric heights is 15.8 cm.