Knowledge Bank

This report examines precisely computed effects of terrain on geoid undulations at a laser tracking station on Mt. Haleakala, Maui, Hawaii. Discrepancies from two to seven meters (Despotakis 1987) between calculated ( using free-air anomalies and reference field OSU86F) and given undulations (from SL6 ellipsoidal heights and spirit-leveled orthometric heights) were lowered to 10-20 centimeters using accurate terrain corrections, improved spherical harmonic reference fields, and new, more computationally accurate software. Twelve 1° x 1° files containing 3" x 3" point elevations were received from DMA which covered all land areas in the Hawaiian Island area (17°≤φ≤24°, 200°≤λ≤207°). These files were merged into one 7° x 7° DTED file containing 8400 x 8400 mean 3" x 3" elevations which was the basis for all further elevation files throughout the study. Terrain corrections (TC's) were calculated on 3", 30" and 2' grids, using an FFT program (COGEOIDV). This program was limited to calculating 600 x 600 TC's at a time. Thus, because of the large number of 3" elevations, the 3" TC's were calculated in small areas (method 1 -- 20' x 20' with 5' border; method 2 -- 10' x 10' with 10' border) and these areas were merged together to get TC coverage over the whole area of interest. This process was burdensome because of the time involved in running the multiple jobs, as well as the mismatch of edges that occurs when merging together the various cells. An RMS difference of TC's along edges of adjoining cells was 2 mgals for method 1 and 0.5 mgals for method 2. To avoid the mismatch of edges, a program (TCLGCRAY) was written to calculate all of the 3" TC's over the entire 5° x 5° area (with a 1° border), by using limited amounts of RAM space at a time. This program was completed, yet wasn't run because of it's expected cpu time (5.4 hours on a Cray Y-MP8/864). It was seen that the use of terrain corrections in this area did not make a significant improvement in the final undulation estimates because the effect of the terrain ( +0.5 meters) was almost completely (1-2 cm) offset by the indirect effect (-0.5 meters). The largest improvement in the undulation estimates was in the use of more recent high degree geopotential models (OSU89B and OSU91A). Their contributions to the undulation estimates were a significant (70-80 cm) improvement over OSU86F. This study shows the 3" elevation file yields the most accurate terrain corrections. However, a disagreement of 15-20 cm between given undulations and undulations estimated using 3" terrain corrections and high degree reference fields was not explained. Sea surface topography in this area could introduce such a bias in the given undulations.