Height systems calculations at Swabian Alb test area

Abstract

This project aims at the consolidation of the data from integrated fieldwork in Swabian Alb test area since 1996 to 2013 as well as the height systems computations. Reliable data were checked by height differences and gravity values, after that they were grouped into 5 closed loops with 56 out of 121 observed points. Potential differences were computed from height differences which acquired from spirit levelling and gravity value, then least square adjustment was adopted. Observation equation (A-matrix) and condition equation (B-matrix) were applied in the adjustment, a weight matrix was also assigned in the adjustment. Geopotential differences were computed based on the Helmert orthometric height at point 580, then geopotenial numbers of the other points were computed by adding the geopotential number with the adjusted potential differences, then height systems could be determined as well as height corrections. In the closed loop adjustment especially adjustment of several loops with many data, condition equation adjustment is preferred because of the smaller size of design matrix compared to the observation equations and the advantage of condition equations over observation equations is that loop misclosures can be determined by condition equation. The results from both equations are the same. The difference of the geopotential numbers between unweighted and weighted adjustment is up to 0.0129 m2/s2 and the difference of height systems between unweighted and weighted adjustment is up to 0.0013 meter or 1.3 millimeter, so the height system computations were not significantly affected by the assigned weight. The difference of height corrections between unweighted and weighted adjustment is up to 10 -8 m so the assigned weights did not affect height correction results. Normal corrections give the smallest values while dynamic corrections give the largest values because the test area is located at latitude 48.485° instead of latitude 45° so the correction values are quite large.