Height transformation models from ellipsoidal into the normal orthometric height system for the territory of the City of Zagreb

The paper presents the testing of the possibility of determining the heights of GPS points in the homogeneous field in the new Croatian Height Reference System (HVRS71) by using the method of height transformation. The testing was made in the area of Zagreb. As part of the field works, normal orthometric heights of 27 GPS points were determined according to the new height system, by transferring the benchmark heights using the geometric levelling method, thus obtaining GPS/levelling points of known ellipsoidal and normal orthometric heights. The GPS/levelling points served as the basis for determining the transformation models that enabled the computation of normal orthometric heights from ellipsoidal heights of any GPS point in the observed area. The empirical data used for modelling were reduced undulation dN values of GPS/levelling points. As part of the dN modelling with parametric functions, the approximation surfaces were obtained on the basis of three polynomials: FN310, FN312 and FN318. The transformation models were also tested using non-parametric Watson and Loess algorithms. The FN318 and Loess models yielded the best results.