A new spherical harmonic approach to residual terrain modeling: a case study in the central European Alps

For decades, the residual terrain model (RTM) concept (Forsberg and Tscherning in J Geophys Res Solid Earth 86(B9):7843–7854, https://doi.org/10.1029/JB086iB09p07843, 1981) has been widely used in regional quasigeoid modeling. In the commonly used remove-compute-restore (RCR) framework, RTM provides a topographic reduction commensurate with the spectral resolution of global geopotential models. This is usually achieved by utilizing a long-wavelength (smooth) topography model known as reference topography. For computation points in valleys this neccessitates a harmonic correction (HC) which has been treated in several publications, but mainly with focus on gravity. The HC for the height anomaly only recently attracted more attention, and so far its relevance has yet to be shown also empirically in a regional case study. In this paper, the residual spherical-harmonic topographic potential (RSHTP) approach is introduced as a new technique and compared with the classic RTM. Both techniques are applied to a test region in the central European Alps including validation of the quasigeoid solutions against ground-truthing data. Hence, the practical feasibility and benefits for quasigeoid computations with the RCR technique are demonstrated. Most notably, the RSHTP avoids explicit HC in the first place, and spectral consistency of the residual topographic potential with global geopotential models is inherently achieved. Although one could conclude that thereby the problem of the HC is finally solved, there remain practical reasons for the classic RTM reduction with HC. In this regard, both intra-method comparison and ground-truthing with GNSS/leveling data confirms that the classic RTM (Forsberg and Tscherning 1981; Forsberg in A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modeling. Report 355, Department of Geodetic Sciences and Surveying, Ohio State University, Columbus, Ohio, USA, https://earthsciences.osu.edu/sites/earthsciences.osu.edu/files/report-355.pdf, 1984) provides reasonable results also for a high-resolution (degree 2160) RTM, yet neglecting the HC for the height anomaly leads to a systematic bias in deep valleys of up to 10–20 cm.