Abstract
Global Positioning System (GPS) kinematic precise point positioning (KPPP) is an effective approach for estimating the Earth’s tidal deformation. The accuracy of KPPP is usually evaluated by comparing results with tidal models. However, because of the uncertainties of the tidal models, the accuracy of KPPP-estimated tidal displacement is difficult to accurately determine. In this paper, systematic vector differences between GPS estimates and tidal models were estimated by least squares methods in complex domain to analyze the uncertainties of tidal models and determine the accuracy of KPPP-estimated tidal displacements. Through the use of GPS data for 12 GPS reference stations in Hong Kong from 2008 to 2017, vertical ocean tide loading displacements (after removing the body tide effect) for eight semidiurnal and diurnal tidal constituents were obtained by GPS KPPP. By an in-depth analysis of the systematic and residual differences between the GPS estimates and nine tidal models, we demonstrate that the uncertainty of the tidal displacement determined by GPS KPPP for the M2, N2, O1, and Q1 tidal constituents is 0.2 mm, and for the S2 constituent it is 0.5 mm, while the accuracy of the GPS-estimated K1, P1, and K2 tidal constituents is weak because these three tidal constituents are affected by significant common-mode errors. These results suggest that GPS KPPP can be used to precisely constrain the Earth’s vertical tidal displacement in the M2, N2, O1, and Q1 tidal frequencies.
Highlights
The tidal force of the Sun and Moon can cause deformation of the solid Earth, which is named “body tide”, and it causes periodic rise and fall of the ocean mass, which is called “ocean tide”.The response of the solid Earth to this mass distribution is known as “ocean tide loading” (OTL).Modern high-precision geodetic technology can determine large-scale deformation at the sub-millimeter level, but the effect of tidal displacement must be considered [1,2,3,4]
Body tide can be modeled with an accuracy of usually less than 1% [5]
OTL displacement can be obtained by convolution integral of an ocean tide model and the Green’s function calculated from an Earth model [6], which we call an OTL model
Summary
The tidal force of the Sun and Moon can cause deformation of the solid Earth, which is named “body tide”, and it causes periodic rise and fall of the ocean mass, which is called “ocean tide”. Modern high-precision geodetic technology can determine large-scale deformation at the sub-millimeter level, but the effect of tidal displacement must be considered [1,2,3,4]. Penna et al [7] reported that the height error of M2 OTL displacement can reach around 20% (~8 mm), depending on the ocean tide model adopted and the handling strategy for the grid cells in coastal areas. The change of the vertical OTL displacement in some areas when using various Earth models can reach 2–3 mm [8]. OTL is still the main uncertain factor in tidal displacement analysis
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