Spectral and Spatial Investigation of Ocean Tide Signatures in GRACE(-FO) Post-Fit Residuals

authored by: Igor Koch
supervised by: Jakob Flury
Abstract: The Gravity Recovery and Climate Experiment (GRACE, 2002–2017) was the first satellite mission to utilize low-low Satellite-to-Satellite Tracking (ll-SST), and the first mission able to monitor mass variations on Earth. Since 2018, the successor mission GRACE Follow-On (GRACE-FO) has been in orbit. The ll-SST concept involves two identical co-orbiting satellites separated by a distance of approximately 220 km. The distance between the satellites is precisely tracked by a K/Ka-band ranging system and serves as the main observable for the derivation of monthly gravity field solutions. These gravity field products are of major importance for studying mass variations within the Earth’s system. The process of computing the monthly gravity field solutions involves satellite orbit modeling and parameter estimation as central components. Since the precise distance measurements provided by the K/Ka-band ranging system contain information on all influences affecting satellite dynamics, various background models are employed during satellite orbit modeling. These models are used to separate the signals that should conventionally be part of the gravity field solutions from disturbances related, for example, to tides, gravitational attraction from celestial bodies, and rapid mass variations in the atmosphere and oceans. Imperfections of ocean tide models are considered among the primary factors limiting the quality of GRACE and GRACE-FO gravity field products. Ocean tide models are known to exhibit significant inaccuracies, especially in polar regions where precise satellite altimetry observations are lacking, and in shallow water regions where ocean tide dynamics are more complex than those in open ocean areas. As part of this work, a spectral analysis was conducted for the first time to examine ocean tide signatures in the ll-SST post-fit residuals. Monthly gravity field solutions and the corresponding range-rate post-fit residuals for the period from April 2002 to September 2023 were computed. The obtained rangerate post-fit residuals were low-pass filtered, numerically differentiated, and assigned to a global 5°×5° grid. Lomb–Scargle periodograms were computed for the time series in each grid, and then analyzed for frequencies with significant amplitudes occurring on a global scale. In total, over 30 prominent tidal frequencies were identified, which correspond not only to the major gravitationally excited tidal constituents but also to minor degree-2 tides, degree-3 tides, non-linear tides, and radiational tides. With the exception of a few tidal constituents, the corresponding amplitude maps almost exclusively show increased amplitudes in polar regions, along coastlines and confined to some regions of the open ocean. The most complex region where a large number of tidal frequencies show increased amplitudes is the Weddell Sea. Although most of the identified tidal frequencies were considered during orbit modeling, meaning that the amplitudes in the periodograms represent residual signal relative to the ocean tide model used, several unmodeled frequencies were identified. These include degree-3 tides 3M1, 3L2, 3N2, 3M3, the compound tides 2SM2 and 2MK3/MO3, and the radiational triple S3, T3, R3, with the latter two sharing their frequencies with the compound tides SP3 and SK3, respectively. All of these unmodeled tides have been scarcely studied or not studied at all thus far. A global altimetry-constrained ocean tide model for 3M3 was just recently published. At the moment, for 3M1, 3L2, 3N2 altimetry-based solutions are only available for the latitudes from −66° to +66°, but not for the polar regions, where according to the performed spectral analysis large tidal variations exist. Data-constrained ocean tide solutions do not exist for the other frequencies. It was shown that purely hydrodynamic solutions can explain a large part of the degree-3 and radiational signal in the post-fit residuals. For the identified compound tides at the moment not even hydrodynamic models have been published yet. An analysis of altimetry data reveals a qualitative agreement with the 2SM2 and 2MK3/MO3 patterns observed in the post-fit residuals. The findings presented suggest that the analysis of ll-SST post-fit residuals offers significant potential for validating ocean tide models. Future research should also explore the potential for assimilating ll-SST measurements into hydrodynamic models.
Organisation(s): Institute of Geodesy
Type: Doctoral thesis
No. of pages: 147
Publication date: 21.01.2026
Publication status: Published
Sustainable Development Goals: SDG 13 - Climate Action
Electronic version(s): https://doi.org/10.15488/20291 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@phdthesis{337338aadf6b47f4865a87b675cb104c,
title = "Spectral and Spatial Investigation of Ocean Tide Signatures in GRACE(-FO) Post-Fit Residuals",
abstract = "The Gravity Recovery and Climate Experiment (GRACE, 2002–2017) was the first satellite mission to utilize low-low Satellite-to-Satellite Tracking (ll-SST), and the first mission able to monitor mass variations on Earth. Since 2018, the successor mission GRACE Follow-On (GRACE-FO) has been in orbit. The ll-SST concept involves two identical co-orbiting satellites separated by a distance of approximately 220 km. The distance between the satellites is precisely tracked by a K/Ka-band ranging system and serves as the main observable for the derivation of monthly gravity field solutions. These gravity field products are of major importance for studying mass variations within the Earth{\textquoteright}s system. The process of computing the monthly gravity field solutions involves satellite orbit modeling and parameter estimation as central components. Since the precise distance measurements provided by the K/Ka-band ranging system contain information on all influences affecting satellite dynamics, various background models are employed during satellite orbit modeling. These models are used to separate the signals that should conventionally be part of the gravity field solutions from disturbances related, for example, to tides, gravitational attraction from celestial bodies, and rapid mass variations in the atmosphere and oceans. Imperfections of ocean tide models are considered among the primary factors limiting the quality of GRACE and GRACE-FO gravity field products. Ocean tide models are known to exhibit significant inaccuracies, especially in polar regions where precise satellite altimetry observations are lacking, and in shallow water regions where ocean tide dynamics are more complex than those in open ocean areas. As part of this work, a spectral analysis was conducted for the first time to examine ocean tide signatures in the ll-SST post-fit residuals. Monthly gravity field solutions and the corresponding range-rate post-fit residuals for the period from April 2002 to September 2023 were computed. The obtained rangerate post-fit residuals were low-pass filtered, numerically differentiated, and assigned to a global 5°×5° grid. Lomb–Scargle periodograms were computed for the time series in each grid, and then analyzed for frequencies with significant amplitudes occurring on a global scale. In total, over 30 prominent tidal frequencies were identified, which correspond not only to the major gravitationally excited tidal constituents but also to minor degree-2 tides, degree-3 tides, non-linear tides, and radiational tides. With the exception of a few tidal constituents, the corresponding amplitude maps almost exclusively show increased amplitudes in polar regions, along coastlines and confined to some regions of the open ocean. The most complex region where a large number of tidal frequencies show increased amplitudes is the Weddell Sea. Although most of the identified tidal frequencies were considered during orbit modeling, meaning that the amplitudes in the periodograms represent residual signal relative to the ocean tide model used, several unmodeled frequencies were identified. These include degree-3 tides 3M1, 3L2, 3N2, 3M3, the compound tides 2SM2 and 2MK3/MO3, and the radiational triple S3, T3, R3, with the latter two sharing their frequencies with the compound tides SP3 and SK3, respectively. All of these unmodeled tides have been scarcely studied or not studied at all thus far. A global altimetry-constrained ocean tide model for 3M3 was just recently published. At the moment, for 3M1, 3L2, 3N2 altimetry-based solutions are only available for the latitudes from −66° to +66°, but not for the polar regions, where according to the performed spectral analysis large tidal variations exist. Data-constrained ocean tide solutions do not exist for the other frequencies. It was shown that purely hydrodynamic solutions can explain a large part of the degree-3 and radiational signal in the post-fit residuals. For the identified compound tides at the moment not even hydrodynamic models have been published yet. An analysis of altimetry data reveals a qualitative agreement with the 2SM2 and 2MK3/MO3 patterns observed in the post-fit residuals. The findings presented suggest that the analysis of ll-SST post-fit residuals offers significant potential for validating ocean tide models. Future research should also explore the potential for assimilating ll-SST measurements into hydrodynamic models.",
author = "Igor Koch",
year = "2026",
month = jan,
day = "21",
doi = "10.15488/20291",
language = "English",
series = "Wissenschaftliche Arbeiten der Fachrichtung Vermessungswesen der Universit{\"a}t Hannover",
publisher = "Fachrichtung Geod{\"a}sie und Geoinformatik der Leibniz Universit{\"a}t Hannover",
}