Abstract
Ocean tide aliasing is one of the largest error sources in satellite gravimetry. Despite its importance, the aliasing mechanism of ocean tides in satellite gravimetry is only partially understood. This paper explains tidal aliasing as a two-step mechanism. The primary aliasing is caused by orbit undersampling of original tidal signals. The secondary aliasing is due to undersampling of the primary aliasing signals through gravity recovery in discrete time intervals. The two-step aliasing mechanism is demonstrated through a closed-loop numerical simulation. The aliasing of the tidal constituents \(M_2\), \(N_2\), \(S_2\), \(K_2\), \(O_1\), \(P_1\), \(Q_1\) and \(K_1\) in CHAMP, GOCE, GRACE and GRACE Follow-On missions is analysed. The primary alias periods of individual constituents change from a few to hundreds of days depending on the orbital geometry. The long-term \(S_2\) aliasing may cause bias in gravity fields derived by GOCE data if the \(S_2\) tide is not well-represented by the ocean tide model applied in the data processing. Comparing the primary aliasing properties of CHAMP with that of GRACE indicates that tuning orbit inclination can improve aliasing properties, i.e. shorter aliasing periods and less couplings with annual/semi-annual signals. The strict definition of secondary alias periods is compromised in case of GRACE and GRACE Follow-On due to non-constant recovery periods, which results in irregular sampling and blurs the sharp spectral lines that are described by the two-step mechanism. The two-step aliasing mechanism can also be used in understanding aliasing of other periodic signals observed by satellite gravimetry.
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Data Availability Statement
The data we used in simulation is ocean tide model EOT08a. The updated version, EOT11a, is available at website page: https://doi.org/10.1594/PANGAEA.834232. We emphasize our closed-loop simulations do not rely on any specific ocean tide model. Inputs to the simulation are the orbital parameters (shown in text) and the known tidal spectral lines. Two-line element data of CHAMP, GOCE, GRACE and GRACE Follow-On missions are available at Space-Track.org.
References
Battrick B (ed) (1999) The four candidate earth explorer core missions - gravity field and steady-state Ocean Circulation. Vols. 1233 of ESA SP. ESA Publications Division, Noordwijk, Netherlands
Bruinsma SL, Förste C, Abrikosov O, Lemoine J-M, Marty J-C, Mulet S, Rio M-H, Bonvalot S (2014) ESA’s satellite-only gravity field model via the direct approach based on all GOCE data. Geophys Res Lett 41:7508–7514. https://doi.org/10.1002/2014GL062045
Chen G, Lin H (2000) The effect of temporal aliasing in satellite altimetry. Photogramm Eng Remote Sens 66(5):639–644
Drinkwater M, Floberghagen R, Haagmans R, Muzi D, PopescuFarahani A (2013) GOCE: ESA’s first earth explorer core mission. Space Sci Rev 108(1–2):419–432. https://doi.org/10.1007/978-94-017-1333-7_36
Farahani HH (2013) Modelling the Earth’s static and time varying gravity field using a combination of GRACE and GOCE data (Doctoral dissertation). Delft Univ Technol. https://doi.org/10.4233/uuid:750401d3-6496-4028-af78-f07f72eb8379
Flechtner F, Neumayer K-H, Dahle C, Dobslaw H, Fagiolini E, Raimondo J-C, Güntner A (2016) What can be expected from the GRACE-FO Laser Ranging Interferometer for Earth Science applications? Surv Geophys. https://doi.org/10.1007/s10712-015-9338-y
Floberghagen R, Fehringer M, Lamarre D, Muzi D, Frommknecht B, Steiger C, Piñeiro J, da Costa A (2011) Mission design, operation and exploitation of the gravity field and steady-state ocean circulation explorer mission. J Geodesy 85:749–758. https://doi.org/10.1007/s00190-011-0498-3
Han S-C, Ray RD, Luthcke SB (2007) Ocean tidal solutions in Antarctica from GRACE inter-satellite tracking data. Geophys Res Lett 34:L21607. https://doi.org/10.1029/2007GL031540
Han S-C, Shum CK, Matsumoto K (2005) GRACE observations of M2 and S2 ocean tides underneath the Filchner-Ronne and Larsen ice shelves. Antarctica. Geophys Res Lett 32:L20311. https://doi.org/10.1029/2005GL024296
Hauk M, Pail R (2018) Treatment of ocean tide aliasing in the context of a next generation gravity field mission. Geophys J Int 214(1):345–365. https://doi.org/10.1093/gji/ggy145
Iran Pour T, Reubelt S, Sneeuw N (2013) Quality assessment of sub-Nyquist recovery from future gravity satellite missions. Adv Space Res 52(5):916–929. https://doi.org/10.1016/j.asr.2013.05.026
Kaula WM (2000) Theory of satellite geodesy: application of satellites to geodesy. Dover Publications inc, Mineola, New York, USA
Knudsen P (2003) Ocean tides in GRACE monthly averaged gravity fields. Space Sci Rev 108(1–2):261–270. https://doi.org/10.1023/A:1026215124036
Knudsen P, Andersen O (2002) Correcting GRACE gravity fields for ocean tide effects. Geophys Res Lett 29(8):19-1-19–4. https://doi.org/10.1029/2001GL014005
Kornfeld RP, Arnold BW, Gross MA, Dahya NT, Klipstein WM, Gath PF, Bettadpur S (2019) GRACE-FO: the gravity recovery and climate experiment follow-on mission. J Spacecr Rockets 56:931–951. https://doi.org/10.2514/1.A34326
Landerer FW, Flechtner FM, Save H, Webb FH, Bandikova T, Bertiger WI, Bettadpur SV, Byun SH, Dahle C, Dobslaw H, Fahnestock E, Harvey N, Kang Z, Kruizinga GLH, Loomis BD, McCullough C, Murböck M, Nagel P, Paik M, Pie N, Poole S, Strekalov D, Tamisiea ME, Wang F, Watkins MM, Wen H-Y, Wiese DN, Yuan D-N (2020) Extending the global mass change data record: GRACE follow-on instrument and science data performance. Geophys Res Lett 47:e2020GL088306. https://doi.org/10.1029/2020GL088306
Liu, W., Sneeuw, N., Iran Pour, S., Tourian, M. J., & Reubelt, T. (2016). A posteriori de-aliasing of ocean tide error in future double-pair satellite gravity missions. In Freymueller J.T., Sánchez L. (Eds.), International symposium on earth and environmental sciences for future generations (Vols. In: 534 ternational Association of Geodesy Symposia, vol 147, pp. 103-109). https://doi.org/10.1007/13452016 259
Lyons RG (2004) Understanding digital signal processing, 2nd edn. Prentice Hall PTR, Upper Saddle River, NJ, USA
Mayer-Gürr T, Savcenko R, Bosch W, Daras I, Flechtner F, Dahle Ch (2012) Ocean tides from satellite altimetry and GRACE. J Geodyn 59–60:28–38. https://doi.org/10.1016/j.jog.2011.10.009
Parke ME, Stewart RH, Farless DL, Cartwright DE (1987) On the choice of orbits for an altimetric satellite to study ocean circulation and tides. J Geophys Res 92(C11):11693–11707. https://doi.org/10.1029/JC092iC11p11693
Ray R, Luthcke S (2006) Tide model errors and GRACE gravimetry: towards a more realistic assessment. Geophys J Int 167(3):1055–1059. https://doi.org/10.1111/j.1365-246X.2006.03229.x
Ray RD, Rowlands D, Egbert G (2003) Tidal models in a new era of satellite gravimetry. Space Sci Rev 108(1–2):271–282. https://doi.org/10.1023/A:1026223308107
Reigber C, Schwintzer P, Lühr H (1999) The CHAMP geopotential mission. Boll Geofisica Teorica Appl 40:285–289
Savcenko, R., & Bosch, W. (2008). EOT0808a-a new global ocean tide model derived by empirical analysis. Geophysical Research Abstract, 10 , EGU2008- A7470
Schlax MG, Chelton DB (1994) Detecting aliased tidal errors in altimeter height measurements. J Geophys Res 99:12603–12612. https://doi.org/10.1029/94JC00568
Seo KW, Wilson CR, Han SC, Waliser DE (2008) Gravity recovery and climate experiment (GRACE) alias error from ocean tides. J Geophys Res 113(B3):B03405. https://doi.org/10.1029/2006JB004747
Sneeuw N (2000) A semi-analytical approach to gravity field analysis from satellite observations (Doctoral dissertation). Technical University of Munich, Institute of Astronomical and Physical Geodesy
Tapley BD, Bettadpur S, Ries JC, Thompson PF, Watkins MM (2004a) GRACE measurements of mass variability in the earth system. Science 305:503–505. https://doi.org/10.1126/science.1099192
Tapley BD, Bettadpur S, Reigber C (2004b) The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett 31:L09607. https://doi.org/10.1029/2004GL019920
Tapley BD, Watkins MM, Flechtner F, Reigber C, Bettadpur S, Rodell M, Sasgen I, Famiglietti JS, Landerer FW, Chambers DP, Reager JT, Gardner AS, Save H, Ivins ER, Swenson SC, Boening C, Dahle C, Wiese DN, Dobslaw H, Tamisiea ME, Velicogna I (2019) Contributions of GRACE to understanding climate change. Nat Clim Change 9:358–369. https://doi.org/10.1038/s41558-019-0456-2
Tourian MJ (2013) Application of spaceborne geodetic sensors for hydrology (Doctoral dissertation). Univ Stuttg. https://doi.org/10.18419/opus-3929
Visser PNAM, Sneeuw N, Reubelt T, Losch M, Van Dam T (2010) Space-borne gravimetric satellite constellations and ocean tides: aliasing effects. Geophys J Int 181(2):789–805. https://doi.org/10.1111/j.1365-246X.2010.04557.x
Acknowledgements
The first author thanks the China Scholarship Council (CSC) for the financial support of her PhD research. Part of this research topic was also supported by the ESA project “Additional Constellation & Scientific Analysis of the Next Generation Gravity Mission Concept” with the contract No. 4000118480/16/NL/FF/gp. We also thank all the reviewers and editors for their clear and constructive comments, as their efforts help us improve the quality of the paper.
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WL designed the research, performed the research and wrote the paper; NS supervised the research and revised the paper.
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Liu, W., Sneeuw, N. Aliasing of ocean tides in satellite gravimetry: a two-step mechanism. J Geod 95, 134 (2021). https://doi.org/10.1007/s00190-021-01586-6
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DOI: https://doi.org/10.1007/s00190-021-01586-6