Earth rotation deceleration/acceleration due to semidiurnal oceanic/atmospheric tides:Revisited with new calculation
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摘要
The global oceanic/atmospheric tides exert decelerating/accelerating secular torques on the Earth rotation. We developed new formulations to accurately calculate amounts of two kinds of secular tidal torques. After Melchior, we found that an additional factor 1+k-l = 1.216, which has been formerly neglected, must be multiplied unto the tidal torque integral. By using our refined formulations and the recent oceanic/atmospheric global tide models, we found that:(i) semidiurnal oceanic lunar/solar tides exert decelerating torques of about-4.462 × 10~(16)/-0.676 × 10~(16) Nm respectively and(ii) atmospheric S_2 tide exerts accelerating torque of 1.55 × 10~(15) Nm. Former estimates of the atmospheric S_2 tidal torque were twice as large as our estimate due to improper consideration of loading effect. We took the load Love number for atmospheric loading effect from Guo et al.(2004). For atmospheric loading of spherical harmonic degree two, the value of k′=-0.6031 is different from that for ocean loading as k′ =-0.3052,while the latter is currently used for both cases-ocean/atmospheric loading-without distinction. We discuss(i) the amount of solid Earth tidal dissipation(which has been left most uncertain) and(ii) secular changes of the dynamical state of the Earth-Moon-Sun system. Our estimate of the solid Earth tidal torque is-4.94×10~(15) Nm.
The global oceanic/atmospheric tides exert decelerating/accelerating secular torques on the Earth rotation. We developed new formulations to accurately calculate amounts of two kinds of secular tidal torques. After Melchior, we found that an additional factor 1+k-l = 1.216, which has been formerly neglected, must be multiplied unto the tidal torque integral. By using our refined formulations and the recent oceanic/atmospheric global tide models, we found that:(i) semidiurnal oceanic lunar/solar tides exert decelerating torques of about-4.462 × 10~(16)/-0.676 × 10~(16) Nm respectively and(ii) atmospheric S_2 tide exerts accelerating torque of 1.55 × 10~(15) Nm. Former estimates of the atmospheric S_2 tidal torque were twice as large as our estimate due to improper consideration of loading effect. We took the load Love number for atmospheric loading effect from Guo et al.(2004). For atmospheric loading of spherical harmonic degree two, the value of k′=-0.6031 is different from that for ocean loading as k′ =-0.3052,while the latter is currently used for both cases-ocean/atmospheric loading-without distinction. We discuss(i) the amount of solid Earth tidal dissipation(which has been left most uncertain) and(ii) secular changes of the dynamical state of the Earth-Moon-Sun system. Our estimate of the solid Earth tidal torque is-4.94×10~(15) Nm.
The global oceanic/atmospheric tides exert decelerating/accelerating secular torques on the Earth rotation. We developed new formulations to accurately calculate amounts of two kinds of secular tidal torques. After Melchior, we found that an additional factor 1+k-l = 1.216, which has been formerly neglected, must be multiplied unto the tidal torque integral. By using our refined formulations and the recent oceanic/atmospheric global tide models, we found that:(i) semidiurnal oceanic lunar/solar tides exert decelerating torques of about-4.462 × 10~(16)/-0.676 × 10~(16) Nm respectively and(ii) atmospheric S_2 tide exerts accelerating torque of 1.55 × 10~(15) Nm. Former estimates of the atmospheric S_2 tidal torque were twice as large as our estimate due to improper consideration of loading effect. We took the load Love number for atmospheric loading effect from Guo et al.(2004). For atmospheric loading of spherical harmonic degree two, the value of k′=-0.6031 is different from that for ocean loading as k′ =-0.3052,while the latter is currently used for both cases-ocean/atmospheric loading-without distinction. We discuss(i) the amount of solid Earth tidal dissipation(which has been left most uncertain) and(ii) secular changes of the dynamical state of the Earth-Moon-Sun system. Our estimate of the solid Earth tidal torque is-4.94×10~(15) Nm.
引文
[1] W.H. Munk, G.J.F. MacDonald, The Rotation of the Earth, Cambridge University Press, 1960 ch.11 and ch.4.
[2] K. Lambeck, The Earth's Variable Rotation:Geophysical Causes and Consequences, Cambridge University Press, 1980, pp. 10-11, ch.5.
[3] K. Lambeck, The Earth's paleorotation, tidal friction and the Earth's rotation,in:P. Brosche, J. S(u|¨)ndermann(Eds.), Springer-Verlag Berlin Heidelberg, New York, 1978, pp. 145-153.
[4] F.R. Stephenson, LV. Morrison, Long-term fluctuations in the Earth's rotation:700 BC to AD 1990, Phil. Trans. Roy. Soc. Lond. A 351(1995)165-202.
[5] R.D. Ray, B.G. Bills, B.F. Chao, Lunar and solar torques on the ocean tides,J. Geophys. Res. 104(1999)17653-17659.
[6] P.M. Mathews, S.B. Lambert, Effect of mantle and ocean tides on the Earth's rotation rate, Astron. Astrophys. 493(2009)325-330.
[7] R.D. Ray, R.M. Ponte, Barometric tides from ECMWF operational analyses, Ann.Geophys. 23(2003)1897-1910.
[8] M. Schindelegger, Atmosphere-induced short period variations of Earth rotation, TU Wien Geowissenschaftliche Mitteillungen Heft Nr 96(2014).
[9] W.B. Shen, S.H. Na, Atmospheric acceleration and earth-expansion deceleration of the earth rotation, Geod Geodyn 8(2017)421-426.
[10] P. Melchior, The Tides of the Planet Earth, Pergamon Press, London, 1978 ch. 3.
[11] W.E. Farrell, Deformation of the Earth by surface loads, Rev. Geophys. Space Phys. 10(1972)761-797.
[12] J.Y. Guo, Y.B. Li, Y. Huang, H.T. Deng, S.Q. Xu, J.S. Ning, Green's function of the deformation of the Earth as a result of atmospheric loading, Geophys. J. Int.159(2004)53-68. https://doi.Org/10.1111/j.1365-246X.2004.02410.x.
[13] S.H. Na, J. Baek, Computation of the load love number and the load green's function for an elastic and spherically symmetric Earth, J. Kor. Phys. Soc. 58(2011)1195-1205. https://doi.org/10.3938/jkps.58.1195.
[14] B. Haurwitz, A.D. Cowley, Diurnal and semidiurnal barometric oscillations,global distribution and annual variation, Pure Appl. Geophys. 102(1973)193-222.
[15] R.S. Lindsen, S. Chapman, Atmospheric tides, Space Sci. Rev. 10(1969)3-188.
[16] R.S. Gross, in:T. Herring, G. Schubert(Eds.), Earth Rotation Variation-Long Period, VoL 3 Geodesy of Treatise on Geophysics, Elsevier, Amsterdam, 2009ch.9.
[17] W.B. Shen, R. Sun, C. Wei, Z. Zhang, J. Li, J. Han, H. Ding, The expanding Earth at present:evidence from temporal gravity field and space-geodetic data, Ann.Geophys. 54(2011), https://doi.org/10.4401/ag-4951.
[2] K. Lambeck, The Earth's Variable Rotation:Geophysical Causes and Consequences, Cambridge University Press, 1980, pp. 10-11, ch.5.
[3] K. Lambeck, The Earth's paleorotation, tidal friction and the Earth's rotation,in:P. Brosche, J. S(u|¨)ndermann(Eds.), Springer-Verlag Berlin Heidelberg, New York, 1978, pp. 145-153.
[4] F.R. Stephenson, LV. Morrison, Long-term fluctuations in the Earth's rotation:700 BC to AD 1990, Phil. Trans. Roy. Soc. Lond. A 351(1995)165-202.
[5] R.D. Ray, B.G. Bills, B.F. Chao, Lunar and solar torques on the ocean tides,J. Geophys. Res. 104(1999)17653-17659.
[6] P.M. Mathews, S.B. Lambert, Effect of mantle and ocean tides on the Earth's rotation rate, Astron. Astrophys. 493(2009)325-330.
[7] R.D. Ray, R.M. Ponte, Barometric tides from ECMWF operational analyses, Ann.Geophys. 23(2003)1897-1910.
[8] M. Schindelegger, Atmosphere-induced short period variations of Earth rotation, TU Wien Geowissenschaftliche Mitteillungen Heft Nr 96(2014).
[9] W.B. Shen, S.H. Na, Atmospheric acceleration and earth-expansion deceleration of the earth rotation, Geod Geodyn 8(2017)421-426.
[10] P. Melchior, The Tides of the Planet Earth, Pergamon Press, London, 1978 ch. 3.
[11] W.E. Farrell, Deformation of the Earth by surface loads, Rev. Geophys. Space Phys. 10(1972)761-797.
[12] J.Y. Guo, Y.B. Li, Y. Huang, H.T. Deng, S.Q. Xu, J.S. Ning, Green's function of the deformation of the Earth as a result of atmospheric loading, Geophys. J. Int.159(2004)53-68. https://doi.Org/10.1111/j.1365-246X.2004.02410.x.
[13] S.H. Na, J. Baek, Computation of the load love number and the load green's function for an elastic and spherically symmetric Earth, J. Kor. Phys. Soc. 58(2011)1195-1205. https://doi.org/10.3938/jkps.58.1195.
[14] B. Haurwitz, A.D. Cowley, Diurnal and semidiurnal barometric oscillations,global distribution and annual variation, Pure Appl. Geophys. 102(1973)193-222.
[15] R.S. Lindsen, S. Chapman, Atmospheric tides, Space Sci. Rev. 10(1969)3-188.
[16] R.S. Gross, in:T. Herring, G. Schubert(Eds.), Earth Rotation Variation-Long Period, VoL 3 Geodesy of Treatise on Geophysics, Elsevier, Amsterdam, 2009ch.9.
[17] W.B. Shen, R. Sun, C. Wei, Z. Zhang, J. Li, J. Han, H. Ding, The expanding Earth at present:evidence from temporal gravity field and space-geodetic data, Ann.Geophys. 54(2011), https://doi.org/10.4401/ag-4951.