Forward and adjoint quasi-geostrophic models of the geomagnetic secular variation

Journal of Geophysical Research: Solid Earth

Volumn 114, Issue 11, 2009, Pages

  Canet, Elisabeth ^a   Fournier, Alexandre ^b   Jault, Dominique ^a  

^a UNIVERSITÉ GRENOBLE ALPES   (France)

^b INSTITUT DE PHYSIQUE DU GLOBE DE PARIS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DATA ASSIMILATION; GEOMAGNETISM; INVERSE PROBLEM; MAGNETIC FIELD; MAGNETOHYDRODYNAMICS; QUASI-GEOSTROPHIC FLOW; SECULAR VARIATION;

EID: 72049106896     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: 10.1029/2008JB006189     Document Type: Article

References (52)

1. Abramowitz, M., and I. A. Stegun (1964), Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, Dover, New York.
2. Amit, H., P. Olson, and U. Christensen (2007), Tests of core flow imaging methods with numerical dynamos, Geophys. J. Int., 168, 27-39, doi:10.1111/j.1365-246X.2006.03175.x. (Pubitemid 46050185)
3. Backus, G., R. L. Parker, and C. Constable (1996), Foundations of Geomagnetism, Cambridge Univ. Press, Cambridge, U. K.
4. Backus, G. E. (1968), Kinematics of geomagnetic secular variation in a perfectly conducting core, Philos. Trans. R. Soc. London, Ser. A, 263, 239-266, doi:10.1098/rsta.1968.0014.
5. Braginsky, S. I. (1970), Torsional magnetohydrodynamic vibrations in the Earth's core and variations in day length, Geomagn. Aeron., 10, 1-10.
6. Buffett, B. A., J. Mound, and A. Jackson (2009), Inversion of torsional oscillations for the structure and dynamics of Earth's core, Geophys. J. Int., 177, 878-890, doi:10.1111/j.1365-246X.2009.04129.x.
7. Chen, J. (2005), Global mass balance and the length-of-day variation, J. Geophys. Res., 110, B08404, doi:10.1029/2004JB003474.
8. Christensen, U. R., and J. Aubert (2006), Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields, Geophys. J. Int., 166, 97-114, doi:10.1111/j.1365- 246X.2006.03009.x.
9. Christensen, U. R., and J. Wicht (2007), Numerical dynamo simulations, in Treatise on Geophysics, vol.8, Core Dynamics, edited by P. Olson, pp. 245-282, Elsevier, Oxford, U. K.
10. Christensen, U. R., V. Holzwarth, and A. Reiners (2009), Energy flux determines magnetic field strength of planets and stars, Nature, 457, 167-169, doi:10.1038/nature07626.
11. Courtier, P. (1997), Variational methods, J. Meteorol. Soc. Jpn., 75, 211-218.
12. Courtier, P., and O. Talagrand (1987), Variational assimilation of meteorological observations with the adjoint vorticity equation. II: Numerical results, Q. J. R. Meteorol. Soc., 113(478), 1329-1347, doi:10.1002/gj. 49711347813.
13. Diamond, P. H., S. I. Itoh, K. Itoh, and T. S. Hahm (2005), Zonal flows in plasma: a review, Plasma Phys. Controlled Fusion, 47, R35-R161, doi:10.1088/0741-3335/47/5/R01.
14. Evensen, G. (2007), Data Assimilation: The Ensemble Kalman Filter, Springer, Berlin.
15. Eymin, C., and G. Hulot (2005), On core surface flows inferred from satellite magnetic data, Phys. Earth Planet. Inter., 152, 200-220, doi:10.1016/j.pepi.2005.06.009. (Pubitemid 41435276)
16. Fournier, A., C. Eymin, and T. Alboussière (2007), A case for variational geomagnetic data assimilation: Insights from a one-dimensional, nonlinear, and sparsely observed MHD system, Nonlinear Process. Geophys., 14, 163-180.
17. Giering, R., and T. Kaminski (1998), Recipes for adjoint code construction, Trans. Math. Software, 24, 437-474, doi:10.1145/293686.293695.
18. Gilbert, J. C., and C. Lemaréchal (1989), Some numerical experiments with variable-storage quasi-Newton algorithms, Math. Program., 45, 407-435, doi:10.1007/BF01589113. (Pubitemid 20660312)
19. Gillet, N., M. A. Pais, and D. Jault (2009), Ensemble inversion of time-dependent core flow models, Geochem. Geophys. Geosyst., 10, Q06004, doi:10.1029/2008GC002290.
20. Glatzmaier, G. A., and P. H. Roberts (1995), A three-dimensional self-consistent computer simulation of a geomagnetic field reversal, Nature, 377, 203-209, doi:10.1038/377203a0.
21. Gross, R. S. (2007), Earth rotation variations-Long period, in Treatise on Geophysics, vol.3, Geodesy, edited by T. Herring, pp. 239-294, Elsevier, Oxford, U. K.
22. Hersbach, H. (1998), Application of the adjoint of the WAM model to inverse wave modeling, J. Geophys. Res., 103(C5), 10,469-10,488, doi:10.1029/97JC03554.
23. Hide, R. (1966), Free hydromagnetic oscillations of the Earth's core and the theory of the geomagnetic secular variation, Philos. Trans. R. Soc. London, Ser. A, 259, 615-647, doi:10.1098/rsta.1966.0026.
24. Holme, R. (2007), Large-scale flow in the core, in Treatise on Geophysics, vol.8, Core Dynamics, edited by P. Olso, pp. 107-130, Elsevier, Oxford, U. K.
25. Holme, R., and N. Olsen (2006), Core surface flow modelling from high-resolution secular variation, Geophys. J. Int., 166, 518-528, doi:10.1111/j.1365-246X.2006.03033.x. (Pubitemid 44082246)
26. Hulot, G., T. Sabaka, and N. Olsen (2007), The present field, in Treatise on Geophysics, vol.5, Geomagnetism, edited by M. Kono, pp. 33-75, Elsevier, Oxford, U. K.
27. Ide, K., P. Courtier, M. Ghil, and C. Lorenc (1997), Unified notations for data assimilation: Operational, sequential and variational, J. Meteorol. Soc. Jpn., 75, 181-189.
28. Jackson, A., and C. Finlay (2007), Geomagnetic secular variation and its applications to the core, in Treatise on Geophysics, vol.5, Geomagnetism, edited by M. Kono, pp. 147-193, Elsevier, Oxford, U. K.
29. Jault, D. (2008), Axial invariance of rapidly varying diffusionless motions in the Earth's core interior, Phys. Earth Planet. Inter., 166, 67-76, doi:10.1016/j.pepi.2007.11.001.
30. Jault, D., C. Gire, and J. L. Le Mouël (1988), Westward drift, core motions and exchanges of angular momentum between core and mantle, Nature, 333, 353-356, doi:10.1038/333353a0.
31. Kalnay, E., et al. (1996), The NCEP/NCAR 40-Year Reanalysis Project, Bull. Am. Meteorol. Soc., 77, 437-471, doi:10.1175/1520-0477(1996) 077〈0437:TNYRP〉2.0.CO;2.
32. Le Dimet, F.-X., and O. Talagrand (1986), Variational methods for analysis and assimilation of meteorological observations, Tellus, 38, 97-110.
33. Lehnert, B. (1954), Magnetohydrodynamic waves under the action of the Coriolis force, Astrophys. J., 119, 647-654, doi:10.1086/145869.
34. Liu, D., A. Tangborn, and W. Kuang (2007), Observing system simulation experiments in geomagnetic data assimilation, J. Geophys. Res., 112, B08103, doi:10.1029/2006JB004691. (Pubitemid 47578252)
35. Olsen, N., and M. Mandea (2008), Rapidly changing flows in the Earth's core, Nat. Geosci., 1, 390-394, doi:10.1038/ngeo203.
36. Olsen, N., H. Lühr, T. J. Sabaka, M. Mandea, M. Rother, L. Tøffner-Clausen, and S. Choi (2006), CHAOS-a model of the Earth's magnetic field derived from CHAMP, Orsted, and SAC-C magnetic satellite data, Geophys. J. Int., 166, 67-75, doi:10.1111/j.1365-246X.2006.02959.x.
37. Pais, M. A., and D. Jault (2008), Quasi-geostrophic flows responsible for the secular variation of the Earth's magnetic field, Geophys. J. Int., 173, 421-443, doi:10.1111/j.1365-246X.2008.03741.x.
38. Pais, M. A., O. Oliveira, and F. Nogueira (2004), Nonuniqueness of inverted core-mantle boundary flows and deviations from tangential geostrophy, J. Geophys. Res., 109, B08105, doi:10.1029/2004JB003012.
39. Plaut, E. (2003), Nonlinear dynamics of traveling waves in rotating Rayleigh-Bénard convection: Effects of the boundary conditions and of the topology, Phys. Rev. E, 67, 046303, doi:10.1103/PhysRevE.67.046303.
40. Rau, S., U. Christensen, A. Jackson, and J. Wicht (2000), Core flow inversion tested with numerical dynamo models, Geophys. J. Int., 141, 485-497, doi:10.1046/j.1365-246x.2000.00097.x. (Pubitemid 30309255)
41. Roberts, P. H. (1967), An Introduction to Magnetohydrodynamics, Longmans, London.
42. Sun, Z., A. Tangborn, and W. Kuang (2007), Data assimilation in a sparsely observed one-dimensional modeled MHD system, Nonlinear Process. Geophys., 14, 181-192. (Pubitemid 46751594)
43. Talagrand, O. (1997), Assimilation of observations, an introduction, J. Meteorol. Soc. Jpn., 75, 191-209.
44. Talagrand, O., and P. Courtier (1987), Variational assimilation of meteorological observations with the adjoint vorticity equation. I: Theory, Q. J. R. Meteorol. Soc., 113, 1311-1328, doi:10.1002/gj.49711347812.
45. Tobias, S. M., P. H. Diamond, and D. W. Hughes (2007), b-plane magnetohydrodynamic turbulence in the solar tachocline, Astrophys. J., 667, L113-L116, doi:10.1086/521978.
46. Turner, G. M., J. L. Rasson, and C. V. Reeves (2007), Observation and measurement techniques, in Treatise on Geophysics, vol.5, Geomagnetism, pp. 93-146, edited by M. Kono, Elsevier, Oxford, U. K.
47. Vallis, G. K. (2006), Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation, Cambridge Univ. Press, Cambridge, U. K.
48. Voorhies, C. V., and G. E. Backus (1985), Steady flows at the top of the core from geomagnetic field models: The steady motions theorem, Geophys. Astrophys. Fluid Dyn., 32, 163-173, doi:10.1080/03091928508208783.
49. Waddington, R., D. Gubbins, and N. Barber (1995), Geomagnetic field analysis - V. Determining steady core-surface flows directly from geomagnetic observations, Geophys. J. Int., 122, 326-350, doi:10.1111/j. 1365-246X.1995.tb03556.x.
50. Wessel, P., and W. H. F. Smith (1991), Free software helps map and display data, Eos Trans. AGU, 72, 441, doi:10.1029/90EO00319.
51. Zatman, S., and J. Bloxham (1997), Torsional oscillations and the magnetic field within the Earth's core, Nature, 388, 760-763, doi:10.1038/41987. (Pubitemid 27375152)
52. Zatman, S., and J. Bloxham (1999), On the dynamical implications of models of Bs in the Earth's core, Geophys. J. Int., 138, 679-686, doi:10.1046/j.1365-246x.1999.00909.x.