Abstract
Inverse technique is a widely used method in oceanography, but it has a problem that the retrieved solutions often violate model prior assumptions. To tune the model has consistent solutions, an iteration approach, which successively utilizes the posterior statistics for next round inverse estimation, is introduced and tested from a real case study. It is found that the consistency may become elusive as the determinants of solution and noise covariance matrices become zero in the iteration process. However, after several steps of such operation, the difference between posterior statistics and the model prior ones can be gradually reduced.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Constable S C, Parker R L, Constable C G. 1987. Occam’s inversion: a practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics, 52(3): 289–300
Dosso S E, Nielsen P L, Wilmut M J. 2006. Data error covariance in matched-field geoacoustic inversion. J Acoust Soc Am, 119(1): 208–219
Engl H W, Hanke M, Neubauer A. 1996. Regularization of Inverse Problems. Dordrecht: Kluwer Academic Publishers, 322
Fiadeiro M E, Veronis G. 1982. On the determination of absolute velocities in the ocean. J Mar Res, 40: 159–182
Fofonoff N P, Millard Jr R C. 1983. Algorithms for computation of fundamental properties of seawater. Paris: UNESCO Technical Paper in Marine Science, 44: 1–53
Golub G H, Heath M, Wahba G. 1979. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics, 21(2): 215–223
Groeskamp S, Zika J D, Sloyan B M, et al. 2014. A thermohaline inverse method for estimating diathermohaline circulation and mixing. J Phys Oceanogr, 44(10): 2681–2697
Hansen P C. 2001. The L-curve and its use in the numerical treatment of inverse problems. In: Johnston P, ed. Computational Inverse Problems in Electrocardiology: Advances in Computational Bioengineering, Vol. 5. Southampton: WIT Press, 119–142
Hoerl A E, Kennard R W. 2000. Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 42(1): 80–86
Levenberg K. 1944. A method for the solution of certain non-linear problems in least squares. Quart Appl Math, 2(2): 164–168
Liu Yonggang, Yuan Yaochu. 1999. Variability of the Kuroshio in the East China Sea in 1992. Acta Oceanologica Sinica, 18(1): 1–15
Marquardt D W. 1963. An algorithm for least-squares estimation of nonlinear parameters. J Soc Indust Appl Math, 11(2): 431–441
McIntosh P C, Rintoul S R. 1997. Do box inverse models work? J Phys Oceanogr, 27(2): 291–308
Nakano T, Takatsuki Y, Kaneko I. 1994. The Kuroshio structure and transport estimated by the inverse method. J Phys Oceanogr, 24(3): 609–618
Scales J A, Snieder R. 1997. To Bayes or not to Bayes? Geophysics, 62(4): 1045–1046
Snieder R, Trampert J. 1999. Inverse problems in geophysics. In: Wirgin A, ed. Wavefield Inversion. Vienna: Springer-Verlag, 119–190
Tarantola A. 2005. Inverse Problem Theory and Methods for Model Parameter Estimation. Philadelphia, Pennsylvania: SIAM, 342
Tikhonov A N, Arsenin V Y. 1977. Solutions of Ill-Posed Problems. John F, Trans. Washington, D C: V H Winston & Sons, 258
Wei Yanzhou, Huang Daji, Zhu Xiaohua. 2013. Interannual to decadal variability of the Kuroshio Current in the East China Sea from 1955 to 2010 as indicated by in-situ hydrographic data. J Oceanogr, 69(5): 571–589
Wei Yanzhou, Pei Yuhua, Zhang Ronghua. 2015. Seasonal variability of the Kuroshio Current at the Section PN in the East China Sea based on insitu observation from 1987 to 2010. Acta Oceanologica Sinica, 34(5): 12–21
Wunsch C. 1978. The North Atlantic general circulation west of 50°W determined by inverse methods. Rev Geophys, 16(4): 583–620
Yuan Yaochu, Su Jilan, Pan Ziqin. 1992. Volume and heat transports of the Kuroshio in the East China Sea in 1989. La mer, 30(3): 251–262
Zhu Xiaohua, Park J H, Kaneko I. 2006. Velocity structures and transports of the Kuroshio and the Ryukyu current during fall of 2000 estimated by an inverse technique. J Oceanogr, 62(4): 587–596
Zika J D, McDougall T J, Sloyan B M. 2010. A tracer-contour inverse method for estimating ocean circulation and mixing. J Phys Oceanogr, 40(1): 26–47
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: The National Natural Science Foundation of China under contract Nos 41490644 and 41490640.
Rights and permissions
About this article
Cite this article
Wei, Y., Kang, X. & Pei, Y. A case study of the consistency problem in the inverse estimation. Acta Oceanol. Sin. 36, 45–51 (2017). https://doi.org/10.1007/s13131-017-1110-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13131-017-1110-3