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Part of the book series: Systems & Control: Foundations & Applications ((SCFA))

Abstract

The Arctic sea ice has been studied intensively in the field of climate and geoscience. One of the main reasons is due to ice-albedo feedback which influences climate dynamics through the high reflectivity of sea ice. The other reason is the rapid decline of the Arctic sea ice extent in the recent decade shown in several observations. These observations motivate the investigation of future sea ice amount. Several studies have developed a computational model of the Arctic sea ice and performed numerical simulations of the model with initial sea ice temperature profile. However, the spatially distributed temperature in sea ice is difficult to recover in real-time using a limited number of thermal sensors. Hence, the online estimation of the sea ice temperature profile based on some available measurements is crucial for the prediction of the sea ice thickness.

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References

  1. A. Alessandri, P. Bagnerini, M. Gaggero, Optimal control of propagating fronts by using level set methods and neural approximations. IEEE Trans. Neural Netw. Learn. Syst. 30(3), 902–912 (2018)

    Article  MathSciNet  Google Scholar 

  2. M. Benosman, Learning-Based Adaptive Control: An Extremum Seeking Approach–Theory and Applications (Butterworth-Heinemann, Oxford, 2016)

    MATH  Google Scholar 

  3. M.K. Bernauer, R. Herzog, Optimal control of the classical two-phase Stefan problem in level set formulation. SIAM J. Sci. Comput. 33(1), 342–363 (2011)

    Article  MathSciNet  Google Scholar 

  4. C.M. Bitz, M.M. Holland, A.J. Weaver, M. Eby, Simulating the ice-thickness distribution in a coupled climate model. J. Geophys. Res. Oceans 106(C2), 2441–2463 (2001)

    Article  Google Scholar 

  5. C.M. Bitz, W.H. Lipscomb, An energy-conserving thermodynamic model of sea ice, J. Geophys. Res. 104(C7), 15–669 (1999)

    Google Scholar 

  6. I. Fenty, P. Heimbach, Coupled sea ice ocean-state estimation in the Labrador Sea and Baffin Bay. J. Phys. Oceanogr. 43(5), 884–904 (2013)

    Article  Google Scholar 

  7. I. Fenty, D. Menemenlis, H. Zhang, Global coupled sea ice-ocean state estimation. Clim. Dyn. 49(3), 931–956 (2015)

    Article  Google Scholar 

  8. S. Gupta, The Classical Stefan Problem. Basic Concepts, Modelling and Analysis (Applied Mathematics and Mechanics, North-Holland, 2003)

    Google Scholar 

  9. D.K. Hall, J.R. Key, K.A. Casey, G.A. Riggs, D.J. Cavalieri, Sea ice surface temperature product from MODIS. IEEE Trans. Geosci. Remote Sens. 42(5), 1076–1087 (2004)

    Article  Google Scholar 

  10. M. Hinze, S. Ziegenbalg, Optimal control of the free boundary in a two-phase Stefan problem. J. Comput. Phys. 223(2), 657–684 (2007)

    Article  MathSciNet  Google Scholar 

  11. T. Kharkovskaia, D. Efimov, E. Fridman, A. Polyakov, J.P. Richard, On design of interval observers for parabolic PDEs, in Proceedings of 20th IFAC World Congress, vol. 50(1) (2017), pp. 4045–4050

    Google Scholar 

  12. S. Koga, M. Krstic, Arctic sea ice state estimation from thermodynamic PDE model. Automatica 112, 108713 (2020)

    Article  MathSciNet  Google Scholar 

  13. S. Koga, D. Bresch-Pietri, M. Krstic, Delay compensated control of the Stefan problem and robustness to delay mismatch. Int. J. Rob. Nonlinear Control 30(6), 2304–2334 (2020)

    Article  MathSciNet  Google Scholar 

  14. M. Krstic, Delay Compensation for Nonlinear, Adaptive, and PDE Systems (Birkhauser, Boston, 2009)

    MATH  Google Scholar 

  15. S. Kutluay, A. R. Bahadir, A. Özdes, The numerical solution of one-phase classical Stefan problem. J. Comput. Appl. Math. 81(1), 135–144 (1997)

    Article  MathSciNet  Google Scholar 

  16. R. Kwok, G.F. Cunningham, Variability of Arctic sea ice thickness and volume from CryoSat-2. Philos. Trans. R. Soc. A 373(2045) (2015). https://doi.org/10.1098/rsta.2014.0157

  17. R. Kwok, D.A. Rothrock, Decline in Arctic sea ice thickness from submarine and ICESat records: 1958–2008. Geophys. Res. Lett. 36(15) (2009). https://doi.org/10.1029/2009GL039035

  18. J. Marshall, A. Adcroft, C. Hill, L. Perelman, C. Heisey, A finite volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J. Geophys. Res. Oceans 102(C3), 5753–5766 (1997)

    Article  Google Scholar 

  19. G.A. Maykut, N. Untersteiner, Some results from a time dependent thermodynamic model of sea ice. J. Geophys. Res. 76, 1550–1575 (1971)

    Article  Google Scholar 

  20. S.J. Moura, N.A. Chaturvedi, M. Krstic, Adaptive partial differential equation observer for battery state-of-charge/state-of-health estimation via an electrochemical model. J. Dyn. Syst. Meas. Control 136(1), 011015-1–011015-11 (2014)

    Google Scholar 

  21. B. Petrus, Z. Chen, J. Bentsman, B.G. Thomas, Online recalibration of the state estimators for a system with moving boundaries using sparse discrete-in-time temperature measurements. IEEE Trans. Autom. Control 63(4), 1090–1096 (2017)

    Article  MathSciNet  Google Scholar 

  22. D.A. Rothrock, D.B. Percival, M. Wensnahan, The decline in arctic sea-ice thickness: separating the spatial, annual, and interannual variability in a quarter century of submarine data. J. Geophys. Res. Oceans 113(C5) (2008). https://doi.org/10.1029/2007JC004252

  23. A.J. Semtner Jr, A model for the thermodynamic growth of sea ice in numerical investigations of climate. J. Phys. Oceanogr. 6(3), 379–389 (1976)

    Article  Google Scholar 

  24. N. Untersteiner, On the mass and heat budget of Arctic sea ice. Arch. Meteorol. Geophys. Bioklimatol. A 12(2), 151–182 (1961)

    Article  Google Scholar 

  25. J.S. Wettlaufer, Heat flux at the ice-ocean interface. J. Geophys. Res. Oceans 96, 7215–7236 (1991)

    Article  Google Scholar 

  26. M. Winton, A reformulated three-layer sea ice model. J. Atmos. Oceanic Technol. 17(4), 525–531 (2000)

    Article  Google Scholar 

  27. C. Wunsch, The Ocean Circulation Inverse Problem (Cambridge University Press, Cambridge, 1996)

    Book  Google Scholar 

  28. C. Wunsch, P. Heimbach, Practical global oceanic state estimation. Phys. D Nonlinear Phenom 230(1–2), 197–208 (2007)

    Article  MathSciNet  Google Scholar 

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Koga, S., Krstic, M. (2020). Sea Ice. In: Materials Phase Change PDE Control & Estimation. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-58490-0_7

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