Journal of Applied Mathematics
Volume 2012 (2012), Article ID 532870, 16 pages
Research Article

Simulation and Domain Identification of Sea Ice Thermodynamic System

1State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Liaoning, Dalian 116024, China
2School of Mathematics and Statistics, Nanyang Normal College, Henan, Nanyang 473061, China
3School of Mathematical Sciences, Dalian University of Technology, Liaoning, Dalian 116024, China

Received 20 January 2012; Accepted 27 April 2012

Academic Editor: Armin Troesch

Copyright © 2012 Bing Tan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Based on the measured data and characteristics of sea ice temperature distribution in space and time, this study is intended to consider a parabolic partial differential equation of the thermodynamic field of sea ice (coupled by snow, ice, and sea water layers) with a time-dependent domain and its parameter identification problem. An optimal model with state constraints is presented with the thicknesses of snow and sea ice as parametric variables and the deviation between the calculated and measured sea ice temperatures as the performance criterion. The unique existence of the weak solution of the thermodynamic system is proved. The properties of the identification problem and the existence of the optimal parameter are discussed, and the one-order necessary condition is derived. Finally, based on the nonoverlapping domain decomposition method and semi-implicit difference scheme, an optimization algorithm is proposed for the numerical simulation. Results show that the simulated temperature of sea ice fit well with the measured data, and the better fit is corresponding to the deeper sea ice.