A coupled thermodynamic system of sea ice and its parameter identification.

*(English)*Zbl 1187.80024In this paper, an inverse coefficient identification thermal problem in a triple layer heat conductor is investigated. The layers represent the snow, sea ice and ocean mixed layer, whilst the unknowns are the thermal properties, i.e. density \(\rho_i\), specific heat \(c_i\), and thermal conductivity \(\kappa_i\), of each layer \(i= 1,2,3\), totalling a number of 9 positive unknown constant parameters. A certain physical constraint is imposed, namely that for the snow \(\kappa_1= a\rho^2_1\), where \(a\) is a given positive constant, such that the number of unknown positive constants is reduced to 9. However, it is impossible to determine \(\rho_2\), \(c_2\), \(\rho_3\) and \(c_3\) separately, but only their products, namely \(\rho_2\cdot c_2\) and \(\rho_3\cdot c_3\), i.e. the heat capacity of the ice and ocean mixed layers, respectively.

The thermodynamic system measures the temperature throughout the triple layer system which is probably too much and impossible in practice. The existence of an optimal control for the least-squares minimization problem is discussed and necessary conditions for optimality are derived. No regularization and no numerical results are presented. There are a few English mistakes and it seems that the paper has not been proof checked properly.

The thermodynamic system measures the temperature throughout the triple layer system which is probably too much and impossible in practice. The existence of an optimal control for the least-squares minimization problem is discussed and necessary conditions for optimality are derived. No regularization and no numerical results are presented. There are a few English mistakes and it seems that the paper has not been proof checked properly.

Reviewer: Daniel Lesnic (Leeds)

##### MSC:

80A23 | Inverse problems in thermodynamics and heat transfer |

86A05 | Hydrology, hydrography, oceanography |

86A22 | Inverse problems in geophysics |

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\textit{W. Lv} et al., Appl. Math. Modelling 32, No. 7, 1198--1207 (2008; Zbl 1187.80024)

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