Properties and optimality conditions of a three-dimension non-smooth thermodynamic system of sea ice

Lv, Wei; Feng, Enmin; Li, Zhijun

doi:10.1016/j.apm.2008.07.002

Cited by 4 publications

(3 citation statements)

References 16 publications

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“…In this paper, a parameter identification method (PIM) is used to determine volumetric heat capacity (product of density and specific heat) and thermal conductivity of sea ice. Using this method, [8,9] presented the optimality conditions of parameter identification for densities, specific heats and thermal conductivities of sea ice. In [10], salinity of sea ice was determined by this method.…”

Section: Introductionmentioning

confidence: 99%

Parameter identification for volumetric heat capacity and thermal conductivity in a quasi-linear thermodynamic system of sea ice

2016

Int. J. Biomath.

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This paper is intended to determine physical parameters describing volumetric heat capacity and thermal conductivity of sea ice in a quasi-linear thermodynamic system using field observations. The quasi-linear thermodynamic system of sea ice with unknown physical parameters is described, and the existence and uniqueness of its solution is proved. Then the physical parameters are taken as control variable, temperature deviations as objective function, and a parameter identification model is established. The existence of its optimal solution is discussed. To solve the identification model, a new algorithm containing genetic algorithm, Hooke-Jeeves algorithm and semi-implicit finite difference scheme is constructed. The physical parameters are calculated using the observations measured at Nella Fjord around Zhongshan Station, Antarctic in CHINARE 2006. For comparability and consistency with other works, a new international standard named TEOS-10 is used. To examine the validity of the identified results, another simulation for temperature profiles in different measurement period is operated. Numerical results show that better simulations of temperature distribution are possible with the identified parameters than EC1993. Therefore not only the identified parameters can be applied in sea ice modeling, but also this study can enrich and supplement observations of sea ice.

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Section: Introductionmentioning

confidence: 99%

Parameter identification for volumetric heat capacity and thermal conductivity in a quasi-linear thermodynamic system of sea ice

2016

Int. J. Biomath.

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“…A semigroup approach to the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient in the quasilinear parabolic equation with Dirichlet boundary conditions was presented [15]. References [16,17] provided the mathematical theory to calculate the ice densities, specific heats, and thermal conductivities. In [18], an ice salinity profile was determined by the parameter identification method abbreviated by THESCI.…”

Section: Introductionmentioning

confidence: 99%

Parameter Identification for Salinity in a Quasilinear Thermodynamic System of Sea Ice

Feng

2014

Mathematical Problems in Engineering

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This study is intended to provide a parameter identification method to determine salinity of sea ice by temperature and salinity observations. A quasilinear thermodynamic system of sea ice with unknown salinity is described and its property is proved. Then, a parameter identification model is established and the existence of its optimal solution is discussed. The salinity profile is calculated by the temperature and salinity data, which were measured at Nella Fjord around Zhongshan Station, Antarctica, during the polar night time by the 22nd Chinese Antarctic Research Expedition. Another simulation for temperature profiles during different measurement periods is operated. Results show that better simulations of the salinity and temperature distribution are possible with the estimated parameters than Eicken’s (Eicken 1992) and THESCI’s (Lv et al. 2009). This method will help people understand the salinity evolution of sea ice more thoroughly.

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“…Refs. [13] and [14] provided the mathematical theory to calculate the thermal conductivities. Semion [3] considered the heat conduction with a piecewise constant conductivity and prove the identifiability for the conductivities by using eigenvalues and eigenfunctions method.…”

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Optimality of piecewise thermal conductivity in a snow-ice thermodynamic system

Lv¹,

Sui²

2015

Numerical Algebra, Control &Amp; Optimization

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This article is intended to provide the optimality of piecewise thermal conductivity in a snow-ice thermodynamic system. Based on the temperature distribution characteristics of snow and sea ice, we construct a piecewise smooth thermodynamic system coupled by snow and sea ice. Taking the piecewise thermal conductivities of snow and sea ice as control variables and the temperature deviations obtained from the system and the observations as the performance criterion, an identification model with state constraints is given. The dependency relationship between state and control variables is proven, and the existence of the optimal control is discussed. The work can provide a theoretical foundation for simulating temperature distributions of snow and sea ice.

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Properties and optimality conditions of a three-dimension non-smooth thermodynamic system of sea ice

Cited by 4 publications

References 16 publications

Parameter identification for volumetric heat capacity and thermal conductivity in a quasi-linear thermodynamic system of sea ice

Parameter identification for volumetric heat capacity and thermal conductivity in a quasi-linear thermodynamic system of sea ice

Parameter Identification for Salinity in a Quasilinear Thermodynamic System of Sea Ice

Optimality of piecewise thermal conductivity in a snow-ice thermodynamic system

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