Non-linear Distributed Parameter System And Identification Of Ice Thermal Diffusivity

With the increasing global warming, much attention has been paid to sea ice in Polar Regions and ice cover at middle and high latitudes and high altitude, as key components of global climate system. Relative to ice dynamics, basis study in ice thermodynamics plays much more crucial role in the climate change. Based on the parameter identification theory of distributed parameter systems and numerical method of partial differential equations, deep study on thermal diffusivity of sea ice and fresh-water ice (lake ice and reservoir ice) is carried by establishing identification model of non-linear distributed parameter system. The dissertation focuses on identification of thermal diffusivity of sea ice and fresh-water ice (lake ice and reservoir ice) according to field measurements from landfast sea ice around Zhongshan Station, east Antarctica, and Hongqipao Reservoir in Heilongjiang and thermokarst lake in the Beiluhe basin of the Qinghai-Tibetan Plateau, respectively, which is very valuable in the deeper understanding of thermodynamic behaviors within ice. The main content and contributions are summarized as follows:1. Based on the thermodynamic process within ice, a non-linear distributed parameter system with ice thermal diffusivity is proposed, and the properties and the existence and uniqueness of the weak solution of the system are given through the theory of partial differential equations. Taking the thermal diffusivity as a parameter to be identified and the temperature deviation of the calculated temperature and the measurements of ice as the performance criterion, we construct a parameter identification model of non-linear distributed parameter system, prove the existence of the optimal parameter and discuss optimality conditions of the model. The identification model simplifies the complexity and uncertainty of simultaneous identification of thermal conductivity, specific heat capacity and density in the previous literatures.2. Considering sea ice thermal diffusivity (an important thermal parameter) is controlled by ice temperature, salinity and density and ice porosity could be as a synthesis physical indicator of ice temperature, salinity and density, study on the direct relationship of sea ice thermal diffusivity and ice porosity is performed. According to the observation data from landfast sea ice around Zhongshan Station during the22nd Chinese Antarctic Research Expedition in2006, we construct a non-linear distributed parameter system in thermodynamics for describing thermal process within sea ice, and propose a parameter identification model of non-linear distributed parameter system taking sea ice thermal diffusivity as the identification parameter, the temperature deviation of the calculated temperature and the measurements of sea ice as the performance criterion and theoretical trend and range of sea ice thermal diffusivity from sea ice physics and thermology as constraints. The relationship between thermal diffusivity and ice porosity of Antarctic sea ice is identified for the first time through the model by using the optimized genetic algorithm. Numerical simulations for Antarctic sea ice temperature in2005are performed by using the identified ice thermal diffusivity and formulas of thermal conductivity, specific heat capacity and density in the previous literatures, respectively, and compared with the measured temperature. The survey reveals that the identified thermal diffusivity is reasonable. The identified result not only realizes to evaluate and understand sea ice thermal diffusivity by using ice porosity as a comprehensive physical indicator for the first time, but also simplifies the complicated and tedious calculations for determining thermal diffusivity by using ice thermal conductivity, specific heat capacity through sea ice temperature, salinity and density in the previous literatures.3. The properties of fresh-water ice is mainly controlled by ice temperature, and thermal diffusivity of fresh-water ice in the previous literatures is determined by indirect calculation or direct numerical method and experiment technology, but their results (numerical and experimental results) have large differences, especially at higher ice temperatures (-3℃to0℃) near the freezing point. Aiming at this situation, on the basis of measurements of ice from Hongqipao Reservoir in Heilongjiang Province and thermokarst lake in the Beiluhe basin of the Qinghai-Tibetan Plateau, a parameter identification model of non-linear distributed parameter system is established by dividing ice layer into small intervals, and thermal diffusivity of reservoir ice and lake ice varied with ice temperature is identified by the model. In general trend, at higher ice temperatures (-3℃to0℃) near the freezing point, thermal diffusivity of reservoir ice and lake ice decreases significantly with increasing ice temperature, and approaches the thermal diffusivity value of fresh-water at temperatures close to the freezing point. At lower ice temperatures (-15℃to-3℃), thermal diffusivity gradually increases with decreasing ice temperature and thermal diffusivity of lake ice is bigger than that of reservoir ice. By comparing the identified thermal diffusivity of reservoir ice and lake ice, we find that there exists dramatic change of thermal diffusivity at higher temperatures (-3℃-0℃) and the thermal diffusivity is affected by the bubble size and content lower temperatures (-15℃～3℃), which provides a reasonable explaination for the change of thermal diffusivity of fresh-water ice. And it is illustrated that the phase transition and the bubble size and content are respectively the dominant factors influencing thermal diffusivity of fresh-water ice at higher temperatures (-3℃-0℃) and lower temperatures (-15℃～3℃). Compared the identified thermal diffusivity with numerical and experimental results of fresh-water ice in the previous literatures, it is indicated that our research results are remarkably consistent with experimental results, and the dramatic change of thermal diffusivity of reservoir ice and lake ice at higher ice temperatures (-3℃to0℃) enriches and supplements previous numerical research on the thermal diffusivity of fresh-water ice in the literature in which the "warm ice" is ignored.