海冰热力学参数辨识及脊帆特征研究
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摘要
海冰作为极地下垫面最重要的特征,对全球大气、海洋环流和气候变化均有极其重要的影响。另外,冰脊作为海冰表面的主要形态特征,对大气、海冰、海水间的动量、热量交换及冰量、冰厚估算起关键作用,对海冰热动力学模式的改进和完善有也起推动作用。本论文以极地海冰热力过程、冰脊形态及动力学特征为研究背景,依据中国第二次北极科学考察期间得到的海冰温度实测数据,研究了一类分片光滑非线性分布参数系统的主要性质及参数辨识问题；又依据德国阿尔弗雷德-魏格纳极地和海洋研究所在南极威德尔海冬季科学考察期间测得的海冰表面起伏数据,研究了一类具有非线性约束的统计优化问题以及聚类算法在数据分析中的应用问题,并对冰-气拖曳系数和脊帆形拖曳力的参数化方案进行了初步改进。以最优化算法、偏微分方程数值方法及概率统计为研究和分析工具,将实测数据与数值计算结合起来,分别对海冰热力学参数、脊帆形态和动力学参数进行了认真探讨和研究。本文的研究内容和取得的主要结果概括如下：
1.针对北极海冰的热力学过程,构造了描述时变区域上海冰热力学过程的抛物型分布参数系统；利用偏微分方程的L2理论证明了该系统弱解的存在唯一性和解对辨识参数的连续依赖性；采用非重叠区域分解法将考虑的区域分为雪层、冰层和海水层三个时变子域,并在内边界上引入连续性条件,使每个子域充分光滑；基于不可微函数的优化理论及方法,分析并得到了系统及其弱解的一些基本性质；基于中国第二次北极科学考察期间现场测得的雪、冰、海水温度数据,提出了以雪、冰厚度为辨识参数,以数值计算值和实测冰温偏差为性能指标的参数辨识模型；证明了最优参数的存在性,并导出了最优性条件；计算结果不但较好地反映了冰温随时间和空间的变化规律,并且与实测冰温吻合良好。
2.依据机载激光高度计测得的海冰上表面高度数据,确定出实测脊帆高度和间距分布的概率密度；以切断高度为优化变量,以脊帆高度和间距分布的概率密度数学模型与实测分布的概率密度之间的误差为目标函数,以对应于优化参数的脊帆高度和间距分布的概率密度为约束条件,建立了具有非线性约束的统计优化模型,得到了最优切断高度,进而从海冰上表面起伏中确定出脊帆；针对传统k均值聚类算法需要事先制定类别数k和容易陷入局部最优的缺陷,将粒子群优化与传统k均值聚类算法相结合搜寻最优聚类中心,在迭代过程中不断更新误差准则以确定出最佳类别数,提出了一种改进的k均值聚类算法；依据脊帆强度(平均脊帆高度和间距的比值),利用所改进的算法将所测剖面分为三类；并通过与卫星图像的比较验证了算法的有效性；在聚类分析基础上通过统计分析和显著性检验讨论了脊帆强度对脊帆高度和间距分布的影响,并分析了脊帆各形态参数之间的相关性。
3.利用拖曳分割理论将冰-气拖曳力分为两部分：由冰面局部粗糙单元产生的摩拖曳力和由脊帆引起的形拖曳力；依据实测数据,利用脊帆形态参数和空间分布对中性条件下对应10m高度处风速的冰-气拖曳系数Cdn(10)和脊帆形拖曳力及其对冰-气总拖曳力的贡献的参数化方案进行了初步改进；讨论了冰-气拖曳系数Cdn(10)和脊帆形拖曳力及其对冰-气总拖曳力的贡献随脊帆强度和冰面粗糙长度的变化趋势：脊帆形拖曳力及其对冰。气总拖曳力的贡献均随脊帆强度减小而减小,随着粗糙长度增大而减小,但变化率和变化幅度不同,冰-气拖曳系数Cdn(10)随脊帆强度增大呈递增趋势,对较小的脊帆强度,Cdn(10)随粗糙长度的增大而增大,但脊帆强度较大时,Cdn(10)随粗糙长度减小而增大。造成不同变化趋势的主要原因是：对应不同脊帆强度与粗糙长度,摩拖曳力和形拖曳力在冰-气总拖曳力中相对优势地位发生变化,即对应较小的脊帆强度,摩拖曳力占优势地位,而对应较大的脊帆强度,形拖曳力占优势地位。本项工作有助于推动海冰动力学模式、热力-动力模式的改进和完善。
As the most important characteristics of the underlying surface in Polar Regions, sea ice has a significantly effect on the global atmosphere, ocean circulations, and climate change. Meanwhile, as one of the important characteristics of the sea ice surface, pressure ridges are the main factor for the estimations of the momentum and thermal transfer between the atmosphere and sea ice, as well as between the ocean and sea ice, ice mass and thickness. On the background of the thermodynamic process of sea ice, and characteristics of morphology and dynamics of pressure ridges, based on the measured sea ice temperature during the Second China Arctic Research Expedition and elevations of sea ice surface in the Weddell Sea measured during the Winter Weddell Outflow Study2006by the Germany Alfred Wegener Institute for Polar and Marine Research, the optimization methods, numerical computation for partial differential equations, and probability theory and mathematical statistics are used to identify the thermodynamic parameters and analyze the parameters of morphology and dynamics of pressure ridges. The main content and contributions are as follows.
1. For the thermodynamic process of the sea ice in the Arctic, a parabolic distributed parameter system is established to describe the thermodynamic process of sea ice. L2theory for partial equations is used to prove the existence and uniqueness of the weak solution of the system and the continuous dependence of this solution on the identified parameters. A non-overlapped domain decomposition method is applied to decompose the time-dependent domain to three sub-domains of snow, ice and sea water, and the continuous condition is introduced at all interfaces to make each sub-domain smooth. Some important properties of the system and its weak solution are analyzed by optimization theory and methods. An optimal model with state constraints is presented with the thicknesses of snow and sea ice as identified parameters, and the deviation between the calculated and the measured sea ice temperature as the performance criterion. The existence of the optimal parameter is proved and the optimal conditions are derived. Numerical simulation is carried out based on the temperature of snow, ice and water measured during the Second China Arctic Research Expedition, and the results not only reflect the variability of sea ice temperature in time and space domains, but also agree well with the observed temperatures.
2. Ice surface elevation profiles measured during Winter Weddell Outflow Study are used to investigate the morphology and distribution of pressure ridges in the northwestern Weddell Sea. To search effective methods for the determination of the cutoff height and the clustering of pressure ridges, an statistical optimal model with nonlinear constraint is presented with the cutoff height as identified parameter, and the deviation between the theoretical and the measured ridge height/spacing distributions as the performance criterion. The obtained optimal cutoff height is then used to separate pressure ridges from other sea ice surface undulations. Next, for the defects of the traditional k means clustering algorithm, an improved k means clustering algorithm is presented to cluster the measured profiles with the ridging intensity (the ratio of mean ridge height to mean spacing), and which are clustered into three regimes. These three ice regimes coincided closely with distinct sea ice regions identified in a satellite radar image. The statistical characteristics of each regime are analyzed and the influences of the ridging intensity on the ridge height and spacing distributions are also discussed. The correlations between the morphology parameters are also discussed.
3. Wind drag is parted into two components according to the drag partition theory:form drag on pressure ridges and the skin drag over rough sea ice surface. The parameterization of form drag on pressure ridges and its contribution to the total drag and air-ice drag coefficient at a reference height of10m under a neutral stability condition are improved by the morphology parameters and distributions of pressure ridges, and the variations of them with increasing ridging intensity and roughness length are discussed. The results revealed that, for the compacted ice field, form drag on ridges and its contribution to total drag both increase with ridging intensity, while decrease with increasing roughness length. There is an increasing trend of the air-ice drag coefficient Cdn(10) with increasing ridging intensity. Meanwhile, Cdn(10) increases for the smaller ridging intensities, whereas decreases for the larger ridging intensity, with increasing roughness length, which is mainly attributed to the change of dominance of form drag on pressure ridges and skin drag over rough ice surface:the form drag on pressure ridges becomes dominant only when ridging intensity is extremely large, while the skin drag over rough ice surface is the dominant component for the profiles with the relative lower ridging intensity. This work will push the study of the sea ice thermodynamic and dynamic models.
1.针对北极海冰的热力学过程,构造了描述时变区域上海冰热力学过程的抛物型分布参数系统；利用偏微分方程的L2理论证明了该系统弱解的存在唯一性和解对辨识参数的连续依赖性；采用非重叠区域分解法将考虑的区域分为雪层、冰层和海水层三个时变子域,并在内边界上引入连续性条件,使每个子域充分光滑；基于不可微函数的优化理论及方法,分析并得到了系统及其弱解的一些基本性质；基于中国第二次北极科学考察期间现场测得的雪、冰、海水温度数据,提出了以雪、冰厚度为辨识参数,以数值计算值和实测冰温偏差为性能指标的参数辨识模型；证明了最优参数的存在性,并导出了最优性条件；计算结果不但较好地反映了冰温随时间和空间的变化规律,并且与实测冰温吻合良好。
2.依据机载激光高度计测得的海冰上表面高度数据,确定出实测脊帆高度和间距分布的概率密度；以切断高度为优化变量,以脊帆高度和间距分布的概率密度数学模型与实测分布的概率密度之间的误差为目标函数,以对应于优化参数的脊帆高度和间距分布的概率密度为约束条件,建立了具有非线性约束的统计优化模型,得到了最优切断高度,进而从海冰上表面起伏中确定出脊帆；针对传统k均值聚类算法需要事先制定类别数k和容易陷入局部最优的缺陷,将粒子群优化与传统k均值聚类算法相结合搜寻最优聚类中心,在迭代过程中不断更新误差准则以确定出最佳类别数,提出了一种改进的k均值聚类算法；依据脊帆强度(平均脊帆高度和间距的比值),利用所改进的算法将所测剖面分为三类；并通过与卫星图像的比较验证了算法的有效性；在聚类分析基础上通过统计分析和显著性检验讨论了脊帆强度对脊帆高度和间距分布的影响,并分析了脊帆各形态参数之间的相关性。
3.利用拖曳分割理论将冰-气拖曳力分为两部分：由冰面局部粗糙单元产生的摩拖曳力和由脊帆引起的形拖曳力；依据实测数据,利用脊帆形态参数和空间分布对中性条件下对应10m高度处风速的冰-气拖曳系数Cdn(10)和脊帆形拖曳力及其对冰-气总拖曳力的贡献的参数化方案进行了初步改进；讨论了冰-气拖曳系数Cdn(10)和脊帆形拖曳力及其对冰-气总拖曳力的贡献随脊帆强度和冰面粗糙长度的变化趋势：脊帆形拖曳力及其对冰。气总拖曳力的贡献均随脊帆强度减小而减小,随着粗糙长度增大而减小,但变化率和变化幅度不同,冰-气拖曳系数Cdn(10)随脊帆强度增大呈递增趋势,对较小的脊帆强度,Cdn(10)随粗糙长度的增大而增大,但脊帆强度较大时,Cdn(10)随粗糙长度减小而增大。造成不同变化趋势的主要原因是：对应不同脊帆强度与粗糙长度,摩拖曳力和形拖曳力在冰-气总拖曳力中相对优势地位发生变化,即对应较小的脊帆强度,摩拖曳力占优势地位,而对应较大的脊帆强度,形拖曳力占优势地位。本项工作有助于推动海冰动力学模式、热力-动力模式的改进和完善。
As the most important characteristics of the underlying surface in Polar Regions, sea ice has a significantly effect on the global atmosphere, ocean circulations, and climate change. Meanwhile, as one of the important characteristics of the sea ice surface, pressure ridges are the main factor for the estimations of the momentum and thermal transfer between the atmosphere and sea ice, as well as between the ocean and sea ice, ice mass and thickness. On the background of the thermodynamic process of sea ice, and characteristics of morphology and dynamics of pressure ridges, based on the measured sea ice temperature during the Second China Arctic Research Expedition and elevations of sea ice surface in the Weddell Sea measured during the Winter Weddell Outflow Study2006by the Germany Alfred Wegener Institute for Polar and Marine Research, the optimization methods, numerical computation for partial differential equations, and probability theory and mathematical statistics are used to identify the thermodynamic parameters and analyze the parameters of morphology and dynamics of pressure ridges. The main content and contributions are as follows.
1. For the thermodynamic process of the sea ice in the Arctic, a parabolic distributed parameter system is established to describe the thermodynamic process of sea ice. L2theory for partial equations is used to prove the existence and uniqueness of the weak solution of the system and the continuous dependence of this solution on the identified parameters. A non-overlapped domain decomposition method is applied to decompose the time-dependent domain to three sub-domains of snow, ice and sea water, and the continuous condition is introduced at all interfaces to make each sub-domain smooth. Some important properties of the system and its weak solution are analyzed by optimization theory and methods. An optimal model with state constraints is presented with the thicknesses of snow and sea ice as identified parameters, and the deviation between the calculated and the measured sea ice temperature as the performance criterion. The existence of the optimal parameter is proved and the optimal conditions are derived. Numerical simulation is carried out based on the temperature of snow, ice and water measured during the Second China Arctic Research Expedition, and the results not only reflect the variability of sea ice temperature in time and space domains, but also agree well with the observed temperatures.
2. Ice surface elevation profiles measured during Winter Weddell Outflow Study are used to investigate the morphology and distribution of pressure ridges in the northwestern Weddell Sea. To search effective methods for the determination of the cutoff height and the clustering of pressure ridges, an statistical optimal model with nonlinear constraint is presented with the cutoff height as identified parameter, and the deviation between the theoretical and the measured ridge height/spacing distributions as the performance criterion. The obtained optimal cutoff height is then used to separate pressure ridges from other sea ice surface undulations. Next, for the defects of the traditional k means clustering algorithm, an improved k means clustering algorithm is presented to cluster the measured profiles with the ridging intensity (the ratio of mean ridge height to mean spacing), and which are clustered into three regimes. These three ice regimes coincided closely with distinct sea ice regions identified in a satellite radar image. The statistical characteristics of each regime are analyzed and the influences of the ridging intensity on the ridge height and spacing distributions are also discussed. The correlations between the morphology parameters are also discussed.
3. Wind drag is parted into two components according to the drag partition theory:form drag on pressure ridges and the skin drag over rough sea ice surface. The parameterization of form drag on pressure ridges and its contribution to the total drag and air-ice drag coefficient at a reference height of10m under a neutral stability condition are improved by the morphology parameters and distributions of pressure ridges, and the variations of them with increasing ridging intensity and roughness length are discussed. The results revealed that, for the compacted ice field, form drag on ridges and its contribution to total drag both increase with ridging intensity, while decrease with increasing roughness length. There is an increasing trend of the air-ice drag coefficient Cdn(10) with increasing ridging intensity. Meanwhile, Cdn(10) increases for the smaller ridging intensities, whereas decreases for the larger ridging intensity, with increasing roughness length, which is mainly attributed to the change of dominance of form drag on pressure ridges and skin drag over rough ice surface:the form drag on pressure ridges becomes dominant only when ridging intensity is extremely large, while the skin drag over rough ice surface is the dominant component for the profiles with the relative lower ridging intensity. This work will push the study of the sea ice thermodynamic and dynamic models.
引文
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