Laplacian Eigenfunctions for Climate Analysis
Laplacian Eigenfunctions for Climate Analysis
复制标题
用于气候分析的拉普拉斯特征函数
DOI：
10.1175/jcli-d-15-0049.1
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发表时间：
2015
影响因子：
4.9
通讯作者：
M. Tippett
中科院分区：
文献类型：
--
作者：
T. DelSole;M. Tippett
本文提出了一种在球面上表示一般域中数据的新方法。该方法是基于本征函数的拉普拉斯运营商，形成一个正交的基集，可以通过测量的长度规模。如果想要通过过滤掉小规模的变异性来降低数据集的维数，用拉普拉斯特征函数表示数据是有吸引力的。虽然拉普拉斯特征函数在气候模拟中无处不在，但由于不规则边界的数值困难，它们在任意区域（如大陆）的使用并不常见。利用机器学习和计算科学的最新进展来推导球面上任意区域上的拉普拉斯算子的本征函数。本征函数仅依赖于域的几何形状，因此不需要来自模型或观测的训练数据，这一特征在小样本量中特别有用。另一个新的特点是，该方法产生的真实…
AbstractThis paper proposes a new method for representing data in a general domain on a sphere. The method is based on the eigenfunctions of the Laplace operator, which form an orthogonal basis set that can be ordered by a measure of length scale. Representing data with Laplacian eigenfunctions is attractive if one wants to reduce the dimension of a dataset by filtering out small-scale variability. Although Laplacian eigenfunctions are ubiquitous in climate modeling, their use in arbitrary domains, such as over continents, is not common because of the numerical difficulties associated with irregular boundaries. Recent advances in machine learning and computational sciences are exploited to derive eigenfunctions of the Laplace operator over an arbitrary domain on a sphere. The eigenfunctions depend only on the geometry of the domain and hence require no training data from models or observations, a feature that is especially useful in small sample sizes. Another novel feature is that the method produces rea...