Multi-variate factorisation of numerical simulations
Multi-variate factorisation of numerical simulations
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DOI：
10.5194/gmd-14-4307-2021
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发表时间：
2021-07-08
影响因子：
5.1
通讯作者：
Valdes, Paul J.
中科院分区：
文献类型：
--
作者：
Lunt, Daniel J.;Chandan, Deepak;Valdes, Paul J.
因子分解（也称为“因子分离”）广泛用于数值模拟分析。它允许将系统属性的变化归因于与该系统相关的多个变量的变化。有许多可能的因子分解方法;在这里，我们讨论了三个先前提出的已应用于气候建模领域的因子分解：线性因子分解，Stein和Alpert（1993）因子分解和Lunt等人（2012）因子分解。我们表明，当被认为是两个以上的变量，这三种方法都不具备所有四个属性的“唯一性”，“对称性”，“完整性”和“纯度”。在这里，我们扩展了这些因子分解，使它们对任何数量的变量都具有这些属性，从而产生三个因子分解-“线性和”因子分解，“共享相互作用”因子分解和“标度残差”因子分解。我们表明，线性和因式分解和共享的相互作用因式分解减少到相同的情况下，四个或更少的变量，我们推测，这适用于任何数量的变量。我们提出的因式分解的背景下，使用先前提出的因式分解的三个过去的研究结果。
Factorisation (also known as "factor separation") is widely used in the analysis of numerical simulations. It allows changes in properties of a system to be attributed to changes in multiple variables associated with that system. There are many possible factorisation methods; here we discuss three previously proposed factorisations that have been applied in the field of climate modelling: the linear factorisation, the Stein and Alpert (1993) factorisation, and the Lunt et al. (2012) factorisation. We show that, when more than two variables are being considered, none of these three methods possess all four properties of "uniqueness", "symmetry", "completeness", and "purity". Here, we extend each of these factorisations so that they do possess these properties for any number of variables, resulting in three factorisations - the "linear-sum" factorisation, the "shared-interaction" factorisation, and the "scaled-residual" factorisation. We show that the linear-sum factorisation and the shared-interaction factorisation reduce to be identical in the case of four or fewer variables, and we conjecture that this holds for any number of variables. We present the results of the factorisations in the context of three past studies that used the previously proposed factorisations.