Correlation Models for Temperature Fields
Correlation Models for Temperature Fields
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温度场的相关模型
DOI：
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发表时间：
2011
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通讯作者：
M. Genton
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作者：
G. North;Jue Wang;M. Genton
本文推导了由白噪声驱动的阻尼扩散方程控制的发展随机场的空间相关性的一些解析形式，该方程在时间上是自回归阶1，在空间上是自回归阶2。这项研究认为，二维平面和表面的一个球，这两个都已经研究过，但在这里的时间被引入到这个问题。这样的模型具有有限的特征长度（大致为自相关福尔斯下降到1/e的间隔）和弛豫时间尺度。特别地，场的特定时间傅立叶分量的特征长度随着特定分量的频率减小而增加到有限值。给出了近似解析的计算公式。一个潜在的应用是表面温度场的相关结构和大面积平均值的估计，这取决于原始数据流如何被过滤成傅立叶频率的分布（例如，移动平均、低通或窄带）。控制方程的形式与简单的能量平衡气候模式一样，在气候研究中有着悠久的历史。从气候模型的推导提供的物理动机提供了一些启发式的呼吁的方法，并建议扩展的工作，以非均匀的情况下。
This paper presents derivations of some analytical forms for spatial correlations of evolving random fields governed by a white-noise-driven damped diffusion equation that is the analog of autoregressive order 1 in time and autoregressive order 2 in space. The study considers the two-dimensional plane and the surface of a sphere, both of which have been studied before, but here time is introduced to the problem. Such models have a finite characteristic length (roughly the separation at which the autocorrelation falls to 1/e) and a relaxation time scale. In particular, the characteristic length of a particular temporal Fourier component of the field increases to a finite value as the frequency of the particular component decreases. Some near-analytical formulas are provided for the results. A potential application is to the correlation structure of surface temperature fields and to the estimation of large area averages, depending on how the original datastream is filtered into a distribution of Fourier frequencies (e.g., moving average, low pass, or narrow band). The form ofthegoverningequationisjustthatofthesimpleenergybalanceclimatemodels,whichhavealonghistoryin climate studies. The physical motivation provided by the derivation from a climate model provides some heuristic appeal to the approach and suggests extensions of the work to nonuniform cases.