TY - JOUR

T1 - Correlation Models for Temperature Fields

AU - North, Gerald R.

AU - Wang, Jue

AU - Genton, Marc G.

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: We acknowledge partial support from both the Harold J. Haynes Endowment at Texas A&M University and NSF Grants CMG ATM-0620624 and DMS-1007504. This publication is based in part on work supported by Award KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2011/5/16

Y1 - 2011/5/16

N2 - 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 of the governing equation is just that of the simple energy balance climate models, which have a long history in 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.

AB - 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 of the governing equation is just that of the simple energy balance climate models, which have a long history in 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.

UR - http://hdl.handle.net/10754/623528

UR - https://journals.ametsoc.org/jcli/article/24/22/5850/33296/Correlation-Models-for-Temperature-Fields

UR - http://www.scopus.com/inward/record.url?scp=79961090651&partnerID=8YFLogxK

U2 - 10.1175/2011jcli4199.1

DO - 10.1175/2011jcli4199.1

M3 - Article

AN - SCOPUS:79961090651

VL - 24

SP - 5850

EP - 5862

JO - Journal of Climate

JF - Journal of Climate

SN - 0894-8755

IS - 22

ER -