Error covariance of a temperature field

• Random variable: T = (T1, …, Tn) where Ti = T(xi,yi)

• Error covariance model:

where pi º (xi,yi).

• Correlations are said to be homogeneous and isotropic since they only depend on the distance between pi and pj.

• Remark: the correlation function can have a non-Gaussian shape. Nevertheless, the probability distribution remains Gaussian.

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