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tical models, in which—for example—the responses Y ( s , t ) and Y ( s $^{′}$, t ) at distinct spatial locations s , s ′ ∈ D$_{Y}$ are only influenced by distinct covariates x ( s , t ) and x ( s $^{′}$, t ). To model the influence of teleconnection phenomena the RESP model lets the remote covariates z ( r , t ) simultaneously influence the responses Y ( s , t ) and Y ( s $^{′}$, t ). 

Geostatistical modeling conventions use mean zero Gaussian processes to specify the randomness of the unknown, spatially correlated components w ( s , t ) and α ( s , r ), and an independent processes to specify the noise ε ( s , t )—the nugget. We complete the Gaussian process specifications by defining the covariance functions for the spatially correlated com- ponents. Let C$_{w}$ and C$_{α}$ respectively be the covariance functions for w ( s , t ) + ε ( s , t ) and α ( s , r ), where 

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Our model may be developed with any spatial covariance function κ , but here we choose to work with the stationary Mat´ ern covariance 

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for spatial locations u and v , and parameter vector θ = ( σ $^{2}$, ρ, ν ) $^{T}$. The function d ( u , v ) must be an appropriate distance function (e.g., great-circle distances for locations on a sphere), σ 2 > 0 is a scaling parameter, ν > 0 is a smoothness parameter, ρ > 0 is a range parameter, and K$_{ν}$ is the modified Bessel function of the second kind with order ν . In covariance function definitions (5) and (6), 1 represents the indicator function and σ 2 ε represents the variance of the nugget process which we specify to be a collection of independent and identically distributed mean zero Gaussian random variables—i.e., ε ( s , t ) iid ∼ N (0 , σ 2 $_{ε}$) ∀ ( s , t ) ∈ D$_{Y}$ × T . 

While the definitions (5) and (6) for the local and remote covariances C$_{w}$ and C$_{α}$ can 

