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temperature and Colorado precipitation in Section 3. 

Complex teleconnection patterns are often based on spatial basis function expansions of the remote covariates z ( r , t ). If there exist weights { a$_{l}$ ( t ) : l = 1 , . . . , K ; t ∈ T } such that the remote covariates z ( r , t ) can be written as a linear combination of continuous, time-invariant basis functions { ψ$_{l}$ ( r ) : l = 1 , . . . , K ; r ∈ D$_{Z}$} via 

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then linearity of the integral in (4) and reduced rank approximation (8) can induce a repa- rameterized, reduced-rank teleconnection effect process α $^{′}$( s , l ) for patterns l = 1 , . . . , K by 

<img src='content_image/326896.jpg'>

Note that the transformation appears naturally because 

<img src='content_image/326895.jpg'>

As with the reduced rank approximation (8), the transformation (13) also relates the RESP model to spatially varying coefficient models (1) and has scientific relevance for teleconnec- tion. The deterministic remote covariate weights a$_{l}$ ( t ) and reparameterized remote coeffi- cients α $^{′}$( s , l ) may be collected into the covariate vector z ( t ) and spatially varying effects θ ( s ) in (1). While the covariate weights a$_{l}$ ( t ) suggest a priori selection of teleconnection indices, the reparameterization may be applied after model estimation. The α $^{′}$( s , l ) addi- 

