HEWITT, HOETING, DONE, AND TOWLER 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 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 Note that the transformation appears naturally because 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- 12 ∫ D$_{Z}$ z ( r , t ) α ( s , r ) d r =$^{∫}$ D$_{Z}$ K ∑ l =1 a$_{l}$ ( t ) ψ$_{l}$ ( r ) k ∑ j =1 h $^{(}$r , r ∗ j $^{)}$α $^{(}$s , r ∗ j $^{)}$d r = K ∑ l =1 a$_{l}$ ( t ) k ∑ j =1 α $^{(}$s , r ∗ j ) ∫ D$_{Z}$ ψ$_{l}$ ( r ) h $^{(}$r , r ∗ j $^{)}$d r = K ∑ l =1 a$_{l}$ ( t ) α $^{′}$( s , l ) . (13) (12) α $^{′}$( s , l ) = k ∑ j =1 α $^{(}$s , r ∗ j ) ∫ D$_{Z}$ ψ$_{l}$ ( r ) h $^{(}$r , r ∗ j $^{)}$d r . (11) z ( r , t ) = K ∑ l =1 a$_{l}$ ( t ) ψ$_{l}$ ( r ) ,