HEWITT, HOETING, DONE, AND TOWLER Figure 3: Estimated teleconnection effects ˆ α $^{′}$( s , 1) for EOF 1 ψ$_{1}$ : D$_{Y}$ → $_{R}$. The overall patterns yield similar interpretations as those made with the Figure 2 exploratory plots, however, the RESP model reduces the regions in which evidence exists for significant tele- connection. Significant teleconnection effects, as determined using 95% highest posterior density intervals, are highlighted. teleconnection likely involves non-linear relationships and additional variables or interactions. Posterior estimates for the transformed remote effects { α $^{′}$( s , 1) : s ∈ D$_{Y}$ } associated with ψ$_{1}$ : D$_{Y}$ → R (Figure 3) largely match the exploratory pointwise correlations between P ( s , t ) and a$_{1}$ ( t ) found in the exploratory plot (Figure 2), indicating the RESP model (3) is capturing known Colorado teleconnections. Fewer locations have significant teleconnection, however, as the estimates incorporate more uncertainty due to spatial correlation; significance is determined with respect to evaluating highest posterior density intervals, separately for each location s ∈ D$_{Y}$ . Leave-one-out cross-validation scores demonstrate the RESP model benefits from including remote covariates and offers improvement over comparison models in the intended prediction- like setting of perfect prognosis downscaling (Figure 4). The RESP and comparison mod- els are trained on all but one year of available data, then used to predict the responses 3.4.2 Model validation 22