LAUSR

AbstractThis paper proposes a regularized regression procedure for finding a predictive relation between one variable and a field of other variables. The procedure estimates a linear prediction model under the constraint that the regression coefficients have smooth spatial structure. The smoothness constraint is imposed using a novel approach based on the eigenvectors of the Laplace operator over the domain, which results in a constrained optimization problem equivalent to either ridge regression or least absolute shrinkage and selection operator (LASSO) regression, which can be solved by standard numerical software. In addition, this paper explores an unconventional procedure whereby regression models are estimated from dynamical model output and then verified against observations—the reverse of the traditional order. The methodology is illustrated by constructing statistical prediction models of summer Texas-area temperature based on concurrent Pacific sea surface temperature (SST). None of the regulari...