The design of statistical predictive models for climate data gives rise to some unique challenges due to the high dimensionality and spatio-temporal nature of the datasets, which dictate that models should exhibit parsimony in variable selection. Recently, a class of methods which promote structured sparsity in the model have been developed, which is suitable for this task. In this paper, we prove theoretical statistical consistency of estimators with tree-structured norm regularizers. We consider one particular model, the Sparse Group Lasso (SGL), to construct predictors of land climate using ocean climate variables. Our experimental results demonstrate that the SGL model provides better predictive performance than the current state-of-the-art, remains climatologically interpretable, and is robust in its variable selection.