Regularized spatial maximum covariance analysis

In climate and atmospheric research, many phenomena involve more than one spatial processes covarying in space. To understand how one process is affected by another, maximum covariance analysis is commonly applied. However, the patterns obtained from maximum covariance analysis may sometimes be difficult to interpret. In this paper, we propose a regularization approach to promote spatial features in dominant coupled patterns by introducing smoothness and sparseness penalties while accounting for their orthogonalities. We develop an efficient algorithm to solve the resulting optimization problem by using the alternating direction method of multipliers. The effectiveness of the proposed method is illustrated by several numerical examples, including an application to study how precipitation in East Africa is affected by sea surface temperatures in the Indian Ocean.