# Regularized Spatial Maximum Covariance Analysis

## TL;DR

This paper introduces a regularized approach to maximum covariance analysis in climate studies, enhancing interpretability of coupled spatial patterns through smoothness and sparsity constraints, with an efficient algorithm for implementation.

## Contribution

It proposes a novel regularization method for MCA that improves pattern interpretability by incorporating spatial smoothness and sparsity, solved via an efficient ADMM algorithm.

## Key findings

- Enhanced interpretability of coupled climate patterns.
- Successful application to precipitation and sea surface temperature data.
- Demonstrated efficiency of the proposed algorithm.

## Abstract

In climate and atmospheric research, many phenomena involve more than one meteorological spatial processes covarying in space. To understand how one process is affected by another, maximum covariance analysis (MCA) is commonly applied. However, the patterns obtained from MCA 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 precipitations in east Africa are affected by sea surface temperatures in the Indian Ocean.