Reduction methods in climate dynamics—A brief review

Currently the number of reduction methods used in practice in climate applications is vast and tends to be difficult to access for researchers searching for an overview of the area. In this work, we review a range of reduction methods that have been, or may be useful for connecting models of the Earth's climate system of differing complexity. We particularly focus on methods where rigorous reduction is possible. We aim to highlight the main mathematical ideas of each reduction method and also provide several benchmark examples for the reduction from climate modelling. In particular, our goal is to provide a broad overview of available methods.