Using Decision Trees for Data-Driven Process Studies: Application to the MJO

The study of Earth system processes can be defined as the understanding of the causal relationships that drive specific subcomponents, such as cloud formation, within a complex dynamical system. Process studies also explain interactions between subcomponents, such as the feedback between radiative transfer and cloud formation. Process studies are analogous to scale analysis of the full set of partial differential equations. Scale analysis identifies the dominant terms on the right-hand side of the equations for given conditions. This allows for the reduction of the complexity of the initial equations and thus focuses on the problem's essential physics. In other words, process studies allow for determining key variables and the conditions under which they influence a physical system.

The number of observations and model-generated data enables machine-learning techniques to develop models that simulate the numerical solver of the governing differential equations. One such ML technique is decision trees, which connect an unconditional distribution of a target parameter in their root node to a particular outcome at each leaf. The path from the tree's root to a leaf represents a set of conditions of dominant variables that lead to a particular outcome. A path or group of similar paths is thus the numerical equivalent of a scale analysis of the physical system's differential equations.

In this paper, we demonstrate the effectiveness of decision trees as a tool for process studies by focusing on the Madden-Julian Oscillation (MJO). We use observed daily Outgoing Longwave Radiation from NOAA’s CDR and daily and hourly values from the ERA5 reanalysis. We then outline the branches of the decision tree that are most probable during periods when the MJO traverses the Maritime Continent as identified by the RMM index. We finally interpret the branches of the decision tree based on physical arguments. We conclude by discussing the generality of the proposed method.