The temporal and spatial scale dependent relation of Convective Available Potential Energy (CAPE) and precipitation is investigated. Using the COSMO-REA6 data set, we ask which of the standard machine learning algorithms: perceptron, support vector machine, decision tree, random forest, k-nearest neighbor and a simple kept deep neural network algorithm can best relate these two variables. Then, we concentrate on decision trees and evaluate the relation of CAPE and precipitation across different scales. We investigate temporal resolutions of 1 hour to 24 hours and horizontal resolutions of 6 km up to 768 km. Regarding ten CAPE and two precipitation classes we find accuracy scores mostly of about 0.7 across all scales. Taking the Dynamic State Index (DSI) as additional predictor into account leads to an overall increase of the scores. We further introduce a theoretical relation of CAPE and precipitation based on the works of Hans Ertel (1933), which will be analyzed in future studies. Today it is natural to tackle complex atmospheric processes using machine learning methods. These data based methods are suggested as additional tool to complement the results gained by the governing equations of atmospheric motion.
