Atmospheric Dynamics - A machine learning approach on the investigation of the scale dependent relation of CAPE and precipitation

Aug 4, 2026

The temporal and spatial, scale-dependent relationship between Convective Available Potential Energy (CAPE) and precipitation is analyzed using the COSMO-REA6 dataset. Standard machine learning models—perceptron, support vector machine, decision tree, random forest, k-nearest neighbor, and a simple kept deep neural network—are compared, with a detailed focus on decision trees. Performance is evaluated across temporal resolutions from 1 to 24 hours and horizontal resolutions from 6 km to 768 km, yielding accuracy near 0.7. Adding the Dynamic State Index (DSI) increases scores overall. A theoretical CAPE–precipitation relation based on Hans Ertel (1933) is proposed for future study, and data-driven methods are positioned as complementary to governing equations.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages11

Reading Time28 min

AccessFree to download

Abstract

Data and machine learning algorithms

Multi-scale evaluation across time and space

Results with DSI as predictor

Theoretical CAPE–precipitation relation and future work

Introduction

Motivation: precipitation predictability and scale effects

Physical background: instability, CAPE, and definitions

Prior studies and rationale for classification

BM©eteor2023olT.Zhe .a(Couthtrib. Atm. Sci.), Vol. 32, No. 6, 487–497 (published online August 17, 2023) Atmospheric Dynamics A machine learning approach on the investigation of the scale dependent relation of CAPE and precipitation Annette Rudolph 1,2∗ and Peter Névir2 1Technische Universität Berlin, Berlin, Germany 2Freie Universität Berlin, Berlin, Germany (Manuscript received January 27, 2022; in revised form March 14, 2023; accepted July 17, 2023) Abstract 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. Keywords: Precipitation, CAPE, DSI, decision tree 1 Introduction Precipitation, its impact and forecast is a present topic in our daily life. But cloud physics is not fully understood leading to uncertainties in the forecast of rainfall. Especially convective precipitation can be very local and the intensity can vary even between different urban districts of one city. Regarding the larger scales, synoptic fronts can be stretched in the order 1000 kilometers. They can be detected on satellite images and their forecasts are quite good. Even though smaller convection can be detected on satellite images too, the exact location of rainfall is hard to predict. From dynamical perspective, precipitation is related to atmospheric instability that is characterized by a large vertical temperature gradient. The relation of extreme precipitation and temperature anomalies is for example shown in Müller et al. (2020) . However, a more accurate parameter that takes the vertical temperature gradient into account and measures hydrostatic instability is the Convective Available Potential Energy, short CAPE, see e.g. Weismanand Klemp (1982), Holton (2004), Khouider (2019) . Assuming adiabatic conditions and that there is no mixing of an air parcel with its environment during ascent, CAPE measures, how much an air parcel can be lifted and how much kinetic energy could be obtained. Let now Tv be the virtual temperature that is approximately ∗Corresponding author: Annette Rudolph, Technsiche Universität, Berlin, e-mail: [annette.rudolph@tu-berlin.de](annette.rudolph@tu-berlin.de) given by Tv ≈ T (1 + 0.61ρρv ) (1.1) with the density of water vapor ρ v and the density of dry air ρ, see e.g. the book of Markowski and Richardson (2011) . Considering a moist air parcel, its virtual temperature is the temperature at which the total pressure and density of the theoretical dry air parcel is equal to the moist air parcel. Following Markowski and Richardson (2011) and expressing the buoyancy B asthe virtual temperature perturbation of a lifted air parcel T divided by the virtual temperature of the environment Tv, CAPE can be deﬁned as follows: CAPE = g 􀀂zZLFECT B dz = g 􀀂zZLFECT TT dz , (1.2) where zLFC is the so-called Level of Free Convection, short LFC. At this h

FAQs

Which machine learning algorithms are compared for relating CAPE and precipitation?

The study compares perceptron, support vector machine, decision tree, random forest, k-nearest neighbor, and a simple deep neural network.

How does the research evaluate scale dependence between CAPE and precipitation?

It tests temporal resolutions from 1 to 24 hours and horizontal resolutions from 6 km up to 768 km, with further focus on decision trees across these scales.

What is the effect of including the Dynamic State Index (DSI)?

Using DSI as an additional predictor leads to an overall increase in the model scores compared with using CAPE-based information alone.

Aug 4, 2026

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