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

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

Kinematic vorticity number - a tool for estimating vortex sizes and circulations

The influence of extratropical vortices on a global scale is mainly characterised by their size and by the magnitude of their circulation. However, the determination of these properties is still a great challenge since a vortex has no clear delimitations but is part of the flow field itself. In this work, we introduce a kinematic vortex size determination method based on the kinematic vorticity number Wk to atmospheric flows. Wk relates the local rate-of-rotation to the local rate-of-deformation at every point in the field and a vortex core is identified as a simply connected region where the rotation prevails over the deformation. Additionally, considering the sign of vorticity in the extended Wk-method allows to identify highs and lows in different vertical layers of the atmosphere and to study vertical as well as horizontal vortex interactions. We will test the Wk-method in different idealised 2-D (superposition of two lows/low and jet) and real 3-D flow situations (winter storm affecting Europe) and compare the results with traditional methods based on the pressure and the vorticity fields. In comparison to these traditional methods, the Wk-method is able to extract vortex core sizes even in shear-dominated regions that occur frequently in the upper troposphere. Furthermore, statistics of the size and circulation distributions of cyclones will be given. Since the Wk-method identifies vortex cores, the identified radii are subsynoptic with a broad peak around 300-500km at the 1000 hPa level. However, the total circulating area is not only restricted to the core. In general, circulations are in the order of 107m2/s with only a few cyclones in the order of 108m2/s

Three-dimensional potential vorticity structures for extreme precipitation events on the convective scale

Three-dimensional potential vorticity (PV) structures on the convective scale during extreme precipitation events are investigated. Using the high resolution COSMO-REA2 data set, 3D composites of the PV, with and without Coriolis parameter and related variables, are evaluated for different classes of precipitation intensity. The development of a significant horizontal dipole structure in the immediate vicinity of the precipitation maximum and the updraft can be explained by the twisting term in the vorticity equation. This is because the vorticity equation is proportional to the PV equation for strong convective processes. This theoretical is important on the convective scale without the consideration of the Coriolis effect, which is a typical characteristic on the synoptic scale. In accordance to previous studies, the horizontal PV dipole is statistically confirmed by 3D composites of the PV and corresponding variables. We show that the dipole structures are especially distinct for the relative PV without Coriolis parameter and the relative vorticity. On the convective scale, the thermodynamical sources and sinks of the potential vorticity indicate the diabatic processes that are related to conservative vortex dynamics via the proportionality of the diabatic heating and the vertical velocity. This work confirms that the PV equation is an important tool in atmospheric dynamics that unifies the thermodynamical processes as well as the dynamical processes into one scalar

blocking events and the stability of the polar vortex

The present study investigates non-linear dynamics of atmospheric flow phenomena on different scales as interactions of vortices. Thereby, we apply the idealised, two-dimensional concept of point vortices considering two important issues in atmospheric dynamics. First, we propose this not widely spread concept in meteorology to explain blocked weather situations using a three-point vortex equilibrium. Here, a steady state is given if the zonal mean flow is identical to the opposed translational velocity of the vortex system. We apply this concept exemplarily to two major blocked events establishing a new pattern recognition technique based on the kinematic vorticity number to determine the circulations and positions of the interacting vortices. By using reanalysis data, we demonstrate that the velocity of the tripole in a westward direction is almost equal to the westerly flow explaining the steady state of blocked events. Second, we introduce a novel idea to transfer a stability analysis of a vortex equilibrium to the stability of the polar vortex concerning its interaction with the quasi-biennial oscillation (QBO). Here, the point vortex system is built as a polygon ring of vortices around a central vortex. On this way we confirm observations that perturbations of the polar vortex during the QBO east phase lead to instability, whereas the polar vortex remains stable in QBO west phases. Thus, by applying point vortex theory to challenging problems in atmospheric dynamics we show an alternative, discrete view of synoptic and planetary scale motion

Atmospheric blocking types: Frequencies and transitions

Abstract. Stationary, long-lasting blocked weather patterns can lead to extreme conditions such as very high temperatures or heavy rainfall. They are defined by a persistent high pressure system in combination with one or two low pressure systems. The mechanisms for the onset of such weather patterns are still not fully understood. Using a novel method based on the kinematic vorticity number we distinguish between two blocking types, namely High-over-Low and Omega block, in previously-identified blocking periods. Our main goal of this work is to study the temporal evolution of the occurrence probability and the onset, offset, and transition probabilities of blocking on the northern hemisphere. We analyze NCEP-DOE Reanalysis 2 data over the30 year period from 1990 to 2019 in two regions: Euro-Atlantic sector (40° W–30° E) and half northern hemisphere (90° W–90° E). First, we use logistic regression to investigate the temporal development of blocking probabilities depending on years, seasons and months. We find no significant difference in blocking numbers over the 30 year period. But we find large differences in the occurrence probabilities on a monthly basis with strongest increases over the 30 year period in February and March that are compensated by a decrease in December and autumn. Second, we use a Markov model to calculate the transition probabilities for two models: One is composed of two states blocking and no blocking, and another Markov model (three states) that additionally distinguishes between the specific blocking types High-over-Low and Omega blocking as well as of the state no blocking. The description with Markov theory reduces the probability to change from one weather regime to another or to stay within the same regime to a dependency only on the previous time step. Over the 30 year period, we found the largest changes in transition probabilities in the summer season, where the transition probability to Omega blocks increase strongly, while the unblocked state becomes less probable. Hence, Omega blocks become more frequent and stable in summer at the expense of the other states. As a main result, we show that Omega blocking is more likely to occur and more persistent than the High-over-Low blocking pattern

Direct Bayesian model reduction of smaller scale convective activity conditioned on large scale dynamics

Abstract. We pursue a simplified stochastic representation of smaller scale convective activity conditioned on large scale dynamics in the atmosphere. For identifying a Bayesian model describing the relation of different scales we use a probabilistic approach (Gerber and Horenko, 2017) called Direct Bayesian Model Reduction (DBMR). The convective available potential energy (CAPE) is applied as large scale flow variable combined with a subgrid smaller scale time series for the vertical velocity. We found a probabilistic relation of CAPE and vertical up- and downdraft for day and night. The categorization is based on the5 conservation of total probability. This strategy is part of a development process for parametrizations in models of atmospheric dynamics representing the effective influence of unresolved vertical motion on the large scale flows. The direct probabilistic approach provides a basis for further research of smaller scale convective activity conditioned on other possible large scale drivers

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

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

On the algebra and groups of incompressible vortex dynamics

An algebraic representation for 2D and 3D incompressible, inviscid fluid motion based on the continuous Nambu representation of Helmholtz vorticity equation is introduced. The Nambu brackets of conserved quantities generate a Lie algebra. Physically,we introducematrix representations for the components of the linear momentum (2D and 3D), the circulation (2D) and the total flux of vorticity (3D). These quantities form the basis of the vortex-Heisenberg Lie algebra.Applying thematrix commutator to the basismatrices leads to the same physical relations as the Nambu bracket for this quantities expressed classically as functionals. Using the matrix representation of the Lie algebra we derive the matrix and vector representations for the nilpotent vortex-Heisenberg groups that we denote by VH(2) and VH(3). It turns out that VH(2) is a covering group of the classical Heisenberg group for mass point dynamics. VH(3) can be seen as central extension of the abelian group of translations. We further introduce the Helmholtz vortex group V(3), where additionally the angular momentum is included. Regarding application-oriented aspects, the novel matrix representation might be useful for numerical investigations of the group, whereas the vector representation of the group might provide a better process-related understanding of vortex flows. Keywords: Nambu mechanics, fluid dynamics, vorticity equation, algebra (Some figures may appear in colour only in the online journal) ∗Author to whom any correspondence should be addressed. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1751-8121

Using the concept of the Dynamic State Index for a scale-dependent analysis of atmospheric blocking

The present study investigates the phenomenon of atmospheric blocking using a cascade of Dynamic State Indices. The different DSI variants signalize model dependent aspects of atmospheric blockings, which allows for a scale-dependent analysis of the corresponding flow pattern. Starting from the primitive equations, approximations lead to the reduced equations of the quasi-geostrophic model and the further approximated barotropic Rossby model. For each model a corresponding Dynamic State Index can be derived. All DSI variants underlie the same concept, such that the three variants capture the stationary and adiabatic state as well as their local deviations. The DSI variants are investigated in the framework of a case study of the atmospheric blocking phenomenon over the European part of Russia in summer 2010. Two main results are presented: (i) The anticyclone of the block is characterized by a large area with nearly vanishing DSI values in all three models. In contrast, the typical DSI dipoles along the jet that surrounds the block differ, dependent on the level of the model reduction, not only in the spatial extent but also in the amplitude. (ii) The DSI variants shows the difference of the impact of the diabatic processes related to precipitation concerning the back and front side of the high. The amplitudes of the negative mean of DSI values on the back side of the high, respectively the amplitudes of the positive DSI mean on the front side, is larger for the primitive equations than for the quasi-geostrophic model. Thus, the DSI is a unified concept for atmospheric dynamics designed to diagnose the scale-dependent footprints of the steady and adiabatic conditions as well as non-steady and diabatic processes depending on the level of the model reduction