53 research outputs found
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
Nambu representation of an extended Lorenz model with viscous heating
We consider the Nambu and Hamiltonian representations of Rayleigh-Benard
convection with a nonlinear thermal heating effect proportional to the Eckert
number (Ec). The model we use is an extension of the classical Lorenz-63 model
with 4 kinematic and 6 thermal degrees of freedom. The conservative parts of
the dynamical equations which include all nonlinearities satisfy Liouville's
theorem and permit a conserved Hamiltonian H for arbitrary Ec. For Ec=0 two
independent conserved Casimir functions exist, one of these is associated with
unavailable potential energy and is also present in the Lorenz-63 truncation.
This Casimir C is used to construct a Nambu representation of the conserved
part of the dynamical system. The thermal heating effect can be represented
either by a second canonical Hamiltonian or as a gradient (metric) system using
the time derivative of the Casimir. The results demonstrate the impact of
viscous heating in the total energy budget and in the Lorenz energy cycle for
kinetic and available potential energy.Comment: 15 pages, no figur
Comprehensive analysis of tornado statistics in comparison to earthquakes: intensity and temporal behaviour
Tornadoes and earthquakes are characterised by a high variability in their properties concerning intensity, geometric properties and temporal behaviour. Earthquakes are known for power-law behaviour in their intensity (Gutenberg–Richter law) and temporal statistics (e.g. Omori law and interevent waiting times). The observed similarity of high variability of these two phenomena motivated us to compare the statistical behaviour of tornadoes using seismological methods and quest for power-law behaviour. In general, the statistics of tornadoes show power-law behaviour partly coextensive with characteristic scales when the temporal resolution is high (10 to 60 min). These characteristic scales match with the typical diurnal behaviour of tornadoes, which is characterised by a maximum of tornado occurrences in the late afternoon hours. Furthermore, the distributions support the observation that tornadoes cluster in time. Finally, we shortly discuss a possible similar underlying structure composed of heterogeneous, coupled, interactive threshold oscillators that possibly explains the observed behaviour
Scale Dependent Analytical Investigation of the Dynamic State Index Concerning the Quasi-Geostrophic Theory
The Dynamic State Index (DSI) is a scalar diagnostic field that quantifies local deviations from a steady and adiabatic wind solution and thus indicates non-stationarity aswell as diabaticity. The DSI-concept has originally been developed through the Energy-Vorticity Theory based on the full compressible flow equations without regard to the characteristic scale-dependence of many atmospheric processes. But such scaledependent information is often of importance, and particularly so in the context of precipitation modeling: Small scale convective events are often organized in storms, clusters up to “Großwetterlagen” on the synoptic scale. Therefore, a DSI index for the quasi-geostrophic model is developed using (i) the Energy-Vorticity Theory and (ii) showing that it is asymptotically consistent with the original index for the primitive equations. In the last part, using meteorological reanalysis data it is demonstrated on a case study that both indices capture systematically different scale-dependent precipitation information. A spin-off of the asymptotic analysis is a novel non-equilibrium time scale combining potential vorticity and the DSI indices
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
The Dynamic State Index with Moisture and Phase Changes
The dynamic state index (DSI) is a scalar field that combines variational information on the total energy and enstrophy of a flow field with the second law of thermodynamics. Its magnitude is a combined local measure for non-stationarity, diabaticity, and dissipation in the flow, and it has been shown to provide good qualitative indications for the onset and presence of precipitation and the organization of storms.
The index has been derived thus far for ideal fluid models only, however, so that one may expect improved and quantitative insights from a revised definition of the quantity that includes more complex aerothermodynamics. The present paper suggests definitions of the DSI for flows of moist air with phase changes and precipitation
Process-oriented statistical-dynamical evaluation of LM precipitation forecasts
International audienceThe objective of this study is the scale dependent evaluation of precipitation forecasts of the Lokal-Modell (LM) from the German Weather Service in relation to dynamical and cloud parameters. For this purpose the newly designed Dynamic State Index (DSI) is correlated with clouds and precipitation. The DSI quantitatively describes the deviation and relative distance from a stationary and adiabatic solution of the primitive equations. A case study and statistical analysis of clouds and precipitation demonstrates the availability of the DSI as a dynamical threshold parameter. This confirms the importance of imbalances of the atmospheric flow field, which dynamically induce the generation of rainfall
From Metastable to Coherent Sets – time-discretization schemes
Given a time-dependent stochastic process with trajectories x(t) in a space \Omega, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable sets M are defined in space M \subset \Omega, coherent sets M(t) \subset \Omega are defined in space and time. Hence, if we extend the space \Omega by the time-variable t, coherent sets are metastable sets in \Omega \times [0,\infty). This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article we show that these well-established spectral algorithms (like PCCA+) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-time-discretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application
Algebraic construction of a Nambu bracket for the two-dimensional vorticity equation
So far fluid mechanical Nambu brackets have mainly been given on an intuitive
basis. Alternatively an algorithmic construction of such a bracket for the
two-dimensional vorticity equation is presented here. Starting from the
Lie--Poisson form and its algebraic properties it is shown how the Nambu
representation can be explicitly constructed as the continuum limit from the
structure preserving Zeitlin discretization
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
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