scholarly journals Predictability of large-scale atmospheric motions: Lyapunov exponents and error dynamics

2017 ◽  
Vol 27 (3) ◽  
pp. 032101 ◽  
Author(s):  
Stéphane Vannitsem
Keyword(s):  
Lyapunov Exponents ◽  
Large Scale ◽  
Atmospheric Motions ◽  
Error Dynamics

scholarly journals Improved moist-convective rotating shallow water model and its application to instabilities of hurricane-like vortices

2018 ◽  
Author(s):  
LMD
Keyword(s):  
Tropical Cyclone ◽  
Shallow Water ◽  
Water Vapour ◽  
Large Scale ◽  
Precipitable Water ◽  
Water Model ◽  
Moist Convection ◽  
Shallow Water Model ◽  
Atmospheric Motions ◽  
Rotating Shallow Water

We show how the two-layer moist-convective rotating shallow water model (mcRSW), which proved to be a simple and robust tool for studying effects of moist convection on large-scale atmospheric motions, can be improved by including, in addition to the water vapour, precipitable water, and the effects of vaporisation, entrainment, and precipitation. Thus improved mcRSW becomes cloud-resolving. It is applied, as an illustration, to model the development of instabilities of tropical cyclone-like vortices.

A physically motivated approach for filtering acoustic waves from the equations governing compressible stratified flow

2008 ◽  
Vol 601 ◽  
pp. 365-379 ◽  
Author(s):  
DALE R. DURRAN
Keyword(s):  
Acoustic Waves ◽  
Large Scale ◽  
Mass Conservation ◽  
Simple Expression ◽  
Reference State ◽  
Small Scale ◽  
Sound Waves ◽  
State Equations ◽  
Planetary Scale ◽  
Atmospheric Motions

An incompressibility approximation is formulated for isentropic motions in a compressible stratified fluid by defining a pseudo-density ρ* and enforcing mass conservation with respect to ρ* instead of the true density. Using this approach, sound waves will be eliminated from the governing equations provided ρ* is an explicit function of the space and time coordinates and of entropy. By construction, isentropic pressure perturbations have no influence on the pseudo-density.A simple expression for ρ* is available for perfect gases that allows the approximate mass conservation relation to be combined with the unapproximated momentum and thermodynamic equations to yield a closed system with attractive energy conservation properties. The influence of pressure on the pseudo-density, along with the explicit (x,t) dependence of ρ* is determined entirely by the hydrostatically balanced reference state.Scale analysis shows that the pseudo-incompressible approximation is applicable to motions for which ${\cal M})$2 ≪ min(1,${\cal R})$2, where ${\cal M})$ is the Mach number and ${\cal R}$ the Rossby number. This assumption is easy to satisfy for small-scale atmospheric motions in which the Earth's rotation may be neglected and is also satisfied for quasi-geostrophic synoptic-scale motions, but not planetary-scale waves. This scaling assumption can, however, be relaxed to allow the accurate representation of planetary-scale motions if the pressure in the time-evolving reference state is computed with sufficient accuracy that the large-scale components of the pseudo-incompressible pressure represent small corrections to the total pressure, in which case the full solution to both the pseudo-incompressible and reference-state equations has the potential to accurately model all non-acoustic atmospheric motions.

The dynamics of large scale atmospheric motions

1983 ◽  
Vol 21 (5) ◽  
pp. 1021 ◽  
Author(s):  
James R. Holton
Keyword(s):  
Large Scale ◽  
Atmospheric Motions

scholarly journals Influence of finite-time Lyapunov exponents on winter precipitation over the Iberian Peninsula

2017 ◽  
Vol 24 (2) ◽  
pp. 227-235 ◽  
Author(s):  
Daniel Garaboa-Paz ◽  
Nieves Lorenzo ◽  
Vicente Pérez-Muñuzuri
Keyword(s):  
Iberian Peninsula ◽  
Lyapunov Exponents ◽  
Finite Time ◽  
Large Scale ◽  
Winter Precipitation ◽  
Seasonal Forecasts ◽  
Sea Level Pressure ◽  
Teleconnection Patterns ◽  
Finite Time Lyapunov Exponents ◽  
Eastern Atlantic Ocean

Abstract. Seasonal forecasts have improved during the last decades, mostly due to an increase in understanding of the coupled ocean–atmosphere dynamics, and the development of models able to predict the atmosphere variability. Correlations between different teleconnection patterns and severe weather in different parts of the world are constantly evolving and changing. This paper evaluates the connection between winter precipitation over the Iberian Peninsula and the large-scale tropospheric mixing over the eastern Atlantic Ocean. Finite-time Lyapunov exponents (FTLEs) have been calculated from 1979 to 2008 to evaluate this mixing. Our study suggests that significant negative correlations exist between summer FTLE anomalies and winter precipitation over Portugal and Spain. To understand the mechanisms behind this correlation, summer anomalies of the FTLE have also been correlated with other climatic variables such as the sea surface temperature (SST), the sea level pressure (SLP) or the geopotential. The East Atlantic (EA) teleconnection index correlates with the summer FTLE anomalies, confirming their role as a seasonal predictor for winter precipitation over the Iberian Peninsula.

Routes of Transport across the Antarctic Polar Vortex in the Southern Spring

2012 ◽  
Vol 69 (2) ◽  
pp. 741-752 ◽  
Author(s):  
Alvaro de la Cámara ◽  
Ana M. Mancho ◽  
Kayo Ide ◽  
Encarna Serrano ◽  
Carlos R. Mechoso
Keyword(s):  
Lyapunov Exponents ◽  
Transport Mechanism ◽  
Large Scale ◽  
Lower Stratosphere ◽  
Polar Vortex ◽  
Horizontal Transport ◽  
The Past ◽  
Lobe Dynamics ◽  
Antarctic Polar Vortex ◽  
The Antarctic

Abstract Transport in the lower stratosphere over Antarctica has been studied in the past by means of several approaches, such as contour dynamics or Lyapunov exponents. This paper examines the problem by means of a new Lagrangian descriptor, which is referred to as the function M. The focus is on the southern spring of 2005, which allows for a comparison with previous analyses based on Lyapunov exponents. With the methodology based on the function M, a much sharper depiction of key Lagrangian features is achieved and routes of large-scale horizontal transport across the vortex edge are captured. These results highlight the importance of lobe dynamics as a transport mechanism across the Antarctic polar vortex.

CHAOS IN A NEAR-INTEGRABLE HAMILTONIAN LATTICE

2002 ◽  
Vol 12 (08) ◽  
pp. 1743-1754 ◽  
Author(s):  
VASSILIOS M. ROTHOS ◽  
CHRIS ANTONOPOULOS ◽  
LAMBROS DROSSOS
Keyword(s):  
Lyapunov Exponents ◽  
Numerical Experiments ◽  
Chaotic Dynamics ◽  
Large Scale ◽  
Hamiltonian Structure ◽  
Chaotic Behavior ◽  
Original System ◽  
Homoclinic Orbits ◽  
Hamiltonian Lattice ◽  
Whiskered Tori

We study the chaotic dynamics of a near-integrable Hamiltonian Ablowitz–Ladik lattice, which is N + 2-dimensional if N is even (N + 1, if N is odd) and possesses, for all N, a circle of unstable equilibria at ε = 0, whose homoclinic orbits are shown to persist for ε ≠ 0 on whiskered tori. The persistence of homoclinic orbits is established through Mel'nikov conditions, directly from the Hamiltonian structure of the equations. Numerical experiments which combine space portraits and Lyapunov exponents are performed for the perturbed Ablowitz–Ladik lattice and large scale chaotic behavior is observed in the vicinity of the circle of unstable equilibria in the ε = 0 case. We conjecture that this large scale chaos is due to the occurrence of saddle-center type fixed points in a perturbed 1 d.o.f Hamiltonian to which the original system can be reduced for all N. As ε > 0 increases, the transient character of this chaotic behavior becomes apparent as the positive Lyapunov exponents steadily increase and the orbits escape to infinity.

scholarly journals Climatology of Lyapunov exponents: The influence of atmospheric rivers on large-scale mixing variability

2017 ◽  
Author(s):  
Daniel Garaboa-Paz ◽  
Jorge Eiras-Barca ◽  
Vicente Pérez-Muñuzuri
Keyword(s):  
Lyapunov Exponents ◽  
Large Scale ◽  
Southern Oscillation ◽  
Baroclinic Instability ◽  
Storm Track ◽  
Wind Fields ◽  
Atmospheric Rivers ◽  
Finite Time Lyapunov Exponents ◽  
Large Correlation ◽  
Large Ensembles

Abstract. Large-scale tropospheric mixing and Lagrangian transport properties have been analyzed for a long-term period 1979–2014 in terms of the finite-time Lyapunov exponents (FTLE). Wind fields reanalysis from the European Centre for Medium-Range Weather Forecasts were used to calculate Lagrangian trajectories of large ensembles of particles. The FTLE climatology shows large correlation values with the baroclinic instability growth rate. Larger values of the inter and intra-annual mixing variabilities highlight El Niño Southern Oscillation, the storm track or the Intertropical Convergence Zone among other large-scale structures. As a case study, the role that atmospheric rivers have on the large-scale atmospheric mixing and the precipitation rates observed in the Sahara-Morocco and British Isles regions have been analyzed. Atmospheric rivers contribution to tropospheric mixing is found to decrease from 15 % in Sahara-Morocco to less than 5 % for UK-Ireland regions, in agreement to their contribution to precipitation that is 40 % larger in the former than for the latter region.

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