scholarly journals Applications of large deviation theory in geophysical fluid dynamics and climate science

2021 ◽  
Author(s):  
Vera Melinda Gálfi ◽  
Valerio Lucarini ◽  
Francesco Ragone ◽  
Jeroen Wouters
Keyword(s):  
Fluid Dynamics ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Large Deviation ◽  
Rare Event ◽  
Low Frequency ◽  
Climate Science ◽  
Geophysical Fluid Dynamics ◽  
Large Deviation Theory ◽  
Deviation Theory

AbstractThe climate is a complex, chaotic system with many degrees of freedom. Attaining a deeper level of understanding of climate dynamics is an urgent scientific challenge, given the evolving climate crisis. In statistical physics, many-particle systems are studied using Large Deviation Theory (LDT). A great potential exists for applying LDT to problems in geophysical fluid dynamics and climate science. In particular, LDT allows for understanding the properties of persistent deviations of climatic fields from long-term averages and for associating them to low-frequency, large-scale patterns. Additionally, LDT can be used in conjunction with rare event algorithms to explore rarely visited regions of the phase space. These applications are of key importance to improve our understanding of high-impact weather and climate events. Furthermore, LDT provides tools for evaluating the probability of noise-induced transitions between metastable climate states. This is, in turn, essential for understanding the global stability properties of the system. The goal of this review is manifold. First, we provide an introduction to LDT. We then present the existing literature. Finally, we propose possible lines of future investigations. We hope that this paper will prepare the ground for studies applying LDT to solve problems encountered in climate science and geophysical fluid dynamics.

Laboratory studies of equatorially trapped waves using ferrofluid

1997 ◽  
Vol 338 ◽  
pp. 35-58 ◽  
Author(s):  
DANIEL R. OHLSEN ◽  
PETER B. RHINES
Keyword(s):  
Fluid Dynamics ◽  
Rotation Rate ◽  
Large Scale ◽  
Rossby Waves ◽  
Low Frequency ◽  
Laboratory Studies ◽  
Geophysical Fluid Dynamics ◽  
Vertical Projection ◽  
Planetary Rotation ◽  
Oceanic Flows

We introduce a new technique to model spherical geophysical fluid dynamics in the terrestrial laboratory. The local vertical projection of planetary vorticity, f, varies with latitude on a rotating spherical planet and allows an important class of waves in large-scale atmospheric and oceanic flows. These Rossby waves have been extensively studied in the laboratory for middle and polar latitudes. At the equator f changes sign where gravity is perpendicular to the planetary rotation. This geometry has made laboratory studies of geophysical fluid dynamics near the equator very limited. We use ferrofluid and static magnetic fields to generate nearly spherical geopotentials in a rotating laboratory experiment. This system is the laboratory analogue of those large-scale atmospheric and oceanic flows whose horizontal motions are governed by the Laplace tidal equations. As the rotation rate in such a system increases, waves are trapped to latitudes near the equator and the dynamics can be formulated on the equatorial β-plane. This transition from planetary modes to equatorially trapped modes as the rotation rate increases is observed in the experiments. The equatorial β-plane solutions of non-dispersive Kelvin waves propagating eastward and non-dispersive Rossby waves propagating westward at low frequency are observed in the limit of rotation fast compared to gravity wave speed.

scholarly journals Post-Born corrections to the one-point statistics of (CMB) lensing convergence obtained via large deviation theory

2020 ◽  
Vol 494 (3) ◽  
pp. 3368-3382 ◽  
Author(s):  
Alexandre Barthelemy ◽  
Sandrine Codis ◽  
Francis Bernardeau
Keyword(s):  
Perturbation Theory ◽  
Large Scale ◽  
Large Deviation ◽  
Weak Lensing ◽  
Microwave Background ◽  
Large Deviation Theory ◽  
Straight Line ◽  
Theoretical Predictions ◽  
The One ◽  
Deviation Theory

ABSTRACT Weak lensing of galaxies and cosmic microwave background (CMB) photons through the large-scale structure of the Universe is one of the most promising cosmological probes with upcoming experiments dedicated to its measurements such as Euclid/LSST and CMB Stage 4 experiments. With increasingly precise measurements, there is a dire need for accurate theoretical predictions. In this work, we focus on higher order statistics of the weak-lensing convergence field, namely its cumulants such as skewness and kurtosis and its one-point probability distribution function (PDF), and we quantify using perturbation theory the corrections coming from post-Born effects, meaning beyond the straight-line and independent lens approximations. At first order, two such corrections arise: lens–lens couplings and geodesic deviation. Though the corrections are small for low source redshifts (below a few per cent) and therefore for galaxy lensing, they become important at higher redshifts, notably in the context of CMB lensing, where the non-Gaussianities computed from tree-order perturbation theory are found to be of the same order as the signal itself. We include these post-Born corrections on the skewness in a prediction for the one-point convergence PDF obtained with large deviation theory and successfully test these results against numerical simulations. The modelled PDF is indeed shown to perform better than the per cent for apertures above ∼10 arcmin and typically in the 3σ region around the mean.

scholarly journals Rare Event Analysis for Minimum Hellinger Distance Estimators via Large Deviation Theory

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 386
Author(s):  
Anand N. Vidyashankar ◽  
Jeffrey F. Collamore
Keyword(s):  
Generating Function ◽  
Large Deviation ◽  
Model Misspecification ◽  
Rare Event ◽  
Hellinger Distance ◽  
Asymptotic Distributions ◽  
Event Analysis ◽  
Large Deviation Theory ◽  
Continuity Properties ◽  
Deviation Theory

Hellinger distance has been widely used to derive objective functions that are alternatives to maximum likelihood methods. While the asymptotic distributions of these estimators have been well investigated, the probabilities of rare events induced by them are largely unknown. In this article, we analyze these rare event probabilities using large deviation theory under a potential model misspecification, in both one and higher dimensions. We show that these probabilities decay exponentially, characterizing their decay via a “rate function” which is expressed as a convex conjugate of a limiting cumulant generating function. In the analysis of the lower bound, in particular, certain geometric considerations arise that facilitate an explicit representation, also in the case when the limiting generating function is nondifferentiable. Our analysis involves the modulus of continuity properties of the affinity, which may be of independent interest.

Large deviations in the supercritical branching process

1993 ◽  
Vol 25 (04) ◽  
pp. 757-772 ◽  
Author(s):  
J. D. Biggins ◽  
N. H. Bingham
Keyword(s):  
Distribution Function ◽  
Large Deviations ◽  
Population Size ◽  
Branching Process ◽  
Large Deviation ◽  
Moment Generating Function ◽  
Large Deviation Theory ◽  
Tail Behaviour ◽  
The Moment ◽  
Deviation Theory

The tail behaviour of the limit of the normalized population size in the simple supercritical branching process, W, is studied. Most of the results concern those cases when a tail of the distribution function of W decays exponentially quickly. In essence, knowledge of the behaviour of transforms can be combined with some ‘large-deviation' theory to get detailed information on the oscillation of the distribution function of W near zero or at infinity. In particular we show how an old result of Harris (1948) on the asymptotics of the moment-generating function of W translates to tail behaviour.

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