Stochastic forcing of quasi-geostrophic eddies

1996 ◽  
pp. 381-395 ◽  
Author(s):  
Peter Müller
Keyword(s):  
Stochastic Forcing

scholarly journals Almost conservation laws for stochastic nonlinear Schrödinger equations

2021 ◽  
Author(s):  
Kelvin Cheung ◽  
Guopeng Li ◽  
Tadahiro Oh
Keyword(s):  
Conservation Laws ◽  
Stopping Time ◽  
Energy Space ◽  
Stochastic Forcing ◽  
Time Dynamics ◽  
Nonlinear Schrödinger ◽  
Time Argument ◽  
Cubic Nonlinear Schrödinger Equation ◽  
Stochastic Setting ◽  
Ito's Lemma

AbstractIn this paper, we present a globalization argument for stochastic nonlinear dispersive PDEs with additive noises by adapting the I-method (= the method of almost conservation laws) to the stochastic setting. As a model example, we consider the defocusing stochastic cubic nonlinear Schrödinger equation (SNLS) on $${\mathbb {R}}^3$$ R 3 with additive stochastic forcing, white in time and correlated in space, such that the noise lies below the energy space. By combining the I-method with Ito’s lemma and a stopping time argument, we construct global-in-time dynamics for SNLS below the energy space.

scholarly journals Inverse-square law between time and amplitude for crossing tipping thresholds

2019 ◽  
Vol 475 (2222) ◽  
pp. 20180504 ◽  
Author(s):  
Paul Ritchie ◽  
Özkan Karabacak ◽  
Jan Sieber
Keyword(s):  
Dynamical System ◽  
Feedback Loop ◽  
Tipping Point ◽  
Dimensional System ◽  
Stochastic Forcing ◽  
Inverse Square Law ◽  
System A ◽  
Asymptotic Expressions ◽  
Higher Dimensional ◽  
Random Disturbances

A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the threshold. We derive a simple criterion that relates how far the parameter exceeds the tipping threshold maximally and how long the parameter stays above the threshold to avoid tipping in an inverse-square law to observable properties of the dynamical system near the fold. For the case when the dynamical system is subject to stochastic forcing we give an approximation to the probability of tipping if a parameter changing in time reverses near the tipping point. The derived approximations are valid if the parameter change in time is sufficiently slow. We demonstrate for a higher-dimensional system, a model for the Indian summer monsoon, how numerically observed escape from the equilibrium converge to our asymptotic expressions. The inverse-square law between peak of the parameter forcing and the time the parameter spends above a given threshold is also visible in the level curves of equal probability when the system is subject to random disturbances.

Dynamics of Interdecadal Climate Variability: A Historical Perspective*

2012 ◽  
Vol 25 (6) ◽  
pp. 1963-1995 ◽  
Author(s):  
Zhengyu Liu
Keyword(s):  
Climate Variability ◽  
Time Scale ◽  
Ocean Dynamics ◽  
Interdecadal Variability ◽  
Driving Mechanism ◽  
Stochastic Forcing ◽  
The Pacific ◽  
Ocean Atmosphere ◽  
Almost All ◽  
Interdecadal Climate Variability

Abstract The emerging interest in decadal climate prediction highlights the importance of understanding the mechanisms of decadal to interdecadal climate variability. The purpose of this paper is to provide a review of our understanding of interdecadal climate variability in the Pacific and Atlantic Oceans. In particular, the dynamics of interdecadal variability in both oceans will be discussed in a unified framework and in light of historical development. General mechanisms responsible for interdecadal variability, including the role of ocean dynamics, are reviewed first. A hierarchy of increasingly complex paradigms is used to explain variability. This hierarchy ranges from a simple red noise model to a complex stochastically driven coupled ocean–atmosphere mode. The review suggests that stochastic forcing is the major driving mechanism for almost all interdecadal variability, while ocean–atmosphere feedback plays a relatively minor role. Interdecadal variability can be generated independently in the tropics or extratropics, and in the Pacific or Atlantic. In the Pacific, decadal–interdecadal variability is associated with changes in the wind-driven upper-ocean circulation. In the North Atlantic, some of the multidecadal variability is associated with changes in the Atlantic meridional overturning circulation (AMOC). In both the Pacific and Atlantic, the time scale of interdecadal variability seems to be determined mainly by Rossby wave propagation in the extratropics; in the Atlantic, the time scale could also be determined by the advection of the returning branch of AMOC in the Atlantic. One significant advancement of the last two decades is the recognition of the stochastic forcing as the dominant generation mechanism for almost all interdecadal variability. Finally, outstanding issues regarding the cause of interdecadal climate variability are discussed. The mechanism that determines the time scale of each interdecadal mode remains one of the key issues not understood. It is suggested that much further understanding can be gained in the future by performing specifically designed sensitivity experiments in coupled ocean–atmosphere general circulation models, by further analysis of observations and cross-model comparisons, and by combining mechanistic studies with decadal prediction studies.

scholarly journals The Linear Response of ENSO to the Madden–Julian Oscillation

2005 ◽  
Vol 18 (13) ◽  
pp. 2441-2459 ◽  
Author(s):  
J. Zavala-Garay ◽  
C. Zhang ◽  
A. M. Moore ◽  
R. Kleeman
Keyword(s):  
Large Fraction ◽  
Surface Wind ◽  
Low Frequency ◽  
Coupled Model ◽  
Cumulative Effect ◽  
Enso Event ◽  
Kelvin Waves ◽  
Madden Julian Oscillation ◽  
Coupled Models ◽  
Stochastic Forcing

Abstract The possibility that the tropical Pacific coupled system linearly amplifies perturbations produced by the Madden–Julian oscillation (MJO) is explored. This requires an estimate of the low-frequency tail of the MJO. Using 23 yr of NCEP–NCAR reanalyses of surface wind and Reynolds SST, we show that the spatial structure that dominates the intraseasonal band (i.e., the MJO) also dominates the low-frequency band once the anomalies directly related to ENSO have been removed. This low-frequency contribution of the intraseasonal variability is not included in most ENSO coupled models used to date. Its effect in a coupled model of intermediate complexity has, therefore, been studied. It is found that this “MJO forcing” (τMJO) can explain a large fraction of the interannual variability in an asymptotically stable version of the model. This interaction is achieved via linear dynamics. That is, it is the cumulative effect of individual events that maintains ENSOs in this model. The largest coupled wind anomalies are initiated after a sequence of several downwelling Kelvin waves of the same sign have been forced by τMJO. The cumulative effect of the forced Kelvin waves is to persist the (small) SST anomalies in the eastern Pacific just enough for the coupled ocean–atmosphere dynamics to amplify the anomalies into a mature ENSO event. Even though τMJO explains just a small fraction of the energy contained in the stress not associated with ENSO, a large fraction of the modeled ENSO variability is excited by this forcing. The characteristics that make τMJO an optimal stochastic forcing for the model are discussed. The large zonal extent is an important factor that differentiates the MJO from other sources of stochastic forcing.

scholarly journals North Atlantic variability driven by stochastic forcing in a simple model

2012 ◽  
Vol 64 (1) ◽  
pp. 18695 ◽  
Author(s):  
Rebecca Legatt ◽  
Igor V. Polyakov ◽  
UmaS. Bhatt ◽  
Xiangdong Zhang ◽  
Roman V. Bekryaev
Keyword(s):  
Simple Model ◽  
North Atlantic ◽  
Stochastic Forcing ◽  
North Atlantic Variability

Ensemble Data Assimilation Using a Unified Representation of Model Error

2015 ◽  
Vol 144 (1) ◽  
pp. 213-224 ◽  
Author(s):  
Chiara Piccolo ◽  
Mike Cullen
Keyword(s):  
Data Assimilation ◽  
Covariance Structure ◽  
Model Error ◽  
Model Errors ◽  
Stochastic Forcing ◽  
Ensemble Forecasts ◽  
Verification Methods ◽  
Physically Based ◽  
Set Up ◽  
Initial Uncertainty

Abstract A natural way to set up an ensemble forecasting system is to use a model with additional stochastic forcing representing the model error and to derive the initial uncertainty by using an ensemble of analyses generated with this model. Current operational practice has tended to separate the problems of generating initial uncertainty and forecast uncertainty. Thus, in ensemble forecasts, it is normal to use physically based stochastic forcing terms to represent model errors, while in generating analysis uncertainties, artificial inflation methods are used to ensure that the analysis spread is sufficient given the observations. In this paper a more unified approach is tested that uses the same stochastic forcing in the analyses and forecasts and estimates the model error forcing from data assimilation diagnostics. This is shown to be successful if there are sufficient observations. Ensembles used in data assimilation have to be reliable in a broader sense than the usual forecast verification methods; in particular, they need to have the correct covariance structure, which is demonstrated.

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