On the Formation Mechanism of the Seasonal Persistence Barrier

The mechanism of the seasonal persistence barrier (SPB) is studied in the framework of an autoregressive (AR) model. In contrast to the seasonal variance, whose minimum is modulated mainly by the minimum growth rate or noise forcing, the SPB is caused primarily by the declining growth rate or increasing noise forcing, instead of the minimum/maximum of the growth rate or noise forcing. In other words, the SPB is caused by the declining signal-to-noise ratio (SNR) rather than the weakest SNR. In a weakly damped system, the phase of the SPB is delayed from that of declining SNR by about a season. The mechanism is further applied to explain the observed SST variability in the tropical and North Pacific. For the tropical Pacific, the spring SPB could be caused by the decreasing growth rate from September to March and weak annual mean damping rate, instead of the minimum growth rate in spring. Over the North Pacific, the increasing noise forcing from March to June may lead to the summer SPB. Our mechanism provides a null hypothesis for understanding the SPB of climate variability.

Decomposition of the Atlantic Multidecadal Variability in a Historical Climate Simulation

The Atlantic multidecadal variability (AMV) modulates various climate features worldwide with enormous societal and economic implications, including variations in hurricane activity in the Atlantic, sea level, West African and Indian monsoon rainfall, European climate, and hemispheric-scale surface temperature. Leading hypotheses regarding the nature and origin of AMV focus primarily on its links with oceanic and coupled ocean–atmosphere internal variability, and on its response to external forcing. The role of another possible process, that of atmospheric noise forcing of the ocean, has received less attention. This is addressed here by means of historical coupled simulations and diagnostic experiments, which isolate the influences of external and atmospheric noise forcings. Our findings show that external forcing is an important driver of the simulated AMV. They also demonstrate that weather noise is key in driving the simulated internal AMV in the southern part (0°–60°N) of the AMV region, and that weather noise forcing is responsible for up to 10%–20% of the multidecadal internal SST variability in some isolated areas of the subpolar gyre region. Ocean dynamics independent from the weather noise forcing is found to be the dominant cause of multidecadal SST in the northern part of the AMV region.

Unique Ergodicity for a Class of Stochastic Hyperbolic Equations with Additive Space-Time White Noise

In this paper, we consider a certain class of second order nonlinear PDEs with damping and space-time white noise forcing, posed on the d-dimensional torus. This class includes the wave equation for $$d=1$$ d = 1 and the beam equation for $$d\le 3$$ d ≤ 3 . We show that the Gibbs measure is the unique invariant measure for this system. Since the flow does not satisfy the strong Feller property, we introduce a new technique for showing unique ergodicity. This approach may be also useful in situations in which finite-time blowup is possible.

Decomposition of the Atlantic Multidecadal Variability in a historical climate simulation

<div> <div class="gmail-page" title="Page 2"> <div class="gmail-layoutArea"> <div class="gmail-column"> <p>The Atlantic Multidecadal Variability (AMV) modulates various climate features worldwide with enormous societal and economic implications, including variations in hurricane activity in the Atlantic, sea-level changes, West African and Indian monsoon rainfall, European climate, and hemispheric‐ scale surface temperature. Leading hypotheses regarding the nature and origin of AMV focus primarily on its links with oceanic and coupled ocean-atmosphere internal variability, and on its response to external forcing. The role of another possible process, that of atmospheric noise forcing of the ocean, has received less attention. This is addressed here by means of historical coupled simulations and diagnostic experiments, which isolate the influences of external and atmospheric noise forcings. Our findings show that external forcing is an important driver of the simulated AMV. They also demonstrate that weather noise is key in driving the simulated internal AMV in the southern part of the (0o-60oN) AMV region, and that weather noise forcing is responsible for up to 10%-20% of the multidecadal internal SST variability in some isolated areas of the sub-polar gyre region. Ocean dynamics independent from the weather noise forcing is found to be the dominant cause of multidecadal SST in the northern part of the AMV region.</p> </div> </div> </div> </div> <p> </p>

Fundamental Behavior of ENSO Phase Locking

El Niño–Southern Oscillation (ENSO) events tend to peak at the end of the calendar year, a phenomenon called ENSO phase locking. This phase locking is a fundamental ENSO property that is determined by its basic dynamics. The conceptual ENSO recharge oscillator (RO) model is adopted to examine the ENSO phase-locking behavior in terms of its peak time, strength of phase locking, and asymmetry between El Niño and La Niña events. The RO model reproduces the main phase-locking characteristics found in observations, and the results show that the phase locking of ENSO is mainly dominated by the seasonal modulation of ENSO growth/decay rate. In addition, the linear/nonlinear mechanism of ENSO phase preference/phase locking is investigated using RO model. The difference between the nonlinear phase-locking mechanism and linear phase-preference mechanism is largely smoothed out in the presence of noise forcing. Further, the impact on ENSO phase locking from annual cycle modulation of the growth/decay rate, stochastic forcing, nonlinearity, and linear frequency are examined in the RO model. The preferred month of ENSO peak time depends critically on the phase and strength of the seasonal modulation of the ENSO growth/decay rate. Furthermore, the strength of phase locking is mainly controlled by the linear growth/decay rate, the amplitude of seasonal modulation of growth/decay rate, the amplitude of noise, the SST-dependent factor of multiplicative noise, and the linear frequency. The asymmetry of the sharpness of ENSO phase locking is induced by the asymmetric effect of state-dependent noise forcing in El Niño and La Niña events.

On fluctuating momentum exchange in idealised models of air–sea interaction

The dynamics of three local models, for momentum transfer at the air–sea interface, is compared. The models differ by whether or not the ocean velocity is included in the shear calculation applied to the ocean and the atmosphere. All three cases are employed in climate or ocean simulations. Analytic calculations for the models with deterministic and random forcing (white and coloured) are presented. The short-term behaviour is similar in all models, with only small quantitative differences, while the long-term behaviour differs qualitatively between the models. The fluctuation–dissipation relation, which connects the fast atmospheric motion to the slow oceanic dynamics, is established for all models with random forcing. The fluctuation–dissipation theorem, which compares the response to an external forcing to internal fluctuations, is established for a white-noise forcing and a coloured forcing when the phase space is augmented by the forcing variable. Using results from numerical integrations of stochastic differential equations, we show that the fluctuation theorem, which compares the probability of positive to negative fluxes of the same magnitude, averaged over time intervals of varying lengths, holds for the energy gained by the ocean from the atmosphere.

On fluctuating momentum-exchange in idealised models of air-sea interaction

The dynamics of three local models, for momentum transfer at the air-sea interface, is compared. The models differ by whether or not the ocean velocity is included in the shear calculation applied to the ocean and the atmosphere. All three cases are employed in climate or ocean simulations. Analytic calculations for the models with deterministic and random forcing (white and coloured) are presented. The short term behaviour is similar in all models, which only small quantitative differences, while the long-term behaviour differs qualitatively between the models. The fluctuation-dissipation-relation, which connects the fast atmospheric motion to the slow oceanic dynamics, is established for all models with random forcing. The fluctuation-dissipation-theorem, which compares the response to an external forcing to internal fluctuations is established for a white-noise forcing and a coloured forcing when the phase space is augmented by the forcing variable. Using results from numerical integrations of stochastic differential equations it is shown that the fluctuation-theorem, which compares the probability of positive to negative fluxes of the same magnitude, averaged over time-intervals of varying length, holds for the energy gained by the ocean from the atmosphere.

On fluctuating air-sea-interaction in local models: linear theory

The dynamics of three local linear models of air sea-interation commonly employed in climate or ocean simulations is compared. The models differ by whether or not the ocean velocity is included in the shear calculation applied to the ocean and the atmosphere. Analytic calculations for the models with deteministic and random forcing (white and colored) are presented. The short term behavior is similar in all models, which only small quantitative differences, while the longterm behavior differs qualitatively between the models. The fluctuation-dissipation-relation, which connects the fast excitation to the slow dissipation, is establised for all models with random forcing. The fluctuation-dissipation-theorem, which compares the response to an external forcing to internal fluctuations is established for a white-noise forcing and a colored forcing when the phase space is augmented by the forcing variable. Using results from numerical integrations of stochastic differential equations shows that the fluctuation-theorem, which compares the probability of positive to negative fluxes of the same magnitude, averaged over time-intervals of varying length, holds for the energy gained by the ocean from the atmosphere.

A Theory for the Seasonal Predictability Barrier: Threshold, Timing, and Intensity

A theory is developed in a stochastic climate model for understanding the general features of the seasonal predictability barrier (PB), which is characterized by a band of maximum decline in autocorrelation function phase-locked to a particular season. Our theory determines the forcing threshold, timing, and intensity of the seasonal PB as a function of the damping rate and seasonal forcing. A seasonal PB is found to be an intrinsic feature of a stochastic climate system forced by either seasonal growth rate or seasonal noise forcing. A PB is generated when the seasonal forcing, relative to the damping rate, exceeds a modest threshold. Once generated, all the PBs occur in the same calendar month, forming a seasonal PB. The PB season is determined by the decline of the seasonal forcing as well as the delayed response associated with damping. As such, for a realistic weak damping, the PB season is locked close to the minimum SST variance under the seasonal growth-rate forcing, but after the minimum SST variance under the seasonal noise forcing. The intensity of the PB is determined mainly by the amplitude of the seasonal forcing. The theory is able to explain the general features of the seasonal PB of the observed SST variability over the world. In the tropics, a seasonal PB is generated mainly by a strong seasonal growth rate, whereas in the extratropics a seasonal PB is generated mainly by a strong seasonal noise forcing. Our theory provides a general framework for the understanding of the seasonal PB of climate variability.

The Role of Stochastic Forcing in Generating ENSO Diversity

Numerous oceanic and atmospheric phenomena influence El Niño–Southern Oscillation (ENSO) variability, complicating both prediction and analysis of the mechanisms responsible for generating ENSO diversity. Predictability of ENSO events depends on the characteristics of both the forecast initial conditions and the stochastic forcing that occurs subsequent to forecast initialization. Within a linear inverse model framework, stochastic forcing reduces ENSO predictability when it excites unpredictable growth or interference after the forecast is initialized, but also enhances ENSO predictability when it excites optimal initial conditions that maximize deterministic ENSO growth. Linear inverse modeling (LIM) allows for straightforward separation between predictable signal and unpredictable noise and so can diagnose its own skill. While previous LIM studies of ENSO focused on deterministic dynamics, here we explore how noise forcing influences ENSO diversity and predictability. This study identifies stochastic forcing details potentially contributing to the development of central Pacific (CP) or eastern Pacific (EP) ENSO characteristics. The technique is then used to diagnose the relative roles of initial conditions and noise forcing throughout the evolution of several ENSO events. LIM results show varying roles of noise forcing for any given event, highlighting its utility in separating deterministic from noise-forced contributions to the evolution of individual ENSO events. For example, the strong 1982 event was considerably more influenced by noise forcing late in its evolution than the strong 1997 event, which was more predictable with long lead times due to its deterministic growth. Furthermore, the 2014 deterministic trajectory suggests that a strong event in 2014 was unlikely.