Ruelle-Pollicott Resonances of Stochastic Systems in Reduced State Space. Part II: Stochastic Hopf Bifurcation

The spectrum of the generator (Kolmogorov operator) of a diffusion process, referred to as the Ruelle-Pollicott (RP) spectrum, provides a detailed characterization of correlation functions and power spectra of stochastic systems via decomposition formulas in terms of RP resonances. Stochastic analysis techniques relying on the theory of Markov semigroups for the study of the RP spectrum and a rigorous reduction method is presented in Part I. This framework is here applied to study a stochastic Hopf bifurcation in view of characterizing the statistical properties of nonlinear oscillators perturbed by noise, depending on their stability. In light of the H\"ormander theorem, it is first shown that the geometry of the unperturbed limit cycle, in particular its isochrons, is essential to understand the effect of noise and the phenomenon of phase diffusion. In addition, it is shown that the spectrum has a spectral gap, even at the bifurcation point, and that correlations decay exponentially fast. Explicit small-noise expansions of the RP eigenvalues and eigenfunctions are then obtained, away from the bifurcation point, based on the knowledge of the linearized deterministic dynamics and the characteristics of the noise. These formulas allow one to understand how the interaction of the noise with the deterministic dynamics affect the decay of correlations. Numerical results complement the study of the RP spectrum at the bifurcation, revealing useful scaling laws. The analysis of the Markov semigroup for stochastic bifurcations is thus promising in providing a complementary approach to the more geometric random dynamical system approach. This approach is not limited to low-dimensional systems and the reduction method presented in part I is applied to a stochastic model relevant to climate dynamics in part III

Observed Tightening of Tropical Ascent in Recent Decades and Linkage to Regional Precipitation Changes

Climate models predict that the tropical ascending region should tighten under global warming, but observational quantification of the tightening rate is limited. Here we show that the observed spatial extent of the relatively moist, rainy and cloudy regions in the tropics associated with large‐scale ascent has been decreasing at a rate of −1%/decade (−5%/K) from 1979 to 2016, resulting from combined effects of interdecadal variability and anthropogenic forcings, with the former contributing more than the latter. The tightening of tropical ascent is associated with an increase in the occurrence frequency of extremely strong ascent, leading to an increase in the average precipitation rate in the top 1% of monthly rainfall in the tropics. At the margins of the convective zones such as the Southeast Amazonia region, the contraction of large‐scale ascent is related to a long‐term drying trend about −3.2%/decade in the past 38 years

Short Warm Distribution Tails Accelerate the Increase of Humid-Heat Extremes Under Global Warming

Humid-heat extremes threaten human health and are increasing in frequency with global warming, so elucidating factors affecting their rate of change is critical. We investigate the role of wet-bulb temperature (TW) frequency distribution tail shape on the rate of increase in extreme TW threshold exceedances under 2°C global warming. Results indicate that non-Gaussian TW distribution tails are common worldwide across extensive, spatially coherent regions. More rapid increases in the number of days exceeding the historical 95th percentile are projected in locations with shorter-than-Gaussian warm side tails. Asymmetry in the specific humidity distribution, one component of TW, is more closely correlated with TW tail shape than temperature, suggesting that humidity climatology strongly influences the rate of future changes in TW extremes. Short non-Gaussian TW warm tails have notable implications for dangerous humid-heat in regions where current-climate TW extremes approach human safety limits

El Niño Dynamics

Bringer of storms and droughts, the El Niño∕Southern Oscillation results from the complex, sometimes chaotic interplay of ocean and atmosphere

El Niño Dynamics

Bringer of storms and droughts, the El Niño∕Southern Oscillation results from the complex, sometimes chaotic interplay of ocean and atmosphere

High dimensional decision dilemmas in climate models

An important source of uncertainty in climate models is linked to the calibration of model parameters. Interest in systematic and automated parameter optimization procedures stems from the desire to improve the model climatology and to quantify the average sensitivity associated with potential changes in the climate system. Building upon on the smoothness of the response of an atmospheric circulation model (AGCM) to changes of four adjustable parameters, Neelin et al. (2010) used a quadratic metamodel to objectively calibrate the AGCM. The metamodel accurately estimates global spatial averages of common fields of climatic interest, from precipitation, to low and high level winds, from temperature at various levels to sea level pressure and geopotential height, while providing a computationally cheap strategy to explore the influence of parameter settings. Here, guided by the metamodel, the ambiguities or dilemmas related to the decision making process in relation to model sensitivity and optimization are examined. Simulations of current climate are subject to considerable regional-scale biases. Those biases may vary substantially depending on the climate variable considered, and/or on the performance metric adopted. Common dilemmas are associated with model revisions yielding improvement in one field or regional pattern or season, but degradation in another, or improvement in the model climatology but degradation in the interannual variability representation. Challenges are posed to the modeler by the high dimensionality of the model output fields and by the large number of adjustable parameters. The use of the metamodel in the optimization strategy helps visualize trade-offs at a regional level, e.g., how mismatches between sensitivity and error spatial fields yield regional errors under minimization of global objective functions