Detecting and Attributing Change in Climate and Complex Systems: Foundations, Green's Functions, and Nonlinear Fingerprints.

Detection and attribution (DA) studies are cornerstones of climate science, providing crucial evidence for policy decisions. Their goal is to link observed climate change patterns to anthropogenic and natural drivers via the optimal fingerprinting method (OFM). We show that response theory for nonequilibrium systems offers the physical and dynamical basis for OFM, including the concept of causality used for attribution.

Gibbs states and Brownian models for coexisting haze and cloud droplets.

Cloud microphysics studies include how tiny cloud droplets grow and become rain. This is crucial for understanding cloud properties like size, life span, and impact on climate through radiative effects. Small weak-updraft clouds near the haze-to-cloud transition are especially difficult to measure and understand.

Optimal parameterizing manifolds for anticipating tipping points and higher-order critical transitions.

A general, variational approach to derive low-order reduced models from possibly non-autonomous systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes more classical notions of invariant or slow manifolds when the breakdown of "slaving" occurs, i.e.

Generic generation of noise-driven chaos in stochastic time delay systems: Bridging the gap with high-end simulations.

Nonlinear time delay systems produce inherently delay-induced periodic oscillations, which are, however, too idealistic compared to observations. We exhibit a unified stochastic framework to systematically rectify such oscillations into oscillatory patterns with enriched temporal variabilities through generic, nonlinear responses to stochastic perturbations. Two paradigms of noise-driven chaos in high dimension are identified, fundamentally different from chaos triggered by parameter-space noise.

Uncovering the Large-Scale Meteorology That Drives Continental, Shallow, Green Cumulus Through Supervised Classification.

One of the major sources of uncertainty in climate prediction results from the limitations in representing shallow cumulus (Cu) in models. Recently, a class of continental shallow convective Cu was shown to share distinct morphological properties and to emerge globally mostly over forests and vegetated areas, thus named . Using machine-learning supervised classification, we identify greenCu fields over three regions, from the tropics to mid- and higher-latitudes, and establish a novel satellite-based data set called , consisting of 1° × 1° sized, high-resolution MODIS images.

Stochastic rectification of fast oscillations on slow manifold closures.

The problems of identifying the slow component (e.g., for weather forecast initialization) and of characterizing slow-fast interactions are central to geophysical fluid dynamics.

Noise-driven topological changes in chaotic dynamics.

Noise modifies the behavior of chaotic systems in both quantitative and qualitative ways. To study these modifications, the present work compares the topological structure of the deterministic Lorenz (1963) attractor with its stochastically perturbed version. The deterministic attractor is well known to be "strange" but it is frozen in time.

Reduced-order models for coupled dynamical systems: Data-driven methods and the Koopman operator.

Providing efficient and accurate parameterizations for model reduction is a key goal in many areas of science and technology. Here, we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal perturbation expansions of the Koopman operator allow us to derive general stochastic parameterizations of weakly coupled dynamical systems.

Efficient reduction for diagnosing Hopf bifurcation in delay differential systems: Applications to cloud-rain models.

By means of Galerkin-Koornwinder (GK) approximations, an efficient reduction approach to the Stuart-Landau (SL) normal form and center manifold is presented for a broad class of nonlinear systems of delay differential equations that covers the cases of discrete as well as distributed delays. The focus is on the Hopf bifurcation as a consequence of the critical equilibrium's destabilization resulting from an eigenpair crossing the imaginary axis. The nature of the resulting Hopf bifurcation (super- or subcritical) is then characterized by the inspection of a Lyapunov coefficient easy to determine based on the model's coefficients and delay parameters.

Data-adaptive harmonic spectra and multilayer Stuart-Landau models.

Harmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure. The corresponding eigenvalues can be grouped per Fourier frequency and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data.

Publisher's Note: Comment on "Nonparametric forecasting of low-dimensional dynamical systems" [Phys. Rev. E 93, 036201 (2016)].

This corrects the article DOI: 10.1103/PhysRevE.93.

Comment on "Nonparametric forecasting of low-dimensional dynamical systems ".

The comparison performed in Berry et al. [Phys. Rev.

Rough parameter dependence in climate models and the role of Ruelle-Pollicott resonances.

Despite the importance of uncertainties encountered in climate model simulations, the fundamental mechanisms at the origin of sensitive behavior of long-term model statistics remain unclear. Variability of turbulent flows in the atmosphere and oceans exhibits recurrent large-scale patterns. These patterns, while evolving irregularly in time, manifest characteristic frequencies across a large range of time scales, from intraseasonal through interdecadal.

Predicting stochastic systems by noise sampling, and application to the El Niño-Southern Oscillation.

Interannual and interdecadal prediction are major challenges of climate dynamics. In this article we develop a prediction method for climate processes that exhibit low-frequency variability (LFV). The method constructs a nonlinear stochastic model from past observations and estimates a path of the "weather" noise that drives this model over previous finite-time windows.