Research Interests


Turbulence Closure with Small, Neural Networks:


Stochastic Strange Attractor (Chekroun et al. (2011), Physica D, 240):

Vimeo movie:


Cloud Physics and Stochastic Strange Attractors (Chekroun et al. (2022), Science Advances, 8 (46)):


Vimeo movie:


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Recent Publications

Santos Gutiérrez, Manuel, Mickaël D. Chekroun, and Ilan Koren. Submitted. “Gibbs states and Brownian models for haze and cloud droplets”. arXiv version Abstract
Clouds microphysics describes the formation and evolution of cloud droplets, rain, and ice particles. It is among the most critical factors in determining the cloud's size, lifetime, precipitation, and radiative effect. Among all cloud types, the small clouds, characterized by weak updrafts, that are close to the haze-to-cloud transition pose challenges in measuring them and understanding their properties. They are superabundant but hard to capture by satellites and often falsely regarded as aerosols. Köhler's theory explains droplet activation and their growth by condensation at the earliest stages of cloud development. It fully describes the thermodynamic state of a single drop but falls short when explaining the collective behavior of large populations of particles. This is especially important when the supersaturation pool is limited. We present an analytical framework to extend Köhler's theory to coexisting cloud droplets. Our results suggest hysteresis and asymmetry in the process of droplet activation and deactivation. The turbulent nature of clouds is incorporated into our model formulation as Brownian noise to provide explicit droplet size distributions and activation timescales. The theoretical findings are confronted with experimental data stemming from laboratory clouds created in the Pi convection chamber, suggesting a new way of understanding haze-to-cloud transitions and small cloud formation processes.
Detection and attribution studies have played a major role in shaping contemporary climate science and have provided key motivations supporting global climate policy negotiations. Their goal is to associate unambiguously observed patterns of climate change with anthropogenic and natural forcings acting as drivers through the so-called optimal fingerprinting method. We show here how response theory for nonequilibrium systems provides the physical and dynamical foundations behind optimal fingerprinting for the climate change detection and attribution problem, including the notion of causality used for attribution purposes. We clearly frame assumptions, strengths, and potential pitfalls of the method. Additionally, we clarify the mathematical framework behind the degenerate fingerprinting method that leads to early warning indicators for tipping points. Finally, we extend the optimal fingerprinting method to the regime of nonlinear response. Our findings indicate that optimal fingerprinting for detection and attribution can be applied to virtually any stochastic system undergoing time-dependent forcing.
Chekroun, Mickaël D., Tom Dror, Orit Altaratz, and Ilan Koren. Submitted. “Equations discovery of organized cloud fields: Stochastic generator and dynamical insights”. arXiv's link Abstract

The emergence of organized multiscale patterns resulting from convection is ubiquitous, observed throughout different cloud types. The reproduction of such patterns by general circulation models remains a challenge due to the complex nature of clouds, characterized by processes interacting over a wide range of spatio-temporal scales. The new advances in data-driven modeling techniques have raised a lot of promises to discover dynamical equations from partial observations of complex systems.
This study presents such a discovery from high-resolution satellite datasets of continental cloud fields. The model is made of stochastic differential equations able to simulate with high fidelity the spatio-temporal coherence and variability of the cloud patterns such as the characteristic lifetime of individual clouds or global organizational features governed by convective inertia gravity waves. This feat is achieved through the model's lagged effects associated with convection recirculation times, and hidden variables parameterizing the unobserved processes and variables.

Koren, Ilan, Tom Dror, Orit Altaratz, and Mickaël D. Chekroun. 2024. “Cloud Versus Void Chord Length Distributions (LvL) as a Measure for Cloud Field Organization.” Geophysical Research Letters 51 (11): e2024GL108435. Publisher's Version Abstract
Cloud organization impacts the radiative effects and precipitation patterns of the cloud field. Deviating from randomness, clouds exhibit either clustering or a regular grid structure, characterized by the spacing between clouds and the cloud size distribution. The two measures are coupled but do not fully define each other. Here, we present the deviation from randomness of the cloud- and void-chord length distributions as a measure for both factors. We introduce the LvL representation and an associated 2D score that allow for unambiguously quantifying departure from well-defined baseline randomness in cloud spacing and sizes. This approach demonstrates sensitivity and robustness in classifying cloud field organization types. Its delicate sensitivity unravels the temporal evolution of a single cloud field, providing novel insights into the underlying governing processes.

Conceptual delay models have played a key role in the analysis and understanding of El Niño-Southern Oscillation (ENSO) variability. Based on such delay models, we propose in this work a novel scenario for the fabric of ENSO variability resulting from the subtle interplay between stochastic disturbances and nonlinear invariant sets emerging from bifurcations of the unperturbed dynamics.

To identify these invariant sets we adopt an approach combining Galerkin-Koornwinder (GK) approximations of delay differential equations and center-unstable manifold reduction techniques. In that respect, GK approximation formulas are reviewed and synthesized, as well as analytic approximation formulas of center-unstable manifolds. The reduced systems derived thereof enable us to conduct a thorough analysis of the bifurcations arising in a standard delay model of ENSO. We identify thereby a saddle-node bifurcation of periodic orbits co-existing with a subcritical Hopf bifurcation, and a homoclinic bifurcation for this model. We show furthermore that the computation of unstable periodic orbits (UPOs) unfolding through these bifurcations is considerably simplified from the reduced systems.

These dynamical insights enable us in turn to design a stochastic model whose solutions—as the delay parameter drifts slowly through its critical values—produce a wealth of temporal patterns resembling ENSO events and exhibiting also decadal variability. Our analysis dissects the origin of this variability and shows how it is tied to certain transition paths between invariant sets of the unperturbed dynamics (for ENSO’s interannual variability) or simply due to the presence of UPOs close to the homoclinic orbit (for decadal variability). In short, this study points out the role of solution paths evolving through tipping “points” beyond equilibria, as possible mechanisms organizing the variability of certain climate phenomena.

Chekroun, Mickaël D., H. Liu, K. Srinivasan, and James C. McWilliams. 2024. “The High-Frequency and Rare Events Barriers to Neural Closures of Atmospheric Dynamics.” Journal of Physics: Complexity 5: 025004. Publisher's version Abstract
Recent years have seen a surge in interest for leveraging neural networks to parameterize small-scale or fast processes in climate and turbulence models. In this short paper, we point out two fundamental issues in this endeavor. The first concerns the difficulties neural networks may experience in capturing rare events due to limitations in how data is sampled. The second arises from the inherent multiscale nature of these systems. They combine high-frequency components (like inertia-gravity waves) with slower, evolving processes (geostrophic motion). This multiscale nature creates a significant hurdle for neural network closures. To illustrate these challenges, we focus on the atmospheric 1980 Lorenz model, a simplified version of the Primitive Equations that drive climate models. This model serves as a compelling example because it captures the essence of these difficulties.