Earth Science

Submitted
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.
2024
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.
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.
Srinivasan, Kaushik, Mickaël D. Chekroun, and James C. McWilliams. 2024. “Turbulence closure with small, local neural networks: Forced two-dimensional and β-plane flows.” Journal of Advances in Modeling Earth Systems 16 (4): e2023MS003795. Publisher's version Abstract

We parameterize sub-grid scale (SGS) fluxes in sinusoidally forced two-dimensional turbulence on the β-plane at high Reynolds numbers (Re ∼25,000) using simple 2-layer convolutional neural networks (CNN) having only O(1000) parameters, two orders of magnitude smaller than recent studies employing deeper CNNs with 8–10 layers; we obtain stable, accurate, and long-term online or a posteriori solutions at 16× downscaling factors. Our methodology significantly improves training efficiency and speed of online large eddy simulations runs, while offering insights into the physics of closure in such turbulent flows. Our approach benefits from extensive hyperparameter searching in learning rate and weight decay coefficient space, as well as the use of cyclical learning rate annealing, which leads to more robust and accurate online solutions compared to fixed learning rates. Our CNNs use either the coarse velocity or the vorticity and strain fields as inputs, and output the two components of the deviatoric stress tensor, Sd. We minimize a loss between the SGS vorticity flux divergence (computed from the high-resolution solver) and that obtained from the CNN-modeled Sd, without requiring energy or enstrophy preserving constraints. The success of shallow CNNs in accurately parameterizing this class of turbulent flows implies that the SGS stresses have a weak non-local dependence on coarse fields; it also aligns with our physical conception that small-scales are locally controlled by larger scales such as vortices and their strained filaments. Furthermore, 2-layer CNN-parameterizations are more likely to be interpretable.

2023
Liu, Huan, Ilan Koren, Orit Altaratz, and Mickaël D. Chekroun. 2023. “Opposing trends of cloud coverage over land and ocean under global warming.” Atmospheric Chemistry and Physics Discussions 23: 6559–6569. Publisher's Version Abstract
Clouds play a key role in Earth's energy budget and water cycle. Their response to global warming contributes the largest uncertainty to climate prediction. Here, by performing an empirical orthogonal function analysis on 42 years of reanalysis data of global cloud coverage, we extract an unambiguous trend and El-Niño–Southern-Oscillation-associated modes. The trend mode translates spatially to decreasing trends in cloud coverage over most continents and increasing trends over the tropical and subtropical oceans. A reduction in near-surface relative humidity can explain the decreasing trends in cloud coverage over land. Our results suggest potential stress on the terrestrial water cycle and changes in the energy partition between land and ocean, all associated with global warming.
Lucarini, Valerio, and Mickaël D. Chekroun. 2023. “Theoretical tools for understanding the climate crisis from Hasselmann’s programme and beyond.” Nature Review Physics 5: 744-765 . Publisher's link Abstract
Klaus Hasselmann’s revolutionary intuition in climate science was to use the stochasticity associated with fast weather processes to probe the slow dynamics of the climate system. Doing so led to fundamentally new ways to study the response of climate models to perturbations, and to perform detection and attribution for climate change signals. Hasselmann’s programme has been extremely influential in climate science and beyond. In this Perspective, we first summarize the main aspects of such a programme using modern concepts and tools of statistical physics and applied mathematics. We then provide an overview of some promising scientific perspectives that might clarify the science behind the climate crisis and that stem from Hasselmann’s ideas. We show how to perform rigorous and data-driven model reduction by constructing parameterizations in systems that do not necessarily feature a timescale separation between unresolved and resolved processes. We outline a general theoretical framework for explaining the relationship between climate variability and climate change, and for performing climate change projections. This framework enables us seamlessly to explain some key general aspects of climatic tipping points. Finally, we show that response theory provides a solid framework supporting optimal fingerprinting methods for detection and attribution.
2022
Chekroun, Mickaël D., Ilan Koren, Honghu Liu, and Huan Liu. 2022. “Generic generation of noise-driven chaos in stochastic time delay systems: Bridging the gap with high-end simulations.” Science Advances 8 (46): eabq7137. Publisher's Version Abstract

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. Noteworthy is a low-dimensional stretch-and-fold mechanism, leading to stochastic strange attractors exhibiting horseshoe-like structures mirroring turbulent transport of passive tracers. The other is high-dimensional , with noise acting along the critical eigendirection and transmitted to deeperstable modes through nonlinearity, leading to stochastic attractors exhibiting swarm-like behaviors with power-law and scale break properties. The theory is applied to cloud delay models to parameterize missing physics such as intermittent rain and Lagrangian turbulent effects. The stochastically rectified model reproduces with fidelity complex temporal variabilities of open-cell oscillations exhibited by high-end cloud simulations.

Dror, Tom, Vered Silverman, Orit Altaratz, Mickaël D. Chekroun, and Ilan Koren. 2022. “Uncovering the Large-Scale Meteorology That Drives Continental, Shallow, Green Cumulus Through Supervised Classification.” Geophysical Research Letters . Publisher's Version Abstract
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 greenCu. 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 greenCuDb, consisting of 1° × 1° sized, high-resolution MODIS images. Using greenCuDb in conjunction with ERA5 reanalysis data, we create greenCu composites for different regions and reveal that greenCu are driven by similar large-scale meteorological conditions, regardless of their geographical locations throughout the world's continents. These conditions include distinct profiles of temperature, humidity and large-scale vertical velocity. The boundary layer is anomalously warm and moderately humid, and is accompanied by a strong large-scale subsidence in the free troposphere.
2021
Chekroun, Mickaël D., Honghu Liu, and James C. McWilliams. 2021. “Stochastic rectification of fast oscillations on slow manifold closures.” Proc. Natl. Acad. Sci. 118 (48): E2113650118. Publisher's Version Abstract
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. In this study, the related rectification problem of slow manifold closures is addressed when breakdown of slow-to-fast scales deterministic parameterizations occurs due to explosive emergence of fast oscillations on the slow, geostrophic motion. For such regimes, it is shown on the Lorenz 80 model that if 1) the underlying manifold provides a good approximation of the optimal nonlinear parameterization that averages out the fast variables and 2) the residual dynamics off this manifold is mainly orthogonal to it, then no memory terms are required in the Mori–Zwanzig full closure. Instead, the noise term is key to resolve, and is shown to be, in this case, well modeled by a state-independent noise, obtained by means of networks of stochastic nonlinear oscillators. This stochastic parameterization allows, in turn, for rectifying the momentum-balanced slow manifold, and for accurate recovery of the multiscale dynamics. The approach is promising to be further applied to the closure of other more complex slow–fast systems, in strongly coupled regimes.
Dror, Tom, Mickaël D. Chekroun, Ilan Koren, and Orit Altaratz. 2021. “Deciphering organization of GOES-16 green cumulus through the empirical orthogonal function (EOF) lens.” Atmospheric Chemistry and Physics 21: 12261–12272. Publisher's Version Abstract
A subset of continental shallow convective cumulus (Cu) cloud fields has been shown to have distinct spatial properties and to form mostly over forests and vegetated areas, thus referred to as “green Cu” (Dror et al., 2020). Green Cu fields are known to form organized mesoscale patterns, yet the underlying mechanisms, as well as the time variability of these patterns, are still lacking understanding. Here, we characterize the organization of green Cu in space and time, by using data-driven organization metrics and by applying an empirical orthogonal function (EOF) analysis to a high-resolution GOES-16 dataset. We extract, quantify, and reveal modes of organization present in a green Cu field, during the course of a day. The EOF decomposition is able to show the field's key organization features such as cloud streets, and it also delineates the less visible ones, as the propagation of gravity waves (GWs) and the emergence of a highly organized grid on a spatial scale of hundreds of kilometers, over a time period that scales with the field's lifetime. Using cloud fields that were reconstructed from different subgroups of modes, we quantify the cloud street's wavelength and aspect ratio, as well as the GW-dominant period.
2020
Wang, Peng, James C. McWilliams, Yusuke Uchiyama, Mickaël D. Chekroun, and Daling Li Yi. 2020. “Effects of wave streaming and wave variations on nearshore wave-driven circulation.” J. Phys. Oceanograhy 50 (10): 3025-3041. Publisher's Version Abstract

Wave streaming is a near-bottom mean current induced by the bottom drag on surface gravity waves. Wave variations include the variations in wave heights, periods, and directions. Here we use numerical simulations to study the effects of wave streaming and wave variations on the circulation that is driven by incident surface waves. Wave streaming induces an inner-shelf Lagrangian overturning circulation, which links the inner shelf with the surf zone. Wave variations cause along shore-variable wave breaking that produces surf eddies; however, such eddies can be suppressed by wave streaming. Moreover, with passive tracers we show that wave streaming and wave variations together enhance the cross- shelf material transport.

2018
Kondrashov, Dmitri, Mickaël D. Chekroun, and Michael Ghil. 2018. “Data-adaptive harmonic decomposition and prediction of Arctic sea ice extent.” Dynamics and Statistics of the Climate System 3 (1): 1. Publisher's Version Abstract

Decline in the Arctic sea ice extent (SIE) is an area of active scientific research with profound socio-economic implications. Of particular interest are reliable methods for SIE forecasting on subseasonal time scales, in particular from early summer into fall, when sea ice coverage in the Arctic reaches its minimum. Here, we apply the recent data-adaptive harmonic (DAH) technique of Chekroun and Kondrashov, (2017), Chaos, 27 for the description, modeling and prediction of the Multisensor Analyzed Sea Ice Extent (MASIE, 2006–2016) data set. The DAH decomposition of MASIE identifies narrowband, spatio-temporal data-adaptive modes over four key Arctic regions. The time evolution of the DAH coefficients of these modes can be modelled and predicted by using a set of coupled Stuart–Landau stochastic differential equations that capture the modes’ frequencies and amplitude modulation in time. Retrospective forecasts show that our resulting multilayer Stuart–Landau model (MSLM) is quite skilful in predicting September SIE compared to year-to-year persistence; moreover, the DAH–MSLM approach provided accurate real-time prediction that was highly competitive for the 2016–2017 Sea Ice Outlook.

Kondrashov, Dmitri, Mickaël D. Chekroun, and Pavel Berloff. 2018. “Multiscale Stuart-Landau Emulators: Application to Wind-Driven Ocean Gyres.” Fluids 3 (1): 21. Publisher's Version Abstract

The multiscale variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper demonstrates how the data-adaptive harmonic (DAH) decomposition and inverse stochastic modeling techniques introduced in (Chekroun and Kondrashov, (2017), Chaos, 27), allow for reproducing with high fidelity the main statistical properties of multiscale variability in a coarse-grained eddy-resolving ocean flow. This fully-data-driven approach relies on extraction of frequency-ranked time-dependent coefficients describing the evolution of spatio-temporal DAH modes (DAHMs) in the oceanic flow data. In turn, the time series of these coefficients are efficiently modeled by a family of low-order stochastic differential equations (SDEs) stacked per frequency, involving a fixed set of predictor functions and a small number of model coefficients. These SDEs take the form of stochastic oscillators, identified as multilayer Stuart–Landau models (MSLMs), and their use is justified by relying on the theory of Ruelle–Pollicott resonances. The good modeling skills shown by the resulting DAH-MSLM emulators demonstrates the feasibility of using a network of stochastic oscillators for the modeling of geophysical turbulence. In a certain sense, the original quasiperiodic Landau view of turbulence, with the amendment of the inclusion of stochasticity, may be well suited to describe turbulence.

Decadal DAH mode

 

Kondrashov, Dmitri, Mickaël D. Chekroun, Xiaojun Yuan, and Michael Ghil. 2018. “Data-adaptive harmonic decomposition and stochastic modeling of Arctic sea ice.” Advances in Nonlinear Geosciences, A. Tsonis, 179-205. Springer. Publisher's Version Abstract

We present and apply a novel method of describing and modeling complex multivariate datasets in the geosciences and elsewhere. Data-adaptive harmonic (DAH) decomposition identifies narrow-banded, spatio-temporal modes (DAHMs) whose frequencies are not necessarily integer multiples of each other. The evolution in time of the DAH coefficients (DAHCs) of these modes can be modeled using a set of coupled Stuart-Landau stochastic differential equations that capture the modes’ frequencies and amplitude modulation in time and space. This methodology is applied first to a challenging synthetic dataset and then to Arctic sea ice concentration (SIC) data from the US National Snow and Ice Data Center (NSIDC). The 36-year (1979–2014) dataset is parsimoniously and accurately described by our DAHMs. Preliminary results indicate that simulations using our multilayer Stuart-Landau model (MSLM) of SICs are stable for much longer time intervals, beyond the end of the twenty-first century, and exhibit interdecadal variability consistent with past historical records. Preliminary results indicate that this MSLM is quite skillful in predicting September sea ice extent.

2017
Boers, N., M. D. Chekroun, H. Liu, D. Kondrashov, D.-D. Rousseau, A. Svensson, M. Bigler, and M. Ghil. 2017. “Inverse stochastic-dynamic models for high-resolution Greenland ice-core records.” Earth System Dynamics 8: 1171–1190. Publisher's Version Abstract

Proxy records from Greenland ice cores have been studied for several decades, yet many open questions remain regarding the climate variability encoded therein. Here, we use a Bayesian framework for inferring inverse, stochastic-dynamic models from δ18O and dust records of unprecedented, subdecadal temporal resolution. The records stem from the North Greenland Ice Core Project (NGRIP) and we focus on the time interval 59 ka–22 ka b2k. Our model reproduces the dynamical characteristics of both the δ18O and dust proxy records, including the millennial-scale Dansgaard–Oeschger variability, as well as statistical properties such as probability density functions, waiting times and power spectra, with no need for any external forcing. The crucial ingredients for capturing these properties are (i) high-resolution training data; (ii) cubic drift terms; (iii) nonlinear coupling terms between the δ18O and dust time series; and (iv) non-Markovian contributions that represent short-term memory effects.

Chekroun, Mickaël D., Honghu Liu, and James C. McWilliams. 2017. “The emergence of fast oscillations in a reduced primitive equation model and its implications for closure theories.” Computers & Fluids 151: 3-22. Publisher's Version Abstract

The problem of emergence of fast gravity-wave oscillations in rotating, stratified flow is reconsidered. Fast inertia-gravity oscillations have long been considered an impediment to initialization of weather forecasts, and the concept of a “slow manifold” evolution, with no fast oscillations, has been hypothesized. It is shown on a reduced Primitive Equation model introduced by Lorenz in 1980 that fast oscillations are absent over a finite interval in Rossby number but they can develop brutally once a critical Rossby number is crossed, in contradistinction with fast oscillations emerging according to an exponential smallness scenario such as reported in previous studies, including some others by Lorenz. The consequences of this dynamical transition on the closure problem based on slow variables is also discussed. In that respect, a novel variational perspective on the closure problem exploiting manifolds is introduced. This framework allows for a unification of previous concepts such as the slow manifold or other concepts of “fuzzy” manifold. It allows furthermore for a rigorous identification of an optimal limiting object for the averaging of fast oscillations, namely the optimal parameterizing manifold (PM). It is shown through detailed numerical computations and rigorous error estimates that the manifold underlying the nonlinear Balance Equations provides a very good approximation of this optimal PM even somewhat beyond the emergence of fast and energetic oscillations.

 

2016
Chen, C., M. Cane, N. Henderson, D. Lee, D. Chapman, D. Kondrashov, and M. D. Chekroun. 2016. “Diversity, nonlinearity, seasonality and memory effect in ENSO simulation and prediction using empirical model reduction.” Journal of Climate 29 (5): 1809–1830. Publisher's Version Abstract

A suite of empirical model experiments under the empirical model reduction framework are conducted to advance the understanding of ENSO diversity, nonlinearity, seasonality, and the memory effect in the simulation and prediction of tropical Pacific sea surface temperature (SST) anomalies. The model training and evaluation are carried out using 4000-yr preindustrial control simulation data from the coupled model GFDL CM2.1. The results show that multivariate models with tropical Pacific subsurface information and multilevel models with SST history information both improve the prediction skill dramatically. These two types of models represent the ENSO memory effect based on either the recharge oscillator or the time-delayed oscillator viewpoint. Multilevel SST models are a bit more efficient, requiring fewer model coefficients. Nonlinearity is found necessary to reproduce the ENSO diversity feature for extreme events. The nonlinear models reconstruct the skewed probability density function of SST anomalies and improve the prediction of the skewed amplitude, though the role of nonlinearity may be slightly overestimated given the strong nonlinear ENSO in GFDL CM2.1. The models with periodic terms reproduce the SST seasonal phase locking but do not improve the prediction appreciably. The models with multiple ingredients capture several ENSO characteristics simultaneously and exhibit overall better prediction skill for more diverse target patterns. In particular, they alleviate the spring/autumn prediction barrier and reduce the tendency for predicted values to lag the target month value.

2014
Roques, Lionel, Mickaël D. Chekroun, Michel Cristofol, Samuel Soubeyrand, and Michael Ghil. 2014. “Parameter estimation for energy balance models with memory.” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 470 (2169). The Royal Society. Publisher's Version Abstract
We study parameter estimation for one-dimensional energy balance models with memory (EBMMs) given localized and noisy temperature measurements. Our results apply to a wide range of nonlinear, parabolic partial differential equations with integral memory terms. First, we show that a space-dependent parameter can be determined uniquely everywhere in the PDE’s domain of definition D, using only temperature information in a small subdomain E⊂D. This result is valid only when the data correspond to exact measurements of the temperature. We propose a method for estimating a model parameter of the EBMM using more realistic, error-contaminated temperature data derived, for example, from ice cores or marine-sediment cores. Our approach is based on a so-called mechanistic-statistical model that combines a deterministic EBMM with a statistical model of the observation process. Estimating a parameter in this setting is especially challenging, because the observation process induces a strong loss of information. Aside from the noise contained in past temperature measurements, an additional error is induced by the age-dating method, whose accuracy tends to decrease with a sample’s remoteness in time. Using a Bayesian approach, we show that obtaining an accurate parameter estimate is still possible in certain cases.
Chekroun, M. D., J. D. Neelin, D. Kondrashov, J. C. McWilliams, and M. Ghil. 2014. “Rough parameter dependence in climate models and the role of Ruelle-Pollicott resonance.” Proceeding of the National Academy of Sciences 111 (5): 1684—1690. Publisher's Version Abstract

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. Based on modern spectral theory of chaotic and dissipative dynamical systems, the associated low-frequency variability may be formulated in terms of Ruelle-Pollicott (RP) resonances. RP resonances encode information on the nonlinear dynamics of the system, and an approach for estimating them—as filtered through an observable of the system—is proposed. This approach relies on an appropriate Markov representation of the dynamics associated with a given observable. It is shown that, within this representation, the spectral gap—defined as the distance between the subdominant RP resonance and the unit circle—plays a major role in the roughness of parameter dependences. The model statistics are the most sensitive for the smallest spectral gaps; such small gaps turn out to correspond to regimes where the low-frequency variability is more pronounced, whereas autocorrelations decay more slowly. The present approach is applied to analyze the rough parameter dependence encountered in key statistics of an El-Niño–Southern Oscillation model of intermediate complexity. Theoretical arguments, however, strongly suggest that such links between model sensitivity and the decay of correlation properties are not limited to this particular model and could hold much more generally.

 

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