arXiv subjects

Manuel Santos Gutiérrez

Publications and source records attributed to Manuel Santos Gutiérrez.

7 recordsLinked to original sources

arXiv2024

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, lifespan, and impact on climate through radiative effects. Small, weak-updraft clouds near the haze-to-cloud transition are especially difficult to measure and understand. They are abundant but hard to capture by satellites. Köhler's theory explains initial droplet growth but struggles with large particle groups. Here, we present a stochastic, analytical framework building on Köhler's theory to account for (monodisperse) aerosols and cloud droplets interaction through competitive growth in a limited water vapor field. These interactions are modeled by sink terms while fluctuations in supersaturation affecting droplet growth are modeled by nonlinear, white noise terms. Our results identify hysteresis mechanisms in the droplet activation and deactivation processes. Our approach allows for multimodal cloud's droplet size distributions supported by lab experiments, offering a new perspective on haze-to-cloud transition and small cloud formation.

physics.ao-ph↗

arXiv2024

The Optimal Growth Mode in the Relaxation to Statistical Equilibrium

Systems far from equilibrium approach stability slowly due to "anti-mixing" characterized by regions of the phase-space that remain disconnected after prolonged action of the flow. We introduce the Optimal Growth Mode (OGM) to capture this slow initial relaxation. The OGM is calculated from Markov matrices approximating the action of the Fokker-Planck operator onto the phase space. It is obtained as the mode having the largest growth in energy before decay. Important nuances between the OGM and the more traditional slowest decaying mode are detailed in the case of the Lorenz 63 model. The implications for understanding how complex systems respond to external forces, are discussed.

cond-mat.stat-mech↗

arXiv2024

Dynamical regimes of CCN activation in adiabatic air parcels

Ubiquitous, yet elusive to a complete understanding: Tiny, warm clouds with faint visual signatures play a critical role in Earth's energy balance. These "twilight clouds", as they are sometimes called, form under weak updraft conditions. Their constituent particles exist in a precarious state, teetering between hazy wisps and activated droplets. This delicate thermodynamic balance creates a limited reservoir of supersaturation, which activated droplets readily consume. Our research presents a novel approach, solving coupled equations for particle growth (Köhler's equation) and supersaturation change. This reveals previously unconsidered activation states for these clouds. Additionally, the analysis predicts conditions where particles can exhibit self-sustained oscillations between haze and activated droplet states.

physics.ao-ph↗

arXiv2023

Steady-state supersaturation distributions for clouds under turbulent forcing

The supersaturation equation for a vertically moving adiabatic cloud parcel is analysed. The effects of turbulent updrafts are incorporated in the shape of a stochastic Lagrangian model, with spatial and time correlations expressed in terms of turbulent kinetic energy. Using the Fokker-Planck equation, the steady-state probability distributions of supersaturation are analytically computed for a number of approximations involving the timescale separation between updraft fluctuations and phase-relaxation, multiplicative noise simplification and droplet or ice particle size fluctuations. While the analytical results are presented in general for single-phase clouds, the calculated distributions are used to compute mixed-phase cloud properties -- mixed fraction and mean liquid water content in an initially icy cloud -- and are argued to be useful for generalising and constructing new parametrisation schemes.

physics.ao-ph↗

arXiv2022

On Some Aspects of the Response to Stochastic and Deterministic Forcings

The perturbation theory of operator semigroups is used to derive response formulas for a variety of combinations of acting forcings and reference background dynamics. In the case of background stochastic dynamics, we decompose the response formulas using the Koopman operator generator eigenfunctions and the corresponding eigenvalues, thus providing a functional basis towards identifying relaxation timescales and modes in physically relevant systems. To leading order, linear response gives the correction to expectation values due to extra deterministic forcings acting on either stochastic or chaotic dynamical systems. When considering the impact of weak noise, the response is linear in the intensity of the (extra) noise for background stochastic dynamics, while the second order response given the leading order correction when the reference dynamics is chaotic. In this latter case we clarify that previously published diverging results can be brought to common ground when a suitable interpretation - Stratonovich vs. Ito - of the noise is given. Finally, the response of two-point correlations to perturbations is studied through the resolvent formalism via a perturbative approach. Our results allow, among other things, to estimate how the correlations of a chaotic dynamical system changes as a results of adding stochastic forcing.

nlin.CD↗

arXiv2021

Reduced-Order Models for Coupled Dynamical Systems: Data-driven Methods and the Koopman Operator

Providing efficient and accurate parametrizations 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 parametrizations of weakly coupled dynamical systems. Such parametrizations yield a set of stochastic integro-differential equations with explicit noise and memory kernel formulas to describe the effects of unresolved variables. We show that the perturbation expansions involved need not be truncated when the coupling is additive. The unwieldy integro-differential equations can be recast as a simpler multilevel Markovian model, and we establish an intuitive connection with a generalized Langevin equation. This connection helps setting up a parallelism between the top-down, equations-based methodology herein and the well-established empirical model reduction (EMR) methodology that has been shown to provide efficient dynamical closures to partially observed systems. Hence, our findings support, on the one hand, the physical basis and robustness of the EMR methodology and, on the other hand, illustrate the practical relevance of the perturbative expansion used for deriving the parametrizations.

nlin.CD↗

arXiv2019

Response and Sensitivity Using Markov Chains

Dynamical systems are often subject to forcing or changes in their governing parameters and it is of interest to study how this affects their statistical properties. A prominent real-life example of this class of problems is the investigation of climate response to perturbations. In this respect, it is crucial to determine what the linear response of a system is to small perturbations as a quantification of sensitivity. Alongside previous work, here we use the transfer operator formalism to study the response and sensitivity of a dynamical system undergoing perturbations. By projecting the transfer operator onto a suitable finite dimensional vector space, one is able to obtain matrix representations which determine finite Markov processes. Further, using perturbation theory for Markov matrices, it is possible to determine the linear and nonlinear response of the system given a prescribed forcing. Here, we suggest a methodology which puts the scope on the evolution law of densities (the Liouville/Fokker-Planck equation), allowing to effectively calculate the sensitivity and response of two representative dynamical systems.

nlin.CD↗