arXiv subjects

Ignacio del Amo

Publications and source records attributed to Ignacio del Amo.

3 recordsLinked to original sources

arXiv2026

Cold Extremes during Dansgaard-Oeschger Oscillations

This paper studies the statistics of extreme cold air surface temperatures in a climate that experiences abrupt changes. We employ a CCSM4 simulation of Last Glacial Maximum conditions that exhibits rapid switching between stadial and interstadial states as data. Non-stationary linear Generalized Extreme Value (GEV) distributions are fitted to find the regions that show the most prominent changes and associate them with physical processes. The results are then compared with a non-linear model, which gives a more detailed picture of how the parameters change as a function of the AMOC strength. While different regions of the world show different extremal behaviours, many regions show an approximately linear relationship between the parameters of the GEV distributions and the strength of the AMOC within the stadial and interstadial states, with some non-linear oscillation or jump where the transition between them takes place. Physical processes such as the expansion and retreat of the sea ice and the relative changes in the strength of the currents are shown to impact the magnitude and variability of the extremes, with significant changes observed in the three parameters of the GEV. They also create teleconnections that are compared whenever possible with various proxies for the temperature of the air and the water. We show how mapping the parameters of the GEV distributions into the AMOC strength gives a way to compare results between different climate models and different climate states. Comparisons, however, need to pay heed to the dynamical characteristics of the state and the location to be meaningful.

physics.ao-ph↗

arXiv2024

Limitations of the Generalized Pareto Distribution-based estimators for the local dimension

Two dynamical indicators, the local dimension and the extremal index, used to quantify persistence in phase space have been developed and applied to different data across various disciplines. These are computed using the asymptotic limit of exceedances over a threshold, which turns to be a Generalized Pareto Distribution in many cases. However the derivation of the asymptotic distribution requires mathematical properties which are not present even in highly idealized dynamical systems, and unlikely to be present in real data. Here we examine in detail issues that arise when estimating these quantities for some known dynamical systems with a particular focus on how the geometry of an invariant set can affect the regularly varying properties of the invariant measure. We demonstrate that singular measures supported on sets of non-integer dimension are typically not regularly varying and that the absence of regular variation makes the estimates resolution dependent. We show as well that the most common extremal index estimation method is ambiguous for continuous time processes sampled at fixed time steps, which is an underlying assumption in its application to data.

math.DS↗

arXiv2024

Escape by jumps and diffusion by α-stable noise across the barrier in a double well potential

Many physical and chemical phenomena are governed by stochastic escape across potential barriers. The escape time depends on the structure of the noise and the shape of the potential barrier. By applying $α$-stable noise from the $α=2$ Gaussian noise limit to the $α<2$ jump processes, we find a continuous transition of the mean escape time from the usual dependence on the height of the barrier for Gaussian noise to a dependence solely on the width of the barrier for $α$-stable noise. We consider the exit problem of a process driven by $α$-stable noise in a double well potential. We study individually the influences of the width and the height of the potential barrier in the escape time and we show through scalings that the asymptotic laws are described by a universal curve independent of both parameters. When the dependence in the stability parameter is considered, we see that there are two different diffusive regimes in which diffusion is described either by Kramer's time or by the corresponding asymptotic law for $α$-stable noise. We determine the regions of the noise parameter space in which each regime prevails, and exploit this result to construct an anomalous example in which a double well potential exhibit a different diffusion regime in each well for a wide range of parameters.

cond-mat.stat-mech↗