arXiv subjects

Javier Amezcua

Publications and source records attributed to Javier Amezcua.

3 recordsLinked to original sources

arXiv2023

Supervised machine learning to estimate instabilities in chaotic systems: estimation of local Lyapunov exponents

In chaotic dynamical systems such as the weather, prediction errors grow faster in some situations than in others. Real-time knowledge about the error growth could enable strategies to adjust the modelling and forecasting infrastructure on-the-fly to increase accuracy or reduce computation time. One could, e.g., change the ensemble size, or the distribution and type of target observations. Local Lyapunov exponents are known indicators of the rate at which very small prediction errors grow over a finite time interval. However, their computation is very expensive: it requires maintaining and evolving a tangent linear model, orthogonalisation algorithms and storing large matrices. In this feasibility study, we investigate the accuracy of supervised machine learning in estimating the current local Lyapunov exponents, from input of current and recent time steps of the system trajectory, as an alternative to the classical method. Thus machine learning is not used here to emulate a physical model or some of its components, but non intrusively as a complementary tool. We test four popular supervised learning algorithms: regression trees, multilayer perceptrons, convolutional neural networks and long short-term memory networks. Experiments are conducted on two low-dimensional chaotic systems of ordinary differential equations, the Rössler and the Lorenz 63 models. We find that on average the machine learning algorithms predict the stable local Lyapunov exponent accurately, the unstable exponent reasonably accurately, and the neutral exponent only somewhat accurately. We show that greater prediction accuracy is associated with local homogeneity of the local Lyapunov exponents on the system attractor. Importantly, the situations in which (forecast) errors grow fastest are not necessarily the same as those where it is more difficult to predict local Lyapunov exponents with machine learning.

physics.comp-ph↗

arXiv2020

Assimilation of atmospheric infrasound data to constrain tropospheric and stratospheric winds

This data assimilation study exploits infrasound from explosions to probe an atmospheric wind component from the ground up to stratospheric altitudes. Planned explosions of old ammunition in Finland generate transient infrasound waves that travel through the atmosphere. These waves are partially reflected back towards the ground from stratospheric levels, and are detected at a receiver station located in northern Norway at 178 km almost due North from the explosion site. The difference between the true horizontal direction towards the source and the backazimuth direction (the horizontal direction of arrival) of the incoming infrasound wave-fronts, in combination with the pulse propagation time, are exploited to provide an estimate of the average cross-wind component in the penetrated atmosphere. We perform offline assimilation experiments with an ensemble Kalman filter and these observations, using the ERA5 ensemble reanalysis atmospheric product as background (prior) for the wind at different vertical levels. We demonstrate that information from both sources can be combined to obtain analysis (posterior) estimates of cross-winds at different vertical levels of the atmospheric slice between the explosion site and the recording station. The assimilation makes greatest impact at the 12-60 km levels, with some changes with respect to the prior of the order of 0.1-1.0 m/s, which is a magnitude larger than the typical standard deviation of the ERA5 background. The reduction of background variance in the higher levels often reached 2-5%. This is the first published study demonstrating techniques to implement assimilation of infrasound data into atmospheric models. It paves the way for further exploration in the use of infrasound observations - especially natural and continuous sources - to probe the middle atmospheric dynamics and to assimilate these data into atmospheric model products.

physics.ao-ph↗

arXiv2012

Ensemble transform Kalman-Bucy filters

Two recent works have adapted the Kalman-Bucy filter into an ensemble setting. In the first formulation, BR10, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-BGR09, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard KF. In the second formulation, BR10, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyze the behavior of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background to observational error covariance, and that using the integration scheme proposed in both BGR09 and BR10 can lead to failure. An integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman-Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model (AGCM) known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.

math.NA↗