Information flow in a two-scale stochastic dynamical system using ordinal symbolic analysis

SANTIAGO ROSA; MANUEL PULIDO; PETER JAN VAN LEEUWEN

Málaga

Conferencia; 11th International Conference on Nonlinear Mathematics and Physics; 2018

Although the resolved dynamical equations of atmospheric or oceanic global numerical models are well established, the development and evaluation of parameterizations that represent subgrid-scale effects pose a big challenge [1]. Small scale waves in the geophysical systems generate in a region, then propagate conservatively long distances to finally break and deposit their momentum far away from their generation location. Therefore, the system is characterized by strong nonlinear and remote interactions between the different scales. To mimic these interactions between subgrid-scale and large-scale dynamics, we use a proof-of-concept two-scale stochastic dynamical system based on Lorenz 1996 with long-range interactions between the two-scales. In this work, time series obtained from these systems are evaluated with information flow measures, i.e. mutual information and transfer entropy[2]. The measures are obtained via ordinal symbolic analysis using the Bandt-Pompe[3] symbolic data reduction in the signals. By comparing different experiments, we show that even when the dynamics of the large-scale variables of the systems has a short-range correlations, small-scale variable may give place to long-range information flow. We evaluate the potencial of information measures as a tool for establishing the structure and functional dependencies to be represented by the subgrid-scale parameterizations. .References[1] Pulido M. and O. Rosso, 2017. Model selection: Using information measures from ordinal symbolic analysis to select model sub-grid scale parameterizations. J. Atmos. Sci., 74, 3253?3269 doi: 10.1175/JAS-D-16-0340.1[2] Staniek, M. and Lehnertz, K., 2008. Symbolic transfer entropy. Phys. rev. lett., 100, p.158101.[3] Bandt, C. and Pompe, B., 2002. Permutation entropy: a natural complexity measure for time series. Phys. rev. lett., 88, p.174102.