Applying Recurrence Analysis to Illustrate the Co-existence of Chaotic and Non-Chaotic Solutions within a Generalized Lorenz Model
Abstract
Based on recent studies using high-dimensional Lorenz models (LMs), a revised view on the nature of weather has been proposed as follows: the entirety of weather is a superset that consists of both chaotic and non-chaotic processes. In other words, both chaotic and non-chaotic may coexist. To illustrate such a coexistence, in this study, we generate recurrence plots and perform recurrence analysis for various types of solutions using a generalized Lorenz model (GLM) with M modes, where M is an odd number that is greater than one. The GLM was derived based on a successive extension of the so-called nonlinear feedback loop within the classical Lorenz model. Using the simplified and full versions of the GLM with M = 3, 5, 7, and 9, we first analyze the following solutions: (1) periodic and quasi-periodic solutions with two, three and four incommensurate frequencies; (2) linear stable and unstable solutions near the non-trivial critical points; (3) a temporal transition from an unstable solution to a limit cycle solution, which is an isolated closed orbit.
Within the GLM with M = 9 (i.e., the 9DLM), two non-trivial critical points are stable for all Rayleigh parameters greater than one and two types of solutions (e.g., steady-state and chaotic solutions) may co-exist with a wide range of Rayleigh parameters, depending on initial conditions (ICs). Therefore, the 9DLM is used to produce the coexistence of two types of solutions for the recurrence analysis. To effectively detect the dependence of the co-existence on ICs, we propose the following methodology: (1) we obtain the non-trivial critical point solutions and derive a system by using the solution as a basic state and decomposing a total field into a basic state and perturbation. The new system, referred to as the version 2 (V2), allows both linear and nonlinear simulations; (2) we conduct ensemble runs with various ICs distributed over a hypersphere centered at a non-trivial critical point; (3) we perform RQA (e.g., the calculation of the recurrence rate (RR) and determinism (DET)) of ensemble runs using various radii for the hypersphere. The feasibility of applying the above method for analyzing the global model data and global reanalysis is discussed near the end.- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2018
- Bibcode:
- 2018AGUFMIN41D0864R
- Keywords:
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- 1855 Remote sensing;
- HYDROLOGYDE: 1908 Cyberinfrastructure;
- INFORMATICSDE: 1914 Data mining;
- INFORMATICSDE: 1942 Machine learning;
- INFORMATICS