Identifying Low-Dimensional Nonlinear Behavior in Atmospheric Data

Abstract

Computational modeling is playing an increasingly vital role in the study of atmospheric?oceanic systems. Given the complexity of the models a fundamental question to ask is, How well does the output of one model agree with the evolution of another model or with the true system that is represented by observational data? Since observational data contain measurement noise, the question is placed in the framework of time series analysis from a dynamical systems perspective. That is, it is desired to know if the two, possibly noisy, time series were produced by similar physical processes. In this paper simple graphical representations of the time series and the errors made by a simple predictive model of the time series (known as residual delay maps) are used to extract information about the nature of the time evolution of the system (in this paper referred to as the dynamics). Two different uses for these graphical representations are presented in this paper. First, a test for the comparison of two competing models or of a model and observational data is proposed. The utility of this test is that it is based on comparing the underlying dynamical processes rather than looking directly at differences between two datasets. An example of this test is provided by comparing station data and NCEP?NCAR reanalysis data on the Australian continent. Second, the technique is applied to the global NCEP?NCAR reanalysis data. From this a composite image is created that effectively identifies regions of the atmosphere where the dynamics are strongly dependent on low-dimensional nonlinear processes. It is also shown how the transition between such regions can be depicted using residual delay maps. This allows for the investigation of the conjecture of Sugihara et al.: sites in the midlatitudes are significantly more nonlinear than sites in the Tropics.