Identifying low-dimensional nonlinear behavior in atmospheric data

Computational modeling is playing an increasingly vital role in the study o f atmospheric-oceanic systems. Given the complexity of the models a fundame ntal question to ask is, How well does the output of one model agree with t he evolution of another model or with the true system that is represented b y observational data? Since observational data contain measurement noise, t he question is placed in the framework of time series analysis from a dynam ical systems perspective. That is, it is desired to know if the two, possib ly noisy, time series were produced by similar physical processes. In this paper simple graphical representations of the time series and the e rrors made by a simple predictive model of the time series (known as residu al 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 d ifferent uses for these graphical representations are presented in this pap er. 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 d irectly at differences between two datasets. An example of this test is pro vided by comparing station data and NCEP-NCAR reanalysis data on the Austra lian continent. Second, the technique is applied to the global NCEP-NCAR reanalysis data. F rom this a composite image is created that effectively identifies regions o f the atmosphere where the dynamics are strongly dependent on low-dimension al nonlinear processes. It is also shown how the transition between such re gions can be depicted using residual delay maps. This allows for the invest igation of the conjecture of Sugihara et al.: sites in the midlatitudes are significantly more nonlinear than sites in the Tropics.