Nonlinear dynamics of hourly ozone concentrations: Nonparametric short term prediction

Jiann Long Chen, Shafiqul Islam, Pratim Biswas

Research output: Contribution to journalArticlepeer-review

95 Scopus citations


Due to inherent spatial and temporal variability of emission concentrations, influence of meteorological conditions, and uncertainties associated with initial and boundary conditions, it is very difficult to model, calibrate, and validate ozone variations from first principles. This paper describes a new procedure, based on dynamical systems theory, to model and predict ozone levels. A model is constructed by creating a multidimensional phase space map from observed ozone concentrations. Predictions are made by examining trajectories on a reconstructed phase space that applies to hourly ozone time series from the Cincinnati area. The proposed phase space model is used to make one-hour to one-day ahead predictions of ozone levels. Prediction accuracy is used as a diagnostic tool to characterize the nature, random vs deterministic, of ozone variations. To demonstrate the utility of this diagnostic tool, the proposed method is first applied to time series with known characteristics. Results for the ozone time series suggest that it can be characterized as a low-dimensional chaotic system. Then, the performance of the proposed phase space and optimum autoregressive model are compared for one-hour and one-day ahead predictions. Three performance measures, namely, root-mean-square error, prediction accuracy, and coefficient of determination yield similar results for both phase space and autoregressive models. However, the phase space model is clearly superior in terms of bias and normalized absolute error of predictions, specially for one-day ahead predictions. In addition, the ability of the proposed model to identify the underlying characteristics from a time series makes it a powerful tool to characterize and predict ozone concentrations.

Original languageEnglish (US)
Pages (from-to)1839-1848
Number of pages10
JournalAtmospheric Environment
Issue number11
StatePublished - Jun 1 1998
Externally publishedYes


  • Nonlinear dynamics
  • Ozone
  • Urban air quality

ASJC Scopus subject areas

  • Environmental Science(all)
  • Atmospheric Science


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