Journal cover Journal topic
Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
Journal topic

Journal metrics

Journal metrics

  • IF value: 1.699 IF 1.699
  • IF 5-year value: 1.559 IF 5-year
    1.559
  • CiteScore value: 1.61 CiteScore
    1.61
  • SNIP value: 0.884 SNIP 0.884
  • IPP value: 1.49 IPP 1.49
  • SJR value: 0.648 SJR 0.648
  • Scimago H <br class='hide-on-tablet hide-on-mobile'>index value: 52 Scimago H
    index 52
  • h5-index value: 21 h5-index 21
Volume 14, issue 4
Nonlin. Processes Geophys., 14, 385–393, 2007
https://doi.org/10.5194/npg-14-385-2007
© Author(s) 2007. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.
Nonlin. Processes Geophys., 14, 385–393, 2007
https://doi.org/10.5194/npg-14-385-2007
© Author(s) 2007. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  12 Jul 2007

12 Jul 2007

Detecting nonlinearity in run-up on a natural beach

K. R. Bryan1 and G. Coco2 K. R. Bryan and G. Coco
  • 1Department of Earth and Ocean Sciences, University of Waikato, Private Bag 3105, Hamilton, 3240, New Zealand
  • 2National Institute of Water and Atmospheric Research, P.O. Box 11–115, Hamilton, New Zealand

Abstract. Natural geophysical timeseries bear the signature of a number of complex, possibly inseparable, and generally unknown combination of linear, stable non-linear and chaotic processes. Quantifying the relative contribution of, in particular, the non-linear components will allow improved modelling and prediction of natural systems, or at least define some limitations on predictability. However, difficulties arise; for example, in cases where the series are naturally cyclic (e.g. water waves), it is most unclear how this cyclic behaviour impacts on the techniques commonly used to detect the nonlinear behaviour in other fields. Here a non-linear autoregressive forecasting technique which has had success in demonstrating nonlinearity in non-cyclical geophysical timeseries, is applied to a timeseries generated by videoing the waterline on a natural beach (run-up), which has some irregular oscillatory behaviour that is in part induced by the incoming wave field. In such cases, the deterministic shape of each run-up cycle has a strong influence on forecasting results, causing questionable results at small (within a cycle) prediction distances. However, the technique can clearly differentiate between random surrogate series and natural timeseries at larger prediction distances (greater than one cycle). Therefore it was possible to clearly identify nonlinearity in the relationship between observed run-up cycles in that a local autoregressive model was more adept at predicting run-up cycles than a global one. Results suggest that despite forcing from waves impacting on the beach, each run-up cycle evolves somewhat independently, depending on a non-linear interaction with previous run-up cycles. More generally, a key outcome of the study is that oscillatory data provide a similar challenge to differentiating chaotic signals from correlated noise in that the deterministic shape causes an additional source of autocorrelation which in turn influences the predictability at small forecasting distances.

Publications Copernicus
Download
Citation