Climate Dynamics

, Volume 43, Issue 1, pp 361–374

Detecting trends that are nonlinear and asymmetric on diurnal and seasonal time scales


DOI: 10.1007/s00382-014-2086-8

Cite this article as:
Fischer, M.J. & Paterson, A.W. Clim Dyn (2014) 43: 361. doi:10.1007/s00382-014-2086-8


Trends in climate time series are often nonlinear and temporally-asymmetric, i.e. the trend is different for different seasons and/or hours of the day. Here a method is developed that allows the nonlinearity and temporal asymmetry of a trend to be investigated simultaneously. First, nonlinear trend components are extracted from a univariate time series, by adapting a nonparametric dimension-reduction method. Then, the nonlinear trend components are substituted into a regression model in which the periodic mean component and the periodic variation in the amplitude of the nonlinear trend are modeled using harmonic functions of the seasonal and diurnal periods. Third, trend patterns in the positive and negative anomalies are investigated, by extending the nonlinear trend model using indicator variables. Fourth, a non-local inferential test is developed to test the statistical significance of the trend patterns. The nonlinear trend model is applied to a simulated time series, as well as to long-term high-resolution temperature records from five Southern Hemisphere sites: Lucas Heights, Sydney Airport, Cape Grim, Macquarie Island and Law Dome. Our method should be generally useful for identifying the effect of both climate-related factors and observation/site-related factors on seasonal and diurnal trends in meteorological data series.


Trend analysisTime series analysisRegressionClimate change

Supplementary material

382_2014_2086_MOESM1_ESM.pdf (267 kb)
PDF (267 KB)

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute for Environmental ResearchAustralian Nuclear Science and Technology OrganisationNSWAustralia