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Atmospheric Measurement Techniques An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/amt-2020-178
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/amt-2020-178
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  17 Jun 2020

17 Jun 2020

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This preprint is currently under review for the journal AMT.

Effects of the prewhitening method, the time granularity and the time segmentation on the Mann-Kendall trend detection and the associated Sen's slope

Martine Collaud Coen1, Elisabeth Andrews2,3, Alesssandro Bigi4, Gonzague Romanens1, Giovanni Martucci1, and Laurent Vuilleumier1 Martine Collaud Coen et al.
  • 1Federal Office of Meteorology and Climatology, MeteoSwiss, Payerne, Switzerland
  • 2Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO, USA
  • 3NOAA/Earth Systems Research Laboratory Boulder, CO, USA
  • 4Universitàdi Modena e Reggio Emilia, Department of Engineering “Enzo Ferrari”, Modena, Italy

Abstract. The most widely used non-parametric method for trend analysis is the Mann-Kendall test associated with the Sen's slope. The Mann-Kendall test requires serially uncorrelated time series, whereas most of the atmospheric processes exhibit positive autocorrelation. Several prewhitening methods have been designed to overcome the presence of lag-1 autocorrelation. These include a prewhitening, a detrending and/or a correction for the detrended slope and the original variance of the time series. The choice of which prewhitening method and temporal segmentation to apply has consequences for the statistical significance, the value of the slope and of the confidence limits. Here, the effects of various prewhitening methods are analyzed for seven time series comprising in-situ aerosol measurements (scattering coefficient, absorption coefficient, number concentration and aerosol optical depth), Raman Lidar water vapor mixing ratio and the tropopause and zero degree levels measured by radio-sounding. These time series are characterized by a broad variety of distributions, ranges and lag-1 autocorrelation values and vary in length between 10 and 60 years. A common way to work around the autocorrelation problem is to decrease it by averaging the data over longer time intervals than in the original time series. Thus, the second focus of this study is evaluation of the effect of time granularity on long-term trend analysis. Finally, a new algorithm involving three prewhitening methods is proposed in order to maximize the power of the test, to minimize the amount of erroneous detected trends in the absence of a real trend and to ensure the best slope estimate for the considered length of the time series.

Martine Collaud Coen et al.

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Martine Collaud Coen et al.

Martine Collaud Coen et al.

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Short summary
The Mann-Kendall trend test requires prewhitening in presence of serially correlated data. The effects of 5 prewhitening methods as well as of time granularity, autocorrelation, temporal segmentation and length of the time series on the statistical significance and the slope are studies for 7 atmospheric datasets. Finally, a new algorithm using 3 prewhitening methods is proposed in order to optimize the power of the test, the amount of erroneous false positive trends and the slope estimate.
The Mann-Kendall trend test requires prewhitening in presence of serially correlated data. The...
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