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Atmospheric Measurement Techniques An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/amt-2019-38
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/amt-2019-38
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 13 Mar 2019

Research article | 13 Mar 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Atmospheric Measurement Techniques (AMT).

Flexible approach for quantifying average long-term changes and seasonal cycles of tropospheric trace species

David D. Parrish1,2, Richard G. Derwent3, Simon O'Doherty4, and Peter G. Simmonds4 David D. Parrish et al.
  • 1Institute for Environmental and Climate Research, Jinan University, Guangzhou, China
  • 2David.D.Parrish, LLC, Boulder, Colorado, USA
  • 3rdscientific, Newbury, Berkshire, RG14 6LH, UK
  • 4Schoo1 of Chemistry, University of Bristol, Cantocks Close, Bristol, BS8 1TS, UK

Abstract. We present an approach to derive a systematic mathematical representation of the statistically significant features of the average long-term changes and seasonal cycle of concentrations of trace tropospheric species. The results for two illustrative data sets (time series of baseline concentrations of ozone and N2O at Mace Head, Ireland) indicate that a limited set of seven or eight parameter values provides this mathematical representation for both example species. This method utilizes a power series expansion to extract more information regarding the long-term changes than can be provided by oft-employed linear trend analyses. In contrast, the quantification of average seasonal cycles utilizes a Fourier series analysis that provides less detailed seasonal cycles than are sometimes represented as twelve monthly means; including that many parameters in the seasonal cycle representation is not usually statistically justified, and thereby adds unnecessary noise to the representation and prevents a clear analysis of the statistical uncertainty of the results. The approach presented here is intended to maximize the statistically significant information extracted from analyses of time series of concentrations of tropospheric species regarding their mean long-term changes and seasonal cycles, including non-linear aspects of the long-term trends. Additional implications, advantages and limitations of this approach are discussed.

David D. Parrish et al.
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Short summary
We present a flexible method that employs a power series expansion and a Fourier series analysis to characterize the average long-term change and seasonal cycle, respectively, from a time series of observations of a trace atmospheric species. This approach maximizes the statistically significant information derived, including non-linear aspects of the long-term trends, without over fitting the data. Generally a small set of parameter values (e.g., 7 or 8) provides this characterization.
We present a flexible method that employs a power series expansion and a Fourier series analysis...
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