Journal cover Journal topic
Atmospheric Chemistry and Physics An interactive open-access journal of the European Geosciences Union
Journal topic

Journal metrics

Journal metrics

  • IF value: 5.668 IF 5.668
  • IF 5-year value: 6.201 IF 5-year
  • CiteScore value: 6.13 CiteScore
  • SNIP value: 1.633 SNIP 1.633
  • IPP value: 5.91 IPP 5.91
  • SJR value: 2.938 SJR 2.938
  • Scimago H <br class='hide-on-tablet hide-on-mobile'>index value: 174 Scimago H
    index 174
  • h5-index value: 87 h5-index 87
Discussion papers
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 19 Mar 2020

Submitted as: research article | 19 Mar 2020

Review status
This preprint is currently under review for the journal ACP.

Statistical regularization for trend detection: An integrated approach for detecting long-term trends from sparse tropospheric ozone profiles

Kai-Lan Chang1,2, Owen R Cooper1,2, Audrey Gaudel1,2, Irina Petropavlovskikh1,3, and Valerie Thouret4 Kai-Lan Chang et al.
  • 1Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO, USA
  • 2Chemical Sciences Division, NOAA Earth System Research Laboratory, Boulder, CO, USA
  • 3Global Monitoring Division, NOAA Earth System Research Laboratory, Boulder, CO, USA
  • 4Laboratoire d’Aérologie, Université de Toulouse, CNRS, UPS, Toulouse, France

Abstract. Detecting a tropospheric ozone trend from sparsely sampled ozonesonde profiles (typically once per week) is challenging due to the noise in the time series resulting from ozone's high temporal variability. To enhance trend detection we have developed a sophisticated statistical approach that utilizes a geoadditive model to assess ozone variability across a time series of vertical profiles. Treating the profile time series as a set of individual time series on discrete pressure surfaces, a class of smoothing spline ANOVA (analysis of variance) models is used for the purpose of jointly modeling multiple correlated time series (on separate pressure surfaces) by their associated seasonal and interannual variabilities. This integrated fit method filters out the unstructured noise through a statistical regularization (i.e. a roughness penalty), by taking advantage of the additional correlated data points available on the pressure surfaces above and below the surface of interest. We have applied this technique to the trend analysis of the vertically correlated time series of tropospheric ozone observations from 1) IAGOS (In-service Aircraft for a Global Observing System) commercial aircraft profiles above Europe and China, and 2) NOAA GMD's (Global Monitoring Division) ozonesonde records at Hilo, Hawaii and Trinidad Head, California. We illustrate the ability of this technique to detect a consistent trend estimate, and its effectiveness for reducing the associated uncertainty in the noisy profile data due to low sampling frequency. We also conducted a sensitivity analysis of frequent IAGOS profiles above Europe (approximately 120 profiles per month) to determine how many profiles in a month are required for reliable long-term trend detection. When ignoring the vertical correlation we found that a typical sampling strategy of 4 profiles-per-month results in 7 % of sampled trends falling outside the 2-sigma uncertainty interval derived from the full data set, with associated 10 % of mean absolute percentage error. We determined that an optimal sampling frequency is 14 profiles per month when using the integrated fit method for calculating trends; when the integrated fit method is not applied, the sampling frequency had to be increased to 18 profiles per month to achieve the same result. While our method improves trend detection from sparse data sets, the key to substantially reducing the uncertainty is to increase the sampling frequency.

Kai-Lan Chang et al.

Interactive discussion

Status: open (until 14 May 2020)
Status: open (until 14 May 2020)
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
[Subscribe to comment alert] Printer-friendly Version - Printer-friendly version Supplement - Supplement

Kai-Lan Chang et al.

Kai-Lan Chang et al.


Total article views: 249 (including HTML, PDF, and XML)
HTML PDF XML Total Supplement BibTeX EndNote
185 62 2 249 14 0 0
  • HTML: 185
  • PDF: 62
  • XML: 2
  • Total: 249
  • Supplement: 14
  • BibTeX: 0
  • EndNote: 0
Views and downloads (calculated since 19 Mar 2020)
Cumulative views and downloads (calculated since 19 Mar 2020)

Viewed (geographical distribution)

Total article views: 227 (including HTML, PDF, and XML) Thereof 226 with geography defined and 1 with unknown origin.
Country # Views %
  • 1



No saved metrics found.


No discussed metrics found.
Latest update: 01 Apr 2020
Publications Copernicus
Short summary
We provide a statistical framework for detecting trends of multiple auto-correlated time series from sparsely sampled profile data. The result is a better and consistent quantification of trend estimate of vertical profile data. The focus was placed on the long-term ozone time series from commercial aircraft and balloon-borne ozonesonde measurements. This framework can be applied to other trace gases in the atmosphere.
We provide a statistical framework for detecting trends of multiple auto-correlated time series...