Estimating daily climatological normals in a changing climate

  • Alix RigalEmail author
  • Jean-Marc Azaïs
  • Aurélien Ribes


Climatological normals are widely used baselines for the description and the characterization of a given meteorological situation. The World Meteorological Organization (WMO) standard recommends estimating climatological normals as the average of observations over a 30-year period. This approach may lead to strongly biased normals in a changing climate. Here we propose a new method with which to estimate daily climatological normals in a non-stationary climate. Our statistical framework relies on the assumption that the response to climate change is smooth over time, and on a decomposition of the response inspired by the pattern scaling assumption. Estimation is carried out using smoothing splines techniques, with a careful examination of the selection of smoothing parameters. The new method is compared, in a predictive sense and in a perfect model framework, to previously proposed alternatives such as the WMO standard (reset either on a decadal or annual basis), averages over shorter periods, and hinge fits. Results show that our technique outperforms all alternatives considered. They confirm that previously proposed techniques are substantially biased—biases are typically as large as a few tenths to more than 1\(^{\circ }\text{C}\) by the end of the century—while our method is not. We argue that such “climate change corrected” normals might be very useful for climate monitoring, and that weather services could consider using two different sets of normals (i.e. both stationary and non-stationary) for different purposes.


Daily climate normals Unbiased estimate Normals accounting for climate change Smoothing splines 



The authors acknowledge Météo-France for supporting this study along with the climate modeling groups involved in CMIP5 for producing and sharing their simulations. They also wish to thank the two anonymous referees for their constructive comments which were of great value in improving the quality of the paper.


Also funded by Météo France.

Supplementary material

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CNRM, UMR3589, Météo-France and CNRSToulouseFrance
  2. 2.Institut de MathématiquesUniversité Paul SabatierToulouse Cedex 09France

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