Climate Dynamics

, Volume 21, Issue 5–6, pp 477–491 | Cite as

Estimating signal amplitudes in optimal fingerprinting, part I: theory

  • M. R. AllenEmail author
  • P. A. Stott


There is increasingly clear evidence that human influence has contributed substantially to the large-scale climatic changes that have occurred over the past few decades. Attention is now turning to the physical implications of the emerging anthropogenic signal. Of particular interest is the question of whether current climate models may be over- or under-estimating the amplitude of the climate system's response to external forcing, including anthropogenic. Evidence of a significant error in a model-simulated response amplitude would indicate the existence of amplifying or damping mechanisms that are inadequately represented in the model. The range of uncertainty in the factor by which we can scale model-simulated changes while remaining consistent with observed change provides an estimate of uncertainty in model-based predictions. With any model that displays a realistic level of internal variability, the problem of estimating this factor is complicated by the fact that it represents a ratio between two incompletely known quantities: both observed and simulated responses are subject to sampling uncertainty, primarily due to internal chaotic variability. Sampling uncertainty in the simulated response can be reduced, but not eliminated, through ensemble simulations. Accurate estimation of these scaling factors requires a modification of the standard "optimal fingerprinting" algorithm for climate change detection, drawing on the conventional "total least squares" approach discussed in the statistical literature. Code for both variants of optimal fingerprinting can be found on


Ordinary Little Square Ensemble Simulation Total Little Square Sampling Uncertainty Internal Climate Variability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Conversations with our collegues Simon Tett, Gareth Jones, William Ingram and John Mitchell were very helpful in the development of this work. We would also like to thank Art Dempster, David Ritson and Francis Zwiers for helpful suggestions and insightful reviews, and Brian Ripley for advice and drawing our attention to the work of Adcock (1878). Myles Allen was supported by an NERC Advanced Research Fellowship with additional support from the Department of the Environment, Food and Rural Affairs (DEFRA) under contract Met1b/2331, the European Commission QUARCC project ENV4-CT97-0501 and the NOAA/DoE Ad Hoc Detection Group. Peter Stott was supported by DEFRA under contract PECD 7/12/37.


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Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Atmospheric, Oceanic and Planetary Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
  2. 2.Hadley Centre for Climate Prediction and Research, Meteorological Office, UK

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