ENSO Model Validation Using Wavelet Probability Analysis

Samantha Stevenson Department of Atmospheric and Oceanic Sciences and Cooperative Institute for Research in the Environmental Sciences, University of Colorado, Boulder, Colorado

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Baylor Fox-Kemper Department of Atmospheric and Oceanic Sciences and Cooperative Institute for Research in the Environmental Sciences, University of Colorado, Boulder, Colorado

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Markus Jochum National Center for Atmospheric Research, Boulder, Colorado

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Balaji Rajagopalan Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, Colorado

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Stephen G. Yeager National Center for Atmospheric Research, Boulder, Colorado

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Abstract

A new method to quantify changes in El Niño–Southern Oscillation (ENSO) variability is presented, using the overlap between probability distributions of the wavelet spectrum as measured by the wavelet probability index (WPI). Examples are provided using long integrations of three coupled climate models. When subsets of Niño-3.4 time series are compared, the width of the confidence interval on WPI has an exponential dependence on the length of the subset used, with a statistically identical slope for all three models. This exponential relationship describes the rate at which the system converges toward equilibrium and may be used to determine the necessary simulation length for robust statistics. For the three models tested, a minimum of 250 model years is required to obtain 90% convergence for Niño-3.4, longer than typical Intergovernmental Panel on Climate Change (IPCC) simulations. Applying the same decay relationship to observational data indicates that measuring ENSO variability with 90% confidence requires approximately 240 years of observations, which is substantially longer than the modern SST record. Applying hypothesis testing techniques to the WPI distributions from model subsets and from comparisons of model subsets to the historical Niño-3.4 index then allows statistically robust comparisons of relative model agreement with appropriate confidence levels given the length of the data record and model simulation.

Corresponding author address: Samantha Stevenson, CIRES, 216 UCB, Boulder, CO 80303. Email: samantha.stevenson@colorado.edu

Abstract

A new method to quantify changes in El Niño–Southern Oscillation (ENSO) variability is presented, using the overlap between probability distributions of the wavelet spectrum as measured by the wavelet probability index (WPI). Examples are provided using long integrations of three coupled climate models. When subsets of Niño-3.4 time series are compared, the width of the confidence interval on WPI has an exponential dependence on the length of the subset used, with a statistically identical slope for all three models. This exponential relationship describes the rate at which the system converges toward equilibrium and may be used to determine the necessary simulation length for robust statistics. For the three models tested, a minimum of 250 model years is required to obtain 90% convergence for Niño-3.4, longer than typical Intergovernmental Panel on Climate Change (IPCC) simulations. Applying the same decay relationship to observational data indicates that measuring ENSO variability with 90% confidence requires approximately 240 years of observations, which is substantially longer than the modern SST record. Applying hypothesis testing techniques to the WPI distributions from model subsets and from comparisons of model subsets to the historical Niño-3.4 index then allows statistically robust comparisons of relative model agreement with appropriate confidence levels given the length of the data record and model simulation.

Corresponding author address: Samantha Stevenson, CIRES, 216 UCB, Boulder, CO 80303. Email: samantha.stevenson@colorado.edu

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