ENSO model validation using wavelet probability analysis

A new method to quantify changes in El Niñ o-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 Niñ o-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 Niñ o-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 Niñ o-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.