El Nino is not well represented by many climate models.
In Nature there is a very high anti correlation between SOI and NINO3.4 in the order of -0.8. I have examined whether that also holds for CMIP5. It does not...
Note: Some runs may have been double counted. However restricting to smaller subsets are qualitatively similar. The few models with positive C are be due to a file mismatch between runs where KNMI-ClimateExplorer did not provide all meta data (I assumed r1i1p1 where this info was missing).
(The models with a correlation coef occasionally greater than -0.5 are: EC-EARTH, GISS-E2-H, GISS-E2-R, IPSL-CM5A-LR, bcc-csm1-1, FIO-ESM - not all were counted in above histogram)
Data were downloaded from KNMI climate explorer. Intervals were 1880-present.
andCoats et al. 2013: Stationarity of the tropical pacific teleconnection to North America in CMIP5/PMIP3 model simulations
The power spectra of Nino3.4 (after removing global warming trend) looks like this.
The model spectra has on average a reasonable shape, but it appears there is a bias towards less variability in modelled nino3.4. There are also models that seem completely off in their shapes.
similar for SOI: