Background
The authors write that "although considerable progress has been made towards more realistic ENSO simulation, systematic errors still persist," citing Capotondi et al. (2006), Guilyardi et al. (2009), Kim and Jin (2011), Lloyd et al. (2009), Lin (2007), and Zhang and Jin (2012)." In particular, they say that "the Coupled Model Intercomparison Project phase 3 (CMIP3) models generally underestimate thermodynamic damping and positive feedbacks including zonal advective and thermocline feedbacks (Kim and Jin, 2011; Lloyd et al., 2009), which are responsible for ENSO variability and display a large diversity of ENSO amplitude, stability and teleconnections (Guilyardi, 2006; Yu and Kim 2010; Cai et al., 2009; Kim and Jin, 2011)."

What was done
Using the Bjerkness stability index as the basis for their analysis, Kim et al. estimated "the overall linear El Niņo-Southern Oscillation (ENSO) stability and the relative contribution of positive feedbacks and damping processes to the stability in historical simulations of Coupled Model Intercomparison Project Phase 5 (CMIP5) models."

What was learned
The four researchers report that "a systematic bias persists from CMIP3 to CMIP5," noting that "the majority of the CMIP5 models analyzed in this study still underestimate [1] the zonal advective feedback, [2] thermocline feedback, and [3] thermodynamic damping terms, when compared with those estimated from reanalysis." And they say that "this discrepancy turns out to be related to [4] a cold tongue bias in coupled models that causes [5] a weaker atmospheric thermodynamical response to sea surface temperature changes and [6] a weaker oceanic response (zonal currents and zonal thermocline slope) to wind changes."

What it means
In light of these several findings, there would appear to be a host of problems that need to be resolved before the studied models are ready to produce reasonably accurate projections of future ENSO behavior.

References
Cai, W., Sullivan, A. and Cowan, T. 2009. Rainfall teleconnections with Indo-Pacific variability in the IPCC AR4 models. Journal of Climate 22: 5046-5071.

Capotondi, A., Wittenberg, A. and Masina, S. 2006. Spatial and temporal structure of tropical Pacific inter-annual variability in 20th century coupled simulations. Ocean Modelling 15: 274-298.

Guilyardi, E. 2006. El Niņo - mean state - seasonal cycle interactions in a multi-model ensemble. Climate Dynamics 26: 329-348.

Guilyardi, E., Wittenberg, A., Fedorov, A., Collins, M., Wang, C., Capotondi, A., van Oldenborgh, G.J. and Stockdale, T. 2009. Understanding El Niņo in Ocean-Atmosphere General Circulation Models: progress and challenges. Bulletin of the American Meteorological Society 90: 325-340.

Kim, S.T. and Jin, F.-F. 2011. An ENSO stability analysis. Part II: results from 20th- and 21st-century simulations of the CMIP3 models. Climate Dynamics 36: 1593-1607.

Lin, J.-L. 2007. The double-ITCZ problem in IPCC AR4 coupled GCMs: ocean-atmosphere feedback analysis. Journal of Climate 20: 4497-4524.

Lloyd, J.E., Guilyardi, E., Weller, H. and Slingo, J. 2009. The role of atmosphere feedbacks during ENSO in the CMIP3 models. Atmospheric Science Letters 10: 170-176.

Yu, J.-Y. and Kim, S.T. 2010. Identification of Central-Pacific and Eastern-Pacific types of El Niņo in CMIP3 models. Geophysical Research Letters 37: 10.1029/2010GL044082.

Zhang, W. and Jin, F.-F. 2012. Improvements in the CMIP5 simulations of ENSO-SSTA meridional width. Geophysical Research Letters 39: 10.1029/2012GL053588.