Background
The authors write that "decadal variability in the climate system from the Atlantic Multidecadal Oscillation (AMO) is one of the major sources of variability at this temporal scale that climate models must properly incorporate because of its climate impact." And, therefore, they say that "the main goal of this paper is to assess the way models from the CMIP3 and CMIP5 projects depict the AMO in the twentieth century climate," which they again emphasize is "a key element for decadal prediction."

What was done
In terms of the data they employed, Ruiz-Barradas et al. say they used real-world sea surface temperature (SST) and precipitation data obtained from observations, together with simulations of 20th-century climate obtained from models participating in the CMIP3 and CMIP5 projects of the Intergovernmental Panel on Climate Change (IPCC), while the observed precipitation data they used were obtained from the University of East Anglia Climate Research Unit's high-resolution gridded station data, as described by Mitchell and Jones (2005).

What was learned
Quoting the three U.S. scientists, they say they found that (1) "the majority of the models have poor correlation with observations and under-estimate the observed variability," that (2) "the models are not up to the task of simulating the impact of the regional hydro-climate," that (3) "the spatial variability of the precipitation anomalies is under-estimated," that (4) "spatial correlations with observations are under 0.3 over the North American domain in either season," that (5) "both CMIP3 and CMIP5 multi-model means do not simulate the intensification of SST anomalies over the Mid-Atlantic from summer to fall, and are colder than observations indicate," that (6) "the multi-model means show wetter North America and drier western Africa than observations in summer and fall," that (7) "spatial correlations of the observed and simulated anomalies do not indicate an improvement of the CMIP5 versus CMIP3 models," that (8) "in the context of North America hydroclimate, particularly over the central US, models are unable to properly simulate the impact of the AMO in summer and fall," that (9) "the evolution of the SST anomalies associated with the warm phase of the AMO in models ... have marked differences in magnitude and structure between the CMIP3 and CMIP5 versions," that (10) in regard to the characteristic period of the AMO, "all models under-estimate the 44-year value suggested from observations with periods in the 16-24 years range," making it clear that (11) both sets of models "are not up to the task of simulating the impact on the regional hydroclimate," and that (12) there have been "no improvements in the oceanic and hydroclimate impacts associated with the AMO from CMIP3 to CMIP5."

What it means
Ruiz-Barradas et al. conclude that "the spurious increase in high 10-20 year variability from CMIP3 to CMIP5 models may be behind the unsatisfying progress in depicting the spatio-temporal features of the AMO." And they say that "this problem, coupled with the inability of the models to perturb the regional low-level circulation" - which is the driver of moisture fluxes - "seem to be at the center of the poor representation of the hydroclimate impact of the AMO."

Reference
Mitchell, T.D. and Jones, P.D. 2005. An improved method of constructing a database of monthly climate observations and associated high resolution grids. International Journal of Climatology 25: 693-712.