We are used to the weather-climate dichotomy, yet the great majority of the spectral variance of atmospheric fields is in the continuous "background" and this defines instead a trichotomy with a "macroweather" regime in the intermediate range from ≈10 days to 10-30 yr (≈100 yr in the preindustrial period). In the weather, macroweather and climate regimes, exponents characterize the type of variability over the entire regime and it is natural to identify them with qualitatively different synergies of nonlinear dynamical mechanisms that repeat scale after scale. Since climate models are essentially meteorological models (although with extra couplings) it is thus important to determine whether they currently model all three regimes. Using last millennium simulations from four GCMs (global circulation models), we show that control runs only reproduce macroweather. When various (reconstructed) climate forcings are included, in the recent (industrial) period they show global fluctuations strongly increasing at scales > ≈10-30 yr, which is quite close to the observations. However, in the preindustrial period we find that the multicentennial variabilities are too weak and by analysing the scale dependence of solar and volcanic forcings, we argue that these forcings are unlikely to be sufficiently strong to account for the multicentennial and longer-scale temperature variability. A likely explanation is that the models lack important slow "climate" processes such as land ice or various biogeochemical processes.