## 3 Results  
### Mean Leaf Area Index (LAI)  
In Figure 1 we present the mean annual LAI (upper panel), the mean annual land precipitation (middle panel), and the mean annual surface temperature (bottom panel) for each model for the period 1986-2005, with the corresponding interannual variability (IAV) and trends. Considering the x-axis of the temperature, models falling at the left of observations (CRU, [89]) indicate a cold bias while models at the right of the reference data have a warm bias. On the y-axis models above the observations have a stronger trend than observations, while the models below the reference value show a lower trend. The same consideration is also valid for the precipitation, namely models falling at the left of observations (CRU) indicate a dry bias (wet bias when falling at the right), while on the y axis models below the observations have a stronger drying trend than observations. It should also be noted that, to be consistent with LAI, we show the precipitation and temperature only over the land points of the Northern Hemisphere. Finally, we selected CRU as reference data for the validation of climatic variables since it has been used as input data in the offline simulations [90]. The evaluation of the simulated precipitation and temperature is needed to assess whether any bias in the simulated LAI can be related to poor performance of the ESMs at reproducing physical variables, or is mainly due to the poor representation of some biogeochemical processes in the land surface models of ESMs. Looking at the LAI (Figure 1), in general, except CanESM2 and INMCM4, all the models overestimate the mean annual LAI over the Northern Hemisphere. The poorest performance has been found in GFDL-EMS2G, which shows a mean value of 2.7, much larger than the reference value (0.83); all the other models show a mean annual LAI ranging from 1.2 and 1.7. Conversely, the trends are well captured by quite a few models; specifically, many models are clustered around the reference value, and, according to the observations, all the models show a greening in the last 20 years. The only far outlier is BNU-ESM, having a positive trend 6 times larger than the observed value. The interannual variability is in general well captured by most of the models, although an overestimation of the year-to-year variability is found for a few models; the exceptions are CanESM2 and MPI-ESM-MR, which show an interannual variability slightly lower than LAI3g. Also, in this case, BNU-ESM is the only outlier in reproducing the IAV, having a year-to-year variability much larger than the reference value. Figure 1: The x-axis shows the observed and simulated mean annual leaf area index (LAI) (**top**), annual land precipitation (**middle**), and mean annual surface temperature over land (**bottom**). The y-axis shows the temporal trend, while the colorbar reports the interannual variability as computed from the annual standard deviation. The large bias found in BNU-ESM could be related in some way to the strong wet bias that this model has in reproducing the observed precipitation. Specifically, whilst the mean annual precipitation as reported by CRU data is 520 mm/yr, BNU-ESM shows a mean value of 802 mm/yr. However, it should also be noted that, except CanESM2, all the other models also have a wet bias. The wet bias found in all the CMIP5 ESM could explain the LAI overestimation: in fact the best agreement between observed and simulated LAI is found for CanEMS2, this being the only model without a wet bias. Although in the boreal and Arctic region the temperature is the main limiting factor for the carbon assimilation, at mid-latitudes the precipitation plays a pivotal role through its control on the soil moisture [91,92]. The precipitation trends in general are well reproduced by the models, being all scattered around the reference data and all showing a wettening over the last 20 years. The exceptions are INMCM4, which does not show any trend in the land precipitation and GFDL-ESM2G, which has a wet bias two times larger than CRU.