\section{CMIP5 multimodel statistics} \label{sec:multimodel}
Fig. \ref{fig:boxplotAmip} shows the East African rainfall annual cycles from different observational datasets, the  ERA-Interim Re-Analysis  and AMIP runs of the 21 CMIP5 models. The observed annual cycles are close to each other,  whether the observation is based on gauge (GPCC and CRU) or satellite (TRMM) or their combination (CMAP and GPCP), establishing a solid reliability for the observed rainfall annual cycle over East Africa. The characteristic bimodal annual cycle is apparent from the observations, with the major rainy season during MAM (long rains) and the second rainy season during OND (short rains). Precipitation from the  ERA-Interim Re-Analysis  generally follows the observed annual cycle except for the short rains where the reanalysis can be  0.5 mm day~$^{-1}$ greater than the observed. Because a reanalysis dataset is influenced both by  the assimilated observations and by the model, reanalyses may share some similar biases with GCMs especially for precipitation.  Rainfall annual cycles from the AMIP runs show some degree of spread among different models but the multimodel mean (the blue line) or their median (red horizontal lines in the boxes) does reproduce the bimodal feature. However, the multimodel mean overestimates the rainfall in all months except April and May. The short rains are positively biased in models such that they are comparable with the long rains. This bias in AMIP runs might arise from the AGCM's excess precipitation response to the SST gradient over the western Indian Ocean as found in previous work \citep[e.g.][]{Bollasina_2013} and will not be addressed here. Instead, we will focus on the bias arising from the atmosphere-ocean coupling by comparing CMIP5 historical runs to the AMIP runs.