\subsection{Convective instatility and MSE}
In order to understand the historical$-$AMIP monthly climatology rainfall difference in MRI-CGCM3, we calculate the convective instability (CI) as measured by near surface moist static energy minus 700 hPa saturated moist static energy \citep{Yang_2015}. The historical$-$AMIP monthly climatology of the CIs are shown in Fig. \ref{fig:ciMon}. The CI differences  generally agree well with  rainfall in Fig. \ref{fig:prMon}. There is also a large scale north-south contrast from January to May over the Indian Ocean. During this period, the northern Indian Ocean and East Africa have negative CI differences, implying that the atmosphere over these regions is more stable and precipitation is suppressed in the historical run compared to in the AMIP run, which explains the dry bias over these regions in Fig. \ref{fig:prMon}. The CI also develops a positive bias over the  western Indian Ocean starting from June,  destabilizing the atmosphere in the historical run and enhancing precipitation there and over East Africa. It should be noted that the evolutions of the CI and rainfall biases are not synchronous over East Africa after June and the CI seems to lead rainfall by one month. For example, the CI bias over East Africa peaks in August and September while the rainfall bias peaks in September and October. Also, the CI bias turns negative over much of East Africa in November while the rainfall bias is still slightly positive and becomes negative in December.