I am not sure about your application, but the total antenna efficiency is the proportion of the input power that is radiated.  If you only want your antenna to radiate in a hemisphere then you need a ground plane to shield the other hemisphere from radiation, and the total radiation efficiency will give what you want.  Otherwise you will need to post-process by integrating the directivity (or the gain) over the hemisphere you are interested in, and over the whole sphere, and multiplying the total efficiency by that ratio.