The problem I can see in your questions is that you never indicated what is your frequency band of interest.
Satellite downlink frequencies from 4/6 t 12/14 and 18 GHz have already been studied for rain attenuation, and ITU Documents have presented the results of ran loss statistics over a year in most Earth locations , according to weather areas.
You can use the ITU data to CALCULATE what you need.
If you want to run an experiment to get your data, then you must specify the frequency, find satellites that carry a beacon transmitter, design and operate a small earth station.To start you can use a spectrum analyzer connected after receiving LNB to try find a stable beacon signal, then design a SDR receiver for that frequency and collect the signal power data over a year or more. You will learn about the stability of your receiver, about the effect of antenna pointing (many satellites "wander" )and other effects beyond that of rain.
Recently, frequency band around 45 GHz is of interest or satellite downlink. In Europe, a satellite with beacons at 20 and 40 GHz is to be launched soon. Building a suitable measuring station to get rain loss data would cost estimated USD 0.5 million or more.
Good luck!