Hi Akash, this seems to me like a rather broad question. There is obviously scientific evidence on the hydrological effects of Climate Change. What is interesting however is that flooding and drought can both be attributed to Climate Change effects, this, of course, varies depending on the part of the world (i.e. it is rare to have both flooding and drought affecting the same flow regime in the same area around the same time). For the case of your project (I presume you are looking at a particular area); you could assign figures (say 1-10, where 10 is extreme flooding, 1 extreme drought that is if you are using ArcGIS) to the set of raster files. The software will then assign colours, usually darker shades for the extreme cases. I am no GIS expert but I understand that is how it kind of works. Also, note that I have only referred to flooding and drought, but there could also be other factors affecting flow regime.
Climate change means increase or decrease in the intensity or amount of rainfall / temperature from the long term average. This will lead to drought or floods or scarcity of water and all these will ultimately affect the discharge pattern in the river flow with time.
One can map the river flow through water spread area making use of remote sensing for different time period, try to understand the deviation from the normal and compare the same with respect to any established climate change pattern in the region and relate.
I agree with Guillermo in saying that river discharge vs time is a direct indicator of change in a river flow system and water resources of a region. Another aspect I would like to add is the recognition of the climate-sensitive component in the river flow system and domonstration of its change with time. We have experience in dealing with glacier rivers, where the snow/ice melt component is a very much climate-sensitive indicator. See our publication: