What would 'adequate' technology to 'deal with' those look like?
Droughts are pretty easy, you can do it right now if you stop trying to maximize evaporation and start doing something reasonable like drip irrigation.
Flooding is a bit different in that I assume we're speaking about the Greenland glaciers and some of Antractica melting. You can either prevent them from melting or just build high walls around particularly valuable pieces of real estate. Shorelines are never stable, anyway -- continental plates rise and sink, estuaries silt up, hurricanes rearrange barrier islands, etc.
Speculation is important for forecasting; it's also fun. Speculation is usually conveyed in two forms: in the form of an argument, or encapsulated in fiction; each has their advantages, but both tend to be time-consuming. Presenting speculation in the form of an argument involves researching relevant background and formulating logical arguments. Presenting speculation in the form of fiction requires world-building and storytelling skills, but it can quickly give the reader an impression of the "big picture" implications of the speculation; this can be more effective at establishing the "emotional plausibility" of the speculation.
I suggest a storytelling medium which can combine attributes of both arguments and fiction, but requires less work than either. That is the "wikipedia article from the future." Fiction written by inexperienced sci-fi writers tends to generate into a speculative encyclopedia anyways--why not just admit that you want to write an encyclopedia in the first place? Post your "Wikipedia articles from the future" below.