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I've done somewhat similar things to predict water levels vs rainfall by creating a watershed model in HEC-HMS (http://www.hec.usace.army.mil/) and working backwards to tweak all of the variables and assumptions in the model to make it agree with the field data. It won't answer all of your questions, but things like evapotranspiration, infiltration, initial abstraction, groundwater storage, time of concentration, and a rainfall-runoff curve will pop right out. Pretty neat and it's free.
Then if you really want to geek out, you can feed the flow data from HEC-HMS into HEC-RAS and develop a water level or gauge reading for minimum paddleable flows, also velocities, erosion, all kinds of neat stuff.
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