A consultant is setting up a hydrologic model using Bayesian inference to evaluate the impacts of raising the Wyangala Dam wall in the Lachlan Valley. A figure of the model is given below. To evaluate the model, they have undertaken sensitivity analysis of some of the model parameters: the maximum surface storage $($Smax$),$ the baseflow rate $($B$),$ and the surface runoff routing time $(Rt).$

a$)$ For this example, explain what the sensitivity analysis shows, and how these results would be helpful for this model.

b$)$ As the model was calibrated via Bayesian inference, the modeller had to define prior distributions for the model parameters. Define the term 'prior distribution', and explain how the modeller could define the prior distribution for the baseflow recharge parameter.

c$)$ Explain what you think would be the biggest source of uncertainty for an exercise like this and why.