1. (4 Points) After recalling the general aspects of the concept of IUH (but without specifying the

expressions it assumes according to the different considered model), find the expression of the flow

q(t) given at an instant t by the convolution integral (i.e. superposition of effects in integral form)

between a generic net rainfall flow and the transformation function (called IUH) representing the

catchment response to it. Mention the two hypotheses required to apply the convolution. Moreover,

demonstrate why the arguments of the rainfall flow function p and of the IUH can be swapped.

Here it is also required to describe the discretized expression of the convolution.

2. {2.0 points} Demonstrate, both analytically and graphically, that the critical rainfall duration for

the peak flow is equal to the concentration time in the case of the kinematic model with linear time-

area curve.

3. {3.0 points}. Describe the Clarke model.

4. {3.0 points}. Describe the framework of the GIUH model.

5. {3.0 points} Show analytically why, for a given return period, the concentration time is also the

critical rainfall duration for in case of rectangular ietograph and linear time-area curve.

6. {2.0 points} Describe the Nash model, mentioning also its relationship with the linear

reservoir model.