The design of hydraulic engineering structures is often based on the definition of extreme events of relevant hydraulic variables (e.g., river discharge) according to the return period concept. The analysis of such extreme events allows for defining their peak value, which may on average occur once in a certain time frame and so be used to define the risk and vulnerability of river engineering structures such as dams, levees, retention basins, weirs, etc. However, not only the functionality of such structures but also the evolution of the river itself result from time-integrated processes, e.g., the scouring around obstacles, bank erosion, and vegetation uprooting. For these analyses, the definition of a reference flow hydrograph and its related return period, more than a single peak value, is required. In this work, we consider the Compound Poisson Process (CPP) as a proxy for the time-varying flow discharge and two threshold values, which we use to calculate the reference hydrograph event shape in relation to a given return period. The lower threshold corresponds to the flow condition triggering the initiation of bedload transport, whereas the higher threshold sets the boundary for the Peak-Over-Threshold return period analysis. We adopt a stochastic approach in order to account for all different trajectories starting from below the lower threshold and eventually reaching the upper one. By this means, we derive the relevant statistical properties of the CPP between the two thresholds and calculate the average duration of the rising and the descending limbs between and above the thresholds so as to mathematically define the reference event and its corresponding return period. This sets the basis for a novel and modern engineering risk and vulnerability design theory, which takes not only the magnitude of events but also their duration and characteristic shape into account.