A scale-invariant Gruss-Markov model for design storm hyetographs

Hyetographs are essential to many hydrological designs. Many studies have s hown that hyetographs are specific to storm types and durations. Recent wor k presented evidence that dimensionless hyetographs are scale invariant. We show that the simple scaling property of rainfall guarantees that the norm alized rainfall rates of different storm durations are identically distribu ted and propose a nonstationary Gauss-Markov model based on the annual maxi mum events that arise from the dominant storm type. We derive the unique es timators for the parameters of the Gauss-Markov model under two constraints that: (a) the typical peak rainfall rate is preserved, and (b) the most li kely hyetograph is obtained. One attractive feature of this model is that i t allows translating hyetographs between storms of different durations. Two examples illustrate our model.