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

Hyetographs are essential to many hydrological designs. Many studies have shown that hyetographs are specific to storm types and durations. Recent work presented evidence that dimensionless hyetographs are scale invariant. We show that the simple scaling property of rainfall guarantees that the normalized rainfall rates of different storm durations are identically distributed and propose a nonstationary Gauss-Markov model based on the annual maximum events that arise from the dominant storm type. We derive the unique estimators for the parameters of the Gauss-Markov model under two constraints that: (a) the typical peak rainfall rate is preserved, and (b) the most likely hyetograph is obtained. One attractive feature of this model is that it allows translating hyetographs between storms of different durations. Two examples illustrate our model.