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\begin{document}

\title{The Perturbed Rainfall Uncertainty Unit Hydrograph Method}



\author[1]{Catalina Corral Fernandez}%
\author[2]{Jorge Leandro}%
\author[3]{Alexandre Silveira}%
\author[3]{Bruna Pessoti}%
\affil[1]{Technical University Munich}%
\affil[2]{Technische Universität München}%
\affil[3]{Federal University of Alfenas}%


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  \date{May 30, 2024}


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\begin{abstract}
The Unit Hydrograph (UH) theory can be used to estimate the discharge
hydrograph of a basin based on precipitation and runoff measurements.
However, uncertainty in those measurements may unable a unique UH to be
derived. It is well known that in comparison with runoff measurements,
the spatial and temporal variability of rainfall is the main source of
uncertainty. Hence, in this work we present a method to derive an
improved unique UH assuming that the rainfall data is the main source of
uncertainty. The Perturbed Rainfall Uncertainty Unit Hydrograph (PeRUUH)
method is verified using a large scale rainfall simulator (LSRS). The
method combines linear programming and reverse modelling to generate a
perturbed rainfall intensity pattern, which accounts for the temporal
and spatial rainfall uncertainty assuming discharge to be true. The
method is validated in three different rainfall events using the LSRS.
The PeRUUH method is more robust than the original UH, as it is shown to
be able to estimate a unique UH for which the discharges have an error
of (approx.) 10 times smaller than its counterpart.%
\end{abstract}%



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