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\begin{document}

\title{Quantifying and Classifying Streamflow Ensembles Using a Broad Range of
Metrics for an Evidence-Based Analysis: Colorado River Case Study}



\author[1]{Homa Salehabadi}%
\author[1]{David Gavin Tarboton}%
\author[2]{Kevin Guy Wheeler}%
\author[3]{Rebecca Smith}%
\author[4]{Sarah Baker}%
\affil[1]{Utah State University}%
\affil[2]{University of Oxford}%
\affil[3]{USBR}%
\affil[4]{US Bureau of Reclamation}%


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  \date{May 16, 2024}


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\begin{abstract}
Stochastic hydrology produces ensembles of time series that represent
plausible future streamflow to simulate and test the operation of water
resource systems. A premise of stochastic hydrology is that ensembles
should be statistically representative of what may occur in the future.
In the past, the application of this premise has involved producing
ensembles that are statistically equivalent to the observed or
historical streamflow sequence. This requires a number of metrics or
statistics that can be used to test statistical similarity. However,
with climate change, the past may no longer be representative of the
future. Ensembles to test future systems operations should recognize
non-stationarity, and include time series representing expected changes.
This poses challenges for their testing and validation. In this paper,
we suggest an evidence-based analysis in which streamflow ensembles,
whether statistically similar to and representative of the past or a
changing future, should be characterized and assessed using an extensive
set of statistical metrics. We have assembled a broad set of metrics and
applied them to annual streamflow in the Colorado River at Lees Ferry to
illustrate the approach. We have also developed a tree-based
classification approach to categorize both ensembles and metrics. This
approach provides a way to visualize and interpret differences between
streamflow ensembles. The metrics presented and their classification
provide an analytical framework for characterizing and assessing the
suitability of future streamflow ensembles, recognizing the presence of
non-stationarity. This contributes to better planning in large river
basins, such as the Colorado, facing water supply shortages.%
\end{abstract}%



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