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\begin{document}

\title{Generalizing Reservoir Operations using a Piecewise Classification and
Regression Approach}



\author[1]{Lucas Ford}%
\author[2]{Arumugam Sankarasubramanian}%
\affil[1]{NC State University}%
\affil[2]{North Carolina State University}%


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  \date{May 27, 2024}


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\begin{abstract}
Inflow anomalies at varying temporal scales, seasonally varying storage
mandates, and multi-purpose allocation requirements contribute to
reservoir operational decisions. The difficulty of capturing these
constraints across many basins in a generalized framework has limited
the accuracy of streamflow estimates in Land Surface Models for
locations downstream of reservoirs. We develop a Piece Wise Linear
Regression Tree to learn generalized daily operating policies from 76
reservoirs from four major basins across the coterminous US. Reservoir
characteristics, such as residence time and maximum storage, and daily
state variables, such as storage and inflow, are used to group similar
observations across all reservoirs. Linear regression equations are then
fit between daily state variables and release for each group. We
recommend two models -- Model 1 (M1) that performs the best when
simulating untrained records but is complex, and Model 2 (M2) that is
nearly as performant as M1 but more parsimonious. The simulated release
median root mean squared error is 49.7\% (53.2\%) of mean daily release
with a median Nash-Sutcliffe Efficiency of 0.62 (0.52) for M1 (M2).
Long-term residence time is shown to be useful in grouping similar
operating reservoirs. Release from low residence time reservoirs can be
mostly described using inflow-based variables. Operations at higher
residence time reservoirs are more related to previous release variables
or storage variables, depending on the current inflow. The ability of
the models presented to capture operational dynamics of many types of
reservoirs indicates their potential to be used for untrained and
limited data reservoirs.%
\end{abstract}%



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