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\begin{document}

\title{Regionalization of Climate Elasticity Preserves Dooge's Complementary
Relationship}



\author[1]{Chandramauli Awasthi}%
\author[2]{Richard M. Vogel}%
\author[1]{Arumugam Sankarasubramanian}%
\affil[1]{North Carolina State University}%
\affil[2]{Tufts University}%


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  \date{May 26, 2024}


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\begin{abstract}
Climate elasticity of streamflow represents a nondimensional measure of
the sensitivity of streamflow to climatic factors. Estimation of such
elasticities from observational records has become an important
alternative to scenario-based methods of evaluating streamflow
sensitivity to climate. Nearly all previous elasticity studies have used
a definition of elasticity known as arc elasticity, which measures
changes in streamflow about mean values of streamflow and climate. Using
observational records in western U.S., our findings reveal that
elasticity definitions based on power law models lead to both regional
and basin specific estimates of elasticity which are physically more
realistic than estimates based on arc elasticity. Evaluating the ability
of arc and power law elasticity estimators in reproducing Dooge's
complementary relationship (DCR) between potential evapotranspiration
and precipitation elasticities reveal that power law elasticities
estimated from at-site, panel and hierarchical statistical models
reproduce DCR, whereas corresponding estimators based on arc elasticity
cannot reproduce DCR. Importantly, our regional elasticity formulations
using either panel and/or hierarchical formulations led to estimates of
both regional and basin specific estimates of elasticities, enabling and
contrasting streamflow sensitivity to climate across both basins and
regions.%
\end{abstract}%



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\verb`978113_0_supp_11541501_s3d6qh.docx`  available at \url{https://authorea.com/users/697148/articles/685418-regionalization-of-climate-elasticity-preserves-dooge-s-complementary-relationship}

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