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\begin{document}

\title{Identification of a lumped, mass-conserving rainfall-discharge model of
the Amazon basin for GRACE data assimilation}



\author[1]{Karim Douch}%
\author[1]{Peyman Saemian}%
\author[1]{Nico Sneeuw}%
\affil[1]{University of Stuttgart}%


\vspace{-1em}



  
  \date{June 18, 2024}


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\begin{abstract}
Previous work based on Gravity Recovery and Climate Experiment (GRACE)
data has shown that for certain large river basins like the Amazon, the
empirical storage-discharge relationship reveals an underlying dynamics
that is approximately linear and time-invariant. This is particularly
true for the catchment upstream of the \selectlanguage{ngerman}Óbidos stream gauge station on
the Amazon river. We build on this observation to put forward, in this
case, a simple first-order differential equation that approximates the
observed dynamics. The model formulation includes one parameter that can
be physically interpreted as an offset determining the total drainable
water stored in the catchment, while a second parameter characterizes
the typical time constant of the draining of the basin. We determine a
value of 1925 km³ for the average total drainable water stored in the
catchment during the period 2004 to 2009 and a draining time constant of
27.4 days. The same approach is also tested over eight smaller
catchments of the Amazon to investigate whether or not the
storage-discharge relationship is governed by a similar dynamics.
Combined with the water mass balance equation, we eventually obtain two
coupled linear differential equations which can be easily recast into a
discrete state-space representation of the rainfall-storage-discharge
dynamics of the considered basin. This set of equations is equivalent to
defining an analytical instantaneous unit hydrograph for the whole
basin. Besides, the proposed model is particularly suitable for Bayesian
filtering and smoothing or the reconstruction of past unobserved states.%
\end{abstract}\selectlanguage{ngerman}%



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