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\begin{document}

\title{Sensitivity Analysis to Uncertain Parameters of Topmodel in Tropical
Regions with Application to the Middle Magdalena Valley}



\author[1]{Maria Cristina Arenas Bautista}%
\author[2]{Duque-Gardeazabal Nicolas}%
\author[2]{Arboleda-Obando Pedro Felipe}%
\author[3]{Guadagnini Alberto}%
\author[3]{Riva Monica}%
\author[2]{Donado-Garzón Leonardo David}%
\affil[1]{Affiliation not available}%
\affil[2]{Universidad Nacional de Colombia Facultad de Ingenieria}%
\affil[3]{Politecnico di Milano Dipartimento di Ingegneria Civile e Ambientale}%


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  \date{May 24, 2024}


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\begin{abstract}
Management of uncertainty in hydrologic modeling is related to our
ability to (a) select appropriate values for model parameters and (b)
assess the extent to which their variation affects a simulated response.
We focus on the application of sensitivity and uncertainty analyses to
assess the influence of main parameters associated with the widely used
distributed watershed model TopModel in estimating surface runoff in the
area of the Middle Magdalena Valley, Colombia. We ground our study on
the GLUE methodology, as included in the MCAT Toolbox. This methodology
is conducive to a Regional Sensitivity Analysis (RSA), rendering global
information about the relative importance of given model parameters
through an a-posteriori probability function. GLUE is viewed as a first
step to undertake a comprehensive global sensitivity analysis based on
the statistical moments characterizing the outputs of the simulations.
We do so upon relying on (a) the Sobol' indices, associated with a
classical decomposition of variance and (b) recently developed indices
quantifying the relative contribution of each uncertain model parameter
to the (ensemble) mean, skewness and kurtosis of the model output. Our
analyses are grounded on a collection of 150.000 model simulations, each
spanning a 12-year temporal window. These are constructed by assuming
those model parameters are random and associated with a uniform
distribution within a support of width selected on the basis of
literature studies and preliminary model calibration against available
data. Results of the global sensitivity analysis enable identifying a
reduced set of model parameter values, showing that the parameter
driving the transmissivity recession curve (associated with an
exponential decrease of saturated hydraulic conductivity with depth),
the maximum root zone storage deficit, and the initial subsurface flow
can be considered as the most sensitive ones. Observed and simulated
high values of surface runoff due to the excess of infiltration suggest
a high water storage capacity of the soil and dominance of subsurface
runoff processes, consistent with the local characteristics of the soils
in the region.%
\end{abstract}%



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