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\begin{document}

\title{Soil-dependent \selectlanguage{greek}β \selectlanguage{english}and \selectlanguage{greek}γ \selectlanguage{english}shape parameters of the Haverkamp infiltration
model for 3D infiltration flow\selectlanguage{english}}



\author[1]{Deniz YILMAZ}%
\author[2]{Laurent Lassabatère}%
\author[3]{David Moret-Fernández}%
\author[4]{Mehdi Rahmati}%
\author[2]{Rafael Angulo-Jaramillo}%
\author[3]{Borja Latorre}%
\affil[1]{Munzur University}%
\affil[2]{Laboratoire d'Ecologie des Hydrosystemes Naturels et Anthropises}%
\affil[3]{Estacion Experimental de Aula Dei}%
\affil[4]{University of Maragheh}%


\vspace{-1em}



  
  \date{May 17, 2024}


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\selectlanguage{english}
\begin{abstract}
Estimating of soil sorptivity ( S ) and saturated hydraulic conductivity
( K s ) parameters by field infiltration tests are widespread due to the
ease of the experimental protocol and data treatment. The analytical
equation proposed by Haverkamp et al. (1994) allows the modeling of the
cumulative infiltration process, from which the hydraulic parameters can
be estimated. This model depends on both initial and final values of the
soil hydraulic conductivity, initial soil sorptivity, the volumetric
water content increase ( [?] \selectlanguage{greek}θ \selectlanguage{english}), and two infiltration constants, the
so-called \selectlanguage{greek}β \selectlanguage{english}and \selectlanguage{greek}γ \selectlanguage{english}parameters. However, to reduce the number of unknown
variables when inverting experimental data, constant parameters such as
\selectlanguage{greek}β \selectlanguage{english}and \selectlanguage{greek}γ \selectlanguage{english}are usually prefixed to 0.6 and 0.75, respectively. In this
study, the values of these constants are investigated using numerical
infiltration curves for different soil types and initial soil water
contents for the van Genuchten-Mualem (vGM) soil hydraulic model. Our
approach considers the long-time expansions of the Haverkamp model, the
exact soil properties such as S , K s , and initial soil moisture to
derive the value of the \selectlanguage{greek}β \selectlanguage{english}and \selectlanguage{greek}γ \selectlanguage{english}parameters for each specific case. We
then generated numerically cumulative infiltration curves using Hydrus
3-D software and fitted the long-time expansions to derive the value of
the \selectlanguage{greek}β \selectlanguage{english}and \selectlanguage{greek}γ \selectlanguage{english}parameters. The results show that these parameters are
influenced by the initial soil water content and the soil type. However,
for initially dry soil conditions, some prefixed values can be proposed
instead of the currently used values. If an accurate estimate of S and K
s is the case, then for coarse-textured soils such as sand and loamy
sand, we propose the use of 0.9 for both constants. For the remaining
soils, the value of 0.75 can be retained for \selectlanguage{greek}γ . \selectlanguage{english}For \selectlanguage{greek}β \selectlanguage{english}constant, 0.75
and 1.5 values can be considered for, intermediate permeable soils
(sandy loam and loam) and low permeable soils (silty loam and silt),
respectively. We clarify that the results are based on using the vGM
model to describe the hydraulic functions of the soil and that the
results may differ, and the assumptions may change for other models.%
\end{abstract}%



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\textbf{Hosted file}

\verb`Numerical study of gamma and beta - vGM -formated for hydrological process.docx`  available at \url{https://authorea.com/users/577331/articles/619767-soil-dependent-%CE%B2-and-%CE%B3-shape-parameters-of-the-haverkamp-infiltration-model-for-3d-infiltration-flow}

\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/fig1-600DPI/fig1-600DPI}

\end{center}
\end{figure}

\begin{figure}[H]
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\includegraphics[width=0.70\columnwidth]{figures/fig2-DPI-600-size-reduced/fig2-DPI-600-size-reduced}

\end{center}
\end{figure}

\textbf{Hosted file}

\verb`figures caption.docx`  available at \url{https://authorea.com/users/577331/articles/619767-soil-dependent-%CE%B2-and-%CE%B3-shape-parameters-of-the-haverkamp-infiltration-model-for-3d-infiltration-flow}

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