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\begin{document}

\title{Investigation of Multi-fidelity Co-Kriging Model for Hydraulic
Conductivity in Sangamon Watershed}



\author[1]{Maryam Ghadiri}%
\author[2]{Chien-Yung Tseng}%
\author[2]{Hadi Meidani}%
\affil[1]{Illinois Water Resources Center}%
\affil[2]{University of Illinois at Urbana Champaign}%


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  \date{May 25, 2024}


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\begin{abstract}
Sangamon watershed is recognized as one of the most worth noting regions
for water and environmental supply planning and management purposes
according to its intensively management for soybean and corn production.
It is also a representative area with limited geological and hydraulic
measurement data, in which sustainable ground water and environmental
management is essential. To better understand the hydraulic properties
of the entire watershed, a multi-fidelity Gaussian Processes (Kriging)
model was applied to predict the hydraulic conductivity of the upper
Sangamon watershed, using previous multi-sources of field observation
data (Electrical Earth Resistivity and pumping test data). The model
also provided a quantification of uncertainty of the predicted values,
which helps us to make reliable suggestions for the future design of
hydraulic observations. The data fidelity effect to the model was
discussed by comparing multi-fidelity and single-high-fidelity Kriging
results. The model predicted values suggest that the accuracy of
multi-fidelity Kriging depends on the locations and the distribution of
both the high- and low-fidelity data. When high-fidelity data points are
sparse and far away from the low-fidelity data points, the information
provided from the low-fidelity data becomes extremely important, which
can greatly enhance the model performance and accuracy. This study has
paved the way to a more efficient parameter estimation in under-sampled
sites by effectively estimating large-scale parameter maps using
small-scale measurements and by applying uncertainty quantification
method to a real watershed observation case. It will also draw upon and
contribute to advances in Bayesian experimental design, and will
optimally result in financial savings.%
\end{abstract}%



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