poster - International Conference of Agricultural Engineering

Stochastic modelling of Contaminants Transport through
Groundwater Using a Moving Least Squares Response Surface
Method with Hermite Polynomials
T. H. Bong 1 , Y. H. Son 1 *, S. K. Noh 1 , J. S. Park 1 , S. P. Kim 2 , J. Heo 2
1 Department of Rural Systems Engineering, Seoul National University, Gwanak-ro, Gwanakgu,
Seoul, 151-921 Korea
2 Rural Research Institute Korea Rural Community Corporation, Haean-ro Sangrok-gu, Ansan,
426-908 Korea
*Corresponding author. E-mail: syh86@snu.ac.kr
Abstract
It is important to understand contaminants transport through groundwater. To obtain reliable
result, uncertainties of parameter should be considered. In this study, uncertainty in Benzene
concentration at various distances is analyzed. Two parameters ( K and K
oc
) are
considered as random variables and probability density distributions of random variables are
estimated using Hermite polynomials. MLS-RSM is performed to improve the efficiency of
uncertainty analysis and can achieve results close to accuracy of MCS with a sample size of
100,000. In conclusion, considering the actual probability density distributions by Hermite
polynomials, more accurate results can be obtained.
Key words: contaminants transport, MLS-RSM, stochastic modelling, Hermite Polynomials
1. Introduction
The groundwater pollution load has been increased as a result of human activities related to
industrial and agricultural production on water resources. Thus understanding contaminants
transport through groundwater is important for water management and remedial action plans.
However, groundwater modelling is not an easy task. To get reliable results, input data
should be accurate and representative of the reality of the field and uncertainties in model
input data including chemical, physical and hydrogeological parameters also needs to be
considered (Baalousha & Köngeter, 2006). Several recent studies have been conducted on
the modelling of contaminants transport though ground water considering uncertainties
(Datta & Kushwaha, 2011; Isukapalli, 1999; Jim yeh, 1992; Ranade et al., 2010).
Probabilistic uncertainty propagation methods available fall into three categories: (a) Monte
Carlo simulation (MCS), (b) analytical method, (c) response surface method (Phoon & Huang,
2007). The MCS is a universal method regardless of the complexities underlying the physical
model and/or input uncertainties. However, when the models are complex, or when there are
numerous parameters, the MCS can be costly and time-consuming. Therefore, a variety of
variance reduction techniques have been proposed to reduce the number of runs.
Among these, the response surface method (RSM) has been used in probabilistic modeling
for various fields. However, the RSM requires transformation of input variable from the
original space (X) to the standard normal space (U). To do this, probability density function
(PDF) of input data is assumed by common PDF (e.g., normal distribution or lognormal
distribution) and transformed using equivalent mean and standard deviation. It is difficult to
estimate PDF from empirical data, especially when sample sizes are small. The reliability of
result relies on input variable, and therefore, a realistic PDF should be considered by actual
measurement rather than assumed probability distributions. Phoon (2003) proved that any
random variable can be expanded as a sum of Hermite polynomials. The remaining issue is
how to improve the efficiency of the calculation. Compared with traditional methods, the RSM