Statistical and Stochastical Approaches to Assess Reasonable Calibrated Parameters in a Complex Multi-Aquifer System
Creators: name: Arlai, Phatcharasak
name: Koch, Manfred
name: Koontanakulvong, Sucharit
name: Arlai, Phatcharasak
Publisher: name: XVI International Conference on Computational Methods in Water Resources
Year: 2006

description: Effective assessment of reasonable calibrated aquifer parameters can be mainly 
divided into three categories; firstly, the conventional analysis of the misfit 
error  between observed and calculated head, secondly, the calculation of 
sensitivity- and correlation coefficients and, finally, the pure stochastical 
approach applying well-known stochastical formulae (cf. Gelhar, 1993 ).

We have applied these three approaches to the Bangkok Multi-Aquifer System. The 
latter consists of eight complex water bearing layers under Bangkok and neighboring 
provinces, namely, Bangkok Aquifer (BK - 50m.), Phra Pradang Aquifer (PD - 100m.), 
Nakhon Luang Aquifer (NL - 150m.), Nonthaburi Aquifer (NB - 200m.), Sam Khok Aquifer 
(SK- 300m.), Phaya  Thai Aquifer (PT - 350m.), Thon Buri Aquifer (TB – 450m.) and 
Pak Nam Aquifer (PN - 550m.). Using first the conventional approach of trial and 
error, the geohydraulic parameters were estimated for this aquifer system by visual 
comparing observed and calculated heads. The regression graphs of observed head (x-
axis) and calculated head (y-axis) showed all points located closely to the 45 
degree-line, which indicates that calculated and observed heads conform closely to 
each other. 

Next, the estimated parameters were assessed by using the automated nonlinear 
regression program, UCODE (Hill, 1998). Relative composite scale sensitivity- and 
correlation coefficients are calculated. The results indicate that every estimated 
parameter has a composite scaled sensitivity higher than 0.01 and a correlation 
coefficient higher than 0.9, which shows that the corresponding geohydraulic 
parameters are well-determined and unique. This means that the observed heads are 
sufficient for a reliable calibration of the named parameters. 

In a third step, the full stochastical approach is used. Applying a random field 
generator (Chiang and Kinzelbach, 2001), 180 realizations of a logarithmic 
transmissivity  field Y=lnT  with a set of variances σY2 for each layer, namely, σY2 
= 0.55, 0.77, 0.59,  in layer 3, 4 and 5, respectively, and  two sets of correlation 
length (λx, λy ) (with x and y corresponding to the EW and NS-direction, 
respectively) that represent 63% and 95% of  the sill of the observed variograms,  
namely,  λx = 9000, 6000, 5500 and λy = 12500, 23000, 7500  for the 63% -sill and 
and  λx = 26000, 21500, 17500 and λy = 33000, 56000, 22500 for the 95%-sill  which 
appears to characterize the possible stochastical range of  the ln T –field  in the 
multi-aquifer system. Using these Monte-Carlo simulations we investigate how σY2 
contributes to the variance σH2 of the head and/or the residual head. It turns out 
that σY2  and σH2  estimated in this way can be related to each other in the form 
σH2  = C*σY2 *λ2  as predicted by stochastical theory (Gelhar,1993). 

Finally, we investigate which factors affect the residual error of the model 
estimation. Obviously, both transmissivity variations and errors in the head 
measurements are mostly responsible for a non-zero estimated residual head. Hence, 
the variances of head that are obtained from stochastically generated 
transmissivities and the intrinsic errors of the head measurements were determined. 
The results show that the stochastically predicted variances of the head are still 
somewhat lower than the variances of the residual head, indicating additional 
uncertainties in the fitted model. Indeed, the pumping rates turn out to be very 
evasive, as pumping rates in the study area are not always correctly reported from 
well owners. To investigate the effects of varying pumping rates on the residual 
head variance, 180 Monte Carlo simulations with randomly disturbed pumping rates of 
varying magnitudes (30 - 80 % of the reference value) are performed. The results 
show that pumping plays a smaller but still significant role for the estimation of 
the residual error, as the residual head variances obtained from stochastic pumping 
are lower than those obtained from the stochastic transmissivity field .


1 Department of Geohydraulics and Engineering Hydrology, University of Kassel, Kurt-
Wolters Str.3, D34109 Kassel, Germany
2 Department of Water Resources Engineering, Chulalongkorn University, Bangkok, 
Thailand