Statistical and Stochastical Approaches to Assess Reasonable Calibrated Parameters in a Complex Multi-Aquifer System

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