Input and parameter uncertainty quantification of groundwater flow models

Abstract

Transient numerical groundwater flow models have been used to understand and forecast groundwater flow systems under anthropogenic and climatic effects, but the reliability of the predictions is strongly influenced by different sources of uncertainty. Hence, researchers in hydrological sciences are developing and applying methods for uncertainty quantification. Nevertheless, spatially distributed flow models pose significant challenges for parameter and spatially distributed input estimation and uncertainty quantification. In this study, we present a general and flexible approach for input and parameter estimation and uncertainty analysis of groundwater models. The proposed approach combines a fully distributed groundwater flow model (MODFLOW) with the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm. To avoid over-parameterization, the uncertainty of the spatially distributed model input has been represented by multipliers. The posterior distributions of these multipliers and the regular model parameters were estimated using DREAM. The proposed methodology has been applied in an overexploited aquifer in Bangladesh where groundwater pumping and recharge data are highly uncertain. The results confirm that input uncertainty does have a considerable effect on the model predictions and parameter distributions. Additionally, our approach also provides a new way to optimize the spatially distributed recharge and pumping data along with the parameter values under uncertain input conditions. It can be concluded from our approach that considering model input uncertainty along with parameter uncertainty is important for obtaining realistic model predictions and a correct estimation of the uncertainty bounds.

Full text

INTRODUCTION
Input and parameter uncertainty quantification
of groundwater flow models
Syed Md. Touhidul Mustafaa, Jiri Nossenta,b, Gert Ghyselsaand Marijke Huysmansa
aDepartment of Hydrology and Hydraulic Engineering, Vrije Universiteit Brussel (VUB), Belgium (E-mail: syed.mustafa@vub.be)
b Flanders Hydraulics Research, Department of Mobility and Public Works, Flemish Government, Antwerp, Belgium
The conventional treatment of uncertainty in groundwater modelling focuses on parameter
uncertainty.
Quantifying input uncertainty in addition to parameter uncertainty separately and
appropriately is important.
The rainfall multiplication method has been applied for lumped and semi-distributed rainfall-
runoff models to quantify rainfall uncertainty in addition to model parameter uncertainty.
As far as the authors are aware, no research incorporating different types of uncertainty has
been carried out so far with a fully-distributed groundwater model.
Model calibration and uncertainty analysis are performed simultaneously with two scenarios .
METHODOLOGY
Consideration of model input uncertainty along with parameter uncertainty is important for obtaining realistic model predictions and a correct estimation of the uncertainty bounds.
The approach using multipliers is useful to quantify the input uncertainty even in a fully-distributed groundwater model.
Additionally, our approach also provides a new way to evaluate and improve the interpretation of spatially distributed recharge and pumping data under uncertain input conditions.
CONCLUSIONS
Recharge Uncertainty
The explicit consideration of recharge uncertainty through the use of recharge
multipliers is feasible even in a fully distributed model, as recharge multipliers were
successfully inferred and identified within their prior ranges.
Objectives
In this study, we present a general and flexible approach for input and parameter
estimation and uncertainty analysis of a fully distributed groundwater model.
The feasibility of our approach using multipliers has been evaluated for fully-distributed
groundwater recharge and pumping data for a fully-distributed, physically-based
groundwater model.
Marginal posterior probability distributions of recharge multipliers
Abstraction multipliers is
able to optimize spatially
distributed abstraction data
under uncertain input
conditions.
Parameter Uncertainty
Different but more realistic parameter values are obtained when input (recharge and
abstraction) uncertainty is explicitly considered.
Prediction Uncertainty
The observation coverage of the 95% confidence interval related to the parameter
uncertainty has increased from 8 % to 45 % when we account for input uncertainty.
The results reveal that ignoring input uncertainty will lead to unrealistic model
simulations and incorrect uncertainty bounds.
Model parameters only
Model + Input parameters
Abstraction Uncertainty
Abstraction multipliers were successfully inferred and identified within their prior ranges.
The use of abstraction multipliers is feasible for considering abstraction uncertainty even
in a fully distributed model.
Prediction uncertaintyPrediction uncertainty
Conventional Method Proposed Method
We introduced groundwater recharge multipliers and groundwater abstraction multipliers to
quantify the uncertainty of the spatially distributed input data
Groundwater abstraction multipliers
(ms-1)(m2s-1)
(m)