Estimation and Impact Assessment of Input and Parameter Uncertainty in Predicting Groundwater Flow With a Fully Distributed Model

Abstract

We present a general and flexible Bayesian approach using uncertainty multipliers to simultaneously analyze the input and parameter uncertainty of a groundwater flow model with consideration of the heteroscedasticity of the groundwater level error. Groundwater recharge and groundwater abstraction multipliers are introduced to quantify the uncertainty of the spatially distributed input data of the groundwater model in addition to parameter uncertainty. The heteroscedasticity of the groundwater level error is also considered in our Bayesian approach by incorporating a new heteroscedastic error model. The proposed methodology is applied in an overexploited aquifer in Bangladesh where groundwater abstraction and recharge data are highly uncertain. The results of the study confirm that consideration of recharge and abstraction uncertainty through the use of recharge and abstraction multipliers is feasible even in a fully distributed physically based groundwater flow model. Heteroscedasticity is present in the groundwater level error and has an effect on the model predictions and parameter distributions. The input uncertainty affects the model predictions and parameter distributions and it is the dominant source of uncertainty in the groundwater flow prediction. Additionally, the approach described also provides a new way to optimize the spatially distributed recharge and abstraction data along with the parameter values under uncertain input conditions. We conclude that considering model input uncertainty along with parameter uncertainty and heteroscedasticity of the groundwater level error is important for obtaining realistic model predictions and a correct estimation of the uncertainty bounds.

Water quality changes and organic matter removal using natural bank infiltration at a boreal lake in Finland

“…As the total discharge from the model area and the mixing ratio at several cells from the two inflow sources were known, detailed data of precipitation or catchment properties were not needed for the model setup. Mustafa et al (2018) demonstrated that the input uncertainty in the catchment properties affects the model predictions and parameter distributions, and this is the dominant source of uncertainty in the groundwater flow prediction. To limit the uncertainties, the model was based on more accurate spring Fig.…”

Integrated Bayesian Multi-model approach to quantify input, parameter and conceptual model structure uncertainty in groundwater modeling

“…The conventional treatment of uncertainty in groundwater modeling primarily focuses on parameter uncertainty, whereas uncertainties due to the model structure are often neglected (Gaganis & Smith, 2006;Rojas et al, 2008). However, many researchers have recently acknowledged that the uncertainty arising from the conceptual model structure has a significant effect on the model predictions and that parameter uncertainty does not cover the whole range of uncertainty (Bredehoeft, 2005;Højberg & Refsgaard, 2005;Mustafa et al, 2018Mustafa et al, , 2019Neuman, 2003;Poeter & Anderson, 2005;Refsgaard et al, 2006Refsgaard et al, , 2007Rojas et al, 2008;Troldborg et al, 2007). Therefore, neglecting conceptual model structure uncertainty may result in unreliable predictions and underestimation of the total predictive uncertainty.…”

“…Hendricks Franssen et al (2011) reported that the EnKF significantly outperformed with synthetic experimental data compare the real data. Mustafa et al (2018) presented a Bayesian approach to simultaneously quantify parameter and input uncertainty of a groundwater flow model. The performance of this approach has been evaluated using a single conceptual real-world groundwater flow model.…”

“…In the proposed integrated fully Bayesian multi-model framework, the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm with a specific likelihood function is combined with the Bayesian Model Averaging (BMA) framework. In this new DREAM-BMA methodology, a likelihood function has been included based on the novel heteroscedastic error model for groundwater levels proposed by Mustafa et al (2018). Like IBUNE of Ajami et al (2007), the current study uses equations for BMA in a similar fashion as BCMA.…”

“…This is the first attempt to apply a fully Bayesian multi-model framework in real-world groundwater modeling to quantify conceptual model structure uncertainty along with uncertainties originating from model input, parameters and measurement error. In this methodology, the fully Bayesian approach proposed by Mustafa et al (2018) has been combined with the Bayesian Combined Model Averaging (BCMA) to simultaneously quantify the uncertainty arising from the conceptual model structural, input and parameter of a fully distributed groundwater flow model. Additionally, the proposed approach is applicable for all types of residual errors i. e. both for homoscedastic and heteroscedastic errors.…”