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Riverbed temperature profiles are frequently used to estimate vertical river–aquifer exchange fluxes. Often in this approach, strictly vertical flow is assumed. However, riverbeds are heterogeneous structures often characterised by complex flow fields, possibly violating this assumption. We characterise the meter-scale variability of river–aquifer interaction at two sections of the Aa River, Belgium, and compare vertical flux estimates obtained with a 1D analytical solution to the heat transport equation with fluxes simulated with a 3D groundwater model (MODFLOW) using spatially distributed fields of riverbed hydraulic conductivity. Based on 115 point-in-time riverbed temperature profiles, vertical flux estimates that are obtained with the 1D solution are found to be higher near the banks than in the center of the river. The total exchange flux estimated with the 3D groundwater model is around twice as high as the estimate based on the 1D solution, while vertical flux estimates from both methods are within a 10% margin. This is due to an important contribution of non-vertical flows, especially through the riverbanks. Quasi-vertical flow is only found near the center of the river. This quantitative underestimation should be considered when interpreting exchange fluxes based on 1D solutions. More research is necessary to assess conditions for which using a 1D analytical approach is justified to more accurately characterise river–aquifer exchange fluxes.

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.

Highlights• Full Bayesian multi-model approach to quantify uncertainty of MODFLOW model • Simultaneously quantifies model structure, input and parameter uncertainty • DREAM with a novel likelihood function is combined with BMA • Neglecting conceptual model uncertainty results in unreliable prediction • Results in more reliable model predictions and accurate uncertainty bounds

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