Geological heterogeneity is a very important factor to consider when developing geological models for hydrological purposes. Using statistically based stochastic geological simulations, the spatial heterogeneity in such models can be accounted for. However, various types of uncertainties are associated with both the geostatistical method and the observation data. In the present study, TProGS is used as the geostatistical modeling tool to simulate structural heterogeneity for glacial deposits in a head water catchment in Denmark. The focus is on how the observation data uncertainty can be incorporated in the stochastic simulation process. The study uses two types of observation data: borehole data and airborne geophysical data. It is commonly acknowledged that the density of the borehole data is usually too sparse to characterize the horizontal heterogeneity. The use of geophysical data gives an unprecedented opportunity to obtain high-resolution information and thus to identify geostatistical properties more accurately especially in the horizontal direction. However, since such data are not a direct measurement of the lithology, larger uncertainty of point estimates can be expected as compared to the use of borehole data. We have proposed a histogram probability matching method in order to link the information on resistivity to hydrofacies, while considering the data uncertainty at the same time. Transition probabilities and Markov Chain models are established using the transformed geophysical data. It is shown that such transformation is in fact practical; however, the cutoff value for dividing the resistivity data into facies is difficult to determine. The simulated geological realizations indicate significant differences of spatial structure depending on the type of conditioning data selected. It is to our knowledge the first time that grid-to-grid airborne geophysical data including the data uncertainty are used in conditional geostatistical simulations in TProGS. Therefore, it provides valuable insights regarding the advantages and challenges of using such comprehensive data.

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Abstract. Uncertainty of groundwater model predictions has in the past mostly been related to uncertainty in the hydraulic parameters, whereas uncertainty in the geological structure has not been considered to the same extent. Recent developments in theoretical methods for quantifying geological uncertainty have made it possible to consider this factor in groundwater modeling. In this study we have applied the multiple-point geostatistical method (MPS) integrated in the Stanford Geostatistical Modeling Software (SGeMS) for exploring the impact of geological uncertainty on groundwater flow patterns for a site in Denmark. Realizations from the geostatistical model were used as input to a groundwater model developed from Modular three-dimensional finitedifference ground-water model (MODFLOW) within the Groundwater Modeling System (GMS) modeling environment. The uncertainty analysis was carried out in three scenarios involving simulation of groundwater head distribution and travel time. The first scenario implied 100 stochastic geological models all assigning the same hydraulic parameters for the same geological units. In the second scenario the same 100 geological models were subjected to model optimization, where the hydraulic parameters for each of them were estimated by calibration against observations of hydraulic head and stream discharge. In the third scenario each geological model was run with 216 randomized sets of parameters. The analysis documented that the uncertainty on the conceptual geological model was as significant as the uncertainty related to the embedded hydraulic parameters.

Abstract:In distributed and coupled surface water-groundwater modelling, the uncertainty from the geological structure is unaccounted for if only one deterministic geological model is used. In the present study, the geological structural uncertainty is represented by multiple, stochastically generated geological models, which are used to develop hydrological model ensembles for the Norsminde catchment in Denmark. The geological models have been constructed using two types of field data, airborne geophysical data and borehole well log data. The use of airborne geophysical data in constructing stochastic geological models and followed by the application of such models to assess hydrological simulation uncertainty for both surface water and groundwater have not been previously studied. The results show that the hydrological ensemble based on geophysical data has a lower level of simulation uncertainty, but the ensemble based on borehole data is able to encapsulate more observation points for stream discharge simulation. The groundwater simulations are in general more sensitive to the changes in the geological structure than the stream discharge simulations, and in the deeper groundwater layers, there are larger variations between simulations within an ensemble than in the upper layers. The relationship between hydrological prediction uncertainties measured as the spread within the hydrological ensembles and the spatial aggregation scale of simulation results has been analysed using a representative elementary scale concept. The results show a clear increase of prediction uncertainty as the spatial scale decreases.

Precipita on is a key input variable to hydrological models, and the spa al variability of the input is expected to impact the hydrological response predicted by a distributed model. In this study, the eff ect of spa al resolu on of precipita on on runoff , recharge and groundwater head was analyzed in the Alergaarde catchment in Denmark. Six diff erent precipita on spa al resolu ons were used as inputs to a physically based, distributed hydrological model, the MIKE SHE model. The results showed that the resolu on of precipita on input had no apparent eff ect on annual water balance of the total catchment and runoff discharge hydrograph at watershed outlet. On the other hand, groundwater recharge and groundwater head were both aff ected. The impact of the spa al resolu on of precipita on input is reduced with increasing catchment size. The eff ect on stream discharge is rela vely low for a catchment size above 250 km 2 , and the eff ect is negligible when the en re catchment area of approximately 1000 km 2 is considered. In the present case the highest resolu on of 500 m was found to result in the best representa on of the hydrological response at subcatchment scale. Stream discharge, groundwater recharge, and groundwater head were also aff ected by the method for correc on of systema c errors in precipita on measurements. The results underscored the importance of using a spa al resolu on of the precipita on input that captures the overall precipita on characteris cs for the considered catchment or subcatchment. As long as the average precipita on of the considered catchment or subcatchment is accurately es mated, the spa al resolu on seems less important when the integrated response in the form of stream fl ow is considered.Precipita on is the most important input to hydrological models, and an accurate representation in space and time is critical for reliable predictions of the hydrological responses. However, a complicating factor is that precipitation oft en exhibits large spatial and temporal variations within a catchment. Particularly it is diffi cult to measure or infer the spatial structure from standard gauge measurements, and an improper spatial representation constitutes a signifi cant source of uncertainty in hydrological modeling (Berne et al., 2004). Spatial variability of precipitation impacts the predictions of the hydrological processes such as seasonal fl ow in streams, fl oods, evapotranspiration, recharge, and groudwater heads. Moreover, it is of signifi cant importance for the closure of the water balance of a watershed or a region (Vischel and Lebel, 2007).Over the years considerable research into the eff ect of precipitation on runoff response has been performed (Obled et al., 1994;Sigh, 1997;Koren et al., 1999;Bell and Moore, 2000;Berne et al., 2004;Smith et al., 2004;Segond et al., 2007). Many studies have analyzed the impact of the spatial density of rain gauges on runoff mechanisms and found that generally the quality of the model simulations deteriorates when the density of the gauge ...

Seasonal variations of tile drainage discharge were simulated in the 6 km2 Fensholt catchment, Denmark, with the coupled surface and subsurface HydroGeoSphere model. The catchment subsurface is represented in the model by 3 m of topsoil and clay, underlain by a heterogeneous distribution of sand and clay units. Two subsurface drainage networks were represented as nodal sinks. The spatial distribution of the heterogeneous units was generated stochastically and their hydraulic properties were calibrated to reproduce drainage discharge for one network and verified with drainage discharge for the other network. Simulated discharge was compared to that of another model for which the heterogeneous sand and clay units were replaced by a homogeneous unit, whose hydraulic conductivity was the mean value of the heterogeneous model. With the homogeneous model, drainage dynamics were correctly simulated but drainage discharge was less accurate compared to the heterogeneous model. Simulated discharge was also compared to that of a larger‐scale model created with the MIKE SHE code, built with the same heterogeneous model. HydroGeoSphere and MIKE SHE generated drainage discharge that was significantly different, with better simulated groundwater dynamics data produced by HydroGeoSphere. Nodal sinks in HydroGeoSphere reproduced drain flow peaks more accurately. Calibration against drainage discharge data suggests that drain flow is controlled primarily by geological heterogeneities included in the model and, to a lesser extent, by the nature of the soil units located between the drains and ground surface.

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