Large-scale hydrological models are important decision support tools in
water resources management. The largest source of uncertainty in such models
is the hydrostratigraphic model. Geometry and configuration of
hydrogeological units are often poorly determined from hydrogeological data
alone. Due to sparse sampling in space, lithological borehole logs may
overlook structures that are important for groundwater flow at larger
scales. Good spatial coverage along with high spatial resolution makes
airborne electromagnetic (AEM) data valuable for the structural input to
large-scale groundwater models. We present a novel method to automatically
integrate large AEM data sets and lithological information into large-scale
hydrological models. Clay-fraction maps are produced by translating
geophysical resistivity into clay-fraction values using lithological
borehole information. Voxel models of electrical resistivity and clay
fraction are classified into hydrostratigraphic zones using

Large-scale distributed hydrological and groundwater models are used
extensively for water resources management and research. We use large scale
to refer to models in the scale of 100 to 1000 km

Such models are typically distributed, highly parameterized, and depend on data availability to sufficiently represent the modeled systems. Model parameterization includes, for example, the saturated and unsaturated zone hydraulic properties, land use distribution and properties, and stream bed configuration and properties. Hydrological forcing data such as precipitation and temperature are also required. Parameters are estimated through calibration, which requires hydrological observation data commonly in the form of groundwater hydraulic heads and stream discharges. Calibration data should be temporally and spatially representative for the modeled system, and so should validation data sets.

One of the main challenges in modeling large-scale hydrogeological systems
is data scarcity (Refsgaard et al., 2010; Zhou et al., 2014). Uncertainty inherent in distributed
hydrological models is well known (Beven, 1989). Incorrect
system representation due to lack of data contributes to this uncertainty,
but the most important source of uncertainty in distributed groundwater
models is incorrect representation of geological structures (Refsgaard
et al., 2012; Seifert et al., 2012; Zhou et al., 2014). In this paper, we
refer to a 3-D subsurface model that delineates the structure of the
hydraulic conductivity (

Lithological borehole logs are the fundamental data source for constructing hydrostratigraphic models. The modeling process is often cognitive, but two-point geostatistical (He et al., 2013; Strebelle, 2002) and multiple-point statistical (e.g. Park et al., 2013) methods are also used. Geostatistical methods have the advantage of uncertainty estimation. Spatially inconsistent sampling pattern and scarcity make lithological borehole logs alone insufficient to capture local-scale geological structures relevant for simulation of groundwater flow and contaminant transport. Cognitive methods have the advantage of using information from geological maps to assist interpretation of larger scale geological features.

Airborne electromagnetic (AEM) data are unique with respect to good spatial
coverage and high resolution. AEM is the only technique that can provide
subsurface information with a resolution down to

Current practice for cognitive hydrostratigraphic and geological model generation faces a number of challenges: structures that control groundwater flow may be overlooked in the manual 3-D modeling process; geological models are subjective, and different geological models may result in very different hydrological predictions; structural uncertainty inherent in the model building process cannot be quantified. Currently there is no standardized way of integrating high-resolution AEM into hydrogeological models.

Sequential, joint and coupled hydrogeophysical inversion methods, as defined by Ferré et al. (2009), have been developed and used extensively in hydrological and groundwater research. In sequential inversion, hydrological and geophysical models and inversions are set up and performed separately (e.g. Binley et al., 2001; Kemna et al., 2002). In joint inversion, hydrological and geophysical models are set up separately but hydrological and geophysical parameters are estimated simultaneously through a joint objective function (e.g. Hyndman and Gorelick, 1996; Hyndman et al., 1994; Linde et al., 2006; Vilhelmsen et al., 2014). In coupled inversion only one model is set up, the hydrological and the geophysical data are evaluated by comparison to translated simulated hydrological states (e.g. Hinnell et al., 2010; Kowalsky et al., 2005). The methods have been applied to capture hydrological processes or estimate aquifer properties and structures from geophysical data. Hydrogeophysical inversion addresses hydrogeological property estimation or delineation of hydrogeological structures. In the context of large-scale groundwater models studies, Dam and Christensen (2003) and Herckenrath et al. (2013) translated between hydraulic conductivity and electrical resistivity to estimate hydraulic conductivity parameters of the subsurface in a joint hydrogeophysical inversion framework. Petrophysical relationships, however, are uncertain, partly because of unknown physical relationship between geophysical and hydrological parameter space. The relationship may vary within and/or between field sites depending on given conditions and cannot be determined a priori. For electrical resistivity versus hydraulic conductivity, relationships suggesting both positive and negative correlation have been found (Purvance and Andricevic, 2000). Herckenrath et al. (2013) concluded that sequential hydrogeophysical inversion was preferred over joint hydrogeophysical inversion due to the uncertainty associated with the petrophysical relationship. Structural inversions are often performed as purely geophysical inversions, where subsurface structures (that mimic geological or hydrogeological features) are favored during inversion by choosing appropriate regularization terms. An example is the layered and laterally constrained inversion developed by Auken and Christiansen (2004), which respects vertically sharp and laterally smooth boundaries found in sedimentary geology. Joint geophysical inversions have been used extensively to delineate subsurface hydrogeological structures under the assumption that multiple geophysical data sets carry information about the same structural features of the subsurface (Christiansen et al., 2007; Gallardo, 2003; Haber and Oldenburg, 1997) but examples of successful joint hydrogeophysical inversion at larger scales are rare.

As a response to lack of global petrophysical relationships, clustering
algorithms as an extension to structural inversion methods have been applied
in geophysics (Bedrosian et al., 2007; Doetsch et al., 2010). Fuzzy

We present an objective and semi-automatic method to model large-scale hydrostratigraphy from geophysical resistivity and lithological data. The method is a novel sequential hydrogeophysical inversion for integration of AEM data into the hydrological modeling process. Hydrostratigraphic structures and parameters are determined sequentially by geophysical/lithological and hydrological data, respectively.

As shown in Fig. 1, the 3-D subsurface zonation is
completed in two parts: (1) a hydrostratigraphic cluster modeling part, and
(2) a hydrological modeling part. In part 1 the hydrostratigraphic
structures are delineated (see Fig. 2c) through

The method is applied to a Danish case study, for which details and results are presented in the following sections.

The Norsminde study area is located on the eastern coast of Jutland, Denmark,
and covers a land surface area of 154 km

Workflow of the two main parts in the method. Top grey box: hydrostratigraphic cluster modeling using the structural information carried in the geophysical data and lithological information. Lower box in bold: hydrological calibration where hydraulic properties of the hydrostratigraphic zones are estimated using hydrological data.

Palaeogene, Neogene, and Quaternary deposits characterize the area. The Palaeogene deposits are thick clays, and define the lower geological boundary. Neogene marine clays interbedded with alluvial sands overlay the Palaeogene deposits in the elevated northern and western parts of the model domain. Quaternary deposits are glacial meltwater sediments and tills found throughout the domain. The west–east striking Boulstrup tunnel valley (2 km by 14 km) incises the Palaeogene clay in the south (Jørgensen and Sandersen, 2006). The unconsolidated fill materials are meltwater sand and gravel, clay tills, and water-laid silt/clay.

Groundwater is abstracted for the drinking water supply, mainly from tunnel
valley deposits and the elevated southwestern part of the domain. The
groundwater resource is abstracted from 66 abstraction wells, with a total
production of 18 000–26 000 m

Northwest–southeast profiles (vertical exaggeration

Map of the Norsminde study area. The map shows the location of the three discharge gauging stations (blue triangles) along the main river, hydraulic head observations for the calibration period (red dots) and the validation period (black crosses), and abstraction wells (stars). The black dashed line delineates the model domain of the hydrological model.

Groundwater hydraulic heads are available from 132 wells at various depths; see Fig. 3 for the spatial distribution. Hydraulic head data are collected from the Danish national geological and hydrological database Jupiter (GEUS, n.d.).

Average annual precipitation is 840 mm yr

Time-domain electromagnetic (EM) data collected through ground and airborne
surveys are available for most of the study area. The AEM survey covers
2000 line kilometers, equivalent to 106 770 1-D models and was carried out with
the SkyTEM

Geophysical and lithological data are used to zone the subsurface. Geophysical data consist of resistivity values determined from the inversion of airborne and ground-based electromagnetic data. Lithological information is represented in clay-fraction values determined through inversion within the clay-fraction concept (CF concept). Zonation is performed in 3-D.

The CF concept is formulated as a least-squares inversion problem to
determine the parameters of a petrophysical relationship (in the inversion
this is the forward model) that translates geophysical resistivities into
clay-fraction values. The concept is described in detail in
Foged et al. (2014) and Christiansen et al. (2014), and
only a brief introduction is given here. The inversion minimizes the
difference between observed clay fraction as determined from borehole
lithological logs (in the inversion this is the data) and translated clay
fraction as determined from geophysical resistivity values (in the inversion
this is the forward data). Clay fraction expresses relative accumulated
thickness of clay material over an interval. In this context clay refers to
material described as clay in lithological logs, and not clay minerals. Clay
definitions include, among others, clay till, marl clay, mica clay, and
silty clay. In the CF inversion, the translator function is a heuristic
two-parameter function defined on a regular 3-D grid that is constrained
vertically and horizontally. Discretization is 1000 m in the horizontal and
4 m in the vertical. The translator function is a scaled inverse error
function (see Eq. (1) and Fig. 4).

Delineation of subsurface structures is performed as a

The translator function is the petrophysical relationship used in the
CF inversion. The parameters

Because clay-fraction values are correlated with geophysical resistivities,

Eleven hydrostratigraphic cluster models consisting of 1–11 zones are set up and calibrated.

Hydrological data are used to parameterize the structures of the hydrostratigraphic model. Stream discharges and groundwater hydraulic heads are used as observation data in the hydrological calibration.

The hydrological model is set up using MIKE SHE (Abbott et al., 1986; Graham and Butts, 2005), which is a physically based hydrological model code simulating evapotranspiration, the unsaturated zone, overland flow, and saturated flow, while stream discharge is simulated by coupling with the MIKE 11 routing model code.

The model has a horizontal discretization of 100 m

The unsaturated zone and evapotranspiration (ET) are modeled using the two-layer water balance method developed to represent recharge and ET to/from the groundwater in shallow aquifer systems (Yan and Smith, 1994). The reference evapotranspiration is calculated using Makkink's formula (Makkink, 1957). Soil water characteristics of the five soil types and the associated 250 m grid product are developed and described by Borgesen and Schaap (2005) and Greve et al. (2007), respectively. Land use data are obtained from the DK-model2009, for which root-depth-dependent vegetation types were developed (Højberg et al., 2010).

Stream discharge is routed using the kinematic wave equation. The stream
network is modified from the DK-model2009 (Højberg et al.,
2010) by adding additional calculation points and cross sections.
Groundwater interaction with streams is simulated using a conductance
parameter between aquifer and stream. Overland flow is simulated using the
Saint-Venant equations (DHI, 2012, 267–281). Manning number
and overland storage depth is 5 m

Saturated flow is modeled as anisotropic Darcy flow,

Forward models are run from 1990 to 2003; the years 1990–1994 serve as warm up period (this was found sufficient to obtain stable conditions); the calibration period is from 2000 to 2003 and the validation period is from 1995 to 1999.

Composite-scaled sensitivity values of selected parameters in the
hydrological model. Sensitivities are shown for head and discharge
observation separately. The two top plots show average, minimum, and maximum
sensitivity of the 11 hydrostratigraphic cluster models. The two lower plots
show sensitivity of subsurface parameters given a 5-cluster model.

Composite-scaled sensitivities (Hill and Tiedeman, 2007) were calculated based on local sensitivity analyses. Figure 5 shows calculated sensitivity for selected model parameters. Sensitivities of the parameters, which are shared by the 11 cluster models, are calculated for each cluster model. The top panel in Fig. 5 shows sensitivities of the shared parameters. The bars indicate the mean value of these sensitivities, and the error bars mark the minimum and maximum value of these sensitivities. The lower panel in Fig. 5 shows subsurface parameters for the 5-cluster model.

The following parameters are a part of the model calibration:

The root-depth scaling factor, which was found sensitive (see Fig. 5, top panel). Because root-depth values vary inter-annually and between crop types, root-depth sensitivity was determined by a root-depth scaling factor, which scales all root-depth values.

The drain time constant. Especially considering discharge observations, the model shows sensitivity towards this parameter. Stream hydrograph peaks are controlled by the drainage time constant (Stisen et al., 2011; Vazquez et al., 2008).

The river leakage coefficient.

The horizontal hydraulic conductivities of all zones of the 11 hydrostratigraphic
cluster models. Figure 5 shows sensitivity to

Calibration is performed using the Marquardt–Levenberg local search optimization implemented in the parameter estimation software, PEST (Doherty, 2005). Observations are 632 hydraulic heads from 132 well filters and daily stream discharge time series from three gauging stations (see Fig. 3). Observation variances are estimated, and, in the absence of information, observation errors were assumed to be uncorrelated. Objective functions for head and discharge have been scaled to balance contributions to the total objective function.

The aggregated objective function,

Uncertainty of stream discharges is mainly due to translation from water
stages to discharge (daily mean discharges). Uncertainties originate from
infrequent calibration of rating curve, ice forming on streams, and
especially stream bank vegetation (Raaschou, 1991). Errors can
be as large as 50 %. Blicher (1991) estimated errors of
5 and 10 % on the water stage measurement and rating curve,
respectively. In cases of very low streamflows (1 L s

Weighted RMSE of hydrological performance of hydrostratigraphic models
consisting of 1 to 11 clusters. Data are shown for all calibration
observations. Blue lines are mean standard deviation on

First, we show results for the hydrological performance of 11 hydrostratigraphic cluster models consisting of 1–11 zones. Second, details of the cluster analysis for the case of a 5-cluster hydrostratigraphy are shown. Finally, the cluster model hydrological performance is benchmarked with comparable hydrological models.

Figure 6 shows the weighted root mean square error (RMSE) of model
performances for a hydrostratigraphic cluster model consisting of 1 to 11 zones,
head and discharge, respectively, is shown in Fig. 6a and b.
The 1-cluster model is a homogeneous representation of the subsurface
resulting in a uniform

Head and discharge contribute by approximately two-thirds and one-third of the total objective function. From the 1-cluster to the 2-cluster model, weighted RMSE for discharge is reduced by more than a factor 2. No significant improvement of the fit to discharge data is observed for more than 2 clusters. Fit to head data improve almost by a factor of 2 from the 1-cluster to the 2-cluster model. Improvement of the fit to head data continues up to the 5-cluster representation of the subsurface. Improvements are a factor of 3 from the 1-cluster to the 5-cluster model. Beyond the 5-cluster model, the fit to head observations stagnates. The 7-cluster and 9-cluster hydrostratigraphic models perform worse than the 3-cluster model. The 8-, 10-, and 11-cluster models obtain an equally good or better fit to head data compared to the 5-cluster model.

2000–2003 calibration and 1995–1999 validation period performance statistics for the 11 hydrostratigraphic cluster models consisting of 1–11 clusters. The top row shows RMSE and the bottom row shows ME.

The blue lines in Fig. 6 illustrate mean standard
deviation on

With the combined information from weighted RMSE values and standard
deviation on

In this paper, we have discussed the performance of the cluster models as a measure of fit to hydraulic head and stream discharge observations. Hydrological models are typically used to predict transport, groundwater age, and capture zones, which are sensitive to geological features. It is likely that the optimal number of clusters is different for these applications. An analysis, as is presented here for head and discharge, for predictive application is more difficult because observations are often unavailable.

The hydrostratigraphic models are constructed under the assumption that subsurface structures governing groundwater flow can be captured by structural information contained in clay-fraction values (derived from lithological borehole data) and geophysical resistivity values. If this is true, an asymptotic improvement of the data fit would be expected for increasing cluster numbers. However, as shown in Fig. 6, this is not strictly the case: weighted RMSE of the 7-cluster and 9-cluster models is higher than weighted RMSE of the 3-cluster, 6-cluster, and 8-cluster models. The likely explanation is that the increasing number of clusters not only corresponds to pure cluster sub-division but also to relocation of cluster interfaces in the 3-D model space. We expect the difference in hydrological performance to be due to changes in interface configuration.

It is well known that an unsupervised

Histograms of

Figure 7 shows RMSE and mean errors for calibration and validation periods for all eleven cluster models. Data used to calculate the statistics are a temporally split sample from 35 wells, which have observations both in the calibration and validation period, and the discharge is for stations 270002 and 270003.

The cluster models perform similarly in the periods 2000–2003 and 1995–1999. With respect to RMSE, Fig. 7a, for head the validation period is approximately 10 % worse than the calibration period. RMSE for discharge (Fig. 7b) is lower in the validation, approximately one-third of the calibration values. Mean errors for head (Fig. 7c) are lower and higher, respectively. The hydrological models analyzed in this study generally under-simulate the average discharge.

Data cloud of geophysical resistivity values and clay-fraction values. Dotted black lines indicate cluster interfaces and cluster are labeled with numbers. The cloud color represents bin-wise data density (300 bins), which are shown in logarithmic scale.

Figure 8 presents histograms of clay-fraction values and resistivity values and how the values are represented in the five clusters, which was chosen to be the optimal number. Counts are shown as percentages of the total number of pixels in the domain. The histograms in Fig. 8 show that the clay fraction attribute separates high resistivity/low clay fraction (sandy sediments) from other high-resistivity portions of the domain, while the resistivity attribute separates low resistivity/high clay fraction (clayey sediments) from other high clay-fraction portions. High resistivity/low clay-fraction values are represented by clusters 1, 3, and 4, and low resistivity/high clay fraction are represented by clusters 2 and 5 (see Fig. 8a). Figure 9 shows the data cloud that forms the basis of the clustering. The data cloud is binned into 300 bins in each dimension and the color of the cloud shows the bin-wise data density. We see that cluster boundaries appear as straight lines in the attribute space. Values with a low resistivity and corresponding high clay fraction, mainly clusters 2 and 5, populate more than half of the domain. Clay is expected to dominate this part of the domain.

The results of the cluster analysis are presented with respect to
geophysical resistivity and clay-fraction values, while the cluster analysis
is performed on the PC of geophysical resistivity and
clay-fraction values. The first PC explains the information where the two
original variables, log resistivity and clay fraction, are inversely
correlated. This corresponds to the situation where a clay fraction of 1
coincides with a low resistivity value, and vice versa for clay-fraction
values of 0 and high resistivities. This is the information that we expect,
i.e. our understanding of how geophysical resistivities relate to
lithological information as represented by the translator function (Eq. 1)
(defined under the assumption that variation in geophysical resistivities
with respect to lithological information depends on the presence of clay
materials). Thus, the first principal component is the “clay” information in
the geophysical resistivities. The second PC is less straight forward to
interpret. Ideally, the second PC represents the data pairs where the
resistivity response is

Calibration and validation statistics for the temporally split sample consisting of observations from 35 wells, which have observations both in the calibration and validation period, and discharge stations 270003 and 270002.

Performance statistics of four Danish hydrological models that are comparable to the Norsminde model. All models are set up using MIKE SHE.

Observed and simulated stream discharge at stations 270003 (top row panels) and 270002 (bottom row panels) from the 1995–1999 validation period. To the left stream discharge hydrographs are shown and to the right scatter plots of observed vs. simulated values. In the scatter plots the dotted and dashed red lines mark misfits of 20 and 50 %, respectively.

Electromagnetic methods are sensitive to the electrical resistivity of the
formation, which is commonly dominated by clay-mineral content, dissolved
ions in the pore water and saturation. Groundwater quality data are available
at numerous sites in the domain. Pore-water electrical conductivity (EC)
values were gathered from the coast and inland following the Boulstrup tunnel
valley. From the coast to 12 km inland values are stable around
50–70 mS m

Table 1 shows RMSE and mean error (ME) for head and discharge based on the 5-cluster model. Weighted RMSE for discharge is below 1, indicating that discharge is over fitted. The standard deviation of discharge is 20 % of the observation, which is a conservative definition. As presented in the methods, section errors may vary between 5 and 50 %. The 1995–1999 hydrograph and scatter plot in Fig. 10 for the 270002 gauging station show good fit to data. Peak and low flows are fitted, but baseflow recession is generally not matched very well. At gauging station 270003, the model fails to capture dynamics and relative magnitudes of the observations. Peak as well as low flows are under-simulated, which is clearly demonstrated in the scatter plot for station 270003 in Fig. 10. With respect to head, the model under-simulates in the elevated parts of the domain (head above 50 m) (see Fig. 11). The head values below 20 m represent the Boulstrup tunnel valley, where head is fitted the best. With weighted RMSE for head of 1.63 and 1.85 the model is almost 2 SD (standard deviations) from fitting head data. Assuming head observation error estimates are correct, this indicates model deficiencies such as structural errors and/or forcing data errors.

Scatter plot of observed and simulated heads values from the 1995–1999 validation period. Dashed lines mark misfits larger than 10 m and dotted lines mark misfits larger than 5 m.

Distributed head results for the validation period 1995–1999;

Figure 12a–b show distributed head results. Generally hydraulic head in the tunnel valley is disconnected from the elevated terrain (Fig. 12a), and groundwater overall flows towards the sea. Figure 12b shows errors (obs–sim) between observed and simulated heads for 1995–1999. The largest errors are found in the southeastern part of the domain, where discharge station 270003, with the worst fit, is located (see Fig. 10, top row panels).

We have compared the hydrological performance of the Norsminde model based
on the 5-cluster hydrostratigraphic model with similar Danish hydrological
models. We have chosen Danish models due to comparability with respect to
data density and quality, and hydrostratigraphy. The model performances are
compared based on RMSE and ME of simulated heads; see
Table 2, as these statistics are reported in the
studies. The horizontal discretization of the models is 100, 200, and
500 m, and the models cover between 202 and 3500 km

We have presented a method for automatic generation of hydrostratigraphic models from AEM and lithological data for groundwater model applications. Other automatic methods of integrating AEM data into geological models are geostatistical methods presented by, for example, Gunnink et al. (2012), using artificial neural networks, or He et al. (2014), using transition probabilities.

The risk of misinterpretation of AEM data, due to effects of saturation, water quality, depth and material dependent resolution, and vertical shielding, are higher with an automatic approach compared to a cognitive approach, as these effects may be identified by a geologist during the modeling process. AEM data can be integrated into geological models using cognitive methods, for example, as presented by Jørgensen et al. (2013), who provide an insightful discussion of the pros and cons of automatic versus cognitive geological modeling from AEM data.

Geological knowledge, which can be incorporated into cognitive geological models (Royse, 2010; Scharling et al., 2009; Sharpe et al., 2007), cannot be included in automatically generated models. Geological knowledge may identify continuity/discontinuity of geological layers, or discriminate between materials based on stratigraphy or depositional environment. For regional-scale groundwater flow, characterization of sedimentation patterns and sequences may not be relevant, but at smaller scales this information is valuable for transport modeling.

The hydrostratigraphic cluster model presented in this paper does not represent a lithological model, but has the advantage of incorporating close to all the structural information contained in the large AEM data sets in a fast and well-documented way. This is not possible in practice for cognitive methods due to spatial complexity and the large amount of AEM data. For hydrological applications hydrostratigraphic model uncertainty, and the resulting hydrological prediction uncertainty, has great value. We believe that the cluster model approach presented in this paper can be extended to address structural uncertainty and its impact on hydrological predictions. Cognitive geological model uncertainty is difficult to quantify.

The CF model is to some degree influenced by smoothing resulting from the AEM data inversion and CF inversion, and the finial kriging of CF values to a regular grid. Smoothing effects causing resistivity transition zones are inconsistent with our understanding of geological interfaces. In future studies different geophysical inversion schemes will be compared to evaluate the effect of smoothing on the final cluster model. This work will partly evaluate how the smooth transition zones impact hydrological results. We expect the geological interfaces to lie in the transition zones, but the exact location is unknown. We will address this problem by generating several cluster models that identify zonal divides at different locations in the transition zones. Hereby hydrological uncertainty as a result of the transition zones may also be assessed.

We have presented an automated workflow to parameterize and calibrate a large-scale hydrological model based on AEM and borehole data. The result is a competitive hydrological model that performs adequately compared to similar hydrological models. From geophysical resistivity data and clay-fraction values, we delineate hydrostratigraphic zones, whose hydrological properties are estimated in a hydrological model calibration. The method allows for semi-automatic generation of reproducible hydrostratigraphic models. Reproducibility is naturally inherent as the method is data driven and thus, to a large extent, also objective.

The number of zones in the hydrostratigraphic model must be determined as part of the cluster analysis. We have proposed that hydrological data, through hydrological calibration and validation, guide this choice. Based on fit to head and discharge observation and calibration parameter standard deviations, results indicate that the 3- and 5-cluster models give the optimal performance.

Distributed groundwater models are used globally to manage groundwater resources. Today large-scale AEM data sets are acquired for mapping groundwater resources on a routine basis around the globe. There is a lack of knowledge on how to incorporate the results of these surveys into groundwater models. We believe the proposed method has the potential to solve this problem.

Hydraulic head observation errors have been estimated using an error budget:

Head measurements are typically carried out with a dip meter, and occasionally
pressure transducers are used. Information about which measurement technique
has been used for the individual observations is not clear from the Jupiter
database. It is assumed that dip meters have been used and

Well elevations are referenced using different techniques. The elevation can
be determined from a 1 : 25 000 topographic map, by leveling or by
differential GPS. The inaccuracies for using topographic maps and DGPS
measurements are on the order of, respectively, 1–2 m and centimeters. The
Jupiter database can have information about the referencing techniques, but
this information is rarely supplied. An implicit information source is the
number of decimal places the elevations have in the database. Elevation
information is supplied with 0, 1, or 2 decimal places. For the wells where
the reference technique is available (checked for cases with topographic map
and DGPS only) the decimal places reflect accuracy of the referencing
technique used. From this information decimal places of 0, 1, and 2 have been
associated with

Errors due to interpolation depend on horizontal discretization of the
hydrological model and the hydraulic gradient. Sonnenborg and
Henriksen (2005, chapter 12) suggested it be estimated as

Within-cell (hydrological model grid) heterogeneity affecting the hydraulic head
was estimated using data from eight wells that are located within the same
hydrological model grid. Temporally coinciding head observations from the
period 2001 and 2002 were used. The error is evaluated as the standard
deviation of a linear plane fitted through the observed heads at the eight
boreholes. This has been done for three dates, which gives a mean

This paper was supported by HyGEM, Integrating geophysics, geology, and hydrology for improved groundwater and environmental management, project no. 11-116763. The funding for HyGEM is provided by The Danish Council for Strategic Research. We are thankful for the support and data provided by the NiCA research project (funded by The Danish Council for Strategic Research under contract no. DSF 09-067260), including SkyTEM data and the integrated hydrological model for the Norsminde study area. Edited by: M. Bakker