Three-dimensional hydrostratigraphy and groundwater flow models in complex Quaternary deposits and weathered/fractured bedrock: evaluating increasing model complexity

A workflow was generated starting with 3D geological modelling using Leapfrog Geo (Seequent Ltd. 2020) followed by 3D hydrostratigraphic modelling and groundwater flow modelling using MODFLOW-NWT (Niswonger et al. 2011). In this study, two 3D geological models, GM1 and GM2, were generated using Leapfrog Geo. In addition, four hydrostratigraphic models, HSM1, HSM2, HSM3 and HSM4, were generated from the GM models to test how model complexity affects groundwater flow patterns and the distribution of recharge and discharge zones (Table 1). The structures of HSM1, HSM2 and HSM3 were based on GM1, whereas the structure of HSM4 was based on GM2.

Leapfrog Geo is designed for rapid implicit modelling. The 3D mesh generation in Leapfrog Geo is based on contact surfaces that define the upper and lower limit of the unit. The interpreted stratigraphy, which defines the relative age of the units, affects the behaviour of the defined contacts. Leapfrog Geo offers three types of contact surfaces: sediment contact, erosive contact and intrusion contact (Seequent Ltd. 2020). The contact surfaces of the 3D geological model were generated with the first two types. The FastRBF interpolation method of Leapfrog Geo, which resembles the kriging method (Oliver 1990), was used to generate the contact surfaces.

The geological models were constructed based on drilling data from the Kersilö database (see Åberg et al. 2017a for the drilling data references) and data obtained from base-of-till (BOT) drilling by AA Sakatti Mining Oy (unpublished data, 2017). In addition, the detailed till geochemistry and bedrock observation databases of the Geological Survey of Finland (GTK) were used. Moreover, ground penetrating radar (GPR) profiles from Åberg et al. (2017a) were utilized.

The geological models GM1 and GM2 were extended and modified from the geological model presented by Åberg et al. (2017a). The extent of the models was set to 6 × 8 km (48 km²) to cover the study area presented in Fig. 1. The GM models consisted of ten units (3D solids), including the River Kitinen, peat, four sorted sediment units, four till units, weathered bedrock and fractured bedrock (Table 1). The geological models were constructed with both explicit and implicit modelling using the methods of Åberg et al. (2017a). The horizontal resolution of both GM models was 20 × 20 m, while the vertical resolution was not applicable in Leapfrog. The River Kitinen was modelled as an erosive contact. However, in GM2, the river bottom was slightly edited compared to GM1 based on the bedrock observations database of GTK.

The peat bottom contact was generated with ArcMap (ESRI) as depth contours. Next, a triangulated irregular network (TIN) surface was generated from the peat contours with ArcMap. After this, the TIN surface that depicted the peat bottom depth was converted into a raster, and the raster was converted to the altitude above sea level by subtracting it from the topography. The converted raster was used as an erosion-type contact defining the peat bottom in a geological model in Leapfrog. However, the peat bottom contact in GM2 was reedited based on new GPR profiles in spring 2019. During contour generation, 0.5-m-thick contours were created 2 m inwards from the border of the mire areas to prevent the peat close to the borders from being too thin. In addition, areas with no peat were defined with 20-m-thick contours 5 m outwards from the border of the mire areas. A random negative height rising above the topography was selected.

Minerogenic Quaternary sediment units (presented in Table 1) were modelled in an explicit manner as sediment contacts with the polyline tool. In GM2, revisions to the Quaternary sediment units were made compared to GM1, including changes to the layer structure of the Sahankangas area (Fig. 1) and expansion of the lowest till unit (Fig. 2).

The bedrock surface contact for both GM models was generated as an erosive contact with implicit modelling. It was adjusted with the polyline tool in those areas where drilling did not reach the bedrock using the methods described in Åberg et al. (2017a).

In both GM models, the bedrock was modelled with two layers: the upper depicted the chemically weathered zone, whereas the lower zone depicted fractured bedrock, as in Durand et al. (2017) and Wright (1992), among others. In GM1, chemically weathered bedrock was modelled with a deposit-type contact above the fractured bedrock surface, as in Åberg et al. (2017a). In GM2, a more precise and extensive chemically weathered zone was generated based on Hall et al. (2015), Raatikainen (2019), AA Sakatti Mining Oy, unpublished data, 2019; and GPR surveys in 2015. The weathering zone was extended to cover the whole model area (Fig. 2), contrary to the restricted coverage of GM1. It was generated with Leapfrog as an offset surface from the bedrock surface with a minimum thickness of 3 m. A few dummy points and polylines were added to offset the surface to manually improve the interpolated bottom contact. In GM1, everything below the bedrock surface was assumed to be fractured bedrock, and the bottom was set to 140 m asl. In GM2, the bottom of the fractured zone was generated as an offset surface from the bedrock surface with a minimum thickness of 5 m (Fig. 2). The offset surface was also adjusted with a few dummy points and polylines. The fractured zone delineated the base of the model.

Model complexity increased from HSM1 to HSM4 (Table 2). HSM1 had a uniform Quaternary sediment package and uniform fractured bedrock, whereas HSM2 had a uniform Quaternary sediment package but variable fractured bedrock. HSM3 had multi-layered Quaternary sediments and a single layer of variable fractured bedrock, whereas HSM4 had multi-layered Quaternary sediments and two-layered variable bedrock.

HSM1 and HSM2 were simple models that consisted of four layers including the units the River Kitinen, peat, Quaternary sediments and fractured bedrock. Simplification from the geological model to the hydrostratigraphic model was performed in Leapfrog by removing contact surfaces between the sediment units (Table 1).

In the complex models, HSM3 and HSM4, most of the units from the GM models were retained (Tables 1, 3 and 4) and the Quaternary sediments consisted of several units, contrary to one combined unit in HSM1 and HSM2. HSM3 had eight layers, whereas HSM4 had ten layers including the units in Table 1. In HSM3, the middle till, lowest till and weathered bedrock units were removed due to their originally assumed small coverage, and the lower sorted and middle sorted units were combined into one unit. In HSM4, middle sorted deposits and lower sorted deposits were likewise combined into one unit, and middle till was removed from the model. Contrary to the construction of HSM3, the weathered bedrock and lowest till units were retained in HSM4 due to the expansion of their coverage.

The hydrogeology tool of Leapfrog was used to convert the 3D hydrostratigraphic models into MODFLOW grids (Figs. 3 and 4). The units of the 3D hydrostratigraphic model were projected within the grid using the evaluation tool of Leapfrog. The resolution of the horizontal cell size was 20 × 20 m, and the minimum allowed cell size was 0.5 m for vertical resolution (Fig. 4c), except in HSM4, in which it was 0.0017 m (Fig. 4d). This minimum thickness appeared between the scattered units as “pinched” cells (e.g. Feinstein et al. 2012), while the basic MODFLOW codes only allow continuous layers. The bases of the MODFLOW grids were edited in HSM1–3 to reach 35 m (assumed average thickness of the fractured bedrock) (Fig. 4c) downwards from the bedrock surface, instead of 140 m asl in GM1 (as in Fig. 4a). In HSM4, the irregularly elevated base of the model (Fig. 4b,d), corresponding to the solid bedrock surface, was used as the base extent as such. The river top was reduced to 0.5 m above the bottom of the river in all HSM models, as described in Åberg et al. (2019). Layer 1 in the mire area was modified in complex models HSM3 and HSM4 to represent two-thirds of the mire thickness, as presented in Åberg et al. (2019), to correspond to the mire acrotelm. Layer 2 in the mire area corresponded to the mire catotelm. Acrotelm is the less decomposed upper part of peat with higher hydraulic conductivity and catotelm is more decomposed peat below the acrotelm (Holden and Burt 2003). In the simple models HSM1 and HSM2, layer 1 was unmodified from GM1 and peat was uniform.

The 3D units of the HSM models were used as zones for horizontal hydraulic conductivity (HK) parameters and vertical anisotropy (VANI) parameters in ModelMuse. The HK and VANI parameters of the HSM models were based on earlier slug test and grain-size analyses, as described in Åberg et al. (2019), and more recent grain-size analyses (SRK, unpublished data, 2019; AA Sakatti Mining Oy, unpublished data, 2019). The HSM models were set as steady-state, which was assumed to be adequate for the generic understanding of groundwater flow patterns since annual water-table variation in most continuous monitoring wells is less than 1 m (Åberg et al. 2019).

The precipitation rate was 560 mm year⁻¹ for the hydrological year lasting from November 2013 to November 2014 to correspond to a single snow-covered period as in Åberg et al. (2019), and this configuration was used for recharge estimations. The recharge rate was interpolated from recharge estimates for two zones called “open water and mire area” and “forested area”, as described in Åberg et al. (2019). The recharge rate of the mire area was assumed to be uniform for simplicity. The recharge rates of the remaining areas were interpolated with multiplier points, as described in Åberg et al. (2019), based on the results of the episodic master recession (EMR; Nimmo et al. 2015) and water-table fluctuation (WTF; Meinzer 1923) methods. All the models were surrounded by constant head boundaries in locations where the mire contacted the model border. Head-dependent flux boundaries were added in sediment boundary areas with the general head boundary (GHB) package. Their heads were calculated from the closest open water bodies, and conductance was defined as in Åberg et al. (2019). The drain package (DRN) was used to simulate discharge within the open mire area and the gravel intake area (Fig. 1). The River Kitinen was modelled with the river package (RIV) to simulate the river discharge.

In the simplest model, HSM1, the fractured bedrock was defined with a uniform initial hydraulic conductivity of 5.3 × 10⁻⁶ m s⁻¹. In models HSM2, HSM3 and HSM4, the fractured bedrock was defined similarly as in Åberg et al. (2019). The hydraulic conductivity of the fractured bedrock was interpolated from hydrogeological testing in boreholes, including packer, spinner and constant head tests (SRK, unpublished data, 2019), along with two slug tests (Golder Associates, unpublished data, 2012). The thrust faults and brittle faults including fractures were defined as their own parameter zones (Table 2).

In HSM4, the type of weathered bedrock zone was defined as gruss type, clay type or nonweathered based on the Weathering Index of Parker (WIP, Parker 1970; Hall et al. 2015). The clay and the gruss zones were delineated based on WIP calculations of till geochemistry data (weathered bedrock samples and fine fraction of till) in Hall et al. (2015) and Raatikainen (2019). Gruss and clay-zone polygons were drawn and used as parameter zones (Fig. 5b). The remaining least weathered areas were included in the same parameter zone as fractured bedrock.

A total of 165 observations, including head observations from groundwater monitoring wells (n = 34), water-table measurements from flarks and other open water bodies (n = 126) on the LiDAR DEM (light detection and ranging digital elevation model) and spring observations (n = 5), were used as the calibration points in all the HSM models. The head observations of the wells were added to the layer that corresponded the depth of the screen of the well (Table 6). The observations from LiDAR DEM were added to layers 1 or 2 depending on the expected water table. The hydraulic conductivities were first manually defined with interpolated HK parameter multipliers in ModelMuse, as presented in Åberg et al. (2019). Then, the hydraulic conductivity of the peat acrotelm, thrust faults, brittle faults and fractures, the gruss zone and clay zone, and RIV and DRN conductance were calibrated with PEST (Doherty 2015), depending on the model version (see Table 5). Parameters that had low sensitivity or indicated ill-posedness were set as fixed parameters. The variation of Marquardt lambda and singular value decomposition were enabled during parameter estimation, which helped to find the best improvement of the objective function of the head observation (see Doherty 2015). The limits for parameter values were set as follows: the maximum allowed value was 0.01 for all calibrated parameters except brittle faults and fractures, which had a maximum of 1, and the minimum allowed value was 1 × 10⁻¹⁰ for all parameters to maintain the convergence of the model. The unit was m s⁻¹ or m² s⁻¹ depending on the parameter. Starting values for RIV and DRN were 1 × 10⁻⁵ and 1 × 10⁻⁶ m² s⁻¹, respectively, based on test calibrations. The starting K of peat, Quaternary sediments and fractured bedrock were 5.4 × 10⁻⁵, 1 × 10⁻⁵ and 5.3 × 10⁻⁶ m s⁻¹ (Table 5), respectively, based on the definition in Åberg et al. (2019). Starting K for gruss and clay were 1 × 10⁻⁵ and 1 × 10⁻⁸ m s⁻¹ (only used in HSM4), respectively. The initial VANI parameters were defined as in Åberg et al. (2019) as 10 for Quaternary deposits, 100 for peat and 1 for all bedrock parameters. The VANI parameters remained fixed due to their low sensitivities (see e.g. Hill 1998; Poeter et al. 2014). Root mean square error (RMSE), mean absolute error (MAE) and bias were calculated from residuals of the head observations. Linear uncertainty was calculated for calibrated parameters with PEST. Since all calibrated parameters used were log-transformed, the uncertainty variances were calculated to logarithms of parameters (Doherty 2018).

Model evaluation was performed with particle tracking with measured mean δ¹⁸O, δD and d-excess isotope values of the water samples in the Viiankiaapa mire based on data presented in Bigler (2019) and measured in September or October 2016. Particle tracking was performed in forward and backward directions with MODPATH (Pollock 1994) to describe the discharge and recharge locations as well as flow routes of the water having certain isotope composition. Isotope compositions were assumed to reflect the evaporation state of water in the recharge area. Neither altitude effect (altitude varies from 180 to 200 m) nor groundwater transport were supposed to affect the isotope values (Gat 2010). The δ¹⁸O, δD and d-excess values were inserted to modelled flow paths with ArcMap to study the flow paths of different isotope compositions in 3D with Leapfrog. Moreover, the isotope values of the particle flow paths were compared to measured isotope values of springs on the shore of the River Kitinen presented in Åberg et al. (2019) measured in August 2015. Firstly, the isotope values of the springs were grouped into five groups based on their locations. Secondly, the flow paths close to the defined five groups were selected and studied in 3D view. Then, the fit between isotope values of the selected flow paths and spring observations were calculated and defined based on the following criteria: the deviation from spring observation is ±1, ±5, and ±1.5‰ in δ¹⁸O, δD and d-excess values, respectively. The difference is assumed to be acceptable if the value is within one-sixth part of the ranges −14.8 to –9.9, −108.8 to –77.0, and −4.4 to 8.6‰ in δ¹⁸O, δD and d-excess values, respectively. If all isotope values of flow paths coincided with the spring observations within acceptable limits, the fit of the group was good. If only some of the spring values coincided with flow path values, the fit of the group was moderate. If all flow path values deviated from spring observations, the fit was poor. If no particle paths crossed the spring observation, the group was categorised as “no-match”. To evaluate the models, overall points were calculated to HSM models with values 2, 1, 0 and empty for good, moderate, poor and no-match fits of the groups, respectively. The final decision of the group match was based on the fit of d-excess, which has a less seasonal variation (Gat 2010).

Based on the geological and hydrostratigraphic models, the study area consists of 51.7–59.0% till, 26.7–34.7% sorted sediments (silt, sand or gravel) and 13.6–14.4% peat, and their volumes are ca. 0.2, 0.1 and 0.05 km³, respectively. The Quaternary sediment package is 8 m thick on average, and it consists of till, sorted sediment and peat units that are 2 m thick on average (Tables 3 and 4). The altitude of the bedrock topography varies from 135 to 206 m asl, with an average altitude of 180 m asl (Fig. 5). According to the most complex models, GM2 and HSM4, the thickness of the fractured bedrock is highly variable (0–77.9 m), with the average thickness being 26.0 m. The average thickness of weathered bedrock is 6 m.

Flow modelling budgets (see Appendix for the second through fifth tables therein) after calibration indicated that the percentage of groundwater discharge to the River Kitinen was a lower proportion of the overall outflow (21.8–29.9%) in the simple models HSM1 and HSM2 than in the complex models HSM3 and HMS4 (34.7–35.5%). However, the percentage of mire discharge in the overall outflow appeared to be higher in the simple models (65.7–74.6%) than the complex models (57.2–59.1%).

In the simple models HSM1 and HSM2, the recharge rate was estimated to be 25% of the precipitation in forested areas. According to the complex models HSM3 and HSM4, the recharge rate in forested areas varied from 28 mm year⁻¹ (5% of precipitation) to 380 mm year⁻¹ (68% of precipitation; Fig. 6). In the mire area, a constant recharge rate of 100 mm year⁻¹ (19% of precipitation) was used in all HSM models based on Åberg et al. (2019). The calibrated hydraulic conductivity of fractured bedrock was 1.7 × 10⁻⁶ m s⁻¹ in HSM1, whereas K of bedrock units varied from 8.4 × 10⁻⁹ to 1.3 × 10⁻³ m s⁻¹ in models HSM2, HSM3 and HSM4 (Table 5). In HSM4, the calibrated hydraulic conductivity for gruss and clay zones was 2.2 × 10⁻⁵ and 8.4 × 10⁻⁹ m s⁻¹, respectively. The hydraulic conductivity of tills varied from 5.0 × 10⁻⁸ to 1.3 × 10⁻⁴ m s⁻¹ and that of sorted sediments from 1.2 × 10⁻⁶ to 6.1 × 10⁻⁴ m s⁻¹ in models HSM3 and HSM4 (Table 11). The root mean square error (RMSE) of the calibrated HSM models varied from 0.38 to 0.33 m, and the residual errors between the simulated and observed water table were within ±1.6 m (Fig. 7) with Pearson correlation coefficient (SPSS ver. 24) of 0.995–0.997 (p value <0.01). The RMSE appeared to decrease when model complexity increased from model HSM1 → HSM2 → HSM3. Overall MAE and bias were similar in all models; however, groundwater wells in Table 12 indicated a notable decrease of RMSE, MAE and bias from HSM1 to HSM4.

The calculated uncertainties with 95% confidence limits indicated that parameters brittle faults and Quaternary sediments (simple models) have similar confidence limits and uncertainty variance (0.05–0.1) regardless of the model. However, some parameters like thrust fault and river parameter had different variance. In HSM3, the variance of the thrust fault was smaller (~0.5) than in HSM2 and HSM4 (>1.5). In HSM 2, the variance of the river parameter was two compared to the smaller variance of ~0.5 in other models. Brittle fault seemed to have the lowest variance in HSM2–4 (<0.1) indicating higher certainty. The variance in drain parameter was high (1.3–1.4) in both simple models. Gruss parameter had low variance (0.1) and clay had high variance (1.7). Peat parameter had high (>1.2) variance in all models except HSM1 with the variance of 0.4.

The flow model results indicated that groundwater mainly flows towards the River Kitinen (Fig. 7). In addition, horizontal flow was dominant in the simple HSM models (Fig. 8a,b), while the downward and upward flow component increased in the complex HSM models (Fig. 8c,d).

The variation in hydraulic conductivity appeared to be an important factor determining groundwater flow patterns. When a high-conductivity zone, e.g. a sand unit, lay below the peat catotelm, vertical flow areas in peat layers expanded. Subtill sorted sediments appeared to cause a similar effect. Moreover, the low hydraulic conductivity of the clay type in weathered bedrock caused a partial increase in the hydraulic gradient in HSM4 (Fig. 7 location C). In addition, the existence of low hydraulic conductivity fractures or faults increased the altitude of the water table (see e.g. Bense et al. 2003).

Flow model results indicated that groundwater discharge appeared to occur in river shoreline and mire areas (Fig. 9). The discharge areas were interpreted from drain cells or flooding cells, as presented in Åberg et al. (2019). The complex models provided more evenly distributed groundwater discharge patterns, reflecting the string and flark pattern of the mire (Fig. 9, location E). The Matarakoski hydroelectric power plant created a recharge area in the river due to the higher river stage compared to the water table on the surrounding shore areas (Fig. 9, location F).

Particle tracking indicated that the groundwater flow in surficial deposits occurred mainly in high hydraulic conductivity zones. The K of brittle faults and fractures seem to affect the particle paths indicating their importance to model results in HSM2–4. The deepest flow paths also seemed to mimic the model bottom indicating the importance of the topography of more competent bedrock, which was used as the model bottom. Moreover, particle tracking indicated groundwater recharge areas in river banks and in the Viiankiaapa mire, as well (Fig. 10).

The simulated flow paths based on the d-excess value dataset from Bigler (2019) were verified with the selected d-excess verification groups (1–5) based on a dataset from Åberg et al. (2019; Fig. 12). The verification groups and the simulated flow paths had the best match of d-excess values in the noncalibrated HSM4 model (Fig. 12, see the last table of the Appendix). Groups 2 and 3 had good fit, and groups 1 and 4 had mainly intermediate or poor fit in all models (Table 13). The intermediate fit of group 1 can be due to the lack of observations in the southwestern area (Fig. 12). In HSM1, group 1 had no match since the southernmost particles discharged already before the river (Fig. 12). Group 5 seemed to have a poor fit or no match in all models. The isotope values of group 5 are probably related to infiltration of evaporated water in the Kärväslampi Pond. Similarly, highly evaporated water in group 4 is probably infiltrated water from the mire (Fig. 12). Since MODPATH considers only advection, the mixing of different isotope compositions was not computed. In addition, evaluation of no match group is challenging since it can be related to a lack of measurements instead of a poor match. However, fairly good overall match with the highly variable d-excess composition in relatively short distances indicated that the flow paths from different sources can be characterized with simple methods like MODPATH.

In this study, the variation in hydraulic conductivities was generated within the predefined hydrostratigraphic units by interpolation with points. Alternatively, the units could be separated into smaller units, either with geostatistical tools such as T-PROGS (Carle 1999) or by defining smaller areas with polygons. There are also mathematical codes and stochastic methods that generate complex hydraulic conductivity fields based on pseudo-genetic models such as braided river bar structures (e.g. Felletti et al. 2006; Pirot 2015).

MODFLOW, which was used in this study, assumes that all units used in the model are equivalent to continuous porous media (CPM), including the fractured bedrock layer. However, Darcy’s law is only valid when the fracture network is dense enough and behaves like a porous medium (Singhal and Gupta 1999). In addition, if the hydraulic conductivity of a fracture is too high, turbulent flow appears and Darcy’s law is not valid. Thus, to improve the modelling accuracy for fractured bedrock, software such as ConnectFlow (Jackson et al. 2000) could be used to generate grids, applying both CPM and a discrete fractured network (DFN) (Hartley and Joyce 2013). Furthermore, ConnectFlow algorithms can be used to calculate K within the Quaternary sediment system underlain by fractured bedrock (Hartley et al. 2009; Hartley and Joyce 2013).

In most of the MODFLOW series codes, including MODFLOW-NWT, horizontally continuous layers are assumed, and the pinched cell approach is the only way to create lens-like structures. MODFLOW 6 (Hughes et al. 2017) could be an option for creating scattered units using unstructured grids, where the number of cells between layers can vary. Unfortunately, the hydrogeology tool of Leapfrog cannot currently create unstructured grids; however, Leapfrog is able to create uneven cell sizes in X and Y directions, enabling denser gridding for river banks, for example, and looser gridding for poorly known or homogeneous sediment areas.

To further develop the modelling workflow used in this study, multiple layers in bedrock units should be added to the MODFLOW grid to create fractures with varying dips. Additionally, fractures could have been generated with the deposit or erosion type of contact in Leapfrog and used as such for the hydrogeology tool, although this would be complicated. Moreover, Leapfrog Geo version 4.4 and older did not allow the use of the vein and intrusion type as contact surfaces in the hydrogeology tool. To model the hydraulic properties of fractures in more detail, the MODFLOW package Horizontal Flow Barrier (HFB) could be used to create low conductivity zones at 90° surrounding the faults and fractures. In addition, in groundwater flow modelling with the code FEFLOW, it is possible to generate discrete features such as conduits or fault structures inside the cell (Diersch 2014). Leapfrog could generate a FEFLOW grid with the hydrogeology tool, and it would therefore be possible to test a corresponding workflow.