Interpretation of hydrogeochemistry of the Upper Freshwater Molasse (Obere Süßwassermolasse) in the Munich area (Bavaria, Germany) using multivariate analysis and three-dimensional geological modelling

The study area is located in Bavaria (Germany) in the greater area of Munich and covers an area of ~550 km² (Fig. 1). The central part of the study area is the Munich Gravel Plain of fluvio-glacial origin, which consists of sandy terraces from Pleistocene glacial periods and modern alluvial and fluvial deposits (Bauer et al. 2006). Coarse-grained carbonate gravels have attained a maximal thickness of 30 m in the city of Munich and up to 60 m in the entire project area, and constitute a very productive porous aquifer (Albarrán-Ordás and Zosseder 2020). The thickness depends on the presence of paleochannel structures carved in the underlying Neogene deposits. Depending on the local geology and the local water table, this aquifer occurs under either confined or (mostly) unconfined conditions. The average hydraulic conductivity is 5 × 10^–3 m/s (Böttcher et al. 2019); however, a wide variability in hydraulic conductivity values has been reported (Theel et al. 2020).

In the south, the landscape and geology are dominated by Pleistocene sediments, including pre-Alpine moraines of four glaciations—Würm, Riß, Mindel, and Günz (from young to old)—and corresponding terraces of gravel accumulations (Doppler et al. 2011). The thicknesses vary a lot and reach mostly from a few meters up to 20 or 30 m, reaching in the south even up to 80 m (Zosseder et al. 2022). The sediments are inhomogeneous and comprise boulders, gravels, and sands, as well as clay and silt. Local, mostly isolated and confined porous aquifers are related to lenses or layers of coarse material (Zosseder et al. 2022).

The Upper Freshwater Molasse (German: Obere Süßwassermolasse – OSM) is the upper part of the North Alpine Foreland Basin, also termed the Molasse Basin. The sedimentary rocks range from the middle to the upper Miocene, ca. 17–11 Ma (Kuhlemann and Kempf 2002). The OSM presents tabular geometry and contains sediments of channel deposits (sands, local gravels) and fine-grained material of the alluvial plain (clays, marls; Maurer and Buchner 2007). The mineral composition is comprised of quartz, mica, clay minerals and minor quantities of calcite and dolomite (Rauert et al. 1993). The thickness of the OSM deposits can reach up to 700 m in the project area (southern part of Isar-valley-paleochannel) and generally increases from north to south (Zosseder et al. 2022). The thicknesses of particular groundwater bodies may reach 200 m (Wagner et al. 2003). The OSM sediments are mostly covered by Quaternary deposits. The outcrops of the OSM are generally in the northern part of the study area, which also constitutes the northern margin of the Molasse Basin. Groundwater occurs in sand and gravel layers. Aquifers can be distinguished between “shallow” and “deeper”. This distinction, however, is of practical meaning and not linked to any specific definition of deep groundwater (e.g. as presented by Frape et al. 2003). Shallow aquifers show evidence of anthropogenic impacts and contain relatively young, meteoric water, whereas deeper aquifers are isolated, containing older groundwater. The deeper OSM aquifers are separated and therefore protected from shallow aquifers by silty and clayey sediments, acting as an aquitard (Rauert et al. 1993). The OSM aquifer conditions are mostly confined and the hydraulic conductivity of the OSM layers is two to five orders of magnitude lower than the overlying Quaternary sediment (Jerz 1993; Böttcher and Zosseder 2022).

With the aim of characterizing the existing and potential uses of the subsurface space and the heterogeneity of deposits, the underground space of Munich has been the subject of geological 3D modelling in recent years (Fig. 1, the boundary of the model is almost the same as the urban area of Munich marked in grey). As a result of these works, the “D_i models” method was conceived as a new methodology for predicting the 3D lithological variability in detrital systems and was proven in a case study in Munich. The details of the model, in particular the input data and sophisticated methodology, can be found in Albarrán-Ordás and Zosseder (2022). The same approach was also implemented in a second model in a broad area located north of Munich (Fig. 1, referred to as Model North; Zosseder et al. 2019). The models were constructed using SKUA-GOCAD™ software (Emerson E&P, St. Louis, USA). The aim of the 3D models was to identify clearly separated aquifers and detect interconnectivity between groundwater bodies.

The focus of the GeoPot project was set as the Munich area, where the need to manage the subsurface resources due to their extensive use is more accentuated, in contrast to its surroundings. Therefore, a detailed lithological and a 3D architectural model was produced for Munich, whereas in the case of the Model North, the priority was given to predicting the lithological composition and no architectural model was implemented.

The first of the models provided the prediction of the lithological composition on a cell-by-cell basis, covering a 310-km² area of Munich. This also revealed the complex reservoir configuration presented in the Quaternary and Upper Freshwater Molasse deposits by means of the 3D architectural model (Albarrán-Ordás and Zosseder 2022). Focusing on the OSM sediments, the architectural model showed four extensive coarse-grained geological bodies in Munich that are separated by impermeable beds (Fig. 2). These four geo-bodies are termed T1–T4, from shallower to greater depths, and they host the aquifer systems with the same notation. The aquifer system T1 represents the first OSM groundwater system from the ground surface, having various aquifer tiers at different depths (referred to in a previous paper as T1A–T1D; Zosseder et al. 2019; Albarrán-Ordás and Zosseder 2022) and showing multiple hydraulic interaction areas with the Quaternary aquifer throughout the city. The architectural 3D model also indicated that the deeper aquifer systems T2–T4 are considered to be isolated from one another.

The second of the models, Model North, implemented using the D_i models method, focuses on the area of the Munich Gravel Plain situated immediately to the north of the city. The modelling area extends northwards to the uncovered molasse sediments in the Tertiary Hills region, covering a total surface area of 2,426 km² (Fig. 1).

A broad range of hydrogeochemical data derived from groundwater samples taken from boreholes at different depths was collected from the records of the Bavarian Environment Agency (Bayerisches Landesamt für Umwelt, LfU) and several water authorities (e.g. City of Munich). Samples revealing high anthropogenic pollution were excluded from further assessment. In particular, piezometers located by dump sites, gravel pits or polluted areas were manually selected based on their location and extreme results for certain chemical parameters (mineralisation, pH) compared to local hydrochemical conditions, and consequently expelled. However, diffuse, ubiquitous contamination from agriculture or in the urban areas were not considered as an exclusion criterion.

In total, ca. 98,000 groundwater analyses coming from 7,300 sampling locations were collected. It is important to note that each sampling location represents one well screen section in a borehole. For clarity, hereafter only the term “well” is used, despite the type of borehole (well, piezometer, etc.). Each level of the multilevel groundwater systems was also treated as a separate “well”.

In addition to the data collection from reviewed literature and external databases, groundwater sampling was carried out in three sampling campaigns during 2017–2019. Samples were collected at 108 sites, which covered private and municipal drilled wells (32), piezometers (21), and springs (55) of the OSM—Fig. A2 in Section S1 of the electronic supplementary material (ESM). Sampling locations were selected mostly outside the city area, in regions that had previously had a less dense programme of sampling, in order to complement the existing data. In-situ measurements were performed by multiparameter field meters (WTW Multi 3430, Xylem Analytics, Weilheim, Germany) for temperature, pH, electrical conductivity, and dissolved oxygen. Groundwater samples were analysed for 46 parameters, including major and minor ions and trace constituents at the Bavarian Environment Agency. The actual design of the applied analytic methods is described in Chavez-Kus et al. (2016). Additionally, water stable isotopes (δ¹⁸O and δ²H) were measured at the TUM using a cavity ring-down spectrometer (IWA-45EP; ABB – Los Gatos Research, San Jose, USA).

The data set was extremely heterogeneous in many aspects, from the kind of raw data format to the range of analysed parameters. Additionally, the data quality, showing diverse limits of detection, varied considerably over time (data from several decades). Hence, intensive processing was essential prior to further analytical steps.

The analyses were checked for their actuality (more recent than 1978, as proposed in the study of the Bavarian Environment Agency (LfU) by Chavez-Kus et al. 2016), completeness (major ions measured) and quality (charge-balance error ≤ 10%). For some wells more than one analysis was available. To ensure the same weighting in spatial statistical assessment and to avoid unwanted clustering effects (e.g. Isaaks and Srivastava 1989), only one analysis for each well was selected. The selection was performed by considering: (1) novelty (newer analyses were favoured), (2) number of analysed parameters and (3) giving priority to the analyses obtained during a sampling campaign conducted for this study case. The last criterion was introduced for the simple reason that full control over quality was possible for these samples. Finally, 1,702 analyses (coming from the same number of distinct wells) were selected. The data points were well distributed over the whole study area; however, with higher density in the city area of Munich (see Fig. 4).

After careful evaluation of each well (in particular: examination of available geological maps and bore logs, as well as analysing the screen lengths and depths in the geological 3D model), the wells were assigned to the hydrogeological units: (1) Quaternary (612 wells), (2) Quaternary – moraines (320), (3) OSM – shallow (581), and (4) OSM – deep (108). The locations of the wells selected for further assessment are presented in Fig. 4. Additionally, the locations of all available wells along with the number of analyses, as well as the position of sampled points in the aquifers, are shown in Fig. A1 in the ESM. In this step, 81 wells were excluded from statistical analysis, namely the boreholes having more than one well screen section, each of them at different depth intervals, therefore, belonging to more than one hydrogeological unit. This facilitated the description of the characteristics of each hydrogeological unit (results presented in Section S2 in the ESM). In the multivariate analysis, however, the wells capturing more than one hydrogeological unit (or geobody derived from 3D modelling) were saved in order to capture the mixing effects.

Multivariate statistical methods were employed in order to capture the variability of the great amount of data for selected parameters derived from groundwater found in complex hydrogeological conditions. These multivariate statistical methods included exploratory factor analysis (EFA) and hierarchical cluster analysis (HCA), followed by the application of a machine learning algorithm. The calculations and diagram preparations were performed with the statistical program R (R Core Team 2021) using the packages stats (integrated in R), class (Venables and Ripley 2002), corrplot (Wei and Simko 2021), psych (Revelle 2020), and ggplot2 (Wickham 2009). Besides, for the Piper diagram preparation, the package hydrogeo (English 2017) was used.

EFA is a statistical method that aims to explore the correlation structure among measured variables and identify relationships between them (Goretzko et al. 2019). The dimensionality of variables is reduced by clustering (Hajji et al. 2021), so the data can be summarized in a smaller set of factors for prediction purposes. Because factor analysis uses a correlation matrix, underlying concerns affecting the correlation should be examined prior to the factor analysis: sample size, missing data, normality, linearity, and outliers (Schumacker 2016). Firstly, because it has implications for the selection of the correlation method, the statistical normality of the data was analysed with the Shapiro-Wilk test. The data size was first validated with the Kaiser-Meyer-Olkin test (KMO should be >0.5). Next, the Bartlett test of sphericity was performed to identify whether the correlations in the matrix were statistically significant (significance level > 0.05; Backhaus et al. 2016). Communality is a measure of how well the variance of each variable is described by a specific set of factors. A measure of sampling adequacy (MSA) shows the proportion of variance in the variables caused by underlying factors (Goretzko et al. 2019). The optimal (lowest) number of factors was determined by generating a scree plot (eigenvalues versus eigenvectors; Conway and Huffcutt 2003). To optimize, variance rotation is applied for better interpretation (e.g. by the oblimin oblique rotation method; Cloutier et al. 2008; Yong and Pearce 2013). As a factor extraction method, maximal likelihood might be preferred (Goretzko et al. 2019).

HCA is a data classification technique, in which the relative positions of all objects in the multidimensional variable space are determined (Odziomek et al. 2017) and distance is used for identification of naturally-occurring groups (clusters). No a priori assumption about the data is made and the classification of the objects into clusters is based on their similarity. In HCA, the squared Euclidean distance metric and Ward’s linkage method were implemented, similar to the methodology presented in Güler et al. (2002) and Cloutier et al. (2008). The Euclidean distance is a measure of similarity performed over all variables included in HCA and is used to identify outlier clusters. Ward’s linkage rule creates separate clusters based on analysis of variance and was next applied to link all nonresiduals into distinct clusters (Raiber et al. 2012). The number of clusters was estimated via elbow-, silhouette-, and gap-statistic methods (Kassambara 2015). The HCA results were than visualised in a dendrogram. Cluster analysis allowed grouping of samples in reference to similarities detected by the algorithm.

EFA and HCA were first conducted for the samples in the area Munich, as the most detailed data as well as a detailed 3D architectural model from the geological 3D modelling were available there (Albarrán-Ordás and Zosseder 2020, 2022). A similar methodological approach to the ones presented by Cloutier et al. (2008), Gilabert-Alarcón et al. (2018) and Heine et al. (2021) was implemented. In this part of the study, 13 parameters were considered—pH, electrical conductivity (EC), dissolved oxygen (DO), calcium, iron, magnesium, manganese, potassium, sodium, chloride, hydrogen carbonate, nitrate, and sulphate—observed in 213 wells. The choice of the wells resulted from the prerequisites of the multivariate statistics; in particular, and also to avoid the concerns of missing data, only the wells for which all 13 parameters were available were selected (Cloutier et al. 2008). Moreover, all wells were directly spatially linked to one of the geological bodies identified in the 3D architectural model of the Quaternary and OSM deposits by Albarrán-Ordás and Zosseder (2019, 2020, 2022). This shortened database comprised data from the time period 1992–2019, representing all the geological bodies and aquifer systems as presented in the preceding 3D model study. HCA procedures were applied using the psych package from the R library (Revelle 2020). For the purpose of the multivariate statistical analysis, the parameters with concentrations lower than the detection limit were replaced with a proxy value ‘0’.

In order to evaluate the characteristics of each cluster more accurately, descriptive statistics were calculated as replenishment for cluster analysis (Ghesquière et al. 2015). The analysis was done on further constituents (e.g. trace elements and water isotopes) not included in the multivariate statistics.

In order to check if the water types from outside of the city can be grouped in the same water type clusters detected for the city area, the records from Munich’s surroundings were fitted to the clusters created for the city. For the classification of data from the entire project area, a k-nearest neighbourhood (KNN) algorithm was used. KNN is a supervised machine learning algorithm (Rebala et al. 2019). A total of 828 wells were considered in this step (together with wells from the city area – 1,041 wells, Fig. 3). It is assumed that similar items are closer to each other. The algorithm was first “trained” and tested on the data from the city area and then applied to the data from Munich’s surroundings. The features were scaled to ensure equal contribution while calculating distance. For each row of the test set, the k = 1 nearest training set vectors were found and classified (Venables and Ripley 2002).

Firstly, the geological 3D models were used in different forms to enhance the understanding of hydrogeological and hydrogeochemical conditions, by the assignment of hydrogeological units and distinguishing between shallow and deeper wells. A set of 2D cross sections along the wells in both Munich and in the area situated to the north of the city (Model North) was selected and generated from the models. These 2D representations show the predicted prevailing lithologies in the vicinity of the well screens where the samples for this study were collected. Analysis of this picture of the continuity of the lithologies resulted in the assignment of the aquifers “OSM-shallow” and “OSM-deep” to the screened well sections. This was inferred individually for each well screen along the 2D profiles.

For simplification purposes, within the present study, the aquifer systems in the OSM are sorted into one of the following two notations—OSM-shallow or OSM-deep. The first group denotes the aquifer system T1, which presents wide interaction areas with the overlying Quaternary aquifer, whereas the second group refers to the aquifer systems T2, T3, and T4, which have no hydraulic interlinkage to other shallow aquifers. The distinction between the aquifer systems T1-T4, i.e. the 3D architectural model, was implemented in 3D only in the city area. However, in order to facilitate the cluster interpretation with depth also in the northern part of the study area, an interpretation of the OSM-shallow and OSM-deep aquifers along the cross section in Model North is provided.

The statistical normality of the data, analysed with the Shapiro-Wilk test, showed that no variable represented the normal distribution. Therefore, a correlation matrix was calculated with the Spearman method because it is nonparametric and used to perform rank-based correlation analysis (Kassambara 2015).

Relevant relationships among the variables are presented as a correlation matrix (Fig. 5), which allows one to distinguish the following relationships: (1) strong positive correlations among chloride, sulphate, nitrate, EC and calcium (0.61–0.83), (2) strong positive correlations between DO and nitrate (0.65), DO and calcium (0.58), iron and manganese (0.53), carbonates and calcium (0.58), and (3) negative correlation of pH and calcium, EC, nitrate, chloride or carbonates (0.52–0.74).

The KMO test gave a moderate overall measure of sampling adequacy (MSA) of 0.71, indicating that the sample size is adequate for factor analysis. In the Bartlett test, high values of chi-squared (χ² = 2,068, p-value ≈ 0, 78 degrees of freedom) were achieved, indicating that statistically significant correlations exist within the matrix. The determinant of the correlation matrix was positive. Internal consistency reliability was measured by Cronbach’s alpha reliability (Revelle 2020) and demonstrated to be good (0.72).

The ideal number of factors in this case was determined by three methods. The scree-elbow plot of eigenvalues and the empirical Kaiser criterion were in favour of four factors, whereas the parallel analysis favoured five. Finally, by trial and error, a number of three was chosen, giving the most satisfying results: minimum number of variables per factor of four and item to factor ratio of 4.3:1.

Maximum likelihood (ML) was implemented as a factoring method and an oblimin oblique rotation method, allowing the resulting factors to be correlated. The Bartlett method was used for factor scores.

Communalities of individual parameters vary between 0.26 and 1.00 (Table 1). The factor loadings and factor scores for the first two factors obtained in the EFA are presented in Fig. 6 (see also Fig. A3 in the ESM). The three factors explain 60% of the total variance; moreover, factors ML1 and ML2 are correlated at 0.47 (Fig. A4 in the ESM).

Factor ML2 explains 27% of the variance and shows the highest loading (>0.7) for positive correlated parameters: Cl^–, SO₄^2– and EC, and also for Na⁺, K⁺ and NO₃^–. This factor matches the concentrations of anions Cl^–, SO₄^2–, and cations Na⁺, K⁺, to the EC, which is known to be related to the total mineralisation.

DO, Ca²⁺ and HCO₃^– load high regarding factor ML1. Also, NO₃^– and DO load secondarily to this factor, as well as pH (negatively). The opposite loadings for HCO₃^– and pH possibly imply that carbonate solubility is controlled by pH (Newman et al. 2016); moreover, the opposite loadings of Ca₂⁺ and Na⁺ reveal the importance of the cation exchange process.

Mn²⁺ has the highest factor loading on the third factor ML3. Similarly, Fe_tot and Mg²⁺ load to ML3. This factor may be connected to the redox conditions in the aquifers, especially with respect to the (admittedly low but not negligible) negative loading of DO.

The estimated number of clusters was diversified depending on the method used (6, elbow method, 4, silhouette method, 9, gap statistics). Therefore, finally, the number was determined arbitrarily on eight clusters and these clusters were the basis for the proceeding interpretation. The cluster analysis allowed grouping of the groundwater samples in reference to similarities in their physicochemical characteristics. In the first attempt at building clusters (not shown), five outliers were identified and excluded from further analysis. The dendrogram in Fig. 7 concerns the remaining 208 data points. This graphical representation of HCA as a dendrogram is presented in combination with pie charts showing the major ions contents.

The clusters built for the city area, resulting from the previous step, were used for the classification of the wells from the entire project area. The classification was performed with the KNN-algorithm. The k-value, which indicates the count of the nearest neighbours, was found in an iterative selection process. For k = 1 the accuracy score of KNN equal to 80 % was found to be satisfactory (95% confidence interval: 69.14, 88.78), with p-value < 2.2e-16 and Kappa = 0.7598; hence, KNN was further used to classify the wells.

Stable isotopes of oxygen and hydrogen in groundwater (expressed as isotope ratios δ²H and δ¹⁸O, respectively) are used, among others, to analyse groundwater flow pathways, including paleo-groundwater and mixing processes (Tweed et al. 2019). For instance, the values of δ²H and δ¹⁸O for water infiltrating to the subsurface in the Pleistocene period were several per-mill lower than the present (Tweed et al. 2019). Additionally, measurements of the radioactive hydrogen isotope tritium (³H) provide further insight into the mean age of groundwater (Małoszewski et al. 1983; Zuber et al. 2001).

Figure 8 presents the stable isotope values, as well as the Global Meteoric Water Line (GMWL) and local meteoric water line (LMWL) calculated for Germany (Stumpp et al. 2014), with the formulae: The observations plot mostly around these lines.

For comparison, an isotopic value for precipitation is presented. Long-term means for stable water isotopes in precipitation were calculated for the measurements from Neuherberg (near Munich) and have the following values: δ¹⁸O –9.89±0.78‰, δ²H –70.5±5.8‰, with d-excess 8.6±1.3‰ (IAEA/WMO 2020).

Groundwater in the study area showed water stable isotope values between –13.2 and –8.9‰ for δ¹⁸O and between –94.7 and –63.9‰ for δ²H (Fig. 8a). Water samples from Quaternary aquifers (Q and Q-moraines) plot mostly close to these values, revealing a relatively young age of groundwater in these compartments. The point-cloud of OSM-shallow is spread towards lower values of δ¹⁸O and δ²H, suggesting that water age reaches Pleistocene, since groundwater recharge occurred during cooler conditions from melt water or precipitation (van Geldern et al. 2014). This trend is even more visible for the wells from deeper OSM levels. The highest δ¹⁸O and δ²H values may be explained by evaporation, either natural (subsurface influx of lake water in the south of Munich) or anthropogenic (industrial cooling water) (Rauert et al. 1993). The variability of δ¹⁸O and δ²H values is greatest in cluster 1 and may reflect a spectrum of groundwater ages or mixing processes (Rauert et al. 1993). Data points of the remaining clusters concentrate mostly around the values of modern precipitation.

Regarding the tritium content (Fig. 8b; Fig. A8 in the ESM), no occurrence was found in most of the wells of the OSM-deep. However, even in some samples associated with cluster 1, typical for deeper aquifers, tritium was observed, suggesting mixing processes. Interestingly, in some wells of shallow OSM and even in Quaternary moraines, no tritium was measured, revealing water age of more than ca. 70 years (recharged prior to the start of above-ground nuclear bomb testing in 1953), suggesting that these units in some parts of the research area are well isolated from the surface.

As described in section ‘Multivariate statistics for the Munich area’, the primary focus was on the city area, where a detailed 3D architectural model of the Quaternary and OSM deposits was available. A map presenting locations of the wells in the Munich city area (Fig. A5 in the ESM) and a Piper diagram for those sites (Fig. A6 in the ESM), as well as a table of the number of wells in each aquifer system and cluster (Table A1 in the ESM) are provided.

The clusters described in the following relate to the entire area. A general overview of all observations is given in Table 2 and Figs. 9 and 10, which present by analogy the number of wells in each aquifer and cluster, the locations of the wells within the study area, and the Piper plot. Additionally, the box-plots obtained for the clusters are shown in Fig. A7 in the ESM. In Figs. 9 and 10, the groundwater samples are coloured according to their cluster. It can be seen in Fig. 9 that clusters do not build any spatial, regional pattern in a 2D view; therefore, in the following, they are described in accordance with their occurrence in a 3D geological system. Additional information for cluster interpretation can be concluded from the bi-variate plots (Fig. 11).

The cluster interpretation provided below presents various examples by means of the two geological 3D models implemented in the greater area of Munich. As mentioned in the section ‘Geological 3D models in the greater area of Munich’, the models refer to (1) the city of Munich (Fig. 12), and (2) the area extending from the north of the city to the Tertiary Hills (Fig. 13). Selected examples are indicated by numbers in Figs. 12 and 13 and described in the text.

In this study, the three main lines of evidence in characterising hydrogeochemistry were: (1) multivariate statistics, complemented by (2) descriptive statistics, and finally coupled with (3) geological 3D modelling. These lines of evidence did not follow one another as listed here, but rather followed each other in a few iterative steps. Coupling the 3D geological models with hydrogeochemical data can be seen from different perspectives: first of all, the model serves as a starting point for grouping hydrochemical data, but at the same time hydrogeochemistry poses an additional validation of the model. Moreover, geological 3D modelling provides a better understanding of the geometry of the aquifers. In older studies, the main criterion for the grouping of wells was their depth. Thanks to the 3D model, other criteria can be examined such as the affiliation of wells to certain aquifers, interconnections between groundwater bodies, etc. On the other hand, the presented utilisation of the 3D geological modelling outcomes reveals a possible qualitative verification of the model, meaning that greater confidence in the model with subdivided horizons was established (after the definition of verification by Diaz-Maurin and Saaltink 2021).

A first understanding of the hydrogeochemical characteristics of the study area was obtained by defining four main hydrogeological units and assigning objects to these units (often taking advantage of the outcomes of the geological 3D modelling), followed by calculating descriptive statistics for 46 parameters (Zosseder et al. 2022; results described briefly in Section S2 of the ESM). The results of this approach were satisfying but did not allow for a deepened assessment of hydrogeochemical patterns; therefore, more sophisticated multivariate statistical methods were implemented.

Multivariate statistics have successfully been applied in hydrogeochemistry studies, especially when dealing with large-scale data (e.g. Heine et al. 2021), when presenting information on human impacts on hydrogeochemistry (Menció and Mas-Pla 2008) and distinguishing between distinct hydrogeochemical zones, as well as increasing the general understanding of hydrogeological processes (Cloutier et al. 2008). All these aspects were addressed in the presented study.

The hydrogeochemical groups (clusters) obtained by multivariate statistical methods and their dependencies could be explained using plots and diagrams, and, finally, being presented in 3D view has thus enhanced their understanding. However, the clusters were based on selected parameters. After creating the clusters by means of multiple statistical methods, it was necessary to fall back on descriptive statistics in order to characterise the hydrogeochemistry more precisely. In this way, descriptive statistics, which constitute a more traditional approach, played an important role in this study, as it enabled further insight into the hydrogeochemistry—for instance, the patterns of trace element occurrence could not be described otherwise.

The clusters obtained in this study, based on the hydrogeochemistry, were not as unambiguous as expected, because the local geology offers multiple pathways for water exchange and mixing at almost all levels and over the whole area, as has already been hinted at in the 3D model (Albarrán-Ordás and Zosseder 2022). Therefore, the authors support the idea that the clusters actually not only present an effective way to highlight distinct water groups where possible, but they also effectively highlight relationships between mixed waters. However, some wells located close to each other and screened at almost the same depths represented different clusters, probably due to some local conditions not captured in the 3D model, or due to the long well screen lengths reaching across different groundwater systems. The latter circumstance is economically explicable, but complicates capturing the hydrogeochemistry characteristics of distinct levels—for example, Rauert et al. (1993) suspected that samples analysed in their study represented mixed waters originating from great depth intervals and, therefore, of different ages.

The two main studies highlighted so far that combined hydrogeochemistry with 3D geological modelling were reported by Martinez et al. (2017) and Raiber et al. (2012). Use of 3D geological models in these studies, similar to the one reported here, has enhanced understanding of the aquifer systems, and their spatial relationships and interconnections. Taking into account the current development of 3D modelling and its numerous applications (Albarrán-Ordás and Zosseder 2022), and a successful implementation as presented in this study, new applications in this thematic area can be expected to follow.

A conceptual regional hydrogeochemical model was developed based on the results of multivariate statistics supported by geological 3D modelling. Based on that, the following can be stated: