A New Water-Based 87Sr/86Sr Isoscape Map of Central and NE Germany, with Special Emphasis on Mountainous Regions

In this study, we present a new 87Sr/86Sr isoscape map of Central and NE Germany. This area is characterized by an alternation of sedimentary basins and mountainous regions with a very variable lithology. Since lithology and rock age have a major impact on the isotopic composition of biologically available strontium, Central and NE Germany should reveal highly variable 87Sr/86Sr ratios. From lithological characteristics, particularly high ratios are expected in the mountainous regions of the Erzgebirge/Fichtelgebirge and the Harz Mountains. In contrast to these predictions, published 87Sr/86Sr isoscape maps of Central and NE Germany record rather uniform and low 87Sr/86Sr ratios. From this observation, we suspected that existing isoscape maps might be computed from an insufficient database, with mountainous regions being underrepresented. Our goal was to gather 87Sr/86Sr baselines for each major lithology of Central and NE Germany and to produce an accurate isoscape map of Central and NE Germany. In the first step, we evaluated the suitability of stream water and groundwater as a proxy for biologically available strontium. In a selected watershed, we present mixing relationships and a stream network model. We show that groundwater is prone to very local geologic and anthropogenic influences and should thus be avoided. Instead, we focussed our further sampling on stream water. Altogether, we used 119 new measurements of groundwater and stream water and a set of 23 auxiliary variables as a database for our new isoscape map of Central and NE Germany. Due to a sampling strategy that focussed on covering each major lithology, our measurements and the final isoscape map show a clear contrast between sedimentary basins and mountainous regions. For regions that have been sufficiently sampled, a direct comparison of the isoscape map with published and new data shows good agreement. Although Central and NE Germany were part of published isoscape maps, our new map is the first that predicts 87Sr/86Sr ratios in mountainous regions with high accuracy.


Introduction
Isoscape (isotope landscape) maps predict the spatial distribution of isotope ratios that contain geographic information, like e.g. strontium, sulphur, hydrogen, or oxygen (West et al. 2010). Since strontium isotopes are not fractionated by metabolic processes when incorporated into living organisms through water or food consumption, they are of particular interest. Isoscape maps of 87 Sr/ 86 Sr can thus be used directly for archaeological or animal migration studies without additional fractionation correction (e.g. Price et al. 2002;Bentley 2006;Bataille et al. 2021). Additionally, strontium isotope ratios ( 87 Sr/ 86 Sr) may vary over short distances because they are largely influenced by the local geological setting (e.g. Beard and Johnson 2000;Bentley 2006;Voerkelius et al. 2010;Bataille et al. 2014). Thus, provenance assignments based on strontium isotopes can reach a relatively high resolution.
Although rocks are the main source of strontium in the environment, provenance studies have to consider the isotopic composition of biologically available strontium, which may differ significantly from the values of the local lithology (e.g. Price et al. 2002). These differences arise from the differential weathering of minerals and from the addition of strontium from other sources such as dust, sea salt deposition, or fertilizers (Böhlke and Horan 2000;Zieliński et al. 2018;Bataille et al. 2018; Thomsen and Andreasen 2019).
Thus, a representative database of measured 87 Sr/ 86 Sr ratios is necessary to produce accurate isoscape maps (Bataille et al. 2020;Holt et al. 2021). To obtain this database, many strontium isotope studies rely on a suite of different samples like soil leachates, small animal tissue, plants, surface water, and groundwater (e.g. Bataille et al. 2018;Ladegaard-Pedersen et al. 2020). While some studies argue that single materials may not reflect the strontium variability as close as a combination of different archives (Crowley et al. 2017;Grimstead et al. 2017), the inter-site variation typically exceeds intra-site variations (Podio et al. 2013;Ladegaard-Pedersen et al. 2020). This advocates the use of only one single material to compute an isoscape map of 87 Sr/ 86 Sr, as done by some researchers (e.g. Hoogewerff et al. 2019;Scaffidi et al. 2020). Such an approach allows focusing on a broad and representative sampling strategy to optimally cover the spatial variability of 87 Sr/ 86 Sr.
For the generation of isoscape maps from a database of measured 87 Sr/ 86 Sr ratios, machine learning algorithms have recently been preferred over all other interpolation methods (e.g. Bataille et al. 2020;Holt et al. 2021). A major advantage of these algorithms is that a relatively small dataset of measured 87 Sr/ 86 Sr ratios can be used to train the algorithm to calculate high-resolution isoscape maps from a bundle of auxiliary variables (Bataille et al. 2018(Bataille et al. , 2020. Auxiliary variables are maps of factors that potentially influence 87 Sr/ 86 Sr ratios. Lithology, rock age, sea salt deposition, evapotranspiration, and aridity are typical factors of high impact in isoscape map calculations of Central Europe (Bataille et al. 2018;Hoogewerff et al. 2019). Bataille et al. (2018) tested different machine learning algorithms and showed that random forest regression outperforms many other methods such as support vector machines, neural networks, or ordinary kriging.
In Central and NE Germany, the surface geology is characterized by an alternation of sediment-filled basins and geologically complex mountainous regions (Fig. 1). These two types of regions should result in distinct 87 Sr/ 86 Sr ratios. For mountainous regions (like the Erzgebirge/Fichtelgebirge, the Harz Mountains, the Lusatian Block, the Thuringian-Franconian Slate Belt, the Thuringian Forest Basin, the Chemnitz Basin, the Granulite Mountains, and the North Saxon Volcanic complex, Fig. 1b, c) with prevalent Precambrian and Palaeozoic granitic gneisses, granites, rhyolites and clastic sediments, highly radiogenic and variable 87 Sr/ 86 Sr ratios are suggested. In difference, lower and more homogeneous 1 3 87 Sr/ 86 Sr ratios are expected in carbonate-bearing Meso-and Cenozoic sediments in the Thuringian Basin, the North German Basin, the Czech Eger Graben, the Bohemian Cretaceous Basin, and the Subhercynian Basin (Fig. 1b, c).
In recently published 87 Sr/ 86 Sr isoscape maps of Central and NE Germany, a clear difference between sedimentary basins and mountainous regions in Central-and NE Germany is not observable (Hoogewerff et al. 2019) or seems to be underestimated (Bataille et al. 2018). Hoogewerff et al. (2019) predicted uniform and low ratios (around 0.705) for entire Central and NE Germany from soil leachate 87 Sr/ 86 Sr data. In contrast, the map of Bataille et al. (2018) predicted differences between mountainous regions (around 0.710 to 0.715) and sediment-filled basins (< 0.710). While the modelled values in sediment-filled basins are in agreement with previous published data (Voerkelius et al. 2010;Maurer et al. 2012) the mountainous region of the Erzgebirge should be characterized by ratios up to 0.720 (Voerkelius et al. 2010;Tichomirowa et al. 2010). A variety of other mountainous regions in Central and NE Germany (the Harz Mountains, the Lusatian Block, the Thuringian-Franconian Slate Belt, the Thuringian Forest Basin, the Chemnitz Basin, the Granulite Mountains, and the North Saxon Volcanic complex) is not represented by published samples (Fig. 1c) or 87 Sr/ 86 Sr isoscape maps.

Fig. 1
Geological and geographical setting with sample locations. a Map of Central Europe with land masses (grey), ocean (white), national borders (black lines), and major streams (blue) b Geological overview map of Central and NE Germany showing the distribution of different rock types based on the Geological Map of Germany 1: 1,000,000 (BGR, 2014). Nine major rock types were defined based on their formation type (sedimentary, metamorphic, igneous rocks) and their ages (e.g. Cenozoic, Cretaceous, Jurassic, and other) c Elevation map of Central and NE Germany with location and type of water samples. Hollow symbols mark previously published data (Voerkelius et al. 2010;Tichomirowa et al. 2010;Maurer et al. 2012), filled symbols mark new samples. The streams were extracted from SRTM DEM (Jarvis et al. 2008), which is shown as a shaded relief map. Mountainous regions are marked with hatched lines. All regions without hatching are sedimentary basins. Abbreviations of regions are: NSVC-North Saxon Volcanic Complex, SGM-Saxon Granulite Mountains, CB-Chemnitz Basin, TFB-Thuringian Forest Basin 1 3 In this study, we designed a sampling strategy that is adapted to complex geological settings. We present a dataset of 119 new 87 Sr/ 86 Sr ratios of water samples from Central and NE Germany and compare the suitability of surface water and groundwater as a proxy for the biologically available 87 Sr/ 86 Sr ratio. In a second step, we used two different approaches to model 87 Sr/ 86 Sr isoscape maps from these data. Because of the dense sampling and the stream network-related sampling strategy, we were able to compute a dendritic model of the strontium isotopic composition of the Freiberger Mulde catchment according to the approach of Brennan et al. (2016). Finally, we used the complete 87 Sr/ 86 Sr dataset to produce an isoscape map of Central and NE Germany by applying the machine learning approach of Bataille et al. (2018), which uses random forest regression to compute an isoscape map from the strontium isotopic composition of the samples and a bundle of auxiliary variables. A comparison with existing isoscape maps of Central Europe highlights the advantages and disadvantages of small-scale and large-scale isoscape maps in migration studies.

Sampling Approach
The small sub-catchment of the Freiberger Mulde (Eastern Erzgebirge) has a very diverse lithology where Paleozoic gneisses and phyllites alternate with granites, volcanic dykes, but also with some Cretaceous sediments. In addition, numerous hydrothermal and mineral deposits occur in this region (Hoth et al. 1995;Rohde 2014;Fig. 2a). To understand the impact of small-scale lithological changes on 87 Sr/ 86 Sr, we took 31 closely spaced samples and determined their strontium isotopic composition and concentration. Additionally, we measured physico-chemical parameters (temperature, pH, electrical conductivity, redox potential, and dissolved oxygen) during sample collection. With the parallel sampling of stream water and groundwater (Fig. 2a), we aimed to define the most appropriate type of water samples.
Because of the complex geological setting in Central and NE Germany, 87 Sr/ 86 Sr ratios of stream water may change over short distances. We distinguished nine major lithological rock types based on their formation (sedimentary, metamorphic, igneous) and their ages (e.g. Cenozoic, Cretaceous, Jurassic and others, compare Fig. 1b). From prevalent rock types, we defined 14 geologically uniform and coherent regions (Fig. 1b,  c). In most cases, these regions correspond to common physiographic regions of Central and NE Germany.
From each physiographic region, we took water samples to cover the entire range of 87 Sr/ 86 Sr ratios. In particular, we sampled several traverses along streams that flow from mountainous regions into sedimentary basins to trace 87 Sr/ 86 Sr changes (Fig. 1c). Altogether, we collected 119 water samples during the summer and early fall from 2016 to 2020 (Table 1). Around 50 ml of sediment-free water from each location was sampled and categorized as groundwater (from wells/springs) or stream water (Table 1, Fig. 1c).

Strontium Isotope Analysis Methods
Water samples were prepared for analysis in the Isotope Geochemistry and Geochronology Lab at TU Bergakademie Freiberg, Institute of Mineralogy. For strontium isotopic composition determination ca. 30 ml of water was evaporated overnight at 85 °C. For the strontium concentration determination weighed aliquots of 7 ml were mixed with a known quantity of a calibrated 84 Sr-enriched spike solution. The mixed solution was also evaporated at 85 °C. Afterwards, the precipitates were re-dissolved in 0.5 ml of 3.5 N HNO 3 for column chemistry. Strontium was separated from the matrix through cation exchange chromatography using 0.2 ml teflon columns with Sr-Spec cation exchange resins (Charlier et al. 2006) and loaded onto pre-degassed W-filaments. Strontium isotope ratios were measured on the Finnigan MAT 262 thermal ionization mass spectrometer (TIMS, Thermo Fischer Scientific) at TU Bergakademie Freiberg. During measurements, the 87 Sr/ 86 Sr ratio was corrected for mass fractionation using an exponential law, normalizing to 86 Sr/ 88 Sr = 0.1194. The standard NBS987 was analysed repeatedly during measurements and yielded an average 87 Sr/ 86 Sr ratio of 0.71023 ± 0.00003 (n = 12). This is within  Fig. 1c) showing the distribution of different rock types together with measured strontium isotopic composition for stream water and groundwater samples (filled circles and squares, respectively) compared to results of spatial stream network modelling (shown as coloured points along streams; colours correspond to the legend). FM: samples from Freiberger Mulde, TR-samples from tributaries, GW -groundwater samples. The streams were extracted from SRTM DEM (Jarvis et al. 2008). b Box plots comparing the strontium concentration of the main stream (Freiberger Mulde), its tributaries and groundwater from the Freiberger Mulde catchment. c Box plots comparing the 87 Sr/ 86 Sr ratios of the Freiberger Mulde, its tributaries and groundwater from the Freiberger Mulde catchment  (Faure and Mensing 2005). Total procedural blanks were < 30 pg strontium, which is much lower than the amount of strontium in the samples and had no impact on our results.

Modelling an 87 Sr/ 86 Sr baseline of the Freiberger Mulde catchment using spatial stream networks
For the Freiberger Mulde catchment, we computed a spatial stream network model, which uses autocovariance structures to account for the spatial dependencies of river networks (Isaak et al. 2014;Brennan et al. 2016). We used all stream water sampling sites of the Freiberger Mulde catchment as input parameters (Fig. 2a (2016), we used upstream and downstream autocorrelation and per cent geology as auxiliary variables.
In the Spatial Tools for the Analysis of River Systems (STARS) toolbox in ArcGIS 10.2 (Peterson and Ver Hoef 2014), a network topology free of geometric errors, a spatial stream network including the sampling and prediction points, the geological information as per cent geology for each sampling and prediction point, and spatial weights depending on the catchment size were prepared. The modelling itself was conducted in R using the spatial stream network (

Modelling an Isoscape Map of Central and NE Germany by a Machine Learning Approach
To create a high-resolution isoscape map of Central and NE Germany, we used the machine learning approach of Bataille et al. (2018), which applies the caret package on R version 3.5.0 (Kuhn 2008). For this, we combined our new 87 Sr/ 86 Sr dataset with appropriate auxiliary variables (  Bataille et al. (2014) were included as their median (r.m1), first quartile (r.ssrq1), and third quartile (r.ssrq3). We extracted the auxiliary variable values for each geographical location to build the regression matrix and used it for training the spatial prediction model in the caret package (Kuhn 2008). We applied the random forest regression model of Bataille et al. (2018) to the whole dataset and the auxiliary variables to create an 87 Sr/ 86 Sr isoscape map for Central and NE Germany. To assess the accuracy and precision of the model, the dataset was randomly split into a training subset (80% of the entire dataset) and a testing holdout subset for validation (20% of the total dataset). A comparison of observed vs. predicted 87 Sr/ 86 Sr ratios of training and testing datasets allows assessing the model performance.
To understand which of the auxiliary variables have the highest impact on the final model, we calculated IncNodePurity using the caret Package (Kuhn 2008) as a measure for variable importance.

Water 87 Sr/ 86 Sr Ratios of Central and NE Germany
The results of strontium analyses are given in Table 1. Figure 2 summarizes the results from 31 samples of the Freiberger Mulde river catchment. On-site parameters and strontium concentrations have been determined together with 87 Sr/ 86 Sr ratios for these samples and are presented in Table 3. Two outliers were defined based on remarkably high electrical conductivity (Table 3). The 87 Sr/ 86 Sr ratios and strontium concentrations of these samples were suspected to be influenced by anthropogenic contaminations and were excluded from Table 1 and the following interpretation and modelling. In the Freiberger Mulde catchment, the 87 Sr/ 86 Sr ratios range from 0.71216 to 0.71881, with a mean of 0.71536. We grouped the Freiberger Mulde dataset into samples from the main stream (FM, Freiberger Mulde), samples from tributaries (TR) and groundwater samples (GW) from springs and wells. The grouped strontium isotopic composition and concentration data are presented in Fig. 2b and c. In entire Central and NE Germany, 87 Sr/ 86 Sr ratios range from 0.70794 to 0.72313, with a mean of 0.71279.

Spatial Stream Network Model of the Freiberger Mulde Catchment
For a part of the Freiberger Mulde catchment, our sampling covered both the topological variation of the stream network and the lithological variation. This is the requirement to model the data in a spatial stream network (Brennan et al. 2016). The result of this modelling is shown in Fig. 2a, together with the measured 87 Sr/ 86 Sr ratios.

Strontium Isoscape Map of Central and NE Germany
We computed our final isoscape map from 23 auxiliary variables and 119 new 87 Sr/ 86 Sr data from water. The relative impact of the single auxiliary variables on our model is summarized in Fig. 3. The resulting isoscape map of Central and NE Germany is presented together with the data in Fig. 4a. In Fig. 4b, we present four swath profiles of the 87 Sr/ 86 Sr ratios across the isoscape map. The swath profiles were derived from the final isoscape map using SAGA (Conrad et al. 2015). In swath profile analysis, the values are not only derived from the defined profile line, but also sampled in a specified width (swath width) perpendicular to the profile. From this dataset, mean, maximum and minimum values can be defined at each point along the profile. In Fig. 4, swath width was 20 km for each profile (indicated in Fig. 4a with triple lines). Major changes in lithology are marked above each profile. The combination of mean 87 Sr/ 86 Sr ratios with lithological changes visualizes the relationship between lithology and the strontium isotopic composition of water. Additionally, minimum and maximum 87 Sr/ 86 Sr ratios along the profiles allow assessing the variability of the strontium isotopic composition within each geologically coherent region.

Comparison of the 87 Sr/ 86 Sr Ratios of Stream Water and Groundwater
From the Freiberger Mulde catchment data, we aimed to define the type of water samples that optimally reflects the local 87 Sr/ 86 Sr ratio. For this, we compared the water of the Freiberger Mulde river with smaller tributaries and with groundwater. The median values of all three groups are similar (ca. 0.1 mg/l Sr, 87 Sr/ 86 Sr ~ 0.715, Fig. 2b, c). However, the variability of 87 Sr/ 86 Sr ratios and strontium concentrations in the Freiberger Mulde catchment is higher for smaller tributaries than for the main stream and highest for groundwater samples (Fig. 2b, c). In comparison with stream water, groundwater is probably much more influenced by very local geologic phenomena like faults, ore lodes, volcanic dykes, and anthropogenic pollution such as fertilizers (Böhlke and Horan 2000; Thomsen and Andreasen 2019), mine waters (Zieliński et al. 2018), or other groundwater contamination (Nigro et al. 2017). Still, in contrast to completely stationary proxies like plant leaves, roots, or soils, a slightly reduced variability in groundwater can be assumed due to some horizontal and vertical groundwater flow (Ladegaard-Pedersen et al. 2020).
These differences in variability between small streams, larger streams, and groundwater are probably related to mixing processes in stream water. Mixing processes can be recognized in mixing diagrams, where two end-members define a line in an 87 Sr/ 86 Sr vs. 1/Sr diagram and the mixed component will plot exactly on this line (e.g. Tichomirowa et al. 2010). However, in the Freiberger Mulde catchment area, a more complex mixing process is observed, because the mixing product (FM4 in Fig. 5a) is not situated on this straight line, so that one or more additional major sources contributed to the 87 Sr/ 86 Sr ratio of sampling point FM 4. The isotope ratio and Sr concentration of sampling points FM5 and FM6 should result from mixing between FM4-and TR3-waters. However, the mixing diagram reveals an additional input from sampling point TR4 (Fig. 5b). This discussion demonstrates that mixing and transport have a high impact on the Sr isotope ratio of stream water, so that each point in the stream network depends on all its upstream points (Brennan et al. 2016).
In difference, the groundwater 87 Sr/ 86 Sr ratios cannot be explained by simple mixing relationships. We found large differences (up to 0.004) between the predicted Sr isotope ratios from the stream network model and the measured 87 Sr/ 86 Sr ratios in groundwater near the streams. This also emphasizes the high influence of local factors on groundwater.
Based on these results, we decided to concentrate on river water instead of groundwater to constrain the local 87 Sr/ 86 Sr ratios of various physiographic regions for Central and North Germany. We avoided groundwater sampling, because very local geologic phenomena and anthropogenic factors should not be included in a local 87 Sr/ 86 Sr signature. Furthermore, the high variability of groundwater 87 Sr/ 86 Sr ratios would require a much higher amount of samples to define a robust mean value for a region. Instead, we sampled large streams to obtain averaged values for larger regions, and smaller streams to represent smaller-scale variations.

Dependency of Stream Water 87 Sr/ 86 Sr on Lithology and Rock Age
As expected, we observe clear differences between stream water that flows on sedimentary basins and water that flows in mountainous regions. The dependency of 87 Sr/ 86 Sr on lithology and rock age is illustrated in swath profiles that include both mountainous regions and sedimentary basins (Fig. 4b) Table 4 Summary of published, measured, and modelled 87 Sr/ 86 Sr ratios in physiographic regions of Central and NE Germany (defined in Fig. 1 (Spiess et al., 1998, Martiklos 2002; occasionally Late Carboniferous to Early Permian granites and rhyolites, (Zech et

Changes of Stream Water 87 Sr/ 86 Sr Ratios Across Geological Boundaries
Due to mixing and transport processes in the stream network, the 87 Sr/ 86 Sr ratio at any point along a stream represents a mixture of the 87 Sr/ 86 Sr ratios of this point´s entire catchment (Brennan et al. 2016). Thus, stream water 87 Sr/ 86 Sr ratios do not necessarily represent the local biologically available strontium, but might be influenced by distant lithologies. Since we used stream water 87 Sr/ 86 Sr data to produce our final isoscape map, this influence of transport and mixing has to be analysed. In the geologically complex area of Central and NE Germany, it is important to know how far 87 Sr/ 86 Sr ratios are transported from mountainous regions into sedimentary basins. Our data and the stream network model of the Freiberger Mulde catchment (Fig. 2a) illustrate that the 87 Sr /86 Sr ratio along streams is strongly influenced by the lithology and rock age, but does not change abruptly when the stream enters or crosses a different rock type. Strong changes are typically observed at confluences of two or more streams of similar size when the influencing catchment increases suddenly (Fig. 2a). From the upper part of the Freiberger Mulde (samples FM1, FM2, and FM3 in Fig. 2a), we conclude that water draining grey gneisses has an 87 Sr/ 86 Sr ratio of 0.7141-0.7148. Frequent occurrences of rhyolitic dykes cut the grey gneisses. These dykes are expected to increase the 87 Sr/ 86 Sr ratio, but do not show a significant impact on the 87 Sr/ 86 Sr ratios of the stream water. However, an increase of 87 Sr/ 86 Sr ratios is observed in the SW of the Freiberger Mulde as an effect of tributary TR2 draining outcrops of red gneisses (Fig. 2a). The Freiberger Mulde returns to the previous values (typical for grey gneisses) after ca. 20 km along stream (after passing sampling point FM 10; Fig. 2a).
In agreement with our observations from the Freiberger Mulde catchment, high 87 Sr/ 86 Sr ratios are transported into the sedimentary basins for not more than a few tens of kilometres in the swath profiles of the final isoscape map (Fig. 4a).
For the area of Central and NE Germany, we conclude that river water 87 Sr/ 86 Sr is strongly influenced by mixing and transport processes along stream, but is nevertheless a suitable proxy for the local biologically available strontium isotopic composition. Although it might change dramatically at confluences, it adapts its 87 Sr/ 87 Sr ratio to the major geology within a few tens of kilometres along stream. However, we cannot assess this effect for larger streams and their tributaries.

Accuracy of the Spatial Stream Network Model of the Freiberger Mulde Catchment
We assessed the accuracy of the stream network model by comparing the mean of the closest upstream-and downstream 87 Sr/ 86 Sr predictions with each measured ratio. Deviations of the modelled from the measured ratios are ≤ 0.0005 and typically below 0.0002.

Auxiliary Variable Impact
A plot of the relative importance of auxiliary variables (Fig. 3) shows that the processbased bedrock model of Bataille et al. (2018) has the largest influence on our model and provides three of the most important variables (the first and third quartiles and mean).
In addition to the bedrock model, we found that the sea salt wet and dry deposition has a major influence on our model (Fig. 3). Central and NE Germany is bordered to approximately ¼ by the coastline to the Baltic Sea. It has a maximum distance from the coast of ca. 430 km. It has been shown that sea salt deposition (sea spray) plays a major role at localities as far as 300 km inland from the coast (Gustafsson and Franzén, 2000;Ladegaard-Pedersen et al. 2020). Possibly, this explains the relatively high impact on the strontium isotopic composition of Central and NE Germany. On the other hand, a crucial contribution of sea salt deposition to Denmark (Frei and Frei 2011) and to Poland (Zieliński et al. 2021), which are located in similar geographic and climatic conditions, was not observed. Thus, it is possible that the correlation between sea salt deposition and surface water 87 Sr/ 86 Sr that was found during random forest modelling, was spurious. Any other parameter that correlates with the distance from the sea could have caused a spurious correlation with sea salt deposition. One possible variable might be the thickness of sediments on the Pre-Permian crystalline basement. These sediments were deposited within the Southern Permian Basin. The southern rim of the Basin was situated close to the recent Fichtelgebirge/Erzgebirge, and the depocenter with the highest sediment thicknesses was located close to the coast line of the recent Baltic Sea (Ziegler 1990) so that the sediment thickness decreased towards South.
The Bouguer anomaly is another auxiliary variable with a high impact. Probably, there is no direct correlation between 87 Sr/ 86 Sr and the Bouguer anomaly. This variable depends, among other things, on the density and thus on the lithology of bedrock. An influence of deep subsurface rocks on the strontium isotopic composition of stream waters and groundwaters can be excluded. Nevertheless, a comparison of the density of surface bedrock and Bouguer anomaly shows good agreement for the Bohemian Massif (Meurers and Steinhauser 1990). Therefore, the Bouguer anomaly is probably a proxy for the surface lithology, which has an undisputable influence on the strontium isotopic composition (e.g. Beard and Johnson 2000;Bentley 2006;Voerkelius et al. 2010;Bataille et al. 2018).
Another important auxiliary variable was dust flux and dust sources, combined in a single variable (r.dust). The relationship between dust and strontium isotopic composition is complex and related to the 87 Sr/ 86 Sr of the provenance region(s) of the dust (Bataille et al. 2020). Especially in regions with slowly weathering rock types, like crystalline felsic rocks in the mountainous regions of Central and NE Germany (Fig. 1a), the influence of exogenous material might be significant. The impact of evapotranspiration (r.pet) on biologically available 87 Sr/ 86 Sr ratios is probably connected to dust and sea salt deposition, since it might control the relative contributions of bedrock-derived strontium versus aerosol-or dust-derived strontium (Bataille et al. 2018).
A potential impact of fertilizers (r.fert) on the 87 Sr/ 86 Sr ratios is typically observed in regions with a high percentage of agricultural land (e.g. Böhlke and Horan 2000;Thomsen and Andreasen 2019). The contribution of agricultural runoff in stream water has been estimated to be as high as 40% in the Karup river (Denmark, Thomsen and Andreasen 2019), and the fraction of agricultural strontium in the Oder river (Poland) has been estimated to Fig. 6 Measured vs. predicted 87 Sr/ 86 Sr ratios for random forest modelling. To assess the accuracy and precision of the model, the dataset was randomly split into a training subset (80% of the entire dataset) and a testing holdout subset for validation (20% of the total dataset). Regression lines are shown in black, 1:1 lines are shown in red. a) Comparison of predicted values with the training dataset. b) Comparison of predicted values with the testing dataset (tenfold cross-validation) be around 50% (Zieliński et al. 2018). We assume that the amount of fertilizer has a comparably low impact on our model, because its IncNodePurity is lower than that of 6 other variables (Fig. 3).
In summary, from the auxiliary variable importance plot (Fig. 3), three sources can be identified that mainly contribute to the 87 Sr/ 86 Sr ratio of bioavailable strontium in Central and NE Germany. These are: (1) rock-type related parameters like the bedrock lithology and rock age (in form of the bedrock model of Bataille et al. 2018) and the Bouguer anomaly (2) transport from external sources, including sea salt wet and dry deposition and dust input, and (3) anthropogenic influences (e.g. fertilizers).

Estimates for the Accuracy of Our Isoscape Map
The accuracy of our final isoscape map can be estimated through a comparison of measured and modelled data. The training and the testing datasets show a high correlation between the modelled and the measured values (Fig. 6a), suggesting a high accuracy of the modelled data. The regression line is close to, but not identical to the 1:1 line, suggesting a slight overestimation of the lowest and a very slight underestimation of the highest 87 Sr/ 86 Sr ratios in the training data. The testing data fit better to the 1:1 line, but several single analyses and the lowest data (measured ratios < 0.711) deviate even more from this line (Fig. 6b).
Another way to quantify the accuracy of the model is the computation of its RSME (root mean square error, Bataille et al. 2018). In our case, the RSME is 0.0015. This is significantly lower than the RSME reported by Bataille et al. (2018) for their strontium isoscape of Central Europe (0.0023). A lower RSME indicates a better fit between modelled and measured data.
For each physiographic region, the accuracy of the final isoscape map can be assessed by the direct comparison between modelled and measured 87 Sr/ 86 Sr ranges. To do this, we extracted the range of 87 Sr/ 86 Sr ratios for each of the defined physiographic regions (Fig. 1c) from our data and the final isoscape map. Since the 87 Sr/ 86 Sr ratios are variable at a certain distance around the boundaries between regions (Fig. 4b), we sampled the range of ratios from the interior of each region. For this, we applied a buffer distance of 5 km from the region boundaries. The data are presented as box plots in Fig. 7. In Table 4, we compile the mean, minimum, maximum and standard deviations of our model for each physiographic region, compare these data with new and published 87 Sr/ 86 Sr ratios, and give a brief summary of the geological setting for each region. While most regions reveal a unimodal distribution around a mean value, others display a bimodal distribution of the 87 Sr/ 86 Sr (Fig. 7, e.g. the North German Basin, and the Thuringian-Franconian Slate belt). In boxplots, this results in a high number of outliers towards higher or lower values. Fig. 7 Box plots of the 87 Sr/ 86 Sr data of the modelled isoscape map, grouped by physiographic regions (Fig. 1c). For comparison, data from this study (red) and literature data from water samples of Central and NE Germany (blue, Voerkelius et al. 2010;Tichomirowa et al. 2010;Maurer et al. 2012) were plotted for each region For our isoscape map, we can show that the mean (Table 4) and median (Fig. 7) modelled value is within the measured data range in most regions. The best fit between the values of the model and measured 87 Sr/ 86 Sr ratios, both in absolute data and in data variability, is reached for the Erzgebirge/Fichtelgebirge region, the Saxon Granulite Mountains, the Harz Mountains, and the Thuringian Franconian Slate Belt (Fig. 7, Table 4). Only in the Eger Graben, the Bohemian Cretaceous Basin, the Thuringian Forest Basins and the Subhercynian Basin, the modelled mean and median 87 Sr/ 86 Sr are outside the range of measured data (Table 4, Fig. 7). We assume that the extremely low number of measured data (0-4 observations for the above mentioned regions) is the reason for this. The absolute deviation of the mean modelled from measured data is as high as around 0.005 in the Eger Graben (no observations), 0.002 in the Bohemian Cretaceous Basin (4 observations), and 0.0016 in the Thuringian Forest Basin (1 observation). We conclude that the accuracy of our model depends on the number of samples that were used for modelling.
In summary, the accuracy of our new isoscape map is generally strong, but our model seems to slightly overestimate 87 Sr/ 86 Sr ratios in several regions, especially in sedimentary basins with generally low 87 Sr/ 86 Sr ratios and a low sampling density, like the N German Basin, the Subhercynian Basin, the Thuringian Basin, and the Bohemian Cretaceous Basin (Fig. 7).

Comparison with Published 87 Sr/ 86 Sr Data and Isoscape Maps of Central and NE Germany
We present the first 87 Sr/ 86 Sr isoscape map that covers entire Central and NE Germany with a very high resolution and accuracy, both in sampling and modelling (Fig. 7, Table 4). Some previously published datasets (Voerkelius et al. 2010;Tichomirowa et al. 2010;Maurer et al. 2012) and isoscape maps (Hoogewerff et al. 2019;Bataille et al. 2018Bataille et al. , 2020 include at least parts of Central and NE Germany and can be compared to our results. Similar to our data and model, Voerkelius et al. (2010) and Tichomirowa et al. (2010) found high 87 Sr/ 86 Sr ratios in the water of the mountainous regions of the Erzgebirge/Fichtelgebirge and the Chemnitz Basin (Table 4). Our new data from the Freiberger Mulde and its tributaries are within the range of published 87 Sr/ 86 Sr ratios from this catchment (Tichomirowa et al. 2010). Additionally, our new data from some sedimentary basins (the Thuringian Basin, the Subhercynian Basin, and the North German Basin) are within the previously published range of data (Table 4; Voerkelius et al. 2010;Maurer et al. 2012). In contrast to this, the previously published 87 Sr/ 86 Sr ratios of the Harz Mountains and the Thuringian Forest Basin (Voerkelius et al. 2010) differ significantly from our new data, which are much higher (Table 4). The reason for such differences might be a too small number of published data from the Harz Mountains and the Thuringian Forest Basin, so that a statistically robust data range could not be defined. Our sampling campaign solved this problem for the Harz Mountains, but not for the Thuringian Forest Basin, where we added only one single measurement to the database.
Our new data reveal a significant difference between 87 Sr/ 86 Sr ratios in mountainous regions (Erzgebirge/Fichtelgebirge, Harz Mountains) and sedimentary basins (North German Basin, Thuringian Basin). We conclude that isoscape maps with uniform and low 87 Sr/ 86 Sr ratios for entire Central and NE Germany (Hoogewerff et al. 2019;Bataille et al. 2020) are not correct. This might be attributed to an insufficient resolution of the maps (Bataille et al. 2020) or an insufficient sampling density (Hoogewerff et al. 2019).
Furthermore, these isoscape maps are not based on water samples, but mainly on soil leachates (Hoogewerff et al. 2019;Bataille et al. 2020). This might induce a small difference in 87 Sr/ 86 Sr, but a generally good correlation between the 87 Sr/ 86 Sr ratios in water and soil leachates has been demonstrated (Ladegaard-Pedersen et al. 2020). Thus, the difference of 87 Sr/ 86 Sr ranges between mountainous regions and sedimentary basins should be recognizable from both materials.
The isoscape map of Western Europe of Bataille et al. (2018) shows strong variability, with higher 87 Sr/ 86 Sr ratios in mountainous regions and lower ratios in sedimentary basins. But here, these differences are obviously not based on measured data, which were sampled in the Thuringian Basin only (Bataille et al. 2018).
As outlined by Bataille et al. (2020), a robust estimate can only be expected in data-rich areas and if sampling covers all geological variations. This is in accord with our observation and a direct comparison of the isoscape map of Bataille et al. (2018) with our new isoscape map can reveal the strengths and weaknesses of both models (Fig. 8). Apparently, the isoscape map of Bataille et al. (2018) underestimates the 87 Sr/ 86 Sr ratios in mountainous regions like the Erzgebirge and the Harz mountains (Fig. 8a, c). Probably, this is because the map was produced without measured data from these regions. In contrast, the modelled 87 Sr/ 86 Sr ratios of the Thuringian Basin, which was part of these authors' sampling approach, are well reproduced (Fig. 8a). In difference, our new isoscape map slightly overestimates the 87 Sr/ 86 Sr ratio in the Thuringian Basin (Fig. 8b), although our 16 new data from the Thuringian Basin do not differ from the dataset used by Bataille et al (2018; Fig. 7).
For our modelling, we used the approach of Bataille et al. (2018) with almost identical auxiliary variables. Thus, the distribution of samples must be the reason for differences in the isoscape maps. Our samples were mainly derived from mountainous regions (Fig. 1c). Consequently, most of the variability in our dataset is found in these regions. Since the machine learning model aims to explain as much as possible of the variability of a dataset, this selective sampling approach optimized our model for mountainous regions. This is  Bataille et al. (2020) and Brennan et al. (2016), who stated that the modelling approach is not adequate for geologically complex areas. Our study demonstrates that geologically complex areas can be modelled correctly if the sampling density is high enough. Nevertheless, a relative uniform sampling approach is necessary to maintain a similar grade of accuracy for an entire isoscape map.

Conclusions
From 119 new stream water and groundwater 87 Sr/ 86 Sr data, we modelled a strontium isoscape map of Central and NE Germany. For this, we used the machine learning method of Bataille et al. (2018) with 23 auxiliary variables.
To support meaningful provenance interpretations in archaeology and animal migration studies, we subdivided the area of Central and NE Germany into 14 geologically coherent regions. We focussed our sampling on the mountainous regions of the Erzgebirge/Fichtelgebirge and the Harz mountains, which were not well represented by measured 87 Sr/ 86 Sr values in previously published isoscape maps (Bataille et al. 2018(Bataille et al. , 2020Hoogewerff et al. 2019) and regional studies (Voerkelius et al. 2010).
In our new data and model, these mountainous regions reveal significantly increased 87 Sr/ 86 Sr ratios in comparison with adjacent sedimentary basins like the Thuringian Basin, the North German Basin, or the Subhercynian Basin. The comparison with existing data and isoscape maps of Central and NE Germany demonstrates that our new isoscape map is the first that resembles stream water 87 Sr/ 86 Sr ratios in mountainous regions with very high accuracy.
Our results demonstrate the need for an increased sampling density in geologically complex areas to cover all possible 87 Sr/ 86 Sr ranges. This is particularly important for studies of migration over short distances, in which the origin and destination of an individual might have similar, but not identical 87 Sr/ 86 Sr. For such studies, isoscape maps are not sufficient to define possible provenance regions, because they do not present uncertainties and ranges of measured data. Instead, each geologically uniform region should be characterized precisely from measured data. Here, we provide a database of Central and NE Germany, in which we present the number and the range of measured data together with mean, minimum and maximum values, and standard deviations of the final isoscape map (Table 4). Such statistical information can be used directly in archaeology and animal migration studies.