The interplay of Malm carbonate permeability, gravity-driven groundwater fow, and paleoclimate – implications for the geothermal feld and potential in the Molasse Basin (Southern ), a foreland- basin play

Tom Vincent Schintgen (  [email protected] ) Leibniz-Institut fur Angewandte Geophysik https://orcid.org/0000-0002-0172-4452 Inga Sigrun Moeck Georg-August-Universität Göttingen, Geowissenschaftliches Zentrum, Goldschmidtstraße 3 37077 Göttingen, Germany

Research

Keywords: Würm glaciation, permafrost, North Alpine Foreland Basin, Molasse Basin, Upper Jurassic, Malm, carbonate aquifer, coupled heat and fuid fow, gravity-driven groundwater fow, geothermal plays

Posted Date: March 31st, 2021

DOI: https://doi.org/10.21203/rs.3.rs-368780/v1

License:   This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License

Page 1/54 Abstract

The Molasse Basin in is part of the North Alpine Foreland Basin and hosts the largest accumulation of deep geothermal production felds in Central Europe. Despite the vast development of geothermal energy utilization projects especially in the metropolitan region, the evolution of and control factors on the natural geothermal feld are still debated. Especially seismic and deep well data from extensive oil and gas exploration in the Molasse Basin led to conceptual hydrogeological and thermal-hydraulic models. Corrected borehole-temperature data helped to constrain subsurface temperatures by geostatistical interpolation and facilitated the set-up of 3D temperature models. However, within the geothermally used Upper Jurassic (Malm) carbonate aquifer, temperature anomalies such as the Wasserburg Trough anomaly to the east of Munich and their underlying physical processes are yet poorly understood. From other foreland basins like the Alberta Basin in Western Canada, it is known that climate during the last ice age has a considerable effect even on subsurface temperatures up to two kilometres depth. Therefore, we study the impact of paleoclimatic changes on the Molasse Basin during the last 130 ka including the Würm glaciation. We consider the hydraulic and thermal effects of periglacial conditions like permafrost formation and the impact of the numerous glacial advances onto the Molasse Basin. The major difference between the thermal-hydraulic regime in the western and eastern parts of the Southern German Molasse Basin are delineated by calculating two contrasting permeability scenarios of the heterogeneously karstifed Malm carbonate aquifer. Thermal-hydraulic modelling reveals the effect of recurrent glacial periods on the geothermally drillable subsurface, which is minor compared to the effect of permeability-related, continuous gravity-driven groundwater fow as a major heat transport mechanism. Practically, the results might help to reduce the exploration risk for geothermal energy projects in the Molasse Basin. More importantly, this study serves as a reference for the comparison and understanding of the interplay of high permeability aquifers, gravity-driven groundwater fow and paleoclimate in other orogenic foreland basins worldwide.

Introduction

Foreland basins are characterized by their typical wedge shaped geometry caused by orogenic mountain belt formation, fexural down-bending of the underlying crust, and loading by erosional products in a compressional plate tectonic setting (Kuhlemann and Kempf (1), Moeck and Beardsmore (2)). Depending on the phase of foreland basin development, lithospheric stretching or extension accompanied by normal faulting due to fexural bending, burial subsidence, thermal contraction and the propagating frontal fault of the orogenic belt into the foreland depocenter environment may be the typical geological factors that infuence the thermal feld in foreland basins. In addition, cross-formational gravity-fow of groundwater acts on geological timescales (Toth (3)). That is why it is obviously very important to quantify its thermal- hydraulic effect in the orogenic foreland-basin geothermal play type, since the driving force of regional groundwater fow is topography, notably the elevation difference between the higher regions close to the mountain belt and the larger streams at lower elevation. Specifcally the down-bending of aquifer rock may signifcantly perturb the geothermal feld, especially if faults or highly permeable layers allow

Page 2/54 advective heat transport from the deeper to the shallower realm of a foreland basin (Moeck (4)). As the only one of seven Alpine foreland basins in Europe (Allen, Homewood (5), Moeck, Uhlig (6)), the North Alpine Molasse Basin was partially covered by piedmont lobes of glaciers during the Quaternary glacial periods, in particular the last (Würm) glaciation (Seguinot, Ivy-Ochs (7), Van Husen (8)). As known from the Alberta Basin in Western Canada, which is another foreland basin covered by two large ice sheets (i.e. the Cordilleran and Laurentide ice sheets) during Quaternary glacial periods (Dyke (9), Seguinot, Khroulev (10)), the glacial cover can exert a signifcant infuence on the thermal feld in the uppermost crust (Demezhko, Gornostaeva (11), Gray, Majorowicz (12), Majorowicz (13), Majorowicz, Gosnold (14)).

Extensive oil and gas exploration data collected in the Molasse Basin since the 1950’s led to conceptual hydrogeological and thermal-hydraulic models. Corrected borehole-temperature data helped to constrain subsurface temperatures by geostatistical interpolation and rendered the set-up of 3D temperature models possible, especially revealing the temperature distribution within the Upper Jurassic (Malm) carbonate aquifer. Many boreholes tap the Malm carbonate aquifer mainly for district heating and balneological use, but some also for electricity generation (GeoMol Team (15)). The Malm carbonate aquifer is considered the largest thermal water resource not only in Germany but also in Central Europe (Goldscheider, Madl-Szonyi (16)). Indeed, carbonate aquifers frequently present a high secondary porosity and permeability due to karstifcation. However, within the geothermally used Malm carbonate aquifer, considerable temperature anomalies such as the Wasserburg Trough anomaly to the east of Munich are known and their underlying physical processes are yet poorly understood. The latter prominent cold temperature anomaly presents a particularly high geothermal exploration risk and therefore has been the subject of recent numerical models (e.g., Przybycin (17), Przybycin, Scheck-Wenderoth (18)).

We use the COMSOL Multiphysics software to perform thermal-hydraulic modelling of the glacial infuence on the present-day thermal and fow regime in the Molasse Basin. We compare the result with the geostatistical evaluation of the 3D thermal feld (Agemar and Tribbensee (19)). Similar to several existing studies in the aforementioned Alberta Basin, the North German Basin and the Paris Basin, we focus on the assessment of the main fuid and heat transport processes for a better understanding of thermal anomalies induced by the interplay of high aquifer permeabiliy, gravity-driven groundwater fow, and paleo-climatic conditions. The recent geothermal play-type concept (Moeck (4), Moeck and Beardsmore (2), Moeck, Beardsmore (20)) aims at classifying geothermal resources according to geological criteria and heat transport mechanisms to assess reservoir quality. The present study is part of the PlayType project, which is concerned with cataloguing the German geothermal provinces according to the play type concept for economic development and internationalisation of the German geothermal sector. Regional geology

The Molasse Basin in Southern Germany is part of the North Alpine Foreland Basin (NAFB). Henceforth, we generally refer to the Southern German Molasse Basin simply as Molasse Basin. It is up to 130 km wide perpendicular to strike and 400 km long parallel to the Alps (Fig. 1). Three main geological units are

Page 3/54 distinguished, each separated by a pronounced hiatus or unconformity. The oldest unit corresponds to the Variscan crystalline basement including continental clastic in graben structures of Permo- Carboniferous age. The basement is covered by Triassic to Cretaceous shallow marine sediments that formed as passive-margin shelf deposits of the European plate. The youngest unit corresponds to Late Eocene to Late Miocene shallow marine and terrestrial sediments that accumulated in the NAFB and represent the Molasse sediments. Henceforth, we generally refer to the Molasse sediments simply as Molasse.

Today, the Malm carbonates crop out at the Swabian and Franconian Albs or Jura to the north of the River. To the south, the carbonate platform is dipping beneath the southwards thickening wedge of Tertiary Molasse (Fig. 1). Lying at a depth of about 2000 m below Munich, the top of the carbonates reach a depth of more than 4000 m at the Alpine front (Bachmann and Mueller (21), Brink, Burri (22), Lemcke (23), Reinecker, Tingay (24)). Marine transgression at the beginning of the Jurassic led to progressive fooding of the Vindelician High and thus submergence of older Mesozoic deposits in the northwest and the Variscan basement in the southeast. In the Late Jurassic, a carbonate platform formed under varying conditions on an epicontinental shelf (Birner (25), Birner, Fritzer (26), Freudenberger and Schwerd (27), Frisch and Huber (28), (29)). The pre-Tertiary sediments and thus the basement of the foreland basin began to subside during the Late Eocene (Schmid, Fuegenschuh (30)), followed by the deposition of Lower Oligocene fysch units and of orogen-derived continental clastics (i.e., the Molasse) from the Late Oligocene to the Late Miocene (Roeder and Bachmann (31)). The depositional evolution of the Molasse Basin is characterized by a complex interaction of supply, basin subsidence and sea-level oscillations that induced diachronous shifts between marine, brackish, lacustrine and continental environments (e.g., Kuhlemann and Kempf (1)). The resulting Molasse sediments are predominantly composed of cyclically deposited clayey and sandy series, which are subdivided from bottom to top into Lower Marine Molasse, Lower Freshwater Molasse, Upper Marine Molasse and Upper Freshwater Molasse (Lemcke (32), Bachmann and Muller (33)). The basement is known from the Variscan in the east and northeast (Fig. 1), where the Malm terminates against the Danube Boundary Fault and the basement is uplifted up to 1700 m (Frisch and Huber (28)). In front of the boundary fault of the Bohemian Massif, another important basement structure, the NW–SE-oriented horst called Landshut-Neuötting High (Fig. 1), with a throw of up to 1300 m, separates the Wasserburg Trough in the west from the Lower Trough in the east (Bachmann, Mueller (34), Frisch and Huber (28)). Numerous faults within the competent Malm carbonate and Tertiary sandstone formed along with the downbending of the European plate in response to thrusting and uplift of the Alps (Schmid, Fuegenschuh (30)). The western and central parts of the Southern German Molasse Basin are characterized by numerous W-E striking faults oriented parallel to the basin axis and to the Alps. These formed as synthetic and antithetic faults due to downbending and extension of the top of the European crust (Bachmann, Dohr (35), Brink, Burri (22)). In the eastern part, the WNW-striking faults are related to the uplift of the Landshut-Neuötting High and the Bohemian Massif (Bachmann, Mueller (34)).

The Quaternary is known as the period of ice ages. Penck and Brückner (36) are the frst who systematically classifed glaciofuvial terraces in the northern Alpine foreland and concluded that there Page 4/54 had been at least four glaciations in the Alps, among which the Würm glaciation (about 115–11.7 ka) is the youngest. The shapes and extent of the ice sheets between glaciations and individual glacial advances can be very different (Ehlers and Gibbard 2008). This study focusses on the Würm glaciation whose traces are best preserved and therefore best studied. Figure 1 shows the extent of Würm glaciers at the Last Glacial Maximum (LGM; Doppler, Kroemer (37), Gibbard, Hughes (38), Van Husen (8)). Recently, Seguinot, Ivy-Ochs (7) numerically modelled the dynamics and extent of the last glaciation in the Alps, and Cohen, Gillet-Chaulet (39) numerically reconstructed the fow and basal conditions of the Rhine Glacier. Beyond the terrestrial regions covered by glaciers at the LGM, periglacial conditions, notably permafrost, prevailed in vast areas of Europe during each glaciation (Lindgren, Hugelius (40), Renssen and Vandenberghe (41), Vandenberghe, French (42)). Permafrost thereby largely hampers groundwater recharge in cold climate, in particular during glaciations (Bertleff, Ellwanger (43), Bertleff and Watzel (44), Jost, Violette (45), Sloan and van Everdingen (46), Woo and Winter (47), Van Vliet-Lanoë (48), Lebret, Dupas (49), Lebret, Dupas (50)). Hydrogeological data and numerical models

The regional pattern of Malm aquifer hydraulic conductivity or permeability has been studied in detail by Birner (25) and Birner, Fritzer (26) for its geothermal potential. Recently, Bohnsack, Potten (53) studied the porosity-permeability relationship derived from drill cores of the Malm carbonate with a focus on the hydraulic matrix properties. The Malm carbonate permeability is very heterogeneous (Homuth, Götz (54)) and closely related to the lithofacies distribution of the Malm carbonates presented by Meyer and Schmidt-Kaler (55). However, the sole consideration of matrix properties leads to an underestimation of permeability on reservoir scale, because high hydraulic conductivities in the Malm are closely linked to karstifed zones in relation to the reef carbonate facies, faults and the proximity of the Danube (Birner, Fritzer (26)). Hydraulic characterization of the Malm aquifer by means of pumping test data shows that the highest hydraulic conductivities of up to 104 m s1 are found at the northern border of the Molasse Basin along the Danube. Hydraulic conductivities of 105 m s1 are characteristic of karstifed Malm carbonate to the south of the Danube. The largest contrast in hydraulic conductivities exists in the southern, deeper realm of the Molasse Basin. In Baden-Württemberg to the west of the river , hydraulic conductivity decreases rapidly to values lower than 108 m s1 towards the clay-rich Helvetic facies in the south, whereas in Bavaria hydraulic conductivity values of 105 m s1 are found in the Wasserburg Trough from Ingolstadt down to the Munich metropolitan region (Fig. 1). The extraordinary high permeability in the deeper parts of the Molasse Basin are likely related to the southeasterly emersion and subsequent extensive karstifcation of the upper 150 to 200 m of the carbonate platform during the Cretaceous (Birner (25), Birner, Fritzer (26), Frisch and Huber (28)). The Munich region itself is located in a transition zone with hydraulic conductivities decreasing from 105 m s1 in the northeast to 107 m s1 in the southwest. In general, zones with hydraulic conductivities higher than 106 m s1 are suitable for geothermal energy production (Birner, Fritzer (26)).

Page 5/54 A major fact is the sub-hydrostatic character of the Malm aquifer (Lemcke and Tunn (56)), with a water table well below terrain level towards the Alpine front and local artesian conditions close to the Danube (Andres and Frisch (57), Frisch and Huber (28)). In general, therefore, the hydrostatic pressure within the Malm overburden is higher than in the Malm aquifer itself (Andres and Frisch (57), Lemcke (58)). Recharge of the Malm aquifer occurs on the one hand along the Danube River, and especially to the north of it through the outcropping Malm (e.g., Heine and Einsiedl (59)), and on the other hand by leakage through the overlying Quaternary and Tertiary sediments (Andres and Frisch (57), Bertleff and Watzel (44), Birner, Fritzer (26), Frisch and Huber (28), Villinger (60), Heidinger, Eichinger (61)). Clear evidence of leakage and the presence of ion exchange water in the deeper Malm aquifer is provided by the hydrochemical indication for mixing with NaCl-rich water originating from the Tertiary overburden (Birner, Mayr (62)). The general groundwater fow is directed from the west to the east and thus follows the gradient of the Danube (Birner (25), Frisch and Huber (28)). By contrast to other sedimentary basins, the existence of freshwater with a mineralization below 1 g L− 1 in the Malm aquifer in large areas of the Molasse Basin is a strong argument for the good hydraulic connection with the Danube (Frisch and Huber (28), Stober, Wolfgramm (63)). Frisch and Huber (28) present a numerical groundwater model for thermal water mass balancing and deduce fow directions within the Malm aquifer. Only a limited recharge is possible from the Alps into the Molasse Basin (e.g., Lemcke (58)). Orogenic belts and their adjacent foreland basins usually are hydraulically disconnected from each other by the frontal fault of the foothills. The reason is that most of the water recharged in the mountains directly discharges in valley foors (i.e., the valley in the present case) and therefore is not available for deeper circulation towards the foreland basin (Toth (3)). The western limit of the fow system is marked by the Rhine-Danube groundwater divide which runs from the northwest to the southeast approximately 30 km to the east of and parallel to Constance (Frisch and Huber (28), Stober and Villinger (64)). From the divide, the fow direction is to the east towards a groundwater depression in the Munich region from where the groundwater fows north and discharges to the Danube between Neustadt and (Fig. 1, Birner, Mayr (62)). As shown by long-term observations of decreasing hydraulic heads caused by production, the total fow rate in the Malm in the central Molasse Basin is relatively low and estimated at 1.5 m3 s − 1 (Frisch and Huber (28)).

Besides these hydrogeological studies, various numerical subsurface models have so far been realized. Kimmeier, Perrochet (65) presented a regional numerical groundwater model for northern Switzerland with a focus on the crystalline basement to investigate the impact on a nuclear waste repository. Clauser, Höhne (66) built the frst 3D numerical model for the western part of the German Molasse Basin based on pure thermal conduction as a reference model. Subsequently, Clauser, Bischof (67) adapted the latter model for steady-state coupled heat and fuid fow. The local thermal anomalies that are obviously related to known faults are caused by free convection within highly permeable vertical faults. Similarly, Rühaak, Rath (68) conclude that temperature deviations from their 3D steady state and conductive model of the western Molasse Basin are likely caused by advective heat fow especially in fault zones. In the western Molasse Basin, the general fow feld suggests that neither in the Tertiary nor in the Malm aquifers signifcant groundwater fow - and thus advective heat fow - occurs from the deeper to the

Page 6/54 shallower parts of the basin. Further 3D numerical modelling of coupled fuid and heat fow processes in the Molasse Basin shows that basin-wide fuid fow strongly affects the shallow thermal feld (Przybycin, Scheck-Wenderoth (18)). Dussel, Lueschen (69) developed a thermal-hydraulic model of the Malm aquifer for the Munich region with the aim to forecast the potential interference of geothermal heating and power plants. Finally, in the context of the GeoMol project, several pilot areas were defned for detailed 3D modelling and the assessment of geopotentials (GeoMol Team (2015)).

Despite the existing numerical models, the geostatistical interpolation of the 3D thermal structure based on temperature measurements in boreholes, namely the composite model implemented in the Geothermal Information System (GeotIS), to date represents the most reliable prognosis of subsurface temperature in the Molasse Basin and in particular at the Top Malm (Fig. 2; Agemar and Tribbensee (19)). Though Vollmayr (70) already mentioned extremely low geothermal gradients in the eastern, Bavarian Molasse Basin, the physical processes leading to that prominent cold temperature anomaly in the Wasserburg Trough to the east of Munich (Dussel, Lueschen (69)) are still poorly understood. The results from hydrochemical and isotopic studies (e.g., Mraz, Wolfgramm (71), Bertleff, Ellwanger (43), Bertleff and Watzel (44), Heidinger, Eichinger (61)) constitute important additional constraints.

The periglacial and glacial infuence over geological times on the thermal feld in sedimentary basins has been investigated for example in the Alberta Basin in Western Canada (Jessop (72), Gosnold, Majorowicz (73), Majorowicz (13), Majorowicz, Gosnold (14), Lemieux, Sudicky (74)), the North Sea and the North German Basin (Boulton, Slot (75), Boulton, Caban (76), Piotrowski (77), Piotrowski (78), van Weert, van Gijssel (79), Majorowicz and Wybraniec (80)), and the Paris Basin (Jost, Violette (45), Lebret, Dupas (50), Dentzer, Lopez (81)). In the Molasse Basin, the geological and geomorphic record allows the differentiation of numerous glacial advances, especially the maximum extent of the Würm glaciation (Figs. 1 and 2). So far, however, no numerical thermal-hydraulic model of the subsurface taking into account the effect of paleoclimate, permafrost and glaciers exists for the Molasse Basin. Bertleff, Ellwanger (43) and Bertleff and Watzel (44) discussed the effect of glaciations using hydraulic, hydrochemical and isotopic data. According to them, the higher hydraulic head produced by foreland glaciers leads to an increased recharge potential in their melting zone, further assuming that larger perennial rivers, and glaciers hamper permafrost formation or preservation in subglacial basins beneath them (Sloan and van Everdingen (46)). Cohen, Gillet-Chaulet (39) show that the basal ice of the Rhine Glacier reaches the pressure melting point in the piedmont lobes as well as in the glacial valleys, and that only the glacier margins and Alpine valleys at higher elevation remained cold based. Rühaak, Rath (68) took into account the transient effect of paleoclimate on their purely conductive model. Here, we numerically simulate for the frst time the effect of the Würm glaciation on the hydrogeology and the thermal feld of the Molasse Basin with a focus on the eastern, Bavarian part and specifcally the region of Munich and the Wasserburg Trough.

Methods

Page 7/54 We use COMSOL Multiphysics to simulate coupled heat and fuid fow in the Molasse Basin. For a faster computation of the basic physical, thermal-hydraulic processes over geological times, we built a simplifed 2D section oriented perpendicular to the strike direction of the Molasse Basin, and therefore containing only the essential geological and structural elements (Fig. 3). The model section represents the geometrical situation to the east and northeast of the Munich region where a prominent cold anomaly occurs (Agemar and Tribbensee (19)). The section is oriented NNW-SSE and extends 180 km from the northern margin of the Franconian Alb via Ingolstadt to the Inn valley near close to the Alpine Front (Figs. 1 and 2). Model depth amounts to 10 km below mean sea level. The model is set up for multiphysics coupling of the subsurface fow module using Darcy’s Law and the heat transfer module. The study is time-dependent and simulates the last 130,000 years to capture the effects of surface paleo- temperature changes and of gravity-driven groundwater fow on the subsurface thermal feld. The major difference between the thermal-hydraulic regime in the western and eastern parts of the Molasse Basin are delineated by calculating two contrasting permeability scenarios of the heterogeneously karstifed Malm carbonate aquifer. We want to emphasize that the focus of our study lies on the signifcance of Malm permeability and glacial conditions for the formation of thermal anomalies, hence we do not consider 3D groundwater fow which could possibly reproduce more exhaustively the entire fow system of the Molasse Basin (e.g., Frisch and Huber (28)). Model geometry and composition of model units

Figure 3 shows the model geometry. The lithological composition of the model units is summarized based on the available literature where the geological evolution is described in detail (e.g., Bachmann and Mueller (21), Bachmann, Mueller (34), Freudenberger and Schwerd (27), GeoMol Team (15), Kuhlemann and Kempf (1), Lemcke (32)). The lithological composition of the model units (Fig. 3) is presented from the oldest to the youngest. The Variscan basement is mostly composed of gneiss and intrusions of plutonic rock dominated by granite (GeoMol Team (15)) and is comparable to the rock exposed in the or the Bohemian Massif. The thin Middle and Lower Jurassic as well as Triassic and Permo- Carboniferous sediments are included in the Variscan basement, corresponding to the upper European continental crust. The Malm carbonates consist of various types of limestones, marls and dolomites that developed in a tropical shallow shelf sea including reefs, lagoons and shallow basins (e.g., Meyer and Schmidt-Kaler (29), Meyer and Schmidt-Kaler (55)). The thickness of the Malm unit is derived from Bachmann, Mueller (34) and Meyer and Schmidt-Kaler (55), and ranges between 500 and 600 m. The Cretaceous period is mainly represented by some hundreds of meters of Middle and Late Cretaceous coastal and shallow marine sediments (Freudenberger and Schwerd (27)) predominantly made up of clay marls (Unger and Meyer (82)), and is here included in the overlying Molasse wedge. The Molasse Basin itself is composed of a wedge of Tertiary Molasse sediments whose base reaches up to 4000 m below mean sea level at the Alpine Front in the south. The thickness of the Molasse (depth of Tertiary or Molasse base) is derived from Lemcke (23), Lemcke (32), Roeder and Bachmann (31), Brink, Burri (22), Bachmann, Dohr (35) and Bachmann and Mueller (21). The Molasse sediments are predominantly composed of cyclically deposited clayey and sandy series (Lemcke (1988), Bachmann and Muller

Page 8/54 (1991)), hydraulically corresponding to an equivalent silt composition (Andres and Frisch (57)). With regard to the scale and the geological time scale of the model, a more detailed subdivision of the Tertiary and Quaternary basin fll is not productive for modelling results with a focus on the Malm aquifer. The physics-controlled mesh was set to extremely fne, which produced a mesh consisting of about 8700 elements with an average element volume of about 0.2 km2. The maximum element size is 1800 m for mesh elements at the base of the model. The minimum element size is 3.6 m in the northern part of the model due to the Altmühl and Danube valleys, a more irregular geometry, and the Molasse unit pinching out. The mesh element volume within the Malm aquifer is about 0.17 km2, whereas it is smaller than 0.1 km2 in the northern shallow part of the model. For verifcation, we also ran the high Malm permeability scenario with a maximum element size of 400 m resulting in about 31,300 mesh elements. Only the resolution is increased, but the solution remains the same. Model set-ups with a fner mesh do not converge. Properties of model units

Table 1 summarizes the properties used in our simplifed model. Clauser, Bischof (67) measured and compiled thermal properties (thermal conductivity, density, porosity, volumetric heat capacity) and hydraulic properties (permeability) of Tertiary sediments from the western part of the Molasse Basin. Subsequently, Clauser, Koch (83) completed the database for the western part of the Molasse Basin by direct laboratory measurements and indirect derivation based on a combination of independent geophysical well logs. Koch, Jorand (84) focused on the eastern (Bavarian) part of the Molasse Basin and particularly analysed the Cretaceous and Upper Jurassic geological units. For their thermal-hydraulic 3D model of the Munich region with a focus on the Malm carbonate aquifer and a multidisciplinary reservoir characterization, Dussel, Lueschen (69) compiled rock properties and references relevant for the present study. We focus on two Malm permeability scenarios, thereby taking into account that the Malm carbonate aquifer presents a large range of permeabilities depending on the carbonate facies, the degree of karstifcation (Birner, Fritzer (26), Fritzer, Settles (85)) and the vertical hydrostratigraphic profle (Bohnsack, Potten (53), Dussel, Lueschen (69)). Except for the Variscan basement, we applied an anisotropic permeability in agreement with Andres and Frisch (57) who noted that generally horizontal permeability is one order of magnitude higher. Rock thermal conductivity is primarily temperature- dependent and therefore signifcantly decreases with increasing depth due to the geothermal gradient. For sedimentary rocks, we applied a temperature correction of thermal conductivity according to Somerton (86). For igneous and metamorphic rocks, we applied a temperature correction of thermal conductivity based on Seipold (87).

Page 9/54 Table 1 Properties of model units.

Model unit Scenario φ κ λ ρ Cp H

horizontal vertical

Molasse (Tertiary, 0.20 10− 14 10− 15 2.0 2000 800 1.2 incl. Cretaceous)

Malm (unconfned) 0.10 1010 1010 2.5 2400 900 0.0

Malm (+ Purbeck) Low 0.10 10− 13 to 10− 14 to 2.5 2400 900 0.0 permeability 10− 15 10− 16

High 0.10 10− 10 to 10− 11 to 2.5 2400 900 0.0 permeability 10− 14 10− 15

Variscan basement 0.03 10− 17 to 10− 17 to 3.5 2700 900 1.8 10− 20 10− 20

Model units refer to model geometry in Fig. 3. Φ = absolute porosity [-], κ = permeability [m2], λ = matrix − 1 − 1 − 3 − 1 thermal conductivity [W m K ], ρ = matrix density [kg m ], Cp = isobaric matrix heat capacity [J kg K− 1], H = radiogenic heat production [10− 6 W m− 3]. Model boundary conditions Heat transfer boundary conditions

At the vertical model boundaries, we defne no-fow conditions for heat transfer. This is a valid assumption since the conductive thermal gradient is largely subvertical between high temperatures at great depth and low temperatures at the surface. Clauser, Bischof (67) applied a basal heat fow of 80 mW m− 2 for an optimal adaptation of their model. After consideration of radiogenic heat production, we apply a conductive basal heat fow of 60 mW m− 2 in the south and 70 mW m− 2 in the north at the base of our model. At the upper boundary, we apply a paleoclimate forcing (Fig. 4). The paleo-temperature data are among the most important model input data. Climate or paleo-temperature forcing is derived using time-dependent temperature offsets from a paleo-climate proxy. For the present study, we chose the EPICA ice core record (European Project for Ice Coring in Antarctica; Jouzel and Masson-Delmotte (88), Jouzel, Masson-Delmotte (89)) which, in a glaciological study by Seguinot, Ivy-Ochs (7), yielded spatially and temporally consistent ice dynamics. Temperature reconstructions from the EPICA record are provided and can be downloaded e.g. from the PANGAEA data repository (Diepenbroek, Fuetterer (90), Diepenbroek, Grobe (91)). The time resolution of the data decreases with age from 10 years to 45 years at 130 ka. For simulation, we use time steps of 50 years. Paleo-temperature forcing is further amended with time-dependent paleo-precipitation reductions and temperature lapse-rate corrections. Seguinot, Ivy-Ochs (7) reduced precipitation with air temperature in order to simulate the potential rarefaction of atmospheric

Page 10/54 moisture in colder climates. The derived relationship results in about 60% less precipitation at the LGM. Accordingly, the linear scaling (f = 1.33) used by Seguinot, Ivy-Ochs (7) was also implemented in this study to calibrate the paleo-temperature forcing in the light of reduced precipitation. According to a present-day mean annual surface temperature map (e.g., Hänel and Staroste (92)), and altitude information, reference temperatures of 9°C at 300 m and of 5°C at 1000 m were determined. The result for Munich at 520 m altitude is 7.7°C and consequently the temperature lapse rate in this part of the North Alpine Foreland corresponds to 0.57°C/100 m. In the Danube and Altmühl valleys, but also in the Franconian Alb, we avoid freezing and thus permafrost formation for numerical stability reasons by disabling the temperature lapse rate and by restricting the minimum temperature to 4°C. These simplifed temperature conditions barely infuence the main fndings. In map view, the top Malm negative thermal anomaly (Agemar and Tribbensee (19)) coincides with the confuence of the and Amper valleys. Since permafrost is frequently absent beneath lakes and larger perennial rivers (Boulton, Slot (75), Sloan and van Everdingen (46)), we here apply particular conditions for river valleys, where paleo-temperature is not allowed to fall below 4°C. The corresponding average and median paleo-temperatures over the last 130 ka are 3.2°C and 2.3°C, respectively. By contrast, we also calculate model scenarios with a constant reference temperature of 9°C at 300 m altitude. The paleo-temperature model input data were smoothed by applying a running average of 21 values and adding an additional running average of 11 values on top of the frst (Fig. 4). We defne the initial model temperature by applying a thermal gradient of 30°C km− 1. Subsurface fow boundary conditions

At the vertical boundaries delimiting the model in the north and the south as well as at the bottom boundary, we defne no-fow conditions for groundwater. The Variscan basement is characterized by a very low permeability and thus is assumed to inhibit groundwater fow from the north and from beneath the studied depth range. Following Toth (3) as well as previous results from the Molasse Basin (e.g., Frisch and Huber (28)), only a limited recharge from mountains into foreland basins is possible. Therefore, we assume hydraulic no-fow conditions at the southern boundary. The confguration of the water table largely controls the driving forces of regional gravity-driven groundwater fow systems. In the Altmühl and Danube valleys where groundwater fows towards these major rivers, we defne an atmosphere or gauge boundary condition. In the northern part of the model corresponding to the Franconian Alb, we specify a hydraulic head in equilibrium with the Altmühl River. In the southern part, at the surface of the Molasse, we apply a hydraulic head replicating the topography (Andres and Frisch (57), Clauser, Bischof (67)). This assumption can be made for low-relief terrain as shown by Freeze and Witherspoon (93), Forster and Smith (94), Lopez and Smith (95), and Toth (3), which also implies that the Molasse sediments are entirely water-saturated and that the availability of meteoric water is always equal to or higher than topography-driven (or gravity-driven) groundwater recharge. Along the chosen section, due to the occurrence of the Inn valley near Rosenheim, the usual gentle rise of the terrain towards the Alps reaches its maximum altitude of 600 m at 30 km to the north of the Alpine Front. This study aims at studying the effect of periglacial conditions (permafrost) and numerous glacial advances onto the

Page 11/54 Molasse Basin. In order to test the effect of recurrent glacier cover in the southern part of the model (Fig. 3), we include scenarios in which the effect of the Inn Glacier is simulated by applying an additional hydraulic head fuctuating as a function of paleo-temperature (Fig. 5). According to Greenwood, Clason (96) and Lemieux, Sudicky (74), the conduit water level in the foreland part of glaciers (i.e., the piedmont lobes) can reach the glacier surface leading to high meltwater supply for recharge beneath the melting zone of glaciers, a condition which had already been argued for by Bertleff, Ellwanger (43). Since the timing and conditions of actual permafrost occurrence beneath foreland glaciers is unknown, we assume that maximum recharge was possible, and subsequently discuss the signifcance of our results. We calculate the evolution of Inn Glacier height in the Alpine foreland using the EPICA paleo-temperature data, and subsequently validate our results with the modelling data presented by Seguinot, Ivy-Ochs (7). We set up an iterative calibration process for simulating the Inn foreland glacier. As a precondition for foreland glacier formation, paleo-temperature must fall below a cut-off temperature of 9°C (with respect to the original proxy data). We also implement a linear proportionality of the maximum glacier height with the coldest paleo-temperature of 14°C (with respect to the original proxy data), once the previously mentioned condition is satisfed. We add another condition on top to prevent foreland glacier formation and to force foreland glacier melting if the running average of glacier height is below respectively falls below a defned threshold of 200 m over the preceding time interval of about 3,000 years. Fluid properties

Since glacial and periglacial climate conditions are taken into account, the formation of permafrost by freezing pore water is implemented by means of the phase change material sub-node of the heat transfer module. Phase change considers specifcally the thermal energy needed or freed at the moment of melting respectively freezing of water. The transition temperature is 273.15 K (i.e., 0°C), the transition interval is 1 K and the latent heat of fusion is 333.5 kJ kg− 1. Table 2 presents the contrast in water properties above and below the freezing point.

Table 2 Properties of water and ice above and below the freezing point. Material property Ice (< 0°C) Water (> 0°C)

Density 918 kg m− 3 999.8443 kg m− 3

Heat capacity at constant pressure 2052 J kg− 1 K− 1 4219.4 J kg− 1 K− 1

Thermal conductivity 2.31 W m− 1 K− 1 0.562 W m− 1 K− 1

Because the model is solved in material coordinates, the ice density and ice thermal conductivity are converted by multiplication with the ratio of water and ice densities at the freezing point. Beyond the phase change of water, the simulation of coupled heat and fuid fow requires the following fuid properties: dynamic viscosity, density, heat capacity at constant pressure and thermal conductivity. A particularly important change is the drastic increase in water dynamic viscosity at the freezing point

Page 12/54 (Fowler (97)). In the model, ice only exists over a relatively small temperature interval, so that we consider the thermal properties of water below 0°C to be independent of temperature and pressure. It is assumed that liquid water is pure, which is a valid assumption since the Malm aquifer has drinking water quality (Frisch and Huber (28), Stober, Wolfgramm (63)). Furthermore, we assume that hydrostatic fuid pressure prevails throughout the model domain. This assumption is valid for the Malm carbonate (Lemcke and Tunn (56), Andres and Frisch (57)) and most of the younger stratigraphic units. We are aware that fuid pressure may tend to lithostatic with depth beneath the Malm carbonate aquifer and that the content in dissolved solids certainly increases in the Variscan basement, but no data for this depth realm are available. Water density would remain almost constant with depth and dynamic viscosity increase due to dissolved solids.

Since our model extends to a depth of 10 km, we extend the properties of liquid water beyond temperature dependency and also take into account the effect of hydrostatic pressure by consulting the international steam tables (Wagner and Kretzschmar (98)). We specifcally calculate the individual property values along the chosen T-P gradient. Based on previous model runs, we choose realistic temperature and hydrostatic pressure gradients of 30°C km− 1 and 95 bar km− 1, respectively. The range of T-P-conditions covered is 0.01–307°C and 1–948 bar. Along the selected T-P-gradient, all relevant water properties show signifcant changes, ranging from + 14% for thermal conductivity, + 6% for isobaric heat capacity and − 92.5% for dynamic viscosity (see also Smith and Chapman (99)). The decrease in water density (-19%) is important because shallower colder water has a tendency to sink, whereas deeper warmer water tends to ascend. Finally, in order to be able to compare our results with standardized hydraulic head data published e.g., by Stober and Villinger (64) and Frisch and Huber (28), we calculate the fresh water head according to the following equation:

‑3 Where hfw is the fresh water head in m, ρfw is the density of fresh water in kg m , ρ is the temperature- and pressure-dependent water density in kg m‑3, ϕ is the pressure head in m, and z is the elevation head in m. For fresh water, we use a temperature of 10°C and a density of 1000.0847 kg m‑3.

Heat transfer in sedimentary basins is typically controlled by the two main mechanisms of conduction and convection by groundwater. In case the groundwater fow is driven by external forces, i.e. forced convection or advection, then the relative importance of the two heat transfer mechanisms is indicated by the geothermal Péclet number (Bachu (100), Bachu (101)) defned as:

Page 13/54 ‑1 ‑1 Where λm is the thermal conductivity of the saturated porous medium in W m K , ρw is the water ‑3 ‑1 ‑1 ‑1 density in kg m , Cpw is the specifc heat of water in J kg K , q is the Darcy velocity in m s , D is the thickness of the respective aquifer in m and are the horizontal and vertical components of the thermal gradient in K m‑1. For Péclet numbers < 0.1, conduction is the dominant heat transport mechanism (Clauser, Bischof (67)). With regard to the long geological time scale considered, aquifer thickness used to derive Péclet numbers corresponds to the vertical extent of the entire model. Results Hydraulic head and groundwater fow

As previously mentioned, the major difference between the thermal-hydraulic regime in the western and eastern parts of the Molasse Basin are delineated by calculating two contrasting permeability scenarios of the heterogeneously karstifed Malm carbonate aquifer, irrespective of the actual 3D thermal-hydraulic fow system. Figure 6 shows the hydraulic head, here the fresh water hydraulic head, which develops at different times in the low Malm permeability scenario (Fig. 6a, b) and in the high Malm permeability scenario (Fig. 6c, d). In particular, Fig. 6a and c visualizes the fresh water hydraulic head which develops in presence of the Inn Glacier. However, at frst, we study only the hydraulic effect of the Inn Glacier, i.e. without applying paleoclimatic conditions. At the upper model boundary corresponding to the surface of the Molasse, the fresh water hydraulic head adequately replicates the topography, including the fuctuation height of the Inn Glacier. If Fig. 6a and c or Fig. 6b and d are compared, the fresh water hydraulic head decrease directly beneath the surface is stronger in the high Malm permeability scenario. The low Malm permeability induces a groundwater fow that is essentially limited to the Molasse. Only a minor fraction of groundwater fows towards the Malm aquifer (Fig. 6a, b). By contrast, the high Malm permeability induces a groundwater fow that is no longer restricted to the Molasse but descends into the Malm aquifer (Fig. 6c, d). A major difference between the LGM, here represented by the hydraulic effect of the Inn Glacier, and the present situation in both low and high Malm permeability scenarios consists in the contrasting groundwater fow patterns. In our models, this particular situation exists because a region of higher altitude is located between the Danube in the north and the Inn in the south of the section. Presently, therefore, two cells of forced convection exist: a southern one draining towards the Inn River, and a northern one draining towards the Danube River (Fig. 6b, d). In the southernmost part of the model, where the surface falls off towards the Inn valley near Rosenheim, groundwater fow descends from the highest fresh water head at 600 m altitude and ascends near the Inn valley (Fig. 6b, d). This groundwater thus forms a separate convection cell, which is decoupled from the fow heading towards the Malm aquifer and to the north. Hydraulic and thermal effect of the Inn Glacier

During cold periods, each foreland advance of the Inn Glacier onto the Molasse Basin induces a reorganization of groundwater fow leading to a single cell of forced convection towards the Danube in the north (Fig. 6a, c). This reorganization of groundwater fow as a hydraulic effect of the Inn Glacier is

Page 14/54 practically immediate (at most a few hundred years) even for the short foreland advance of the Inn Glacier 40 ka ago (Fig. 5). A valuable tool to visualize the effect of changes between scenarios consists in combining the respective solutions of different model scenarios to show the difference between the solutions over time or for a specifc time. By simulating for instance the hydraulic effect of the Inn Glacier on subsurface fow in the Molasse Basin, the results clearly show that the hydraulic head in the southernmost part of the model periodically increases when the Inn Glacier advances into the foreland (Fig. 7a). Surprisingly, a supposedly higher quantity of cold water infltrating into the basin barely infuences the thermal feld, except for a small negative anomaly at the southern model boundary (Fig. 7b). In our models, the southern convection cell induces an upfow of groundwater and heat mostly within the Molasse near the Alpine Front and towards the Inn valley near Rosenheim in the south of the section (Fig. 6b, d). In fact, the hydraulic effect of the Inn Glacier produces the small negative anomaly by temporarily precluding this upfow. Flow reversal and cold-water infltration causes temperatures at the same depth (0–4 km) to decrease by up to 40°C. Thermal feld as a result of low and high Malm permeabilities

Figure 8a and b shows the thermal feld in the Molasse Basin in the low Malm permeability scenario with permafrost development under paleoclimatic conditions. The permeability of the Malm aquifer varies linearly from low anisotropic values of 1013 m2 horizontally and 1014 m2 vertically at the Danube valley to low anisotropic values of 1015 m2 horizontally and 1016 m2 vertically in the southernmost part of the model. By contrast, Fig. 8c and d shows the high Malm permeability scenario with permafrost development under paleoclimatic conditions. The permeability of the Malm aquifer varies linearly from high anisotropic values of 1010 m2 horizontally and 1011 m2 vertically at the Danube valley to low anisotropic values of 1014 m2 horizontally and 1015 m2 vertically in the southernmost part of the model. In the low Malm permeability scenario, groundwater fow limited to the Molasse causes cooling mainly in the Molasse and does not affect the Malm aquifer (Fig. 8a, b). In the high Malm permeability scenario, groundwater fow descending from the surface into the Malm aquifer causes subsurface cooling extending to signifcantly greater depth (Fig. 8c, d). In the latter case, the general fow and temperature pattern results from the downfow or leakage of cold meteoric water through the Molasse of relatively low permeability, slow heating of this water and fnally upfow of the heated groundwater through the karstifed Malm aquifer to the surface in the Danube valley. The coupled fuid and heat fow thereby signifcantly modifes the initial, homogeneous and conductive geothermal gradient. A comparison of Fig. 8a and c also reveals a different maximum permafrost thickness depending on the Malm permeability scenario. High Malm permeability causes much more pronounced cooling of the shallow subsurface (Fig. 8c). When the paleo-temperature starts to decrease, cold-water downfow through the Molasse forms a dark blue curtain moving down towards the Malm aquifer. About 35 ka ago, at the start of the coldest period of the last glaciation (Fig. 4), permafrost develops to greater depth where cold water has previously fown down and thus where the subsurface has been undercooled (Fig. 8c). Permafrost thickness reaches on average up to 600 m in the high Malm permeability scenario (Fig. 8c). As a

Page 15/54 comparison, permafrost thickness is only 150–200 m in the low Malm permeability scenario (Fig. 8a). At the end of the LGM, permafrost has largely melted 15 ka ago, but patches of permafrost remain until about 10 ka ago. Again, after the permafrost has melted, cold-water downfow forms a dark blue curtain. The effect of permafrost formation and thawing is regionalization of cold-water downfow over the entire width of the Molasse Basin. Indeed, after 10 ka of simulation time, the 25, 50 and 75°C-isotherms show a maximum downward curvature in the northern part of the Molasse Basin between section km 40 and 70 where groundwater mass fow, or recharge, is highest due to the very high Malm permeability and the relatively low thickness of the Molasse cover in the range of 1500 to 2500 m (Fig. 8c, d). After 30 ka of simulation time, the maximum downward curvature of these isotherms has shifted southwards to a zone between section km 55 and 75. After 50 ka of simulation time, the maximum downward curvature of the 20°C-isotherm is located at section km 70. A second downward curvature begins to develop underneath the highest hydraulic head at profle km 100. After 70 ka of simulation time and the frst phase of permafrost formation, the 25°C-isotherm has become almost horizontal between profle km 60 and 100, i.e. parallel to the base of permafrost. The latter zone extends even further between section km 50 and 110 after 110 ka of simulation time (i.e., at the LGM 20 ka ago; Fig. 8c). Thermal anomaly with paleoclimatic forcing

More illustrative than the absolute thermal feld shown in Fig. 8 is the temperature difference over time between the low and high Malm permeability scenarios under paleoclimatic conditions (Fig. 9). A visible cold anomaly has developed in the northern part of the Molasse wedge after 20 ka of simulation time (110 ka ago) and gets colder with time, reaching a near steady-state minimum temperature after 50 ka of simulation time (80 ka ago; Fig. 9a). Cooling is thus very slow and the average cooling rate amounts to about 0.76°C ka1. Later, after 110 and 130 ka of simulation time (i.e., 20 ka ago and at present), it extends through the Malm aquifer and beyond into the Variscan basement (Fig. 9b, c). The maximum temperature difference or thermal anomaly generated between high and low Malm permeability scenarios amounts to about 38°C (Fig. 9). Strikingly, the negative thermal anomaly even continues cooling after the last glaciation. In addition, the Inn Glacier that advances periodically onto the Molasse Basin produces the cold anomaly observed at the southern boundary of the section at 110 and 130 ka. The Inn Glacier imposes a high hydraulic head and so squeezes a larger volume of cold meltwater into the subsurface in the high Malm permeability scenario. The yellowish colors in Fig. 9 represent the upfow of warmer water through the Malm aquifer towards the Danube in the high Malm permeability scenario. This shows that cooling of the Molasse in the downfow zone results in heat transfer towards the Danube in the upfow zone. Thermal anomaly without paleoclimatic forcing

Figure 9 clearly shows that the thermal anomaly already exists after 50 ka of simulation time (i.e., 80 ka ago), before permafrost formation (Fig. 4) or the frst foreland advance of the Inn Glacier (Fig. 5). In order to evaluate the specifc effect of periglacial climate conditions and thus paleo-temperature forcing on coupled, gravity-driven groundwater and heat fow, we also simulated both permeability scenarios with a Page 16/54 constant reference temperature of 9°C at 300 m altitude as a surface-temperature boundary condition. Figure 10 shows the temperature difference between the corresponding permeability scenarios without paleoclimate forcing. The resulting thermal felds with and without paleoclimate forcing look similar. As anticipated by the results after 50 ka of simulation time shown in Fig. 9a, the calculated temperature difference shown in Fig. 10 equally reveals a cold anomaly centered on the Molasse Basin. Even without paleoclimatic conditions applied, temperatures in the Molasse are up to 50°C colder in the high Malm permeability scenario. Here, the average cooling rate amounts to about 1°C ka1. The negative thermal anomaly still shows extremely slow cooling after 110 ka of simulation time. In our 2D section, without any perpendicular groundwater fow along the Danube, the temperature of the water ascending through the Malm aquifer is up to 18°C warmer near the Danube. Thermal effect of different surface temperature conditions

Instead of comparing the thermal effect of different surface-temperature boundary conditions on each Malm permeability scenario, Fig. 11 and Fig. 12 show the thermal effect of each surface temperature boundary condition on the low and high Malm permeability scenarios, respectively. Both combined sections reveal a negative temperature difference about 100°C colder in the southernmost part of the models. The reason is the predicted ascent of warm water towards the depression of the Inn valley near Rosenheim in the scenarios with constant reference surface temperature. By contrast, in the scenarios with paleoclimatic conditions applied, permafrost formation and the hydraulic head induced by the recurrent advance of the Inn Glacier inhibit this ascent of warm water by repeated reorganization of the groundwater fow systems. Figure 12 can be directly compared to Fig. 7 and shows, besides the hydraulic and thermal effect of the Inn Glacier, the hydraulic blanketing effect of permafrost, which in turn amplifes the overall effect of the Inn Glacier. Moreover, in both combined sections, the applied paleoclimatic conditions cause a few degrees C colder temperatures in the shallow subsurface. These are an aftereffect of permafrost formation.

In the low Malm permeability scenario, a relatively small, up to 12.5°C warmer thermal anomaly forms in the southern part of the model (Fig. 11). The latter likely is an expression of two combined processes leading to a reduced hydraulic conductivity: (1) a primary low Malm permeability and (2) a higher dynamic viscosity of the infltrating water due to the lower surface temperatures. First, the relatively low permeability yields an overall more conductive, warmer model, and second, further reduction in hydraulic conductivity results in even less heat redistribution in the deepest part of the Molasse Basin.

In the high Malm permeability scenario (Fig. 12), the most surprising result is the prominent positive thermal anomaly centered on the Molasse Basin and the Malm aquifer, which reaches a maximum temperature of about 25°C during the LGM about 20 ka ago (Fig. 12b). Actually, the positive anomaly related to the last glaciation is presently weakening and thus cooling very slowly due to resumed groundwater fow. The cooling rate amounts on average to about 0.5°C ka1. Figure 12 actually captures the interplay of extensive groundwater fow and the hydraulic blanketing effect of permafrost. Despite the on average higher reference surface temperature of 9°C compared to an average of 3.2°C and a median

Page 17/54 of 2.3°C for paleo-temperature (Fig. 4), the thermal anomaly caused by the model with paleo-temperature forcing is paradoxically about 16°C warmer than the model with a constant reference surface temperature up to the present day. Most surprisingly, the thermal anomaly is warmest (about 25°C) at the LGM when paleo-temperature is the coldest (about 5°C) and permafrost is the thickest. Péclet number

Figure 13 shows the Péclet number for the low and high Malm permeability scenarios, respectively, with a constant reference surface-temperature condition. In both model scenarios, heat conduction characterizes the Variscan basement, which is in agreement with the cataloguing of the Molasse Basin as conduction-dominated play-type foreland basin. In the low Malm permeability scenario, the Malm aquifer presents isolated zones dominated by heat conduction as well as zones dominated by heat convection, which shows that heat convection dominates only locally and thus makes large-scale heat transfer much less effective. By contrast, the Malm aquifer in the high Malm permeability scenario presents a contiguous pattern of high Péclet numbers, which demonstrates that advective heat transfer is signifcant. Only in the deepest part close to the Alpine Front, where the Malm permeability equals 10− 14 m2, does the Péclet number indicate that heat conduction dominates in both Malm permeability scenarios. The Péclet-number range within the Molasse is also signifcantly different in the low and high Malm permeability scenarios. In the low Malm permeability scenario, isolated zones of relatively low Péclet numbers consistently characterize the Molasse (Fig. 13a). By contrast, in the high Malm permeability scenario, the Molasse exhibits higher Péclet numbers especially in its northern part and above the highly permeable Malm aquifer (Fig. 13b). Here, leakage of groundwater through the Molasse – combined with heat evacuation through the karstifed Malm – explains the slow cooling and thus the formation of a negative thermal anomaly. Heat-fow density

Figure 14 shows the vertical component of the conductive heat-fow density in the low and high Malm permeability scenarios, respectively. In the Franconian Alb to the north of the Danube, the conductive heat-fow density increases from 70 mW m2 at the base of the model to about 100–105 mW m2 at the top of the Variscan basement. The heat-fow density rises upwards due to radiogenic heat production within the Variscan basement, which is characteristic of a conductive regime. In the Molasse Basin part of the model, the conductive heat-fow density distribution is in both low and high Malm permeability scenarios infuenced more or less by heat convection. In the low Malm permeability scenario, the conductive heat-fow density ranges relatively uniformly between 65 and 75 mW m2 in the central part of the section, not much higher than the heat-fow density range of 60 mW m− 2 in the south and 70 mW m− 2 in the north at the base of the model. The conductive heat-fow density is extremely low beneath the highest point (about 25 mW m2) and increases to 65 mW m2 at 2000 m depth (Fig. 14a). In the high Malm permeability scenario, the conductive heat-fow density ranges between 70 and 90 mW m2 in the central part of the section. The Malm stands out with a conductive heat-fow density reaching up to 120

Page 18/54 mW m2. Within the upper part of the Molasse, convective heat redistribution is so intense that the conductive heat-fow density is close to zero (5–10 mW m2) at the surface and rapidly increases to 60– 65 mW m2 at 1500–2000 m depth (Fig. 14b). Darcy’s velocity magnitude

Figure 15 shows Darcy’s velocity magnitude as a measure of how fast groundwater is fowing. In agreement with the very low permeability range, groundwater fow is extremely slow in the Variscan basement. A contrast of up to three orders of magnitude exists between Darcy’s velocity magnitude in the Malm aquifer and in the Molasse. In both the low and high Malm permeability scenarios, Darcy’s velocity magnitude within the Malm aquifer is lower than 0.1 m a1 in the deepest part of the Molasse Basin, whereas it progressively increases to about 1 m a1 in the centre of the Molasse Basin (section km 65) and further increases to about 10 m a1 near the Danube. Darcy’s velocity magnitude within the Molasse ranges between about 0.01 m a1 and 0.1 m a1 (Fig. 15). In the Franconian Alb to the north of the Danube where the karstifed Malm carbonate is exposed, our models show that Darcy’s velocity magnitude exceeds 10 m a1 with a maximum of more than 1000 m a1. As shown in Fig. 15b, the higher Malm permeability causes a signifcantly higher Darcy’s velocity magnitude within the Molasse and in the direction of the Danube, especially in the northern two-thirds of the Molasse Basin. The about twice as high Darcy’s velocity magnitude leads to the heat fow redistribution shown in Fig. 14b, and eventually to the cold anomaly shown in Fig. 9c. The higher Malm permeability also signifcantly affects the groundwater regime within the Molasse Basin by causing an increase and a decrease of Darcy’s velocity magnitude in the deeper and shallower parts, respectively.

Discussion Hydraulic head and groundwater fow

The hydraulic head corresponds to the sum of two components, which are the elevation head z on the one hand and the pressure head ϕ on the other hand (Toth (3)). The hydraulic head is a direct measure of the fuid`s potential energy in a given point of the fow region. However, since water density is temperature-dependent in our models, the pressure head and thus the hydraulic head increases with depth. Therefore, in order to be able to compare our results with standardized hydraulic head data published e.g., by Stober and Villinger (1997) and Frisch and Huber (2000), we calculate the fresh water head as mentioned in the methodology section. The groundwater fow is from the recharge to the discharge areas and always in the direction of decreasing hydraulic head (Fig. 6). In our model, the Danube and Altmühl Rivers lie at 300 and 305 m altitude, respectively. The river altitude implemented in our model is lower than the actual altitude of 370 m of the Danube near Ingolstadt, but closer to the 330 m altitude of the discharge zone near Regensburg, because we retained the geometry of the initial conceptual model. The Inn River lies at 440 m altitude near Rosenheim. Overall, however, the discrepancy between the conceptual model and the actual geologic situation is negligible. Figure 6a and b show that

Page 19/54 in the low Malm permeability scenario the hydraulic head within large parts of the Malm aquifer corresponds to about 400–500 m altitude. The latter result is, however, not directly comparable to the fresh water head derived for regions to the west of Munich (Frisch and Huber (28)), because the groundwater fow in the western part of the Molasse Basin is directed from the west to the east, whereas the groundwater fow in the eastern part of the Molasse Basin is directed from the south to the north. In Fig. 6c, the stronger hydraulic head decrease in the high Malm permeability scenario is explained by the faster dissipation of the hydraulic pressure induced by topography or the Inn Glacier. When permafrost occurs, the hydraulic head also decreases fast beneath the permafrost layer, because it hampers recharge while groundwater stored within the Molasse sediments continues fowing towards the Malm aquifer. The water table in the low Malm permeability scenario rises signifcantly faster aside the Danube, and is thereby less sub-hydrostatic than in the high Malm permeability scenario, because the lower Malm permeability reduces the hydraulic connection with the Danube. By contrast, the hydraulic head along the highly permeable Malm aquifer is clearly sub-hydrostatic, which is in agreement with Lemcke and Tunn (56) and Andres and Frisch (57) who observed a water table up to 200 m below terrain level towards the Alpine front. Accordingly, the high Malm permeability scenario in Fig. 6c and d indicates that the hydraulic head within the Malm aquifer in the central part of the section can theoretically be as low as the Danube in case the permeability contrast between Malm and Molasse is very high. Frisch and Huber (28) indicate a relatively low fresh water head of 370 m in the Munich region, reaching southwards as far as the Starnberger See and being only 40 m higher than the Danube near Regensburg over a distance of more than 100 km. A similar low fresh water head over 80 to 100 km distance results from our high Malm permeability scenario (Fig. 6d). Therefore, the low hydraulic head values in the Malm aquifer confrm the excellent hydraulic connection with the Danube, which was postulated by Frisch and Huber (28) and Stober, Wolfgramm (63) because of the existence of freshwater with a mineralization below 1 g L1 in the Malm aquifer in large areas of the Molasse Basin. Mraz, Wolfgramm (71) also recently provided further evidence that a continuous infuence of descending meteoric fuids explains the low salinity and the isotope values observed within the Malm. Groundwater dating performed by Heidinger, Eichinger (61) using Krypton isotopes are in agreement with a relatively dynamic groundwater recharge of the Malm aquifer across the thick Molasse, potentially under sublglacial conditions. Strikingly, Tertiary reservoir layers located to the south of the negative thermal anomaly and within the conduction-dominated zone close to the Alpine Front comprise numerous oil and gas felds (Bachmann, Dohr (35), Bachmann, Mueller (34), Bachmann and Mueller (21)) and are known for their signifcant overpressure (Drews, Bauer (102)). Regarding the impact of groundwater leakage on hydrocarbon reservoirs, as well as brines in the Tertiary Molasse and Cretaceous sediments, we refer to Lemcke (23), Lemcke and Tunn (56) and further Andres and Frisch (57). The latter authors argue that oil and gas have largely been fushed out and destroyed by groundwater fow except for their preservation in sheltered structural traps (see e.g., Bachmann, Dohr (35)). Similarly, mineralized formation waters have progressively been diluted except for salt accumulations in isolated zones (Andres and Frisch (57)). Hydrocarbon trapping and hydrodynamic regimes are not mutually exclusive, but are frequently coexisting and interrelated in many geological basin types (Wendebourg, Biteau (103)). Hydraulic and thermal effect of the Inn Glacier Page 20/54 The model results about periodic reorganization of groundwater fow in response to glacier cover (Fig. 6, Fig. 7) are in accordance with fndings by Boulton, Caban (76) and Piotrowski (77) who studied the large- scale patterns of groundwater fow beneath ice sheets. Glacial cycles produce cyclical pulses of pressure and groundwater fow through the subsurface. Thus, glaciations represent the strongest impacts on groundwater during recent geological time. Figure 6 best shows the observations of Boulton, Caban (76) and Piotrowski (77) by exemplifying the reorganization of the relatively small, topographically controlled groundwater catchments typical of interglacial periods, such as the present, to produce basin-scale integration of groundwater fow when glaciers advance into the foreland. The consequence is signifcant groundwater fow in deep aquifers (i.e., in the deep Molasse and in the Malm) and the complete replacement of pre-existing groundwater by colder water in shallow aquifers, where permafrost is absent, such as in the Quaternary and the shallow Molasse beneath larger perennial rivers and lakes, and probably beneath piedmont lobes of glaciers (Fig. 7b). Similar to the present study, Lemieux, Sudicky (74) numerically simulated the surface-subsurface water exchange fux in Canada and demonstrated that large quantities of meltwater, i.e. on average 43%, episodically infltrate beneath glaciated areas. However, Piotrowski (78) fnds evidence that relatively fne-grained substratum like in the Molasse Basin can drain only about 25% of subglacially produced meltwater. Mraz, Wolfgramm (71) studied the fuid and temperature evolution of the Malm aquifer by analysing fuid inclusions and performing stable isotope measurements of different cement phases in carbonate rock. Their results reveal that the least saline fuids from the Malm occur in the Traunreut well near Lake Chiemsee to the east of the Inn valley. In addition, they conclude that the reservoir temperature must have decreased more strongly in the eastern part (Traunreut area) than in the central part (Munich area) of the Molasse Basin. According to our model results for the high Malm permeability scenario (Fig. 6c; Fig. 7b), it is possible that cold meltwater from the Inn and Achen glaciers (Van Husen (8)) infltrated down to the Malm aquifer under an increased hydraulic head in the course of several glaciations, but without producing an appreciable cold anomaly in the deeper Molasse Basin. Equally, the much larger Rhine Glacier (Cohen, Gillet-Chaulet (39)) apparently does not produce a signifcant cold anomaly in the deeper Molasse Basin and the Malm aquifer (Fig. 2, Agemar and Tribbensee (19)). This obvious fact shows that the hydraulic and thermal effect of relatively large, recurrent foreland glaciers is not sufcient and causative for signifcant cold anomalies in the relatively deep Malm aquifer.

The particular situation along our section, where a topographic high generates two opposite cells of forced convection, actually illustrates a groundwater divide between the Danube and Inn Rivers (Fig. 6b and d). A similar situation exists between the Danube and the Rhine Rivers in the Molasse Basin near , where the potentiometric surface provides evidence that the Rhine drains the Malm aquifer in the eastern part of the Molasse Basin (Bertleff, Ellwanger (43), Stober and Villinger (64)). Bertleff, Ellwanger (43) studied the paleogroundwaters that are found in various Tertiary aquifers (i.e., in the Molasse) and in the karstifed Malm. Their interpretation of hydrochemical and hydroisotopical measurements indicate a high altitude origin of the water and a recharge of the intermediate and regional (i.e., deep) circulation systems under colder climatic conditions than today. They outlined a possible hydrodynamic model of groundwater recharge in which groundwater recharge during glacial periods

Page 21/54 occurred in distinct subglacial environments. In the present study, recharge areas under cold conditions in presence of permafrost are essentially confned to deep, relatively permafrost-free glacial basins where glacier cover causes an increased recharge due to a higher water table or hydraulic head (Fig. 7a), which confrms similar results obtained by Bertleff, Ellwanger (43). However, in the bulk of the Molasse Basin, recharge under periglacial conditions certainly was appreciably lower compared to the present temperate climate, mainly because of reduced precipitation (Cohen, Gillet-Chaulet (39), Seguinot, Ivy-Ochs (7)) and recurrent, persistent permafrost. Therefore, contrary to Bertleff, Ellwanger (43) who put forward that recharge rates under recent climatic conditions are comparatively low, we suggest that recharge in the Molasse Basin generally was lower during colder climatic conditions. Thermal feld as a result of low and high Malm permeability

In all Malm permeability scenarios, three regions with distinct geothermal gradients can be differentiated (Fig. 8). In the Franconian Alb to the north of the Danube valley, groundwater mainly cools the shallow subsurface by fowing laterally towards the Altmühl valley as well as towards the Danube valley. The isotherms are subhorizontal and the undisturbed geothermal gradient is characteristic of the relatively low permeability of basement rocks. In the region of the Danube valley, the subsurface heats up because the region between Neustadt and Regensburg represents a regional upfow zone. Evidence for the regional discharge of the Malm aquifer in the latter region had already been provided by Bertleff, Ellwanger (43), Birner, Mayr (62), and Frisch and Huber (28). Groundwater from the Molasse Basin circulates deep enough to take up heat and discharge it in the Danube valley. At Bad Gögging, which is located 30 km downstream of Ingolstadt, a 120-m-deep well produces 14°C-warm water in the Malm aquifer (Wirth and Andres (104)), which is signifcantly more than the mean annual surface temperature of about 8°C (Hänel and Staroste (92)). Groundwater and heat upfow due to forced convection causes the distance between isotherms to increase at medium depth, resulting eventually in a higher geothermal gradient and higher temperatures at shallow depth. According to our model, the 25°C-isotherm is located just about 150 m below the surface to the south of the Danube valley (Fig. 8). Temperatures of 25°C in the shallow subsurface of the Molasse Basin or Malm aquifer do not exist, mainly because a signifcant groundwater fow is expected in the Malm parallel to the Danube (Frisch and Huber (28), Heine and Einsiedl (59)). Nevertheless, the top Malm temperature presented in GeotIS (Agemar and Tribbensee (19)) shows that temperatures are higher by up to 20°C in the realm of an der Ilm and Landshut, a region located about 40 km to the south of the Danube. Only a 3D model could reveal thermal-hydraulic processes perpendicular to our 2D section. Specifcally, the studied 2D section is appropriate to reproduce maximum hydraulic gradients across the Molasse Basin, from the Alps in the south towards the Danube in the north. Topography along the section reaches up to 600 m compared to 300 m at the Danube and 440 m at the Inn Rivers, which is why forced convection induces a large downfow zone in the Molasse Basin. The geothermal gradient within the Molasse is relatively undisturbed in the low Malm permeability scenario (Fig. 8a, b), whereas it is signifcantly reduced in the high Malm permeability scenario with the 25°C-, 50°C- and 75°C-isotherms at depths of about 1 km, 1.8 km and 2.4 km, respectively (Fig. 8c, d).

Page 22/54 In order to validate our results, we compare the isotherms of our Malm permeability scenarios to representative 2D sections extracted from the 3D temperature model of the Molasse Basin implemented in GeotIS (Agemar and Tribbensee (19)). A frst section with isotherms and fve projected deep wells, generated in GeotIS just to the west of Munich, is comparable our low Malm permeability scenario. The subhorizontal and equidistant isotherms translate into a thermal feld typical for a conduction-dominated regime. By comparison, our low Malm permeability scenario shows a thermal perturbation in the southern part of the model section, which is related to the convection cell induced by deep fow towards the Inn valley in the south. By contrast, the extracted GeotIS section shows a typical ramp towards the Alpine front and therefore the mentioned convection cell cannot form. In addition, Molasse permeability may be lower near the Alpine front due to a higher horizontal stress and thus a higher compaction. A second section with isotherms and numerous projected deep wells, generated in GeotIS along the trace of our 2D section to the east of Munich, is comparable to our high Malm permeability scenario. The curved and irregular isotherms are characteristic for a thermal feld in a convection-dominated regime. Like our results of the high Malm permeability scenario, the GeotIS section shows three regions with distinct geothermal gradients. Beneath the Franconian Alb to the north of the Danube valley, the isotherms are subhorizontal and show a regular spacing, which is typical for conduction in this northern part of the model dominated by the Variscan basement. In the northern part of the Molasse Basin, higher temperatures exist at shallow depth and thus produce a higher geothermal gradient. Here, ascending groundwater in the Malm aquifer due to forced convection is responsible for heat upfow. In the southern part of the Molasse Basin, numerous deep wells mainly drilled by the oil and gas industry confrm a large downfow zone of relatively cold surface water through the Molasse by leakage into the underlying Malm aquifer.

With regard to model sensitivity to changes in permeability, the Molasse permeability is worth mentioning because it also has a different and complex composition along strike (GeoMol Team (15), Kuhlemann and Kempf (1), Schwerd, Doppler (105), Zweigel, Aigner (106)), and presents a varying number of typically more permeable sandstone reservoir layers (Brink, Burri (22)). Bertleff, Ellwanger (43) indicate a very low permeability range of 1016 to 1018 m2 for the Lower Freshwater Molasse, which consists mainly of lacustrine and fne-grained fuvial sediments. Comparatively low average permeabilities of the Molasse and a very low recharge by leakage (Bertleff and Watzel (44)) seem to be representative of the western Molasse Basin in Baden-Württemberg where only a single sandstone reservoir layer is known (Brink, Burri (22)). Villinger (60) specifed a permeability range of 1015 to 1016 m2. Andres and Frisch (57) discussed various estimates available in literature and derived a (vertical) Molasse permeability of 2∙1016 m2 hydraulically representative of an equivalent silt composition of the Molasse sediments. Although the focus of our study lies on the variation of the Malm permeability, we checked the model sensitivity to a Molasse permeability lower than given in Table 1. If the Molasse permeability is one order of magnitude lower, the simulated negative anomaly reaches only about 10°C. Clearly, in our models, the lower constraint needed to produce the observed negative thermal anomaly corresponds to a minimum Molasse permeability of 1014 m2 horizontally and 1015 m2 vertically. The latter conclusion suggests that permeable sandstone layers within the Molasse are not only a prerequisite for hydrocarbon trapping, but

Page 23/54 also may be essential for hydrodynamic regimes able to signifcantly perturb the thermal feld. This would support the observation that hydrocarbon trapping and hydrodynamic regimes are frequently coexisting and interrelated in many geological basin types (Wendebourg, Biteau (103)).

In agreement with the geological setting, the heat input into the Molasse Basin is characterized by conduction through the Variscan basement, which is characteristic of the foreland-basin play type (Moeck (4), Moeck and Beardsmore (2), Moeck, Beardsmore (20)). Our model results confrm the main fndings of thermal-hydraulic modelling performed by Przybycin, Scheck-Wenderoth (18). The Malm and the Tertiary sediment fll of the Molasse Basin present a sufciently high formation permeability for basin-wide gravity-driven fuid fow and convective heat fow. Since the range of Darcy’s velocity magnitude is mostly between 0.01 and 1 m a1 (Fig. 15), and thus relatively low, Darcy’s law remains valid. Although we did not explicitly model the thermal-hydraulic effect of faults within the Malm, we agree with Przybycin, Scheck-Wenderoth (18) that faults have a subordinate, relatively local infuence on the thermal feld (see e.g., Rühaak, Rath (68)). Subvertical faults tend to increase the overall permeability of the karstifed Malm (Birner (25)), but strong basin-wide forced convection likely overprints free convection within faults (Lopez and Smith (95)). Unlike Przybycin, Scheck-Wenderoth (18) who suggest that heterogeneities in thermal conductivity contribute to the generation of pronounced positive and negative thermal anomalies in the Molasse Basin, we put forward formation permeability and gravity-driven groundwater fow as a key factor for heat redistribution. In their model of the Upper – area, Pfeiderer, Götzl (107) concluded that hydraulic and geothermal gradients show similar regional trends caused eventually by the strong effect of groundwater convection on the redistribution of heat in the Malm karst aquifer.

Our models predict a maximum permafrost thickness of 150–200 m in the low Malm permeability scenario (Fig. 8a). These fndings are in reasonable agreement with previous modelling results about maximum permafrost thickness in Central and Western Europe. For the last glaciation, numerical modelling satisfactorily shows a permafrost thickness of less than 100 m in the Paris Basin (Lebret, Dupas (50)), more than hundred meters in north-central Europe (Delisle, Caspers (108)), and up to 150 m to the north of the Rhine Glacier in Switzerland (Cohen, Gillet-Chaulet (39)). This is much less than several hundred meters up to some 500 m of permafrost currently subsisting at high latitude in Alaska and Canada (Lebret, Dupas (50), Sloan and van Everdingen (46)). The main factors infuencing the permafrost thickness are the heat fow density, mean annual ground temperatures, and thermal properties of rocks related to their lithology and their water content (Lebret, Dupas (50)). Since ground temperatures and rock properties are identical in both Malm permeability scenarios, the signifcantly higher maximum permafrost thickness of up to 600 m in the high Malm permeability scenario (Fig. 8c) can largely be explained by the drastically reduced conductive heat fow density as a consequence of extensive downward groundwater fow (Fig. 14b). Precise and reliable fossil indicators of past deep permafrost are difcult to fnd and direct evidence often linked to physical markers like indications of frost cracking (Lebret, Dupas (50)) or disturbed geothermal gradients, like e.g. in the Alberta Basin in Western Canada (Gray, Majorowicz (12), Majorowicz (13), Majorowicz, Gosnold (14)). In the realm of the Amper and Isar

Page 24/54 valleys, we implemented a zone where the minimum temperature is limited to 4°C to prevent permafrost formation. Permafrost is often absent beneath lakes and larger perennial rivers because deep and fowing water locally inhibits freezing of the subsurface (Boulton, Slot (75), Dagher, Su (109), Sloan and van Everdingen (46)). Besides the general leakage of shallow groundwater into the karstifed Malm, unhindered infltration of cold groundwater in the Amper and Isar valleys even at cold surface temperatures may explain the local correlation of the Amper and Isar valleys with the coldest zone of the underlying thermal anomaly (Fig. 2; Agemar and Tribbensee (19)). As Bertleff, Ellwanger (43) and Bertleff and Watzel (44) put forward, our models corroborate the fact that recharge during cold periods can only occur when and where permafrost is absent (compare Fig. 6 and Fig. 8). Indeed, a frozen sediment has a hydraulic conductivity many orders of magnitude lower than the same sediment in an unfrozen state (e.g., Piotrowski (77), Piotrowski (78)) because the dynamic viscosity of water drastically increases when it becomes ice, taking a value of some 1012 Pa s, about 1015 times that of water (Fowler (97)). Permafrost is absent when surface temperature is cold but above the freezing point (Fig. 4) and in subglacial basins when periodic glacier cover impedes permafrost formation in the melting zone (Boulton, Slot (75), Piotrowski (77)). Likewise, our models promote the assumption by Bertleff, Ellwanger (43) that the discharge areas of the Malm between Neustadt and Regensburg remained active even during pleniglacial times, making the Malm aquifer the only drainage system possible. The present modelling implements a suggestion by Pfeiderer, Götzl (107) to set up a transient conductive model for consideration of paleoclimatic signals and subsequently a coupled thermal-hydraulic model to test possible hydraulic concepts. Thermal anomaly with paleoclimatic forcing

The simulation of the low Malm permeability scenario along profle A, by contrast to the high Malm permeability scenario (Fig. 8), serves to illustrate the major difference in subsurface heat redistribution to the west and east of Munich. Figure 9 shows the resulting temperature difference under paleoclimatic conditions and thus visualizes the strongly modifed thermal feld. As shown by Birner, Fritzer (26), the range of hydraulic conductivities or permeabilities spans three to four orders of magnitude between the least permeable, marl-dominated Helvetic facies in the southwest and the most karstifed Malm carbonate in the east of the Molasse Basin. The much higher Malm carbonate permeability due to karstifcation drastically increases the gravity-driven coupled groundwater and heat fow, and thus heat redistribution. The higher the Malm carbonate permeability, the stronger and deeper the gravity-driven groundwater fow, which by descending through the Molasse towards the Malm aquifer also signifcantly cools down the Molasse as well as the Malm aquifer. The geostatistically evaluated thermal feld (Fig. 2; Agemar and Tribbensee (19)) validates the thermal anomaly produced in our study. This result therefore confrms that the model is able to replicate the cold anomaly occurring in the Wasserburg Trough to the east of Munich. Thermal anomaly without paleoclimatic forcing

Our model results confrm that a signifcant negative thermal anomaly forms within 50 ka (Fig. 9a). Even without paleoclimatic conditons applied, temperatures in the Molasse are up to 50°C colder in the high

Page 25/54 Malm permeability scenario (Fig. 10). The main explanation for this counterintuitive result is that the extreme conditions linked to cold periods such as glacier cover and permafrost formation are relatively sporadic events in comparison to the geological time scale of persistent groundwater fow. Over the 130 ka simulated in the present study, the advances of the Inn Glacier into the foreland and onto the Molasse Basin are sporadic (Seguinot, Ivy-Ochs (7)). The duration of glacier cover makes up only about 26.6 ka (Fig. 5), which represents 20% of the simulated time and 25% of the Würm glaciation (Fig. 4). Similarly, the duration of sustained temperatures below the freezing point and thus the prerequisite of permafrost formation represents only a fraction of the Würm glaciation (Jouzel, Masson-Delmotte (89)). The duration of continuous permafrost makes up only about 45.2 ka (Fig. 4), which represents 35% of the simulated time and 44% of the Würm glaciation. Unlike these relatively sporadic events, the permeability of geologic units is a permanent, primary geological control factor of the magnitude of forced convection and heat redistribution. Moreover, formation permeability already controlled coupled groundwater and heat fow probably since the end of Molasse Basin development in the Late Miocene. The existence of the Danube River is equally important because it strongly infuences the discharge of thermal water by the Malm karst between Neustadt and Regensburg. The Pre-Danube River started to form and evolve as soon as the sea retreated from the Molasse Basin some 7 Ma ago (Kuhlemann and Kempf (1)). The Pre- Danube also plays a major role in removing the Molasse sediments exposed to erosion due to uplift of the Molasse Basin. The drainage of the Danube is highly dynamic over geological time, especially at the transition from the Tertiary to the Quaternary when it loses several headwaters to the Rhine River. The youngest events are the loss of the Alpine Rhine about 800 ka ago and the rerouting of the Danube during the Riss glaciation about 300 ka ago (Jerz and Peters (110), Schaefer (111)) or more recently during the Würm glaciation (Fiebig and Preusser (112), Doppler, Kroemer (37)). River systems are highly sensitive to environmental changes, including the effects of tectonic, climatic, glacial and anthropogenic forcing (Cordier, Adamson (113)). In particular, the glaciations in the Alpine realm directly or indirectly control the changes in the drainage pattern of the Danube. It is therefore possible that the thermal anomaly observed to the east of Munich (Agemar and Tribbensee (19)) progressively developed over the last 800 ka with the onset of the frst major glaciations recorded in the North Alpine Foreland and as a consequence of the dynamic reaction and evolution of the Danube. Thermal effect of different surface temperature conditions

Figure 11 and Fig. 12 visualize the sole effect of the two contrasting surface temperature boundary conditions, including permafrost formation and recurrent glacial advances under paleoclimatic conditions, on the low and high Malm permeability scenarios, respectively. Clearly, as mentioned e.g. by Bertleff, Ellwanger (43), Lemieux, Sudicky (74), Piotrowski (77), Piotrowski (78), permafrost acts as a barrier for groundwater fow since it drastically reduces the hydraulic conductivity within sediments. Therefore, permafrost formation hampers heat redistribution by forced convection. In a sense, permafrost formation brings the high Malm permeability scenario closer to the low Malm permeability scenario. In Fig. 11c and Fig. 12c, the signature of colder surface temperature locally remains in the shallow subsurface up to the present day with a temperature difference of more than 2°C. In both permeability scenarios, the colder zones in the shallow subsurface of the Molasse Basin are remnants of permafrost,

Page 26/54 which retards warming-up. Our results corroborate those obtained by Gray, Majorowicz (12) who investigated the geothermal state of sedimentary basins, specifcally the northern Alberta Basin, using oil industry thermal data. With regard to studies of the deeper thermal feld ideally devoid of the paleoclimatic effect, they concluded that reliable data should be derived from deep wells (> 2000 m) with precise, continuous temperature logs and measured thermal conductivities.

Our model shows that cooling of the shallow subsurface and recharge essentially during colder climatic conditions is preserved in the low permeability scenario up to the present, mainly because it reacts slower to warming due to the relatively low rock thermal conductivity (Fig. 11). As a matter of fact, low permeability lithologies tend to capture and preserve the long-term climatic evolution of the Pleistocene (e.g., Bertleff, Ellwanger (43)), which is clearly dominated by colder climatic conditions in the last 800 ka if not the entire Quaternary (Ehlers and Gibbard (114)). More permeable geologic units, in particular the karstifed Malm, and the corresponding groundwater fow systems react much faster or dynamically to warm periods like the Holocene (Bertleff, Ellwanger (43), Bertleff and Watzel (44)). Thereby, the signature of colder climatic conditions is largely overprinted (Fig. 12). Péclet number

Clauser, Bischof (67) concluded that no signifcant heat redistribution occurs in the Malm in the western part of the Molasse Basin. This situation refers to the low Malm permeability scenario. In the eastern part of the Molasse Basin, in particular between Munich and the Landshut-Neuötting High, however, our results demonstrate a substantial heat redistribution. This is visualized by the differing Péclet number distribution in the low and high Malm permeability scenarios (Fig. 13). The Péclet number calculation also confrms the interpretation by Bertleff, Ellwanger (43) and Bertleff and Watzel (44) that the southern, deepest part of the Malm is characterized by a relatively stagnant groundwater system dominated by heat conduction. This groundwater is also referred to as Pleistocene paleogroundwater and can only be renewed by leakage through the Tertiary Molasse (Fig. 6), whereby an ion-exchange water composition formed (Bertleff, Ellwanger (43), Birner, Mayr (62)). Heat-fow density

Surface heat-fow density data are available from several geothermal atlases (Legrand, Balling (115), Hänel and Staroste (92), Hänel and Hurter (116)) and updated maps (e.g., Cloetingh, van Wees (117)). However, the resulting surface heat-fow density maps differ largely. Data compiled by Hänel and Hurter (116) yield surface heat fow density values ranging from about 90–95 mW m− 2 in the northwest in the realm of Stuttgart and the Danube River, and values of about 70 mW m− 2 in the realm of the German- Austrian border and the Alpine front. The European heat fow map by Cloetingh, van Wees (117) shows a south to north heat fow range of 70 to 85 mW m− 2 for the Munich region studied here. The published surface heat fow density values are in the range of values typical for the geodynamic setting of Paleozoic extended crust in Europe (Balling (118), Norden, Foerster (119)). The low Malm permeability model scenario, which is representative of the largest part of the Molasse Basin, quite confdently reproduces the surface heat-fow density pattern presented by Hänel and Hurter (116). For the high Malm

Page 27/54 permeability scenario, our model results clearly demonstrate that the conductive surface heat-fow density values, which are typically derived from temperature measurements in subvertical wells, are aficted with a signifcant convective heat fow perturbation due to groundwater fow towards the highly karstifed Malm (Fig. 14b). Most importantly, our results provide evidence that heat-fow density distribution is heterogeneous and depth-dependent. Therefore, in regions dominated by (free or forced) convection, the determination of background heat-fow density, crucial as a constraint for thermal- hydraulic models, is not straightforward. The complexity obviously increases with the magnitude of groundwater fow and convective heat transfer. The published heat-fow density maps do not refect the results of the high Malm permeability scenario. The reason is the sparsity of deep boreholes and temperature data, and most substantially derived heat-fow density values, in the realm of the negative thermal anomaly. Heat-fow density maps generally correspond to interpolated data points and do neither include geological information nor consider physical processes. Darcy’s velocity magnitude

Our results about Darcy’s velocity magnitude of up to 1000 m a1 in the exposed Malm aquifer are conservative compared to values of at least 87,600 m a1 actually measured in the Swabian Alb (Hölting and Coldewey (120)). Similar to previous conclusions based on hydraulics, hydrochemistry and isotope signature, our model results generally confrm the subdivision of the Malm aquifer in two main zones (Bertleff and Watzel (44)). The zone along the northern basin margin contains recently regenerated groundwater, whereas the zone in the basin centre contains water of Pleistocene age characterized by a very low regeneration. However, the higher permeability of the karstifed Malm in the Wasserburg Trough to the east of Munich regionally induces signifcant leakage of meteoric water through the Quaternary, Tertiary and Cretaceous overburden, and thereby causes a faster groundwater regeneration also in this more central zone of the Molasse Basin (Heidinger, Eichinger (61)). Comparison with the Alberta Basin – another formerly glaciated foreland basin

One major objective of this study is to compare and understand the interplay of high permeability aquifers, gravity-driven groundwater fow and paleoclimate in different orogenic foreland basins worldwide. Like the Molasse Basin in Southern Germany, the Alberta Basin in Western Canada has been extensively explored for oil and gas. Recently, the available data have been used for heat fow studies and to assess its geothermal potential. From the analysis of geothermal gradients throughout the Alberta Basin, it is long known that climate during the last ice age has a considerable effect even on subsurface temperatures up to two kilometres depth.

The Alberta basin is part of the West Canada Sedimentary Basin (WCSB), which is about 25 times larger than the NAFB. The Alberta Basin is about 700 km wide perpendicular to strike and more than 1000 km long. The thickness of the sedimentary wedge increases to about 6000 m close to the Rocky Mountains. The Alberta Basin formed above the Precambrian basement corresponding to the Canadian Shield. A single regional-scale groundwater fow model across the entire Alberta Basin and its sedimentary

Page 28/54 succession was previously observed e.g. by Majorowicz, Jones (121), Majorowicz, Jones (122) and Jones, Lam (123). However, the fow of formation waters in the Alberta Basin is more complex, both areally and stratigraphically (Bachu (101)). According to Bachu (124) and Bachu (100)), basin-wide groundwater fow is not possible because extensive basin-scale aquitards and aquicludes preclude full- scale basin-wide groundwater fow and the regional-scale permeability of aquifers is too low (< 1015 m2). The resulting overall groundwater velocities of 0.01 m a1 are similar to Darcy velocities in the Southern German Molasse sediments (Fig. 15a). Like in the Molasse Basin (Fig. 13), heat conduction at Péclet numbers < 0.1 dominates in the Alberta Basin, except for the Devonian Elk Point aquifer system at the northern edge of the basin (Bachu (101)). Similar to the Malm aquifer in the Molasse Basin, reefs, dolomitization, fracturing and karst processes are responsible for the high permeability of the Elk Point aquifer system. This causes fow channelling along the Presqu’ile reef barrier and to relatively strong heat advection by groundwater. The discharge from the Elk Point aquifer occurs at outcrop near the Great Slave Lake, which explains the signifcant thermal anomaly and high geothermal gradients observed at shallow depth near the Precambrian Shield (Bachu (101)). Majorowicz, Garven (125) built a 2D hydrogeological model across the Alberta Basin and obtained maximum groundwater velocities of 1.1 m a1, which are similar to Darcy velocities in the Malm aquifer in the central part of our model section, but signifcantly lower than Darcy velocities of 10 m a1 near the Danube (Fig. 15a). Gupta, Wilson (126) performed fuid-fow rate simulations in the Alberta Basin and obtained for the present situation fuid-fow velocities in the range of 0.0001 to 0.01 m a1 for the most permeable formations in the deeper parts of the basin. Such velocities are much lower than Darcy velocities at comparable depth in the Molasse Basin (Fig. 15), even in the low Malm permeability scenario (about 0.01 to 1 m a1).

The fndings of Majorowicz, Garven (125) confrm that no single, deep, large, regional-scale groundwater fow can account for the heat fow variations observed along the strike of the Alberta Basin. Bachu (100) and Bachu (127) concluded that the geometry and the aspect ratio of the fow system is crucial for heat redistribution across a basin under realistic hydraulic conditions. Therefore, with regard to foreland-basin surface topography, Majorowicz, Garven (125) infer a lateral scale of less than 200 km for effective horizontal heat transfer. Moreover, by comparison to the Molasse Basin, the simulated freshwater heads in the Alberta Basin are relatively high in the central part (Gupta, Wilson (126)), which inversely demonstrates that the hydraulic connection of the Molasse Basin to major rivers (here, the Danube) is considerably better in the high Malm permeability scenario (Fig. 6d).

In the Alberta Basin, a major difference compared to the structurally equivalent Mesozoic formations in the Molasse Basin are the various evaporite formations and the generally highly saline formation waters with more than 100 g L1 Cl in the Paleozoic aquifers (Connolly, Walter (128), Gupta, Wilson (126), Hitchon, Bachu (129)). Less saline formation waters of meteoric origin characterize the shallower foreland-stage Mesozoic formations (Gupta, Wilson (130)), which are equivalent to the Tertiary Molasse in Southern Germany, whereas meteoric water in the Alberta Basin is only known in small regions in recharge and discharge areas. The Malm carbonate aquifer in the Molasse Basin is largely characterized by a chloride content below 1 g L1 (Fritzer, Settles (85)). Higher chloride contents of 15 g L1 are mainly known in the

Page 29/54 Malm near the Alpine Front (Stober (131), Stober, Wolfgramm (63)). NaCl content in the Tertiary Molasse mostly ranges from 1 to 25 g L1, except for the Chattian Sands with up to 60 g L1 (Fritzer, Settles (85)). In the Alberta Basin, salinity increase with depth offsets the decrease in density resulting from temperature increase (Bachu (101)), such that Paleozoic formation waters in the basement are heavier than Mesozoic waters. Consequently, buoyancy is signifcant in the Alberta Basin and impedes full-scale groundwater fow from the surface to the basement (Bachu (101), Ferguson, McIntosh (132), Gupta, Wilson (130)).

Thanks to the exceptional abundance of oil and gas exploration data, the thermal feld of the WCSB, more specifcally the Alberta Basin, presently appears to be more heterogeneous than the thermal feld of the Molasse Basin. Despite numerous studies, the controlling factors of the thermal feld in the Alberta Basin are still poorly understood (Weides and Majorowicz (133)). So far, a coherence between heat fow and heat generation could not been established for the entire WCSB. However, convective heat redistribution by fuid fow across the basin partially accounts for observed variations of thermal gradients (Weides and Majorowicz (133)). Decades ago, Jessop (1971) discovered that a glacial perturbation of heat fow exists in Canada. Under extreme conditions the observed perturbation can be as high as 20 mW m2, but in most cases is of the order of 10 % or less of the background heat fow. With regard to the thermal-hydraulic impact of Quaternary glaciations, the entire Alberta Basin was repeatedly covered by two large ice sheets (i.e. the Cordilleran and Laurentide ice sheets; Dyke (9), Seguinot, Khroulev (10)), whereas the Molasse Basin was only covered by comparatively small piedmont lobes of Alpine glaciers that recurrently advanced onto the foreland basin (Seguinot, Ivy-Ochs (7), Van Husen (8)). Lemieux, Sudicky (74) numerically simulated the surface-subsurface water exchange fux in Canada and demonstrated that large quantities of meltwater episodically infltrate beneath glaciated areas, but without consideration of the thermal effect of cold meltwater infltration into the subsurface. Gosnold, Majorowicz (73), Majorowicz (13) and Majorowicz, Gosnold (14) studied the implications of post-glacial warming for northern Alberta heat fow. Based on the recent depletion of heat fow in the upper 2 km, and assuming heat conduction, they were able to derive the glacial base surface temperature of about 4.4°C during the last glaciation. Recently, Demezhko, Gornostaeva (11) and Demezhko, Gornostaeva (134) obtained similar results for ground surface temperature and surface heat-fow density changes at the base of the Laurentide and Fennoscandian ice sheets, respectively, during the Late Würm (or Wisconsin, Weichselian) glaciation. By contrast, our results of particularly low geothermal gradients (Fig. 8d) and low heat fow density (Fig. 14b) in the shallow subsurface of the Molasse Basin are clearly related to signifcant groundwater and heat fow drained downwards to the sufciently permeable Malm carbonate aquifer.

Conclusions

This study aimed at using numerical thermal-hydraulic modelling in the Southern German Molasse Basin along a 2D section to assess the magnitude of gravity-driven coupled groundwater and heat fow under the paleoclimatic conditions of the last 130 ka, including the Würm glaciation. The Molasse Basin serves as a reference play in order to quantify the potential effect of paleoclimate on basins of the foreland- basin play type worldwide.

Page 30/54 Our model is able to replicate the cold anomaly occurring in the Wasserburg Trough to the east of Munich. The fndings are, however, unexpected concerning the fundamental reason of the observed thermal anomaly. The thermal-hydraulic model scenarios clearly show that neither colder mean annual surface temperatures, nor permafrost formation, nor glaciers advancing onto the foreland explain the observed cold anomaly. The cause clearly is forced convection in the high Malm permeability scenario. Among the effects of cold periods, permafrost formation has the largest impact on the thermal-hydraulic regime, because it signifcantly reduces groundwater fow, and thereby forced convection. Therefore, permafrost produces not a thermal, but a hydraulic blanketing or shielding effect and effectively reduces heat redistribution. When Malm permeability scenarios are compared, this hydraulic shielding creates a positive thermal anomaly centered on the Molasse Basin and the Malm carbonate aquifer. In fact, the latter positive thermal anomaly is currently still chilling very slowly. Conversely, models performed without paleoclimatic forcing, i.e. with the higher reference surface-temperature condition, yield a signifcantly colder thermal anomaly because groundwater fow reduction due to permafrost is absent. The sensitivity analysis reveals that the development of a negative thermal anomaly with the observed intensity is relatively abrupt and forms within a permeability range of one order of magnitude, which, for the high Malm permeability scenario, implies a Molasse permeability not lower than 1014 m2 horizontally and 1015 m2 vertically. Practically, the results suggest that exploration risk for geothermal energy projects in the Molasse Basin is thermally and hydraulically optimal in the transition zone between the conduction- and convection dominated areas, corresponding to hydraulic conductivities in the range of 105 and 106 m s1. The transition zone comprises the Munich metropolitan region.

Our results are in agreement with known recharge of the Malm aquifer along the Danube and through the outcropping Malm north of the Danube, as well as discharge in the Danube valley between Neustadt and Regensburg. Secondly, considerable recharge and leakage through the overlying Quaternary and Tertiary sediments combined with signifcant drainage by the underlying Malm aquifer are essential to explain the reduction of heat-fow density and the related depression of geothermal gradients. Unlike previous suggestions that heterogeneities in thermal conductivity contribute to the generation of pronounced positive and negative thermal anomalies in the Molasse Basin, we put forward that formation permeability and gravity-driven groundwater fow are key factors for heat redistribution, largely overprinting moderate disparities in thermal conductivity. Our results also disagree with previous fndings of generally increased recharge under cold climate and especially under glacial conditions. Subglacial permafrost-free basins may have promoted increased recharge under a higher hydraulic head. However, in the bulk of the Molasse Basin, recharge under periglacial conditions certainly was appreciably lower compared to the present temperate climate, mainly because of reduced precipitation and recurrent, persistent permafrost. Both the Molasse Basin and the Alberta Basin are essentially conduction- dominated except for areas where reefs, dolomitization, fracturing and karst processes generate a high permeability in typical reservoir rock like carbonate. Beyond the overall permeability, essential key factors controlling the magnitude of convection are the foreland-basin geometry and aspect ratio, the depth of the sloping aquifer, aquifer discharge at outcrop, and the number of relatively impermeable shale and

Page 31/54 evaporite formations, since all these factors control the depth of fuid circulation and the magnitude of thermal perturbation in sedimentary basins.

To sum up, the main cause for the occurrence and magnitude of the cold anomaly is the signifcantly higher Malm permeability due to karstifcation in the eastern (Bavarian) part as opposed to the western part of the Molasse Basin, and thus the magnitude of gravity-driven groundwater fow. Finally, the comprehensive understanding of the fundamental thermal-hydraulic processes of geological systems over geological time scales requires the consideration not only of the main aquifer or geothermal reservoir, but also of classical aquitards like the basement and the overburden.

Abbreviations

EPICA European Project for Ice Coring in Antarctica

GeotIS Geothermal Information System

LGM Last Glacial Maximum

MB Molasse Basin

NAFB North Alpine Foreland Basin

WCSB Western Canada Sedimentary Basin

Declarations Availability of data and materials

The datasets analysed and used as paleo-temperature forcing during the current study are publicly available in the PANGAEA data repository, https://doi.pangaea.de/10.1594/PANGAEA.683655. (Jouzel and Masson-Delmotte (88), Jouzel, Masson-Delmotte (89)). All other relevant data generated or analysed during this study are included in this published article.

Competing interests

The authors declare that they have no competing interests.

Funding

The study and current project “PlayType – Cataloguing geothermal provinces according to the concept of rate of success (play type) for economic development and internationalisation of the German geothermal

Page 32/54 sector” is fnanced by the German Federal Ministry for Economic Affairs and Energy (grant number 0324210). The funding body did not infuence the content of this study.

Author’s contributions

TVS designed the present study, built the 2D model, investigated and applied the boundary conditions, model unit and fuid properties, performed the coupled thermal-hydraulic simulations and fnally interpreted the results. ISM initiated the PlayType project, helped to draft the manuscript and contributed with productive discussions to the interpretation of the results. All authors read and approved the fnal manuscript.

Acknowledgements

The study has been carried out at the Leibniz Institute for Applied Geophysics (LIAG) in Hannover and supported by the Bayerisches Landesamt für Umwelt (LfU Bayern). The authors would like to thank the project partners and the colleagues at the LIAG for constructive discussions. In particular, M. Dussel provided helpful comments to a draft version of the present paper.

Author’s information

Not applicable

References

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Page 40/54 107. Pfeiderer S, Götzl G, Bottig M, Brüstle A-K, Porpaczy C, Schreilechner M, et al. GeoMol - geologische 3D-Modellierung des österreichischen Molassebeckens und Anwendungen in der Hydrogeologie und Geothermie im Grenzgebiet von Oberösterreich und Bayern. Abhandlungen der Geologischen Bundesanstalt. 2016;70:1-88. 108. Delisle G, Caspers G, Freund H. Permafrost in north-central Europe during the Weichselian: how deep? In: Philips M, Springman SM, Arenson LU, editors. Eighth International Conference on Permafrost; 21- 25 July; Zürich, Switzerland. Lisse, The Netherlands: Swets & Zeitlinger; 2003. p. 187-91. 109. Dagher EE, Su G, Nguyen TS. Verifcation of the numerical simulation of permafrost using COMSOL Multiphysics(R) software. 2014 COMSOL Conference Boston; 8-10 October; Newton, MA, United States. Stockholm, Sweden: COMSOL AB; 2014. 110. Jerz H, Peters M. Flussdynamik der Donau bei Ingolstadt in vorgeschichtlicher, geschichtlicher und heutiger Zeit, mit Ergebnissen zur Landschafts- und Vegetationsentwicklung. Katastrophe oder Chance? Hochwasser und Ökologie : Rundgespräch am 22 Oktober 2001 in München. Rundgespräche der Kommission für Ökologie. 24. München, Germany: Verlag Dr. Friedrich Pfeil; 2002. p. 95-108. 111. Schaefer I. Der Talknoten von Donau und ; zur Frage des Laufwechsels der Donau vom 'Wellheimer Trockental' ins 'Neuburger Durchbruchstal'. Zeitschrift für Geomorphologie. 1966;51:59- 110. 112. Fiebig M, Preusser F. Das Alter fuvialer Ablagerungen aus der Region Ingolstadt (Bayern) und ihre Bedeutung für die Eiszeitenchronologie des Alpenvorlandes. Zeitschrift für Geomorphologie. 2003;47(4):449-67. 113. Cordier S, Adamson K, Delmas M, Calvet M, Harmand D. Of ice and water; Quaternary fuvial response to glacial forcing. Quaternary Science Reviews. 2017;166:57-73. 114. Ehlers J, Gibbard P. Extent and chronology of Quaternary glaciation. Episodes. 2008;31(2):211-8. 115. Legrand R, Balling N, Saxov S, Bram K, Gable R, Meunier J, et al. Atlas of Subsurface Temperature in the European Community. Luxembourg, Luxembourg: Commission of the European Communities, Subprogramme Geothermal Energy; 1979. 36 p. 116. Hänel R, Hurter S. Atlas of Geothermal Resources in Europe. Luxembourg, Luxembourg: Commission of the European Communities; 2002. 92 p. 117. Cloetingh S, van Wees JD, Ziegler PA, Lenkey L, Beekman F, Tesauro M, et al. Lithosphere tectonics and thermo-mechanical properties: An integrated modelling approach for Enhanced Geothermal Systems exploration in Europe. Earth-Science Reviews. 2010;102(3):159-206. 118. Balling N. Heat fow and thermal structure of the lithosphere across the Baltic Shield and northern Tornquist Zone. Tectonophysics. 1995;244(1):13-50. 119. Norden B, Foerster A, Balling N. Heat fow and lithospheric thermal regime in the Northeast German Basin. Tectonophysics. 2008;460(1-4):215-29. 120. Hölting B, Coldewey WG. Hydrogeologie. Einführung in die Allgemeine und Angewandte Hydrogeologie. 8 ed. Berlin Heidelberg, Germany: Springer-Verlag; 2013. 438 p.

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Figures

Page 42/54 Figure 1

Regional geological map of the Southern German Molasse Basin, modifed after Bousquet, Schmid (51) and Doben, Doppler (52). Maximum extent of the Würm glaciation according to digital maps by Gibbard, Hughes (38). Dark red line AA’ indicates the studied cross section. Inset map shows the location of the map in Germany (MB = Molasse Basin).

Page 43/54 Figure 2

3D structural model of top Malm (Upper Jurassic) for Baden-Württemberg, Bavaria and . Temperature at top Malm derived from the geostatistical 3D temperature model of the LIAG (Agemar and Tribbensee (19)).

Figure 3

Page 44/54 Model geometry representing the simplifed Molasse Basin geology along cross section AA’ shown in Figure 1. It spans from the Franconian Alb in the north (left) over Ingolstadt to the Inn valley (near Rosenheim close to the Alpine Front) in the south (right).

Figure 4

Paleo-temperature for a reference mean annual surface temperature of 9°C at 300 m altitude adapted from the European Project for Ice Coring in Antarctica (EPICA; Jouzel, Masson-Delmotte (89)). Linear scaling for paleo-precipitation forcing implemented following Seguinot, Ivy-Ochs (7). Red and blue colouring represents mean annual surface temperature above and below zero degrees C, respectively.

Figure 5

Evolution of the Inn Glacier height in the Alpine foreland during the Würm glaciation (see also Seguinot, Ivy-Ochs (7)). Glacier height is applied as time-dependent hydraulic head at the southern model boundary (Inn Glacier in Figure 3).

Page 45/54 Figure 6

Fresh water hydraulic head and streamlines in the low Malm permeability scenario with the sole hydraulic effect of the Inn Glacier (a) at the Last Glacial Maximum 26.3 ka ago, and (b) at present. By comparison, fresh water hydraulic head and streamlines in the high Malm permeability scenario with the sole hydraulic effect of the Inn Glacier (c) at the Last Glacial Maximum 26.3 ka ago, and (d) at present. Streamlines indicate Darcy’s velocity feld resulting from model properties and a constant reference

Page 46/54 surface temperature. White lines are isopotential levels at 50 m intervals. Vertical exaggeration equals three.

Figure 7

Hydraulic and thermal effect of the Inn Glacier. (a) Hydraulic head difference and (b) temperature difference induced by the Inn Glacier at its maximum extent 26.3 ka ago in the high Malm permeability scenario under paleoclimatic conditions. Vertical exaggeration equals three.

Page 47/54 Figure 8

Thermal feld including permafrost development in the low Malm permeability scenario under paleoclimatic conditions (a) 20 ka ago and (b) at present, and in the high Malm permeability scenario under paleoclimatic conditions (c) 20 ka ago and (d) at present. Red lines are isotherms at 25°C intervals. White line marks base of permafrost (0°C). Vertical exaggeration equals three.

Page 48/54 Figure 9

Temperature difference between both scenarios of high and low Malm permeabilities under paleoclimatic conditions: (a) 80 ka ago, (b) 20 ka ago, and (c) at present. Vertical exaggeration equals three.

Page 49/54 Figure 10

Temperature difference between both scenarios of high and low Malm permeabilities with a constant reference surface-temperature condition: (a) 80 ka ago, (b) 20 ka ago, and (c) at present. Vertical exaggeration equals three.

Page 50/54 Figure 11

Temperature difference between a paleo-temperature condition and a constant reference surface- temperature condition in the low Malm permeability scenario, (a) 80 ka ago, (b) 20 ka ago, and (c) at present. Vertical exaggeration equals three.

Page 51/54 Figure 12

Temperature difference between the paleo-temperature condition and the constant reference surface- temperature condition in the high Malm permeability scenario, (a) 80 ka ago, (b) 20 ka ago, and (c) at present. Vertical exaggeration equals three.

Page 52/54 Figure 13

Péclet number distribution showing the relative importance of heat advection versus conduction with a constant reference surface temperature in (a) the low Malm permeability scenario, and (b) the high Malm permeability scenario.

Figure 14

Page 53/54 Vertical component of the conductive heat fow density under paleoclimatic conditons in (a) the low Malm permeability scenario, and (b) the high Malm permeability scenario. Vertical exaggeration equals three.

Figure 15

(a) Darcy’s velocity magnitude for the high Malm permeability scenario with a constant reference surface temperature, and (b) Difference of Darcy’s velocity magnitude between the high and low Malm permeability scenarios. Darcy’s velocity magnitude is expressed as logarithm base 10 and unit m a 1. Vertical exaggeration equals three.

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