A hydrogeological conceptual model of aquifers in catchments headed by temperate glaciers

. Achieving understanding and quantification of unknown aquifer systems in glacial context is crucial to forecast the evolution under climate change of water resources and of potential floods and landslides hazards. We focus on four south-eastern outlet glaciers of the main Icelandic icecap, Vatnajökull. New data are being acquired in the field to characterise groundwater dynamics. From this we propose a hydrogeological conceptual model: two distinct aquifers and their hydraulic conductivities are identified. A comprehensive water balance at the scale of the watershed has been obtained. Recharge to the aquifers is 4 times higher under the glaciers than on the plain, and we demonstrate the glacial melt recharge impact on the groundwater dynamic.


Introduction
The research addressing glacier evolution under climate change is well developed, looking not only at changes in mass balance (e.g.: Aðalgeirsdóttir et al., 2020;Björnsson et al., 2013;Gardner et al 2013;Jóhannesson et al., 2020), but also at the associated effects on basal and downstream hydrology (e.g. Li et al., 2015). However, aftermath changes to the groundwater component are rarely considered (Vincent et al., 2019), though evolving groundwater recharge, discharge and storage in glacierised catchments is required to forecast the future changes in water resources and of water-related hazards (landslides, floods) under climate change.
Available studies in similar glacierised catchments show: high recharge to aquifers by glacial meltwater (Mackay et al.,   The studied glaciers are temperate and warm based. They have undergone a complex evolution since their last maximum of extension at the end of the 19 th century (Hannesdóttir et al., 2015). There recession since the mid 1990s (Björnsson et al., 2013) is linked to climate change (e.g. Aðalgeirsdóttir et al., 2020). It has slowed down since 2010 (Noël et al., 2022), underlying the high sensitivity of glaciers to climate and oceanic factors. The retreat rate is predicted to increase again in the next decades (Noël et al., 2022). Breiðamerkurjökull has a particularly quick retreat rate because of its unique situation, with its proglacial lake in direct and close communication with the ocean, which currents are made monthly manual measurements from March or May to September of the groundwater level, water temperature and water EC with a manual piezometric probe (Solinst TLC Meter 107). The springs are controlled visually, and their temperature and EC monitored with the TLC Meter. We monitored 4 boreholes in the till and glacio-fluvial deposits and 7 boreholes in the basalt using automatic pressure and temperature probes, at an hourly time step (6 TD-Diver type DI802, 3 TD Micro-Diver type DI501) and 2 probes measuring in addition electro-conductivity (2 CTD-Diver type DI217). To correct for the atmospheric pressure we used 3 Baro Diver type DI800 and 1 Baro Micro-Diver DI500 . A participatory approach involving Glacier Adventure, a tourism and educational company based in Hali, allows the monthly monitoring of 3 of the boreholes in the basalt aquifer all year round with an Hydrotechnik Water level meter.
All boreholes and springs were localised using a differential GPS in September 2021 (elevations obtained in table 1).
Finally we carried slug tests out in July and September 2022 in the 5 boreholes in the till and glacio-fluvial deposits and in 6 boreholes in the basalt formation, using slugs (diameters 10 cm and 5 cm) and an automatic pressure probe. One to three repetitions of the test were conducted in each borehole, with data acquired every half second.

Data Analysis
We used numerous methodologies to analyse the data gathered and acquired; they are listed below.
The potential evapotranspiration was calculated using Thornthwaite method (Thornthwaite, 1948) for evolution since 1966 and with Penman method (Monteith, 1965;Penman, 1948, with CropWat 8.0)  Leptosol and Andosols that compose the area (Arnalds, 1999;Arnalds, 2015). As rainfall and snow events are not completely distinguished in the precipitation chronicle provided by the IMO, the effective rainfall we calculate does not represent the effect of the snow melt (delayed recharge to the aquifers).
We used estimates of glacier melt to deduce a recharge rate to the underlying till and glacio-fluvial deposits or basalt aquifers. To estimate the glaciers melt, we used two datasets: ( infiltrate to the aquifers. This ratio is deduced from a 2012-2013 surface runoff data set (Young et al., 2015). In this study a 67.3 km 2 catchment of the glacier is studied, with daily surface runoff measurements in a river south of Skálafellsjökull, discharge which is assumed equal to the discharge emerging 500 m upstream from under the glacier (Young et al., 2015). The surface runoff measured and extrapolated (for days without data) accounts for 50 % (± 10%) of the volume of ice melt during the same period.
The thicknesses of the geological formations were estimated combining the thicknesses extracted from the existing geological logs and literature.
We calculated hydraulic conductivities with two different methods: from grain size data for the till and glacio-fluvial deposits and from slug tests for both aquifers. For the grain size data method, we used d10 from samples collected in the Skálafellsjökull area. Their representativeness is local and up to 2 m depth. We carried out the calculation using the We interpreted the slug tests with the Bouwer and Rice solution (Bouwer and Rice, 1976) for the unconfined boreholes (only on the rising parts of the tests) and with the Hvorslev method (Hvorslev, 1951) for the confined boreholes. The results are representative for a few meters distance in radius from the borehole and for the whole depth of the screen in the borehole (table 1).
We estimated specific yield (Sy) for both aquifers using grain size data (graph in Robson, 1993)  with R the recharge in m, and Δh the increase in groundwater table in m. Only recharge events due exclusively to rainfall should be considered, thus we excluded days with snow precipitation and/or snow cover, as well as periods of potential significant glacial melt recharge.
The topographic map used for the plain and the top of the glaciers is IslandsDEMv1 ( fig. 1), a seamless and biascorrected mosaic from ArcticDEM (Porter et al., 2018) and lidar (Jóhannesson et al., 2013)

New data
We present here the new data set allowing the characterisation of the dynamic of each aquifer.

Groundwater level
The groundwater level in the till and glacio-fluvial deposits aquifer is often near or at the surface topography.
South of Fláajökull especially groundwater levels are very close to the topography ( fig. 7), which is not a surprise as many temporary swamps can be found in this area. The county that contains this area is actually called "mýrar", which means swamps. Groundwater level amplitudes of the temporal variations are decreasing with the distance to the glacier

Electro-conductivity
Water with an EC < 700 μS cm -1 is considered non-saline, between 700 and 2000 μS cm -1 slightly saline and between 2000 and 10 000 μS cm -1 moderately saline (Rhoades et al., 1992). Values of EC above 700 μS cm -1 have been measured in three boreholes, by order of decreasing values: VG1, HA16, and HA23 (table 2). Values measured in HA26 are just below or just over 700 μS cm -1 . In ASK104, groundwater is completely fresh until -8 m b.g.l., but below that level, EC values are significantly above 700 μS cm -1 . These boreholes are close to the coastline or to the brackish lake connected to the sea ( fig. 3). The closer they are to one or the other, the higher their EC values are. EC has also been measured hourly in HA16 from May to September 2022: EC is varying from 700 to 1850 μS cm -1 with regular cycles (period of 24 hours due to the tide and period of 3 to 4 days).   Table 3 summarizes the results of the slug tests conducted in 11 boreholes. Hydraulic conductivities (K) of till and glacio-fluvial aquifer range from 5.8E-6 m s -1 to 3E-5 m s -1 while those of basalt aquifer range from 1.1E-10 to 4.9E-6 m s -1 . Thus, there is a wider heterogeneity of K in the basalt aquifer.

FLA1
Till and g-f unconfined 6 Bouwer and Rice 5.

Results
We will first detail the recharge rates obtained, then go through the characteristics and dynamic of both aquifers, and finally propose a conceptual model of the system.

In the plain
The total effective rainfall, based on the Potential Evapotranspiration calculated with Thornthwaite method, has increased by 165 mm (from 975 to 1140) since 1990, following the precipitation trend ( fig. 4).
The monthly variation of the effective rainfall, based on the Potential Evapotranspiration (PET) calculated from 1990 to 2021, shows that several months each year have no effective rainfall at all (PET with Thornthwaite method: 2-5 months, very rarely none; Penman-Monteith method: 1-4 months, very rarely 0, 5 or 7 months). Months with no effective rainfall are most of the time between April and August. These months have an inter-annual average of effective rainfall < 30 mm. The winter's months, October to March, all have an average effective rainfall above > 100 mm, with a maximum in January and February.
The estimation of the recharge of the aquifers occurring between the glacier terminus and the coastline (i.e. the plain) is based on the effective rainfall. The surface runoff being important, and with a lack of data allowing a more accurate estimation, a scaling coefficient of 0.5 (with a range of 0.25-0.75) is applied to the effective rainfall to obtain the recharge rate (table 6).

Scaling coefficient applied to the effective rainfall
Recharge in the area between the glaciers terminus and the coastline (mm year -1 )  On the plain the interannual average hydrologic balance on 1990-2021 is the following: 1540 mm (± 310 mm) of precipitations, 520 mm (± 80 mm) of evapotranspiration (both methods used), 500 mm (± 150 mm) of runoff and 500 mm (± 150 mm) of recharge to the aquifers.

Aquifers storage coefficients
Aquifer storage coefficient S is composed of two parts, specific yield Sy and specific storage Ss: Sy + Ss*e (e being the thickness of the aquifer), Sy being dominant in unconfined aquifers, and Ss*e dominant in confined aquifers. We calculated Sy using the WTF method for three to seven distinct rainfall-recharge events depending on the borehole and the length of the available groundwater record (  (Heath, 1983)

Aquifers dynamics
In the studied area groundwater is flowing towards the sea. Hydraulic gradients can be deduced from the difference of groundwater levels between two boreholes on the same potential groundwater flow line. Hydraulic gradient in the till and glacio-fluvial deposits aquifer is around 4.5/1000 south of Fláajökull. Hydraulic gradient in the basalt aquifer is around 3.5/1000 south of Fláajökull, around 3.9/1000 south of Skálafellsjökull and around 30/1000 in Hali. Time evolution of the groundwater level in the till and glacio-fluvial deposits aquifer show clear recharge events by rainfall, by snow melt, and by glacial meltwater. Recharge by rainfall events occur within 24 hours of the precipitation event, at least when the rain is > 10 mm ( fig. 7 and 8). Snow melt events are identified in February-March 2022 ( fig. 7 and 8), and also on a shorter time scale in January 2022. When precipitation is snowfall and the snow cover last for more than one day, the lag between a snowfall precipitation event and the recharge of the groundwater is visible ( fig. 7 and 8), corresponding to the time for the snow to melt. In September the quicker increase of the water level in borehole September 2022 that can not be accounted for only by the precipitation events during the same period. ASK105 lies at 4.2 km from the nearest glacier terminus; boreholes further away show a similar but smaller increase during the same period of time: ASK103 at 6.2 km: +0.2 m; ASK102 at 7.4 km: +0.22 m; HA16 at 7.4 km: +0.19 m.
Temperature data from FLA4 borehole exhibit 4 plateaux (constant value over a period of time) of temperatures between 4.2 to 5.4 °C ( fig. 12). These plateaux correspond to every time the water level is lower than 24.1 m a.s.l. (fig.   12). We interpret that as an upward leakage from the basalt aquifer, triggered when the water level in the till and glaciofluvial deposits aquifer is lower than the piezometric level in the confined basalt aquifer. The groundwater level in the basalt aquifer must then be very constant. The temperature measured in the basalt aquifer in ASK105 (1.6 km from FLA4), from 5 to 9 °C, corroborates that hypothesis.
The high EC values near the coastline (table 2)