Modern silicon dynamics of a small high-latitude subarctic lake

. High biogenic silica (BSi) concentration occurs sporadically in lake sediments throughout the world, however, the processes leading to high BSi concentrations varies. While BSi formation and preservation is expected to occur in silica-rich environments with high dissolved silicon (DSi) concentrations such as volcanic and hydrothermal inputs, the factors and mechanisms explaining high DSi and BSi concentrations in lakes remain unclear. We explored the factors responsible for the high BSi concentration in sediments of a small, high-latitude subarctic lake (Lake 850). To do this, we combined 5 measurements of variations in stream discharges, DSi concentrations and stable Si isotopes in both lake and stream water with measurements of BSi content in lake sediments. Water, radon, and Si mass balances revealed the importance of groundwater discharge as a main source of DSi to the lake, with groundwater-derived DSi inputs 3 times higher than those from ephemeral stream inlets. After including all external DSi sources (i.e., inlets and groundwater discharge) and estimating the total BSi accumulation in the sediment, we show that diatom production consumes up to 79% of total DSi input. Additionally, low 10 sediment accumulation rates were observed based on the dated core. Our ﬁndings thus demonstrate that groundwater discharge and low mass accumulation rate can account for the high BSi accumulation during the last 150 cal. yr BP. Globally, lakes have been estimated to retain one ﬁfth of the annual DSi delivery into the Challa, Tanzania/Kenya (Barker et al., 2013) or as shown here in lakes with sufﬁcient DSi inputs from groundwater source that supply DSi during the growing season to alleviate potential DSi limitation of diatom growth. In addition, lakes with high autochthonous carbon production and deposition combined with very low mean sedimentation rates generally found in Arctic lake sediments (Wolfe et al., 2004), as well as lakes with low-relief watershed morphology and with low stream input that yield low quantities of ﬁne-grain clastic input, are potential systems for high BSi accumulation (Conger, 1942). These water bodies with high BSi accumulation act as important sinks of Si in the global Si cycle. Our results support the importance of groundwater in the lake silicon budget and suggest that this process should not be overlooked in future investigations on BSi in lakes and global estimates of the terrestrial lake BSi sink.

where Q gw is the unknown groundwater discharge [m 3 d −1 ]; Q in and Q out are the discharge from inlet and outlet streams The calculation of Rn loss to the atmosphere was based on the empirical equation by MacIntyre et al. (1995): where k is the gas transfer coefficient [m d −1 ] based on an empirical relationship that relates k with wind speed and lake area (Vachon and Prairie, 2013), and α is the air-water partitioning of Rn corrected for salinity and temperature (Schubert et al.,95 2012).
Groundwater discharges (Q gw ) were estimated for August and September 2019. For the remainder months, we interpolated the estimated values by assuming two different scenarios of i) constant or ii) variable groundwater inflows over the year (see Appendix A1) for variable groundwater inflows scenario).

Water balance 100
The lake water balance was calculated from the volumetric water balance equation: where ∆V is the change in lake water volume, Q in and Q out are the stream inflow and outflow, respectively, Q gw is the groundwater inflow, P is precipitation, E is evaporation. Monthly summer precipitation of 48 mm (ANS, 2020a) has been considered to be included in the stream inflow term. Evaporation and precipitation have been shown to only have a small 105 contribution to the lake water balance, and thus they are considered negligible here (Shemesh et al., 2001).

Silicon mass balance
The DSi flux into and from the lake is calculated as φ = Q · c, where Q is discharge [l s −1 ] and c is DSi concentration [mg SiO 2 l −1 ]. The DSi balance is then calculated as: where ∆DSi is the change of lake DSi [mg SiO 2 yr −1 ], and φ in , φ out and φ gw are the DSi fluxes of the inlet, outlet, and groundwater discharge [mg yr −1 ], respectively. Finally, φ BSi represents the flux of BSi into the sediment [mg SiO 2 yr −1 ], and it was calculated as: φ BSi = (SAR · ρ dry · BSiwt% · A sed ) · 1000, 4 https://doi.org/10.5194/bg-2020-441 Preprint. Discussion started: 11 December 2020 c Author(s) 2020. CC BY 4.0 License.
where SAR is sediment accumulation rate [cm yr −1 ] calculated from the age-depth model (see Methods section 4.1.2), ρ dry is dry bulk sediment density [g cm −3 ], BSiwt% is the mean of BSi content in sediments, A sed is the area of sedimentary basin of the lake [cm 2 ] and 1000 is unit conversion.
Assuming steady-state (∆DSi = 0), DSi concentration in groundwater was then calculated by dividing φ gw from Equation 4 by Q gw . The groundwater DSi flux in ice-free period is dependent on inlet (φ in ), outlet DSi flux (φ out ) and BSi flux to sediment (φ BSi ). However, during ice-covered period, the φ gw is dependent only on φ BSi , if there is some (scenario 1, Appendix B) and 120 on differences of lake volume and DSi concentration. Thus, in order to solve Equation 4, φ BSi and lake DSi concentration changes in ice-covered period are required. The φ gw during ice covered period is calculated by a mixing model (see Appendix A2).
To constrain DSi concentrations in groundwater, we have examined 3 different scenarios considering different BSi fluxes (φ BSi ) to the sediment driven by the length of diatom production. Two scenarios with maximal and minimal monthly BSi 125 flux appear in the Appendix B aiming to describe maximal and minimal diatom production period and thus groundwater DSi concentrations. The scenario better describing recent diatom production considers that the diatom growing season and, thus, the BSi flux occurs in 4 months, from June until August, in a year (Shemesh et al., 2001), and that scenario is presented here.

Silicon isotope mass balance
The variability of the isotopic Si signature of the lake water is likely to be biologically driven and, therefore, was described 130 using a Si isotopic fractionation model. We hypothesize that the lake has sufficient inlet and groundwater supply to allow for DSi concentrations to remain high and that DSi is unlimited for diatom growth, thus, an open system model was used. The open system model (Varela et al., 2004) describes the expected diatom δ 30 Si BSi , as well as the post-uptake signature of the lake water δ 30 Si postuptake .
where δ 30 Si initial is the isotopic signature of the initial DSi source, ε is the fractionation factor of freshwater diatoms˘1.1±0.41 La Rocha et al., 1997), and f is the fraction of remaining DSi calculated as f = cout c initial , where c initial and c out are DSi concentrations before and after diatom production uptake. Thus, (1 − f) is the DSi utilization by diatom production. The initial DSi concentration is calculated through mixing model with knowledge of the discharges (Q in and Q gw ) and DSi concentrations 140 (c in and c gw ) of the endmembers .
The initial isotopic signature of lake DSi before diatom uptake is back calculated from δ 30 Si postuptake (Appendix A3). The known variables are the (1 − f) and the δ 30 Si postuptake represented either in the lake isotopic composition or in the lake outlet δ 30 Si out , if δ 30 Si lake = δ 30 Si out . Further, the groundwater isotopic composition can be calculated from the initial isotopic Si mixture before diatom uptake and fractionation through isotope mixing model (see Appendix A3).

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Similar to the Si mass balance, the isotope Si mass balance was examined through three scenarios that differ in BSi flux to the sediment representing different length of diatom production (Appendix B). As differences in BSi fluxes alter groundwater DSi concentrations, the isotopic composition is also changing. However, the scenario describing the recent lake functioning is used for the model presented here. Results of this model were compared with measured data of δ 30 Si BSi and δ 30 Si postuptake (which equals to δ 30 Si lake ). For validation, the groundwater δ 30 Si gw for monthly steady-state was calculated and compared 150 with data in the literature.  Table S1). Additionally, samples of two profiles of lake water from the deepest and a shallower part of the lake were collected in August and September 2019. All water samples were filtered directly in the field through a 0.45 µm cellulose Sterivex™-HV Durapore filter and acidified with HCl to pH 2 in the laboratory. DSi concentrations were analyzed by the automated molybdate-blue method (Strickland and Parsons, 1972) with a Smartchem 200, AMS System™ discrete analyzer at Lund University with an instrumental error of ±3.7%.

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For Rn analyses, surface water samples (maximum of 1.5 m depth from the surface or 0.5 m depth at the shallow depths) were collected from 5 different stations ( Figure 1, Table S1). A deeper water sample (4 m depth) was collected from the central deeper point of the lake to evaluate the potential stratification of Rn concentrations. Samples of water from the main inlet and the outlet stream were also collected. Water samples were collected in 1.5 l polyethylene terephthalate (PET) bottles with no headspace using a peristaltic pump. Water was pumped directly into the bottle and left overflowing to replenish the volume 165 at least three times to ensure minimal contact with air. Shortly after collection, Rn concentrations were determined using a Rn-in-air alpha spectrometer RAD7 (Durridge Inc.) coupled to the Big Bottle RAD H 2 O accessory (Durridge Inc.). All Rn concentrations were decay corrected for the time of collection.
Discharges from the inlet and outlet streams were determined by measuring the water velocity at 60% of the sampling point depth using the six-tenths-depth method (Turnipseed and Sauer, 2010) and creating a cross section through the tributary.

Sediment sampling
Two short (∼ 15 cm) sediment cores were sampled with a HTH gravity corer in March and August 2019 (Table S1). Both cores showed an undisturbed water-sediment interface. One of the cores was sliced directly in the field in 1 cm sections. Each section was weighed before and after freeze drying to determine water content, porosity, and wet and dry bulk densities. Total organic carbon (TOC) and total nitrogen (TN) analyses were carried out on all freeze dried samples, after packing 5 to 10 mg of dry 175 sediment into tin capsules. Five samples throughout the core were tested for carbonate content by acidifying with HCl and heating to 60 • C before the TOC measurements (Brodie et al., 2011). The measurements were done on a COSTECH ECS4010 elemental analyzer at the Department of Geology, Lund University, with the average analytical uncertainty for TOC of 0.3 wt% 6 https://doi.org/10.5194/bg-2020-441 Preprint. Discussion started: 11 December 2020 c Author(s) 2020. CC BY 4.0 License. based on duplicate analysis (n = 14). The carbonate content calculated as a difference in TOC between de-calcified and bulk sample was below 0.5 wt%, thus considered negligible.
Biogenic SiO 2 content in the sediment was analyzed by sequential alkaline extraction (Conley and Schelske, 2001). Freeze dried and homogenized samples were digested in 0.1 M Na 2 CO 3 (sample reagent ratio 0.03/40 g/ml) in a shaking bath at 85 • C for 5 hours. Subsamples of 100 µl were taken at 3, 4, and 5 hours and neutralized in 9.9 ml of HCl to examine for the dissolution of minerals. As no changes in the amount of total Si extracted during the time course of the dissolution, the mean BSi concentration from all the values was used to estimate BSi concentration with no mineral correction applied (Conley,185 1998).
All sediment samples were analyzed for radionuclide concentrations ( 210 Pb, 226 Ra, and 137 Cs) at Lund University. 210 Pb, 226 Ra, and 137 Cs were determined by direct γ-counting using a high-purity germanium detector ORTEC (Model GEM FX8530P4-RB). Freeze-dried and ground samples were sealed for at least 3 weeks before counting to ensure secular equilibrium of 226 Ra daughters. 210 Pb was determined through the 46 keV γ-emission and 226 Ra through the 351 and 609 keV γ-emission of its 190 daughter nuclide 214 Pb and 214 Bi, respectively. 137 Cs was measured by its emission at 662 keV. Self-absorption was measured directly, and the detector efficiency was determined by counting a National Institute of Standards and Technology sediment standard.
Sediment core chronologies were obtained by applying the Bayesian statistics approach with software package Plum (Aquino- To constrain the Rn mass balance, the second sediment core was used for equilibration experiments in order to determine Rn diffusion from underlying sediments and the Rn concentration representative of the groundwater discharging into the lake.

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Briefly, diffusive flux experiments were carried out in the laboratory by incubating ∼ 200 g of dry sediment placed into 500 ml PET bottles with Milli-Q® water, as described in Chanyotha et al. (2014). Using the RAD7 coupled to the Big Bottle RAD H 2 O accessory (Durridge Inc.), Rn concentrations were monitored for 14 hours. The rate of Rn diffusion from the sediment (F diff ) was derived from the exponential ingrowth of Rn concentrations with time. The bottles containing grab sediments were then stored for more than a month and periodically shaken. After this time, the Rn concentration in water was measured using 205 the RAD7 and converted into groundwater endmember activities using porosity and bulk density as described in Chanyotha et al. (2014).

Stable Si isotopes analyses
Stable Si isotope analyses were performed on diatoms recovered from sediment, lake, and stream water samples. Cleaned diatom material from a previous study (Shemesh et al., 2001) was processed for stable Si isotopes. Briefly, pure diatom samples 210 (∼ 0.8 mg) were digested with 0.5 to 1 ml of 0.4 M NaOH (analytical purity) at 50 • C for at least 48 hours. When all diatoms were dissolved, samples were diluted with Milli-Q® water to prevent precipitation and fractionation of amorphous silica, then neutralized by 0.5 to 1 ml of 0.4 M suprapur® HCl. The solutions were measured for their DSi concentration to obtain the Si recovery, which was between 90 and 100%. Sample solutions were purified for Si isotope analysis by cation-chromatographic separation using 1.5 ml cation-exchange DOWEX® 50W-X8 (200-400 mesh) resin following the method of Georg et al. (2006).

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Silicon from filtered water samples was purified using the same cation-exchange method (Georg et al., 2006). The international Si standard NIST reference material RM-8546 (former NBS-28) and laboratory standard Diatomite were prepared by alkaline NaOH fusion and purified following protocol by Georg et al. (2006).
The reference material RM-8546 (former NBS-28) and laboratory standards IRMM-018, Big-Batch, and Diatomite used in the VegaCenter were prepared by another type of fusion with LiBO 2 (Sun et al., 2010). Thus, our alkaline NaOH fused NBS-28 220 and Diatomite standards (Georg et al., 2006), purified in identical way as the samples, were matrix matched to contain 3 mg l −1 Li IPC-MS standard. Similarly, all purified samples were diluted to a concentration of 3 mg l −1 of Si in 0.12 M SeaStar HCl matrix and doped with Li to contain 3 mg l −1 Li to match the standard matrix.
The stable isotope measurements were carried out on a NuPlasma (II) HR multi-collector inductively conducted plasma mass spectrometry (MC-ICP-MS, Nu Instruments™) with an Apex HF desolvation nebulizer at the Vegacenter, Swedish Museum 225 of Natural History, Stockholm. The 28 Si signal intensity of full procedural blanks was determined to be less than 0.35% of the total signal intensity, thus no sample contamination was observed. Silicon isotope data are reported as deviations of 30 Si 28 Si and 29 Si 28 Si from the NBS-28 reference solution in ‰, denoted δ 30 Si and δ 29 Si as follows: Each sample was measured three times, bracketed by NBS-28 in between, and full chemical replicates for all samples 230 (n = 25, total measurements = 180) were measured. Secondary reference materials Diatomite, Big-Batch, and IRMM-018 were measured throughout all measuring sessions in a period of 3 years, with averages of δ 30 Si = 1.26 ± 0.19 ‰ (2SD repeated , n = 219) for Diatomite, δ 30 Si = −10.64 ± 0.18‰ (2SD repeated , n = 77) for Big-Batch, and δ 30 Si = −1.77 ± 0.18‰ (2SD repeated , n = 100) for IRMM-018 for quality control purposes. All secondary reference material values were in good agreement with values from a previous interlaboratory comparison (Reynolds et al., 2007). The reproducibility of all samples was > 0.2 ‰. At 235 the Vegacenter laboratory, the long-term precision for δ 30 Si is 0.15‰ (2SD).

Lake water chemical and isotopic properties
Lake 850 is a subarctic lake in a region with strong seasonality. The discharge from inlets and the outlet streams show a decreasing trend throughout the ice-free period from June through September (Table 1). The highest water flow rates are 240 observed during the snowmelt period (June and July). Inflow from the stream inlet to the lake in August is low, and both inlets are dry in September.
During the ice-free period direct surface precipitation contribution from the watershed, was estimated from the average precipitation of 48 mm month −1 (ANS, 2020a). With the watershed area of 0.35 km 2 (Rubensdotter and Rosqvist, 2003), precipitation results in 0.65 l s −1 , which represents only 1.4% of the lake volume. Similar or higher discharges are observed 245 in the stream inlets from July to August. Therefore, the influence of precipitation on the water mass balance is limited. The calculated lake water residence time during the high-flow regime in June, defined as lake volume (1.2 · 10 5 m 3 ) divided by the lake outlet discharge (Table 1), is 55 days. During the rest of the year, the lake water residence time is more than 1 year.
A lower inlet DSi concentration of 2.34 ± 0.05 mg l −1 is observed during snow melt in June compared to July and August, when the inlet DSi concentrations increase to 4.79 ± 0.05 mg l −1 and 5.05 ± 0.12 mg l −1 , respectively. The lake outlet DSi concentration shows little variability, with the lowest concentration of 0.94 ± 0.01 mg l −1 in July and only a small increase up 255 to 1.12±0.03 mg l −1 towards the end of the summer season in August. In September, when the inlet streams are snow covered, the DSi concentration in the outlet stream is the same as the lake water concentration at 1.37 ± 0.01 mg l −1 .
The stable Si isotope signatures of the lake, inlet, and outlet streams vary during the year. The heaviest lake δ 30 Si lake signature, 1.27 ± 0.15‰, is observed during the ice-cover period, and the lightest signature, 0.73 ± 0.10‰, occurs during the snowmelt in June (Table 1). In June, the inlet has a lighter δ 30 Si in of 0.02 ± 0.10‰, whereas in August the inlet isotopic 260 signature 0.78 ± 0.15‰ has similar values as the lake. The δ 30 Si out of the outlet in June is slightly heavier (0.89 ± 0.10‰) compared to the lake δ 30 Si lake . In July the outlet δ 30 Si out is lighter than the inlet one (Table 1). During the remainder of the year, the outlet δ 30 Si out is closely similar to the lake and inlet δ 30 Si lake .

Groundwater discharge
Surface lake Rn concentrations range between 94 Bq m −3 to 136 Bq m −3 in August and from 96 Bq m −3 to 126 Bq m −3 in 265 September. Dissolved Ra in lake waters is assumed to be similar to those found in other lakes in the region (1.4 ± 0.6 Bq m −3 ).
However, the measured Rn inputs (the stream inlets) due to Ra decay were below 0.5%, compared to the net excess of Rn delivered by groundwater discharge. Thus, the inlet Rn flux was neglected in the total Rn balance.
There was no significant vertical stratification of Rn concentration with Rn concentrations in deep waters (105 ± 26 and 79 ± 24 Bq m −3 ) in August and September, respectively. Equation 1 was solved analytically to obtain the amount of ground-270 water discharging into the lake (Q gw ) in August and September 2019. Uncertainties of individual terms were included in the estimation of the associated uncertainty (NORM, 1995;Taylor and Kuyatt, 1994).
Using the average wind-speed for 48 h period prior sampling ( Rn inputs from groundwater are required to balance the Rn losses from the lake. The Rn flux into the lake through groundwater discharge is calculated to be 166 ± 43 Bq m −2 d −1 and 180 ± 40 Bq m −2 d −1 in August and September, respectively. Considering the lake area of 20 000 m 2 and the Rn concentration in groundwater obtained from incubation experiments (10626 ± 1720 Bq m −3 ), groundwater fluxes are 3.56 ± 1.25 l s −1 and 3.88 ± 1.06 l s −1 for August and September, respec-290 tively. Note that this is a conservative estimate for groundwater fluxes, because we use the highest measured Rn concentration as the endmember.
Due to the lack of Rn measurements for the entire year, we estimated groundwater inputs for the months where no sampling was carried out using two scenarios: (i) constant groundwater inflow of 3.73 ± 1.25 l s −1 , calculated as the mean of the August and September data; and (ii) modelled groundwater inflow based on groundwater fluxes obtained from a lake survey in the 295 Abisko region in 2018-2019 (C. Olid, unpublished data), which ranged from 1.55 ± 1.09 L s −1 to 11.20 ± 2.34 l s −1 ( Figure   2). The annual Rn fluxes follow a pattern of a distinct peak in discharge in June and a gradual decrease towards July -October, reaching the base-flow level in November ( Figure 2). The ratio between the groundwater Rn flux in September in Lake 850 and the groundwater Rn fluxes from the lake survey was used to model the missing groundwater Rn fluxes in Lake 850 ( Figure   2, Appendix A1).

Age-depth model, lithology and mass accumualtion rates
The age-depth model for the sediment core is shown in Figure 3. The average sediment accumulation rate (SAR) was estimated to be 0.083±0.041 cm yr −1 , which equals a sediment accumulation rate of 12±6 yr cm −1 and a mass accumulation rate (MAR) of 16.0 ± 9.3 mg cm −2 yr −1 . The presence of mosses in the sediment was observed during the core processing and also was described in the sediment lithology by Shemesh et al. (2001). Changes in the sediment content of aquatic or terrestrial mosses, are a result of a potential groundwater inflow. This accumulated water is released through the outlet when the lake ice starts to melt in May-June, and the outlet discharge is thus high (Table 1). After this period, lake-level is stabilized and groundwater 325 replenishes the lake original volume during short periods over the summer.
When groundwater discharge is assumed to be constant (Scenario i, 3.73 ± 1.25 L s −1 ) based on our data from August and September, the lake shows annual lake-level changes up to 1.9 m ( Figure 5 and A1, blue line). From July to December, the lake volume is restored by the groundwater inflow, and, on the annual time scale, the lake-level would increase around 2 m every year ( Figure 5, blue line).

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Using the modelled annual groundwater inflow (Scenario ii, Figure 2), limited lake-level changes were observed. The maximum lake-level decrease is 95 cm during summer ( Figure 5 and A1, green line), but groundwater discharge restores lake-level during upcoming months. Taking into account the uncertainties, lake-level variation can be as great as 2.4 m or none ( Figure   5 and A1, green shading). This scenario with the smallest lake-level changes is in agreement with previous results of oxygen isotopes mass balance (Shemesh et al., 2001). Therefore, we used this water balance model further for the Si balances.

Silicon and Silicon isotope mass balance
BSi accumulation occurs in conditions when the total DSi influx is higher that the stream DSi outflux. Therefore, we construct a Si mass balance based on stream inlets and the outlet. The DSi influx through the inlet stream is not sufficient to maintain lake DSi concentration at steady-state in June (red and blue triangles, Figure 6A). In contrast, in July and August sufficient DSi enters the lake to supply the outlet DSi flux. The monthly inlet DSi flux is between 0.22 ± 0.11 to 0.62 ± 0.31 kg SiO 2 day −1 , 340 while the outlet DSi flux ranges from 0.19 ± 0.10 to 2.21 ± 1.11 kg SiO 2 day −1 . However, diatom production is an additional sink of Si by creating a BSi flux into the sediment. The DSi influx is, thus, not sufficient to account for both the DSi outflux and the BSi flux into the sediment ( Figure 6A). Therefore, an additional external source (i.e., groundwater discharge) must supply additional DSi to compensate for the average BSi flux (2.9 mg SiO 2 cm −2 yr −1 ) into the sediment.
Groundwater discharges from scenario ii ( Figure 2) were used to build a Si mass balance and a Si isotope mass balance.

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Here, we assume that the recent BSi flux into the sediment occurs only during the growing season (from June until September) ( Figure 6A; Shemesh et al., 2001). The missing DSi flux resulting from the mass balance was considered to originate from the groundwater flux, and thus, we use this flux to calculate back the groundwater DSi concentration and isotopic signature.
During the diatom growing season, BSi flux into the sediment increases up to 1.76 ± 0.87 kg SiO 2 day −1 (magenta line, Figure 6A), which produces DSi deficiency in the lake. To balance this deficiency, groundwater discharge must supply between 350 1.62±1.21 and 3.39±1.77 kg SiO 2 day −1 during the diatom growing season (cyan line, Figure 6A). Considering the modelled groundwater discharges derived from Rn mass balance, the DSi concentration in the groundwater is estimated to range from 3.50±1.68 mg l −1 to 5.85±2.99 mg l −1 from diatom growth (cyan line, Figure 6B). During the ice-covered period, the diatom growth ans thus BSi flux into the sediment is considered to be negligible, while groundwater is still flowing into the lake.
The winter groundwater concentration is calculated from the difference in the lake concentration from September (1.02 ± 355 0.91 mg l −1 ) to March (2.51 ± 0.35 mg l −1 ) (Appendix A2). Therefore, the groundwater discharging into the lake from late-October until mid-June is the only water inflow with a DSi concentration of 6.95 ± 4.90 mg l −1 .
The Si isotopes mass balance using the open fractionation model (Varela et al., 2004) shows that the higher demand of DSi in the productive months ( Figure 6A, B) needs to have a lighter isotopic composition in order to produce the δ 30 Si BSi of 0.07 ± 0.43‰ measured on diatoms preserved in the sediment. The isotopically lighter source is assumed to be groundwater 360 discharge, with calculated ranges from −0.55 ± 0.55‰ in July to 0.23 ± 0.58‰ in September ( Figure 6C). Using the modelled groundwater δ 30 Si, the expected δ 30 Si BSi in all productive months varies from −0.49±0.49‰ to −0.01±0.56‰ (not shown), values that are in agreement with the sediment BSi of δ 30 Si BSi = 0.07 ± 0.43‰. The production consumes from 63% of the initial DSi in June, 77% in July and September, and 79% in August. During the ice-covered period from late-October until mid-June, the groundwater base flow is considered to be constant, calculated from the difference of the lake isotopic signatures 365 from September until March (Appendix A3), and thus the δ 30 Si gw = 1.45 ± 2.58‰ ( Figure 6C).

Discussion
Lake 850 is unusual in terms of both the DSi and BSi concentration in water and sediment, respectively. The maximum DSi concentration of 2.51 mg SiO 2 l −1 in March is among the top 10% of lakes in Northern Sweden (Bigler and Hall, 2002). The average BSi content in the lake sediment of 40 wt% (Rosén et al., 2010) places Lake 850 in the upper 6% of lake sediments 370 studied worldwide (Frings et al., 2014). Although several factors, including the morphology of the watershed (Jenny, 1941;Rubensdotter and Rosqvist, 2003), diatom production and low detrital input (Conger, 1942), vegetation (Struyf et al., 2010), and preservation potential (Ryves et al., 2003) are known to affect sedimentation regimes and BSi accumulation resulting in a diatom-rich sediment, we show here that groundwater input is an important factor leading to the large BSi accumulation in Lake 850.

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The combined results from the water, Rn, and Si mass balances indicated the importance of an external source of DSi through groundwater discharge. Groundwater inflow was the primary water and DSi supply to the lake, with a contribution about 3 times higher than the stream inlets ( Figure 6A). The Si and Si isotope mass balance models showed that groundwater DSi concentration and isotopic composition varied during the ice-free period, compared to the ice-covered period, when they were stable ( Figure 6B, C).

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The significance of groundwater on lake Si cycle is also evidenced by the relatively lighter stable Si isotope signature of diatoms from sediment, which suggests that groundwater is the primary DSi source for diatoms. Stream inputs could also be a source of DSi for diatoms, especially in early spring, when snowmelt can deliver isotopically lighter DSi by displacement of shallow groundwater into the stream inlet (Campbell et al., 1995). However, spring snowmelt water and groundwater in June are likely to have the same isotopic composition ( Figure 6C) because the same factors, e.g., short residence time in 385 the watershed are present in both types of water. Thus, only by using mass balance is the quantification of each DSi source apparent, providing evidence that groundwater supplies almost 4 times more DSi compared to streamflow in June. Our results suggest that the groundwater supply plays a crucial role in providing DSi for the production of diatoms and accumulation of BSi in Lake 850.

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The water balance coupled with the Rn mass balance indicated that groundwater discharge is an essential water source for the lake. Both models of groundwater inflow (constant and varying groundwater inputs) demonstrated changes in lake volume as a result of high-water discharge at the outlet of the lake during spring snowmelt. More pronounced changes in lake volume were observed in scenario i, where constant groundwater inflow was assumed ( Figure 5, blue line). However, because the oxygen isotope data showed negligible evaporation and precipitation effect on lake volume change (Shemesh et al., 2001), this model is 395 not considered to be the most realistic. Scenario ii, which considered a variable groundwater flow ( Figure 5, green line) seems to be more realistic. The modelled groundwater hydrograph (Figure 2) is comparable with the hydrograph of the neighbouring river Miellejokha ( Figure S1) and resembles the hydrographs of groundwater discharge in studies of high-altitude lakes from other regions (Clow et al., 2003;Hood et al., 2006;Huth et al., 2004;Liu et al., 2004). The results from this model show that groundwater discharge is up to 5 times higher values than the lake water outflow through the outlet. Similarly, groundwater 400 discharge brings from 3 to 24% of the lake volume depending on the month.
The water balance based on modelled groundwater inflow suggests that lake-level changes throughout the year are within a range of 0.95 m ( Figure 5, green line), and, thus, lake area and average depth also vary throughout the year. Therefore, the underlying assumptions of constant depth and area are likely overestimating lake-level change.
For a more precise model of lake-level, lake volume variations and a detailed bathymetry of Lake 850 is needed. However, the importance of the ground-405 water contribution to Lake 850 supports the evidence that groundwater should be considered as an important water and DSi 13 https://doi.org/10.5194/bg-2020-441 Preprint. Discussion started: 11 December 2020 c Author(s) 2020. CC BY 4.0 License.

The role of groundwater in Si concentration mass balance and Si isotope mass balance
The lake Si mass balance ( Figure 6A) shows that modelled groundwater concentration and flux of BSi vary through the year, 410 which is similar to observations from Crystal Lake in Wisconsin (Hurley et al., 1985). Seasonal variations in groundwater DSi concentration related to discharges were also observed in Canadian rivers with groundwater inputs (Maavara et al., 2018).
Moreover, the calculated BSi flux into the sediment is comparable (or higher) with BSi fluxes observed in some of the North American Great Lakes (Conley, 1988;Newberry and Schelske, 1986;Schelske, 1985) and lakes with diatomaceous sediment in the Arctic (McKay et al., 2008;Kaplan et al., 2002;Tallberg et al., 2015).

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The model of stable Si isotopes shows little variation during the ice-covered period, as no diatom production is expected. The δ 30 Si of groundwater for the ice-covered period ( Figure 6C) falls into the range of measured groundwater isotopic composition worldwide, which ranges from −1.5 to 2‰ (Frings et al., 2016). However, the groundwater signature δ 30 Si gw is heavier than found in other groundwater studies (Georg et al., 2009;Opfergelt et al., 2011;Ziegler et al., 2005), which may reflect lower dissolution of primary minerals, longer groundwater residence time, and possibly some clay mineral formation in the 420 groundwater pathway (Frings et al., 2016;Pokrovsky et al., 2013) during the ice-covered period. Further, no diatom production, and thus no associated Si isotope fractionation, is expected in winter. Therefore, the δ 30 Si lake is influenced by the input of δ 30 Si gw only and not by diatom production. The δ 30 Si lake measured in March is slightly lighter than all modelled δ 30 Si gw for the ice-covered period, which can be explained by diatom dissolution in the uppermost sediment layers. However, if the uncertainties of the modelled groundwater isotopic composition are taken into account, the lake signature is within the same 425 range as the groundwater signature. Therefore, no additional processes must be present during the ice-covered period, and the groundwater isotopic signature is reflected in the lake isotopic signal. With snowmelt, the decrease of the δ 30 Si gw reflects the increase in weathering of primary minerals and decrease in the groundwater residence time due to higher discharges, as also observed in Arctic rivers (Pokrovsky et al., 2013).
The greatest variation in the isotopic signature of groundwater occurs in August, when the groundwater isotopic composition 430 is fully dependent on the changes in BSi flux into the sediment. As the yearly BSi accumulation occurs during the growing season which is only 4 month, the groundwater must bring additional DSi to supply diatom production. Hence, the isotopic model calculating the groundwater isotopic composition shows δ 30 Si gw comparable with values for groundwater reported in the small number of other studies (Frings et al., 2016;Opfergelt et al., 2011). Further, the calculated δ 30 Si BSi based on the initial mixture of the modelled groundwater and stream inlet signature gives results within the range of the measured δ 30 Si BSi .

Model uncertainties
The largest sources of uncertainty in the water and silicon balance models ( Figure 5, SA1 and 6) are the discharge uncertainties of the inlet and outlet and the winter groundwater discharges. The spring snowmelt is dynamically changing the inlet and outlet discharges, as has been observed on rivers in the area, such as Miellejohka ( Figure S1). With only a single sample every month, there is no information on variation of the stream on a finer temporal scale. Thus, monthly stream flow and the modelled groundwater discharges might be over-or underestimated. Further, the uncertainties in isotopic model and the isotopic composition of the groundwater were propagated from the mass balance model and from the stable isotopic measurements, especially in the outlet water in August.
Another source of uncertainties in the Si and Si isotope mass balance models originates from the uncertainties on the agedepth model. The uncertainties on MAR, which are calculated from the SAR and the densities are as high as 50%. It is 445 likely due to changes in the sediment composition and increased content of mosses. Therefore, the BSi flux to the sediment carries similar or higher uncertainty. As a result of those uncertainties, the modelled groundwater concentrations and isotopic composition are ranging greatly.
Additionally, the diatom preservation efficiency, which is globally around 3% in the oceans (Treguer et al., 1995), and, in deep lakes around 1−2% (Ryves et al., 2003) of the total diatom production, suggests that 97−99% of diatom BSi is redissolved 450 in the water column in those environments. However, no estimates of sediment preservation efficiency are available for small, cold lakes such as Lake 850. Therefore, the mass balance can be slightly underestimated, in case that the BSi flux into the sediment, which was calculated from the sediment record represents only a fraction of the total production. To eliminate this source of uncertainty annual monitoring of diatom production and accumulation would be needed.
Uncertainty also results from the variability among sediment cores in their BSi content. BSi concentrations in the sediment 455 vary from 13 to 40 wt% in different cores (this study; Rosén et al., 2010). We have tested the combination of the MAR (16.0 mg cm −2 yr −1 ) reported from this study with the highest BSi of 40.3 wt% from a companion core from Lake 850 (Rosén et al., 2010) to evaluate the impact of BSi flux on the groundwater concentrations. The yearly BSi flux would increase 2.2 times, which would result in 1.6 to 2.3 times higher groundwater DSi concentration to support the BSi flux and keep the Lake 850 at steady-state. However, the BSi content is variable within the sedimentary basin, and thus the sedimentation rate is a 460 crucial factor for the estimate of BSi accumulation. For future model improvement a monitoring of all inlets, groundwater, pore water, and the outlet together with sediment traps to constrain the production, BSi flux and dissolution would be needed.

Conclusions
The diatom-rich sediment in Lake 850 is formed because of high DSi supply by groundwater during the growing season for diatoms coupled with low sedimentation rates, which fosters a large accumulation of diatoms in the form of BSi. Water and Si 465 mass balance demonstrated the importance of groundwater as a source of water and DSi, with fluxes that are 3 times greater than stream input. Groundwater supplies lighter δ 30 Si, which is reflected in the lighter diatom δ 30 Si signature. By quantifying the groundwater inputs, the Si and Si isotopic mass balances allowed for the estimate of the stable Si isotope signatures of groundwater throughout the year. The modelled isotopic signature of groundwater falls into the same range as the world groundwater δ 30 Si signature (Frings et al., 2016;Sutton et al., 2018).

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The results from our study can be applied more broadly to other lakes to evaluate factors governing the accumulation of diatom-rich sediment. BSi rich sediments are likely to be found in lakes situated on silica-rich bedrock, such as in Lake that supply DSi during the growing season to alleviate potential DSi limitation of diatom growth. In addition, lakes with high autochthonous carbon production and deposition combined with very low mean sedimentation rates generally found in Arctic 475 lake sediments (Wolfe et al., 2004), as well as lakes with low-relief watershed morphology and with low stream input that yield low quantities of fine-grain clastic input, are potential systems for high BSi accumulation (Conger, 1942). These water bodies with high BSi accumulation act as important sinks of Si in the global Si cycle. Our results support the importance of groundwater in the lake silicon budget and suggest that this process should not be overlooked in future investigations on BSi in lakes and global estimates of the terrestrial lake BSi sink.   available (June, July and September). Rn fluxes through groundwater during the ice-covered period were assumed to be 40% lower than those measured in September (C. Olid, unpublished data; Table A1). The groundwater Rn flux from November to April was assumed to be constant and equal to April estimations. A2 Groundwater DSi and δ 30 Si calculations during the ice-covered period The groundwater concentration c gw in during the ice-covered period was calculated from the groundwater discharge, the lake 660 volume from the water balance, and the lake DSi differences between September and March though a mixing model: where c Mar is the lake concentration in March, c Sept is the lake concentration in September, V Sept is the lake volume in September, and V gw in is the total volume of water brought by groundwater in 8 months. The total water volume brought by groundwater in 8 months was calculated from the modelled groundwater winter discharges (Figure 2). The lake volume in 665 September is taken from the water balance model, where the modelled groundwater discharges were used ( Figure 5 and A1, green line).
Similarly, the c gw in during the ice-covered period in the scenario with continuous BSi flux to the sediment for period of 8 month was calculated by adding flux into the sediment into the mixing model: where the φ BSi is the total flux of BSi to sediment in 8 months. The BSi flux into the sediment for 8 months was calculated as a sum of the continuous monthly BSi flux from September until March. Figure A1. Estimated lake-level variation between neighbouring months throughout the year with uncertainties as shading. No lake-level change is depicted by the solid purple line. The blue line presents lake-level increase or decrease from one to another month with constant groundwater discharge (scenario i), and the green line is the rate of lake-level variation with modelled groundwater discharges (scenario ii).
The isotopic composition of the groundwater during the ice-covered period, based on measured data was calculated as: where δ 30 Si Mar is the lake isotopic composition in March, δ 30 Si Sept is the lake isotopic composition in September, c Sept is 675 the lake concentration in September, c gw in is the concentration of groundwater during the ice-covered period (eq. A1 or A2, depending on model), V gw in is the total volume of water brought by groundwater in 8 months, and V Sept is the lake volume in September. Due to the high groundwater input in Lake 850 proven by the Rn mass balance ( see section Results: 5.2 Groundwater dis-680 charge), the inlet δ 30 Si does not represent the initial δ 30 Si used by diatoms. Therefore, the initial δ 30 Si of DSi is a mixture of groundwater δ 30 Si and inlet δ 30 Si flux weighted. The δ 30 Si initial in was calculated from δ 30 Si postuptake , which equals to δ 30 Si lake as: Further the groundwater δ 30 Si gw which fits the measured data and keeps the steady-state, was calculated as: Appendix B: Mass balance models: Extreme Si and Si isotope mass balances The Si and Si isotopic mass balances models were tested for two extreme scenarios to model the highest and the lowest possible concentration of groundwater brought into the lake. Further, a scenario based on recent diatom growth season is modelled (Table   B1). The DSi concentration and isotopic composition from the inlet and outlet streams are similar in all three scenarios. The

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groundwater DSi concentrations and isotopic composition are calculated from the groundwater fluxes influenced by the three potential BSi fluxes into the sediment, representing three possible lengths of diatom production. All scenarios are using the open system isotopic model (Varela et al., 2004) to describe the effect of diatom production on the lake water δ 30 Si signature.
The difference between the first and second scenario is the BSi flux into the sediment: (1) considers BSi flux into the sediment throughout the whole year representing lack of ice-covered period, and (2) BSi flux into sediment is present only from June 695 until September (Shemesh et al., 2001). Scenario (3) utilizes the open system isotopic model only for June, with no diatom production the rest of the year, and thus no fractionation in the lake, which describes lake behaviour with only short ice-free period. Here we describe only scenario 1 and 3, whereas in the main text scenario 2 is presented and discussed.  isotopic signature is δ 30 Si BSi = −0.01 ± 0.47‰, which is in agreement with the average measured δ 30 Si BSi in the diatoms from sediment.
This scenario assumes that the groundwater concentration during the ice-covered lake is recharging the lake DSi, while the BSi flux into the sediment is still present ( Figure B1B). Applying the mixing model (equation A2 and A3), groundwater DSi concentration (11.29 ± 1.07 mg l −1 ), groundwater discharge, lake volume change during the ice-covered period, and the 740 difference of the isotopic composition of the lake water between September (1.02 ± 0.24‰ ) and March (1.27 ± 0.10‰ ), the isotopic signature of the groundwater is calculated to be 1.45 ± 2.58‰ ( Figure B1C).

B2 Scenario 3: only 1 month of BSi flux into the sediment
The third scenario is based on the inlet and outlet DSi fluxes but assumes that diatom production occurs only in June. This scenario could occur if the climate would experience cooling and the diatom growth period would be extremely shortened.

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Additionally, this scenario demonstrated the highest groundwater concentrations during the growing season. The rest of the year diatom production, and so the BSi flux into the sediment, is negligible or zero. Therefore, the yearly accumulated BSi settles into the sediment within one month, which yields a BSi flux of 7.08 ± 3.62 kg SiO 2 per day (magenta line, Figure B1G).
In this scenario, groundwater input must be from 0.15±0.37 kg SiO 2 to 8.70±4.59 kg SiO 2 per day, and the DSi concentration ranges between 0.37 ± 0.69 mg l −1 to 8.99 ± 4.35 mg l −1 during the ice-free period (cyan line, Figure B1H). Similar to the 750 second scenario (in the main text), to restore the lake DSi concentration during the ice-covered period from lake-October to mid-June, groundwater DSi concentration is around 6.95 ± 4.90 mg l −1 .
Scenario 3 assumes the BSi flux into the sediment occurs only in June, and the rest of the year there are no processes causing stable Si isotope fractionation. This scenario originates from data in August and September, when the δ 30 Si of inlet, outlet and the lake are very similar. Only in June is there fractionation between the lake stream inlets and the lake, which is described by 755 the open-system-fractionation model. Therefore, the groundwater concentration in June increases to 8.99±4.35 mg l −1 ( Figure   B1H), with an isotopic signature of −0.04 ± 0.52‰( Figure B1I) to sustain the diatom production represented by BSi flux into the sediment. The production consumes 84% of the available DSi.
In July, August, and September the groundwater DSi concentration is low, as the lake does not have any production, thus no demand on the DSi. The isotopic composition of the groundwater is 0.23 ± 1.41‰, 0.75 ± 2.83‰, and 1.02 ± 0.53‰, 760 respectively ( Figure B1I). High uncertainties in the isotopic composition of the groundwater reflect the uncertainties in the stream and groundwater discharges and fluxes. the changes in climate and thus the ice-free period length. Our models aimed to estimate the changes in the lake DSi and Si balance in those extreme changes of growing season driven by changes in climate. However, the groundwater concentrations are commonly higher than the superficial streams (Frings et al., 2016;Maavara et al., 2018;Opfergelt et al., 2011), which is not the case in scenario 1 and 3. The groundwater DSi concentrations are lower than in the stream inlet during the ice-free period in those two scenarios ( Figure B1B and B1H), which suggest that those scenarios have either missing or surplus data 770 of the inlet and outlet DSi concentration and discharges. A more complex model with variable discharges of groundwater and stream inlets and outlet depending on precipitation end evaporation changes would be needed. Therefore, those two scenarios bring only a rough estimate hinting the changes in DSi and Si isotopic mass balances connected to changes in climate.