Quantifying nitrate dynamics in an oligotrophic lake using Δ17O

. The stable isotopic compositions of nitrate, including the 17 O anomalies ( 1 17 O), were determined twice in 1 yr (June and August 2007) in the oligotrophic water column of Lake Mashu, Japan. These data were then used to quantify the geochemical dynamics of nitrate in the lake, by using the deposition rate of the atmospheric nitrate onto the entire catchment area of the lake. The total amount of nitrate in the lake water decreased from 4.2 to 2.1 Mmol during the period between the observations, while the average 1 17 O values remained uniform at +2.5‰. The 1 17 O values corresponded to an small and uniform mixing ratio of atmospheric nitrate to total nitrate of 9.7 ± 0.8%. These results indicate that 0.52 ± 0.34 Mmol of the remineralized nitrate was fed into the water column through nitriﬁcation, while 2.6 ± 0.4 Mmol of nitrate was simultaneously removed from the water column by assimilation, during the period between the observations. The lake water dissolved nitrate was characterized by rapid removal through assimilation during summer until it was almost completely removed from


Introduction
Anthropogenic activities have led to increased emissions of fixed nitrogen from land to the atmosphere. Indeed, the amount of emitted nitrogen has almost doubled globally, with much greater increases occurring in some regions, and this fixed-nitrogen flux is expected to double again by 2030 . The increase in NO x emissions in East Asia has been particularly dramatic over the last decade (Akimoto, 2003;Zhang et al., 2007;Uno et al., 2007) owing to rapid growth in both industry and the number of automobiles. Most of the emitted NO x is transported eastward by the Asian monsoon and deposited in the western North Pacific, which includes Japan, as atmospheric nitrate (NO − 3 atm ) (Akimoto, 2003;Uno et al., 2007).
Excess fixed-nitrogen input has been linked to various environmental problems such as forest decline (e.g. Fenn et al., 1998), degradation of groundwater quality (e.g. Murdoch and Stoddard, 1992;Williams et al., 1996), eutrophication of coastal and open oceans (e.g. Paerl, 1997;Duce et al., 2008), and shifts in biodiversity (e.g. Tilman et al., 1996). In addition, significant declining trends in clarity have been detected in some highly transparent oligotrophic lakes, such as Danish Lake in Europe (Riis and Sand-jensen, 1998), Lake Tahoe in North America (Jassby et al., 1999), and Lake Mashu in East Asia (Figs. 1 and 2;CGER NIES et al., 2004). Atmospheric input of excess fixed-nitrogen nutrients could play a major role in this decline in clarity through an increase in phytoplankton in the water column (Riis and Sand-jensen, 1998;Jassby et al., 1994;Fukazawa, 2008).
Although water chemistry has routinely been measured in lakes, our understanding of the nitrogen cycle in oligotrophic lakes is limited, especially with respect to the fate of deposited atmospheric nitrate. Indeed, the fate of atmospheric nitrate deposited onto the hydrosphere is determined through a combination of several processes including (1) di- where the constant β is 0.5247 (Miller, 2002;Kaiser et al., 2007). In addition, 17 O is stable in the mass-dependent isotope fractionation processes; therefore, we can use 17 O as a novel conserved tracer of NO − 3 atm to determine the NO − 3 atm /NO − 3 total ratio ([NO − 3 atm ]/[NO − 3 total ]), regardless of partial removal through denitrification and/or assimilation subsequent to deposition using the following equation: where 17 O atm denotes the average 17 O value of NO − 3 atm , and 17 O lake denotes the average 17 O value of nitrate dissolved in the lake. Using both the estimated NO − 3 atm /NO − 3 total ratio and the rate at which NO − 3 atm is deposited into the lake, Michalski and Thiemens (2006) also successfully estimated the average nitrification rate in the lake.
The average δ 15 N, δ 18 O and 17 O values of atmospheric nitrate deposited onto the East Asian region have been determined through continuous monitoring at Rishiri Island ( Fig. 1; Tsunogai et al., 2010), which is located in the same prefecture as Lake Mashu in Japan. Moreover, the deposition rate of atmospheric nitrate has been monitored precisely at many observation sites in the East Asian region due to the transboundary air pollution in the area (EANET, 2008). Accordingly, the results will be applicable to atmospheric nitrate deposited onto Lake Mashu. Thus, in this study, we determined both the concentrations and stable isotopic compositions of nitrate in Lake Mashu, including the 17 O values, to quantify the NO − 3 atm /NO − 3 total ratio of nitrate and clarify the geochemical dynamics of nitrate in the water column. This study was conducted with a special emphasis on the fate of atmospheric nitrate deposited into the ultra-oligotrophic environment of the lake. In addition to evaluating the distribution, we also determined the temporal variations in nitrate in the lake to enable accurate quantification of the geochemical dynamics of nitrate in the water column, including the average seasonal variations throughout the year. The results of this study will be useful to clarify the reasons for the significant declines in clarity detected in highly transparent oligotrophic lakes. The findings presented herein will also help clarify the fate of atmospheric nitrate deposited onto the hydrosphere in general.

Site description
Lake Mashu is a dimictic crater lake located in the northern part of Japan(43 • 35 N, 144 • 32 E; Fig. 1), situated in a subalpine area 355 m above sea level and encircled by a steep and rocky caldera wall. The surface of the lake is covered with ice and snow from February to March. The autumn overturn occurs around December to January, while the spring overturn occurs around April to May (Nojiri et al., 1990).
The lake has a catchment area of about 32.4 km 2 , most of which is occupied by the lake surface, which comprises 19.6 km 2 ( Fig. 1; Horiuchi et al., 1985). The maximum depth of the lake is 211.5 m and the lake bottom is almost flat and covered with pumice deposits. There are no perennial streams entering or exiting the lake, and the surface level is approximately in a state of equilibrium, suggesting that the lake water supplied as rain water to the catchment area seeps out through the porous bottom, in addition to being lost via evaporation. The mean residence time of the lake water is around 110 yr (Ambe et al., 1988).
The lake water is ultra-oligotrophic, showing PO 3− 4 concentrations less than 0.1 µM (µM = µmol L −1 ) and NO − 3 concentrations less than 3 µM at the epilimnion (CGER NIES et al., 2004). In addition, the lake water is well oxygenated, regardless of depth or season, showing dissolved oxygen (DO) saturation ratios of 100 ± 5% (Fig. 3). Furthermore, the transparency (Secchi depth) of the lake was 41.6 m on 31 August 1931, which was the highest ever recorded among lakes worldwide (Yoshimura, 1932), surpassing that of Lake Baikal (40.5 m). However, the transparency has decreased to less than 30 m in recent years (Fig. 2;CGER NIES et al., 2004), likely in response to increased levels of phytoplankton in the water column (Haga et al., 1994;Fukazawa, 2008). The phytoplankton in the lake is primarily composed of diatoms and dinoflagellates, such as Fragilaria lapponica, Ceratium hirundinella, Dinobryon sertularia and Dinobryon sp. (Haga et al., 1994). The maximum chlorophyll-a concentrations in the water column are around 1 µg L −1 , being observed in the subsurface zone at depths ranging from 10 to 75 m in summer (Fig. 3;CGER NIES et al., 2004).
The entire catchment area of the lake has been designated as a specially restricted zone of the Akan National Park of Japan since 1934 to preserve the lake in its pristine form. Even trespassing on the lake shore has been strictly prohibited. As a result, atmospheric input of nutrients rather than local human activities are likely responsible for the increase in phytoplankton that has occurred in the water column (Fukazawa, 2008). The chances for lake water sampling have been restricted as well, usually to just a few days in summer. Furthermore, lake water sampling/monitoring that requires heavy instruments or high power electricity has been difficult because all equipment must be carried to the lake via a steep path on the caldera wall.

Sampling
Water samples were collected on 25 June and 24 August 2007 from the central sampling station of the lake (43 • 35 02 N, 144 • 32 03 E; Fig. 1) using a 2.0 L Niskin sampler (Nishimura et al., 1999) at depths of 0, 20, 50, 100, 150 and 200 m (Table 1). Each sample was transferred into 250 mL polyethylene bottles on the boat subsequent to being rinsed at least twice with the sample itself and then filtered through a pre-combusted Whatman GF/F filter (0.7 µm pore size) within a few hours of collection, after which the filtrate was stored in a refrigerator (4 • C) until analysis. The maximum retention period until analysis was two months. Additionally, the seston that collected on the filter was washed with pure water, placed in a plastic case and then stored in a deep freezer (−20 • C) to analyze the particulate organic nitrogen (PON) in the lake water.

Analysis
The concentrations of nitrate (NO − 3 ) and nitrite (NO − 2 ) were measured using a UV-detector HPLC by introducing 200 µl of the filtrate sample solution (Ito et al., 2005). To determine the stable isotopic compositions, nitrate in each filtrate sample was chemically converted to N 2 O using a method  . A summary of the procedures is presented below.
Aliquots of 45 ml were pipetted into 60 mL clean screwcap vials with butyl rubber septum caps. Next, 2 g of spongy cadmium were added, followed by 450 µl of a 1 M NaHCO 3 solution and 1.3 g of a reagent grade sodium chloride, which resulted in a pH of approximately 8.5 and a Cl − concentration of 0.5 mol L −1 . The samples were then shaken for 20-30 h on a horizontal shaker at a rate of 2 cycles s −1 to convert the nitrate in each sample to nitrite (NO − 2 ). Subsequently, 30 mL aliquots of the samples were decanted into clean 60 ml vials and then capped tightly with Teflon-lined septum caps. After evacuating the air from the head space and the sample solution for 20 min, 1.2 ml of degassed azide/acetic acid buffer was added to each vial via a syringe and the mixture was shaken vigorously to convert the nitrate (NO − 2 ) in the sample to nitrous oxide (N 2 O) using HN 3 . Because of the volatility and toxicity of HN 3 , all reactions were conducted using an original automatic reaction line. In addition, all exhaust was vented via a fume hood. After 30 min, the solution was made basic (pH > 13) by adding 0.6 mL of 6 M NaOH with a syringe and shaking to prevent residual HN 3 from escaping into the laboratory during subsequent isotopic analysis.
The stable isotopic compositions of N 2 O were determined using our Continuous-Flow Isotope Ratio Mass-Spectrometry (CF-IRMS) system Hirota et al., 2010), which consists of an original helium purge and trap line, a gas chromatograph (Agilent 6890) and a Finnigan MAT 252 (Thermo Fisher Scientific, Waltham, MA, USA) with a modified Combustion III interface (Tsunogai et al., 2000(Tsunogai et al., , 2002. First, approximately 5 ml of head space gas in each vial was sampled in a gas-tight syringe and injected into a helium sparging line via an injection port (Ijiri et al., 2003). The sample was then sent through a purification port packed with Ascarite II and magnesium perchlorate to remove both the CO 2 and residual H 2 O, after which it was collected into a final stainless steel trap immersed in liquid nitrogen. After changing the flow path, the liquid nitrogen bath was removed to introduce the sample into a PoraPLOT-Q analytical capillary column (0.32 mm i.d. × 50 m) at a column oven temperature of 30 • C, where the N 2 O was separated from any remaining CO 2 . The eluted N 2 O was then carried continuously into a Finnigan MAT 252 isotope-ratio-monitoring mass spectrometer with a specially designed multicollector system via an open split interface to monitor isotopologues of N 2 O + at m/z ratios of 44, 45 and 46 to determine δ 45 and δ 46 . Each analysis was calibrated using a machine-working reference gas (99.999% N 2 O gas in a cylinder) introduced into the mass spectrometer via an open split interface according to a definite schedule to correct for sub-daily temporal variations in the mass spectrometry. In addition, a working-standard gas mixture containing N 2 O of a known concentration (ca. 1000 ppm N 2 O in air) that was injected from a sampling loop attached to the sparging unit was analyzed in the same way as the samples at least once a day to correct for daily temporal variations in the mass spectrometry.
After the analyses based on the N 2 O + monitoring were conducted, another aliquot of head space was introduced into the same purge and trap line to determine the 17 O for N 2 O . Using the same procedures as those used in the N 2 O + monitoring mode, purified N 2 O eluted from the PoraPLOT-Q analytical capillary column was introduced into our original gold tube unit , which was held at 780 • C for the thermal decomposition of N 2 O to N 2 and O 2 . The produced O 2 purified from N 2 through separation using a MolSieve 5A PLOT column was subjected to CF-IRMS to determine the δ 33 and δ 34 by simultaneous monitoring of O + 2 isotopologues at m/z ratios of 32, 33 and 34. Each analysis was calibrated with a machine-working reference gas (99.999% O 2 gas in a cylinder) that was introduced into the mass spectrometer via an open split interface according to a definite schedule to correct sub-daily temporal variations in the mass spectrometry. In addition, a working-standard gas mixture containing N 2 O of known concentration (ca. 1000 ppm N 2 O in air) that was injected from a sampling loop attached to the sparging unit was analyzed in the same way as the samples at least once a day to correct for daily temporal variations in the mass spectrometry.
All δ values are expressed relative to air (for nitrogen) and VSMOW (for oxygen) in this paper. The obtained values of the sample-derived N 2 O were compared with those of international standards to calibrate the δ values of the sample nitrate on an international scale, as well as to correct for both the isotope fractionation during the chemical conversion to N 2 O and the progress of the oxygen isotope exchange between the nitrate-derived reaction intermediate and water (ca. 20%). We used both , the internationally distributed isotope reference materials for nitrate, to normalize the primary isotopic scale (Böhlke et al., 2003;Kaiser et al., 2007). In addition, several local laboratory standards that had been calibrated using the internationally distributed isotope reference materials were used for routine calibration purposes by measuring them in the same manner in which we measured the samples.
To calculate δ 15 N, δ 18 O or 17 O in the samples, the values in N 2 O derived from nitrate standards were first determined . The δ 15 N and 17 O values in the samples were then simply calibrated using calibration curves generated from the N 2 O derived from the nitrate standards. In the case of calculating δ 18 O for NO − 3 , we also corrected the oxygen exchange between the δ 18 O of NO − 3 and water to consider cases in which the δ 18 O of the water used to prepare the standards differed from the δ 18 O of the sample water. Thus, we used the following formula to correct for δ 18 O, where b is the intercept of the standards, m is the slope obtained using the standards and 18 O water is the δ 18 O difference between the sample water and standard water. Most samples had nitrate concentrations of more than 1 µM, which corresponds to nitrate quantities of more than 30 nmol in a 30 ml sample and is sufficient to determine δ 15 N,  (Michalski et al., 2002). Specifically, our 17 O values would be 0.02 ± 0.02‰ lower for the lake water nitrate if we had used linear approximation.
Nitrite (NO − 2 ) in the samples also interferes with the final N 2 O produced (McIlvin and Altabet, 2005) when the chemical conversion method is used to determine the stable isotopic compositions of nitrate (NO − 3 ). Therefore, it was necessary to correct for the contribution to accurately determine stable isotopic compositions of the sample nitrate. The lake water samples analyzed in this study contained NO − 2 at concentrations less than the detection limit, which corresponded to NO − 2 /NO − 3 ratios less than 10%. These findings indicated that there was minimal interference; thus, the results were used without any corrections.
The δ 18 O values of H 2 O in the filtrate samples were also analyzed using the method described by Ijiri et al. (2003), within an error of ±0.2‰. Both VSMOW and VSLAP were used to calibrate the values to the international scale. The concentrations and δ 15 N values of PON on the GF/F filters were analyzed using the method developed by . In this method, organic nitrogen on the filter is oxidized to nitrate using persulfate. Subsequent processes to determine δ 15 N values of nitrate were generally the same as the nitrate analyses described above. To calibrate the value to the international scale, several local laboratory standards that had been calibrated using the internationally distributed isotope reference materials (IAEA N1, USGS 25, and IAEA N2; Böhlke and Coplen, 1995) were used for routine calibration purposes by measuring them in the same manner in which the samples were measured. The PON data presented in this study had an error of ±0.3‰ for δ 15 N.

Distribution and temporal variations in nitrate in the water column
The concentrations and δ 15 N, δ 18 O and 17 O values of nitrate in the water column are presented in Table 1 and Fig. 4. The δ 15 N values of nitrate in Lake Mashu were characterized by 15 N-depletion. Indeed, the δ 15 N values in June were lower than those in Lake Superior, which had the lowest reported nitrate among temperate lakes worldwide in 1998 (Ostrom et al., 1998). The reasons for these findings are discussed in detail in Sect. 3.5. Moreover, all of the nitrate in Lake Mashu had low, but positive 17 O values ranging from +1.6 to +4.3‰, suggesting that the lake water contained some NO − 3 atm . In June, the concentrations of nitrate were almost uniform at 1.6 ± 0.1 µM (Fig. 4a), suggesting that the water was vertically well mixed during the spring overturn in 2007 and the removal rate of nitrate through assimilation was slow during the period between spring mixing and observation in June. To verify these findings quantitatively, we roughly estimated the apparent kinetic isotopic effects for the nitrate decrease from June to August, while assuming the lake to be a closed system. The extent to which a biological unidirectional transformation fractionates the values of δ 15 N and δ 18 O is given by the kinetic isotope effects, 15 ε and 18 ε, respectively. These are functions of the ratio of the reaction rate constants (k) for the molecules containing the two isotopes: where 14 k and 15 k denote reaction rate constants of the 14 N and 15 N isotopologues of nitrate, respectively, and 16 k and 18 k denote reaction rate constants of the 16 O and 18 O isotopologues of nitrate, respectively. The nitrate N and O isotope discrimination during nitrate assimilation have been quantified by mono-cultures of marine unicellular eukaryotic algae (Granger et al., 2004) and unicellular prokaryotic and eukaryotic plankton culture (Granger et al., 2010). While the range of N and O isotope effect amplitudes that were observed for cultures of assimilators ( 15 ε = 5-20‰) was large, O isotope effects were always equivalent to the corresponding N isotope effect ( 15 ε = 18 ε). Thus, nitrate N and O isotope ratios appear to co-vary linearly with a constant ratio of 1 (i.e., δ 18 O= δ 15 N) during nitrate assimilation. This biological imprint is also reflected in marine environments, with δ 18 O/ δ 15 N ratios of 1 being associated with nitrate assimilation on the surface of the ocean (Casciotti et al., 2002). In contrast, 15 ε: 18 ε ratios observed for denitrification in freshwater environments such as lakes or groundwater are generally around 0.6 (Bottcher et al., 1990;Lehmann et al., 2003). The fractionation factor of the 15 ε: 18 ε ratio during molecular diffusion of nitrate must be a function of the square root of the reduced molecular mass and should be around 0.5. Accordingly, we can differentiate the fractionation processes based on the relationship between 15 ε and 18 ε.
To calculate both 15 ε and 18 ε for the variation from June to August, the total inventory of nitrate in the lake water (N total ) and their average δ 15 N, δ 18 O and 17 O values (δ avg ) were calculated for each observation from the data describing their vertical distributions in the water column and the vertical distribution of area in the caldera (Horiuchi et al., 1985) using the following equations (Tsunogai et al., 2000): where C z , δ z and A z denote the nitrate concentration, each isotopic value (δ 15 N, δ 18 O and 17 O), and the area of the caldera at a depth z, respectively. We obtained the N total , δ 15 N avg , δ 18 O avg and 17 O avg for each observation in Tables 1 and 2, assuming that the data obtained at 0, 20, 50, 100, 150, and 200 m represented the average value from 0 to Table 2. Variations in the total inventory of nitrate (N total ) in Lake Mashu, together with those of atmospheric nitrate (N atm ) and remineralized nitrate (N re ). Each net and gross variation are presented as well, together with gross variation in atmospheric nitrate through depositions ( N atm ), remineralized nitrate through nitrification ( N nit ), and nitrate uptake through assimilation ( N up ) in the lake during the observations. All units are in Mmol N.  Table 2, the total nitrate inventory in the lake decreased from 4.2 to 2.1 Mmol (Mmol = 10 6 mol) from June to August. In accordance with this decrease, both δ 15 N and δ 18 O increased from −6.5 to −2.5‰ (δ 15 N) and from +3.4 to +7.6‰ (δ 18 O), while the 17 O values were almost uniform around +2.5‰ (Table 1). As a result, the observed variations in the δ 15 N and δ 18 O of nitrate between June and August in the lake corresponded to the apparent kinetic isotopic effects of 15 ε = 6.0‰ and 18 ε = 6.1‰. Both the 15 ε and 18 ε values, as well as the 15 ε: 18 ε ratios were reasonable when compared with values commonly observed during assimilation by eukaryotic phytoplankton (Granger et al., 2004(Granger et al., , 2010, such as diatoms or chlorophytes. Based on these findings, it turns out that the lake water is almost closed for nitrate from external/internal sources during the observation period. In addition, the assimilation of nitrate by phytoplankton (or by periphyton to some extent) in the lake was the major process that controlled temporal variation of nitrate in the lake. The uniform average 17 O values between June and August also support this conclusion because 17 O values of nitrate must be stable during partial removal through assimilation.
We even found evidence of nitrate removal through assimilation for depths below 150 m, where it was probably difficult for in situ assimilation to occur. This can be explained by the combination of active removal through assimilation in the upper hypolimnion (around the depths of 50 to 100 m) and vertical mixing of the water mass within the hypolimnion through vertical advection and/or eddy diffusion in the water column (Nojiri et al., 1990). The observed uniform profile of temperature and DO within hypolimnion also supported the active vertical mixing within the hypolimnion (Fig. 3).
Although in lake assimilation was the major process that controlled both the concentration and isotopic compositions of nitrate in the lake, we found definite evidence of a trace contribution of new nitrate from internal/external sources as well. Evaluation of the variations in the δ 15 N and δ 18 O values of nitrate at each depth assuming a closed system for each depth revealed that the 15 ε: 18 ε relationship was not 1 (Fig. 5). For example, the 15 ε: 18 ε was 3 at 20 m, while it was around 0.3 at 200 m (Fig. 5). These findings were partly due to vertical mixing with the surrounding layer. In other words, each layer was not as rigidly closed as we assumed when calculating 15 ε and 18 ε for each depth, but was vertically mixed with the surrounding layer through eddy diffusion and/or advection. The δ 15 N and δ 18 O values of nitrate at 20 m in August, which were close to those observed at 0 m, can be explained by the contribution of the 0 m nitrate to the 20 m nitrate. Most of the original nitrate at the 20 m depth in June was likely exhausted until August through active assimilation at that depth, so that the relative contribution ratio of nitrate from the surrounding layer might become significant in the 20 m layer.
In addition to vertical mixing, a slight contribution of new nitrate must have been responsible for the deviations in the 15 ε: 18 ε ratios from 1. The maximum 17 O value, which was obtained at the surface in August, was substantially higher than that obtained in June, suggesting that NO − 3 atm was deposited from the atmosphere onto the lake surface during summer stratification. Conversely, the minimum 17 O value obtained at the bottom (200 m) in August was lower than that obtained in June, suggesting that the accumulation of NO − 3 re remineralized from sinking organic nitrogen via nitrification at the bottom during summer stratification. Except for samples collected from the surface and the bottom, the 17 O values were almost uniform around +2.5 ± 0.4‰. Thus, while assimilation of nitrate was the major process that controlled the distribution and temporal variation of nitrate in the lake, deposition of NO − 3 atm to the surface and production of NO − 3 re through nitrification in and around the lake (i.e. nitrification within the water column and at the sediment-water interface) and accumulation to the bottom also contributed to the distribution and temporal variation of nitrate in the lake. The magnitude of each flux is discussed in Sects. 3.3 and 3.6.

Mixing ratio of NO − 3 atm to nitrate
The estimated average 17 O values of NO − 3 in the lake ( 17 O lake ) were uniform at +2.5‰ for both June and August ( (2). We concluded that 9.7 ± 0.8% of the total nitrate in the lake originates directly from the atmosphere; therefore, the remainder of nitrate that was of remineralized origin (NO − 3 re ) and was produced through nitrification in and around the lake.
The average mixing ratio of NO − 3 atm to NO − 3 total in Lake Mashu corresponds to those estimated for Lake Tahoe (13%) based on the same 17 O method (Michalski and Thiemens, 2006). These findings indicate that the mixing ratios observed in the present study are representative mixing ratios of NO − 3 atm to NO − 3 total in oligotrophic lakes. In Lake Superior, atmospheric deposition was assumed to be the primary source of nitrate in the water column based on the 15 Ndepleted δ 15 N values of nitrate (average of −4.1‰; Ostrom et al., 1998). Similar 15 N-depleted δ 15 N values were observed in Lake Mashu (Table 1). However, the results of the present study suggest that it is difficult to assume atmospheric nitrate is the primary source of nitrate. The same conclusion was suggested based on the δ 18 O values of nitrate in Lake Superior (Finlay et al., 2007). Thus, we must assume that other sources and/or isotopic fractionation pro- cesses led to the 15 N-depleted nitrate in the lakes. These are discussed in detail in Sect. 3.5.

Quantification of gross nitrate cycling rate during the observations
Because diazotrophs occurred in minute amounts in Lake Mashu (Haga et al., 1994), primary production in the lake requires either nitrate or ammonium to be supplied to the euphotic layer of the lake as the source of nitrogen. The nitrate in the euphotic zone of the lake must be supplied through nitrification in and around the lake, as well as through atmospheric deposition onto the catchment area of the lake (Fig. 6). While the average mixing ratio of NO − 3 atm to NO − 3 total was almost uniform in the lake water for the period, we already found evidence of the accumulation of NO − 3 atm deposited from the atmosphere at the lake surface, as well as the accumulation of NO − 3 re from sinking organic nitrogen within the bottom water during summer stratification. These findings indicate that NO − 3 re must have been produced at a rate that could compensate for the deposition of NO − 3 atm at the surface while maintaining a uniform mixing ratio of NO − 3 atm to NO − 3 total in the lake water (Fig. 6). By applying Eq. (2), the total inventory of NO − 3 atm in the lake water (N atm ) in the initial and temporal observations can be estimated from the following equations: where (N atm ) 0 and (N atm ) t denote the initial and temporal inventory of NO − 3 atm in the lake, (N total ) 0 and (N total ) t denote the initial and temporal inventory of NO − 3 total in the lake, and ( 17 O lake ) 0 and ( 17 O lake ) t denote the initial and temporal 17 O lake of NO − 3 total in the lake, respectively. In addition, 17 O atm denotes the 17 O value of NO − 3 atm . Adopting the inventory of NO − 3 total in the lake water in June as (N total ) 0 and that in August as (N total ) t results in (N atm ) 0 and (N atm ) t being 0.41 Mmol and 0.20 Mmol, respectively (Table 2).
Because the 17 O value of nitrate is stable during the partial uptake of nitrate through assimilation or denitrification, ( 17 O lake ) t can be expressed by the gross nitrate feeding rate through both atmospheric deposition ( N atm ) and nitrification in and around the lake ( N nit ) to the initial inventories of nitrate in the lake ((N atm ) 0 and (N total ) 0 ), By using Eqs. (8) and (10), we can obtain N nit as follows: The gross uptake rate of nitrate through assimilation ( N up ) can then be estimated from N nit using the following equation: The background monitoring station of atmospheric deposition, Cape Ochiishi (43 • 9 34 N, 145 • 30 50 E), was located on the southeastern side of the lake at a distance of 90 km from the lake center. The monthly wet deposition rate of NO − 3 atm measured at the station was 0.62 mmol m −2 for July 2007 and 0.53 mmol m −2 for August 2007 (EANET, 2008). Because the dry deposition rate of nitrate consists of 21% of the total (wet + dry) deposition rate in the northern district of Japan (Ministry of the Environment, 2009), we estimated that 0.047 Mmol of NO − 3 atm was deposited onto the entire catchment area of the lake (32.4 km 2 ) during the approximately two month period between observations. Using the NO − 3 atm deposition rate as N atm and the annual average 17 O atm as 17 O atm in Eqs. (11) and (12), we estimated that 0.52 ± 0.34 Mmol of the remineralized nitrate had been fed into the lake water through nitrification, while 2.6±0.4 Mmol of the nitrate had been removed from the lake water through assimilation during the period between sampling events ( Table 2).
The errors in the estimated values of N nit and N up were mostly derived from errors in determination of the deposition rate of nitrate ( N atm ), not 17 O determination, under the observed 17 O values around +2.5‰. Conversely, the error derived from 17 O would be significant when 17 O lake was much smaller than the observed. For example, if the value was less than +0.1‰, accurate values for both N nit and N up cannot be estimated in the lake under the same error during 17 O determination. Thus, analysis of 17 O with much higher precision will be needed to apply the 17 O method to lakes with low 17 O lake values.

Comparison with primary production rates
To determine if the estimated gross nitrate uptake rate in summer (2.6 ± 0.4 Mmol per 2 months) was reasonable, we compared it with the rate of primary production measured in the lake. The rates of gross primary production measured in the lake water column at depths of 0 to 70 m on 2 September 1985 using the 13 C-tracer method (Hama et al., 1983) ranged from 0.81 to 2.50 mg C m −3 d −1 (CGER NIES et al., 2004). Integrating the gross primary production rates to the entire water column shallower than 70 m gave a gross primary production rate of 0.14 Mmol C d −1 for the lake water. Assuming a C:N ratio of 6.6 (Redfield ratio) for primary production, this is equivalent to an N uptake rate of 0.022 Mmol N per day and 1.3 Mmol N per 2 months. The N uptake rate was in the same order as the nitrate uptake rate of 2.6 ± 0.4 Mmol per 2 months that was estimated based on 17 O.
However, further corrections are necessary to convert the gross N uptake rate to the gross nitrate uptake rate in the lake, such as (1) subtracting the primary production using ammonium and urea, (2) subtracting the primary production using atmospheric N 2 (N 2 fixation), (3) adding the primary production that occurs at depths greater than 70 m, (4) correcting temporal changes and seasonal variations in primary production, (5) adding the nitrate uptake fractions other than phytoplankton in the water column, such as periphyton (Axler and Reuter, 1996), and (6) correcting uncertainties in the C:N ratio during assimilation in oligotrophic freshwater environments (Axler et al., 1982). Among these possible corrections, important corrections for the present study might be Nos. (1), (5) and (6), because the reported parameters for their correction were significant, as presented below. If the parameters estimated in Castle Lake (a meso-oligotrophic subalpine lake in California, USA; Axler and Reuter, 1996) were applied to Lake Mashu, the assimilation rate would have to be reduced by half through correction (1), but then multiplied by approximately 10 according to correction (5) (Axler and Reuter, 1996), and then reduced by 1/5 following correction (6) (Axler et al., 1982). Although adding the corrections results in a similar value (1.3 Mmol N per 2 months) as that obtained without the correction, we must take into account the significant propagation of errors to the estimated gross nitrate uptake rate during the corrections, because the parameters in Nos. (1), (5) and (6) could be much higher or lower in Lake Mashu. Furthermore, significant correction could be anticipated for No. (4) as well. Thus, we estimated the gross nitrate uptake rate from the primary production in the lake to range from 0.1 Mmol to 10 Mmol per 2 months. 696 U. Tsunogai et al.: Quantifying nitrate dynamics using 17 O Although it is impossible to estimate the exact nitrate uptake rate from primary production data alone, the data regarding the primary production also support our finding that the nitrate uptake rate is highly reliable for the studied lake. Further studies considering the 15 N tracer incubation data simultaneously with monitoring 17 O of nitrate will confirm this conclusion.

Origin of 15 N-depleted nitrate
As described in Sect. 3.1, the δ 15 N values of nitrate in Lake Mashu were characterized by 15 N-depletion, which was especially low in June (−6.5‰ on average; Table 1). The δ 15 N value was much lower than the annual average δ 15 N value of atmospheric nitrate deposited onto the area (−1.1‰; Tsunogai et al., 2010). However, comparably 15 N-depleted δ 15 N-NO − 3 values as low as −4.1‰ have been found in Lake Superior (Ostrom et al., 1998), which is an undisturbed oligotrophic lake in North America. Moreover, in the case of oceanic nitrate, δ 15 N values as low as −6.5‰ (Conception Bay, Newfoundland, Canada; Ostrom et al., 1997) and −8.5‰ (Ise Bay, Japan; Sugimoto et al., 2008) have been reported for some coastal water columns. All of these sites were well oxygenated when the depleted 15 N nitrate levels were found, which suggests that dissolved nitrate is produced through nitrification, while denitrification plays a minor role in nitrogen cycling.
Nitrification is accompanied by significant fractionations in nitrogen isotopes (Wada et al., 1975;Mariotti et al., 1981); therefore, nitrogen cycling in a water column in which most nitrate is derived from NH + 4 through nitrification typically results in lower δ 15 N-NO − 3 levels than δ 15 N-NH + 4 levels. For example, in the case of Lake Michigan, the δ 15 N-NO − 3 is 9‰ lower than the δ 15 N-NH + 4 level and 2‰ lower than the δ 15 N-PON level (McCusker et al., 1999). Thus, the observed δ 15 N values are reasonable for those produced through nitrification under the condition in which the δ 15 N values of the total fixed-nitrogen pool were less than 0‰. To determine if the total fixed-nitrogen pool in Lake Mashu had depleted 15 N values, we also determined the δ 15 N values of PON in samples collected from the upper 50 m of the lake in August 2007 (Table 1). The 15 N-depleted δ 15 N values of PON in August (around −2‰; Table 1) suggested that the total fixednitrogen pool was low in Lake Mashu. Thus, the primary source of the observed 15 N-depleted nitrate in Lake Mashu was nitrification under the condition in which the δ 15 N values of the total fixed-nitrogen pool were low (around −2‰).
However, denitrification in the lake results in 15 Nenrichment of residual nitrate through isotopic fractionation (Wada et al., 1975;Lehmann et al., 2003;Granger et al., 2008). Thus, not only nitrate production through nitrificationunder total δ 15 N values of the fixed-nitrogen pool of around −2‰, but also low potential for the denitrification process in and around the lake could be responsible for the 15 N-depleted δ 15 N values of nitrate that were observed in the lake water column. The low potential for denitrification in the lake is supported by the low rates of carbon burial in the lake sediment (CGER NIES et al., 2004), as well as the apparent low potential for denitrification due to oxygen enrichment of the water column (Fig. 3). The 15 N-depleted feature in the total fixed-nitrogen pool in comparison with other lakes can also be explained by the low potential for denitrification in the lake because active denitrification during nitrogen cycling results in 15 N-enrichment of the residual total fixed-nitrogen pool through isotopic fractionation during denitrification.
The δ 18 O values of nitrate in June (+3.4‰) also indicate that nitrification is the major source of nitrate in the lake. By using the linear 17 O-δ 18 O relationship observed in samples of well oxygenated groundwater (n = 19) eluted from the background forested watersheds of Rishiri Island, Japan, Tsunogai et al. (2010) estimated the average δ 18 O value of remineralized nitrate produced through nitrification within the forest ecosystem to be −4.2 ± 2.4‰ by extrapolating the linear relationship to the endmember having 17 O = 0. While the exchange of oxygen atoms between nitrification intermediates and the ambient water is the dominant process that determines the δ 18 O value of nitrate produced through nitrification (Casciotti et al., 2002), we can expect similar δ 18 O values for nitrate produced through nitrification in and around the lake because groundwater and lake water in Rishiri showed similar δ 18 O values with those in and around Lake Mashu (from −14‰ to −7‰; Yasuhara et al., 2005). As a result, similar δ 18 O values in ambient water during nitrification can be expected in Lake Mashu and Rishiri Island.
Although the δ 18 O values of nitrate in June (+3.4‰) were higher than those estimated for nitrate produced through nitrification (−4.2 ± 2.4‰), this discrepancy can be explained by the contribution of atmospheric nitrate. This is because the lake water nitrate contained 9.7 ± 0.8% atmospheric nitrate. Atmospheric nitrate can be characterized by significant 18 O-enrichment (Durka et al., 1994;Burns and Kendall, 2002), as well as 17 O. Thus, we can anticipate slight 18 Oenrichment in nitrate when compared with pure nitrate produced through nitrification. The quantitative relationship is shown in Fig. 7, in which the average δ 18 O value of nitrate in the lake water in June was plotted as a function of 17 O together with the hypothetical mixing line between atmospheric nitrate having 17 O and δ 18 O values of +26.2‰ and +87.1‰, respectively , and the nitrification-derived nitrate having 17 O and δ 18 O values of 0‰ and −4.2‰, respectively . Contribution of the atmospheric nitrate (ca. 10%) to the remineralized nitrate reasonably explains the δ 18 O value of the lake water nitrate in June (Fig. 7). The δ 18 O value of surface nitrate (0 m) in the lake water in June was also plotted on the mixing line at the side closer to the endmember of atmospheric nitrate (Fig. 7). The results of this analysis also suggest that, prior to starting assimilation in the lake, the mixing ratio of the atmospheric nitrate to the remineralized nitrate governed the δ 18 O value of nitrate in the lake. Furthermore, an approximately 10% contribution of the atmospheric nitrate to the remineralized nitrate produced through nitrification can reasonably explain the δ 18 O value of nitrate in the lake water column. Moreover, the hypothetical endmember values of both atmospheric nitrate (NO − 3 atm ) and remineralized nitrate (NO − 3 re ) represented those in Lake Mashu well. Such mixing of atmospheric nitrate of around 10% does not contradict the finding that nitrification is the primary source of the 15 N-depleted nitrate because the atmospheric nitrate is depleted in 15 N as well. The annual average δ 15 N value has been estimated to be −1.1‰ in East Asia . Accordingly, a mixing ratio of atmospheric nitrate to remineralized nitrate of around 10% with remineralized nitrate could increase δ 15 N by only 0.5‰ under the conditions in which remineralized nitrate has δ 15 N values around −6‰. Thus, we conclude that the isotopic fractionation during the nitrification reaction (from which ca. 90% of nitrate in the lake was derived) was responsible for the 15 Ndepletion in the lake. In addition to the δ 15 N values, the δ 18 O values of nitrate in Lake Superior (around +2.4‰; Finlay et al., 2007) resembled those of Lake Mashu, suggesting that nitrification in the lake might be the major source of nitrate as well, with atmospheric nitrate serving as a minor source.
Unfortunately, it has been difficult to determine δ 15 N values of trace nitrate present at concentrations lower than 5 µM using traditional analytical methods (Bremner and Edwards, 1965;Amberger and Schmidt, 1987;Sigman et al., 1997;Silva et al., 2000). Thus, past δ 15 N data describing nitrate in lakes have primarily been limited to mesotrophic/eutrophic lakes in which nitrate is abundant in the water column (more than 5 µM). These mesotrophic/eutrophic lakes can be characterized by active denitrification in their water column and/or within the sedimentary layer, so that most δ 15 N data describing nitrate in lakes indicate values greater than 0‰. Recent advances in analytical methods have enabled determination of trace levels of nitrate less than 1 µM (Sigman et al., 2001;Casciotti et al., 2002;McIlvin and Altabet, 2005;Tsunogai et al., 2010). Additional δ 15 N data describing nitrate in oligotrophic lakes could reveal similar nitrification nitrate with low δ 15 N values around −6‰.

Annual variation in nitrate in Lake Mashu
When an infinitely long duration for the period of accumulation of both atmospheric nitrate ( N atm ) and remineralized nitrate produced through nitrification ( N nit ) is considered in Eq. (10), the initial nitrate in the lake, (N atm ) 0 and (N total ) 0 , can be removed from the equation. Because the observed average 17 O value of nitrate in the lake represented the average NO − 3 atm /NO − 3 total ratio of the entire amount of nitrate that was dissolved in the lake at the point of observation, the observed average 17 O value in June ( 17 O lake ) reflected the long range mean value in the relationship between N atm and N nit that was fed into the lake prior to the observation. Thus, we can estimate the average feeding flux of nitrate through nitrification (F nit ) using the average feeding flux of nitrate through atmospheric deposition (F atm ) from the following equation: where 17 O atm denotes the 17 O value of NO − 3 atm . Based on the average annual wet deposition flux of NO − 3 atm measured on Cape Ochiishi over the last 5 yr (EANET, 2008), the annual deposition flux of NO − 3 atm onto the entire catchment area of the lake (F atm ) is 0.35 ± 0.2 Mmol a −1 , so that the annual gross feeding flux of nitrate through nitrification (F nit ) becomes 3.2±0.3 Mmol a −1 in the lake.
The estimated flux is greater than the lower boundary condition for the annual feeding flux of nitrate in the lake to compensate for the net loss of nitrate during the observations in 2007 (2.1 Mmol; Table 2). Furthermore, the estimated nitrification fluxes coincided with those obtained by applying the estimated instantaneous gross feeding rate during summer (0.57 ± 0.33 Mmol per 2 months; Table 2) to the annual rate (3.4 ± 2.0 Mmol a −1 ), suggesting that the estimated annual gross flux is highly reliable and the gross nitrification rate in the lake is almost stable, regardless of the season.
Conversely, if the estimated instantaneous gross uptake rate in summer (2.6 ± 0.4 Mmol per 2 months) remained the same, even after the observations at the end of August, all of the residual nitrate in the lake (2.1 Mmol) would be exhausted by the end of October. In the case of nitrate in the euphotic layer, the assimilation would be completed much earlier, by early September. Thus, the gross uptake rate in other seasons should be much smaller than the instantaneous rate during summer. Assuming steady state annual variation in nitrate in Lake Mashu, the estimated total annual gross feeding flux (F atm + F nit = 3.6 ± 0.4 Mmol a −1 ) also corresponds to the annual gross uptake flux of nitrate in the lake through assimilation (Fig. 6). Thus, the rapid instantaneous gross uptake rate (2.6 ± 0.4 Mmol per 2 months) can be expected to last only another three weeks in the lake. In other words, all of the nitrate assimilation will be completed by the middle of September at the latest. During continuous monitoring using a mooring system from 2008, the annual maximum chlorophyll-a concentration at 20 m was observed in August, after which it rapidly decreased to the background level in the beginning of September (Tanaka et al., 2009). Although no data for 2007 is available, the temporal variation in chlorophyll-a concentration seemed reasonable when compared with our estimation. In conclusion, while both atmospheric deposition and nitrification fed nitrate into the lake at a similar rate regardless of seasons, nitrate removal through assimilation was concentrated in summer, occurring for less than three months.
The estimated annual gross uptake mass of nitrate (3.6 ± 0.4 Mmol) was similar to the total nitrate inventory in the upper 100-120 m in June of 2007. Thus, the primary production in the lake appears to be complete when all of the nitrate in the upper euphotic layer is exhausted. Although we have little direct information regarding the limiting nutrients in the lake, the observed annual variation of nitrate in Lake Mashu implies that nitrogen could be a limiting nutrient. Past data describing the distribution of nitrate revealed nitrate concentrations lower than 0.1 µM in August or September in the epilimnion (CGER NIES et al., 2004), which also supports this suggestion.
Dividing the total mass of nitrate in June (4.2 Mmol) by the annual average gross uptake/feeding rate (3.6 ± 0.4 Mmol a −1 ) gave an approximate residence time of nitrate in the lake of 1.2 ± 0.1 yr. The residence time of nitrate corresponds to less than 1/10 of that in Lake Superior (Kumar et al., 2008), suggesting that nitrate in Lake Mashu has an ephemeral property. Thus, we can expect atmospheric nitrate deposited into the lake to be rapidly assimilated.

Implications for the loss of transparency in Lake Mashu
Because nitrogen appears to be one of the nutrients limiting primary production in the lake, an increase in the deposition rate could result in a direct increase in primary production.
However, as revealed in this study, atmospheric nitrate is not the only source of nitrate assimilated in the lake through primary production. Rather, it comprises only ca. 10% of the entire nitrate assimilated; therefore, any direct increase in the rate would be only ca. 10% of the increase in the deposition rate. In other words, even if the annual nitrate deposition rate suddenly increased by 20%, the direct increase in primary production using nitrate would be only 2%, and therefore, difficult to detect. Nevertheless, this does not mean that atmospheric nitrate will not have a significant effect on primary production in the lake. The present study also revealed a rapid turnover of nitrate in the summer euphotic layer through assimilation, as well as active remineralization of assimilated nitrogen to nitrate, which was probably due to the absence of denitrification processes within the well oxygenated water environment (Fig. 6). Thus, an increase in the deposition flux of atmospheric nitrate will indirectly increase the primary production in the lake by increasing the entire fixed nitrogen pool cycling in the lake (Fig. 6). Because the indirect effects that occur through accumulation of fixed nitrogen are long lasting, such an indirect effect would be more important for primary production in the lake.
It should be noted that this conclusion is based on the assumption that nitrogen is always the limiting nutrient in the lake. While Fe is abundant in the lake water (ca. 40 nM;Nojiri, 1992), dissolved inorganic phosphate is always present at levels below the detection limit (less than 0.1 µM) in the lake water (CGER NIES et al., 2004). As a result, phosphorous components may also be limiting nutrients, especially when nitrogen accumulates in the lake water. To clarify the potential for the effects of phosphorous components available in the lake, the distribution of their concentration and their temporal variations must be determined using highly sensitive analytical methods (e.g. Patey et al., 2008). Some incubation experiments to clarify the limiting nutrients are also needed. Furthermore, there is little knowledge available regarding the dynamics of ammonium in the lake, especially with respect to how much primary production occurs due to the presence of ammonium. The f -ratio of primary production in Lake Superior was estimated to be 0.2 (Kumar et al., 2008); thus, a similar low f -ratio can be expected for the primary production in Lake Mashu as well. Accordingly, further studies are needed to clarify the geochemical dynamics of nutrients in the lake, including ammonium. It is important to understand these dynamics to evaluate future primary production in the lake. Monitoring of the loss rate of fixed-N to the sedimentary layer is also important for evaluation of the total fixed-N pool in the lake.

Comparison with the traditional 15 N-labeled tracer method
In most studies that have been conducted to date, the gross uptake rate of nitrate has been estimated by incubation experiments using 15 N tracer techniques. In this conventional approach, which was originally introduced by Dugdale and Goering (1967), 15 N labeled NO − 3 is added into bottles or mesocosms that simulate in situ conditions, which leads to the production of particulate organic-15 N (PO 15 N) through assimilation over a known incubation period of several hours to several days. This PO 15 N is then gathered and quantified by mass spectrometry. However, these experimental procedures are generally costly, complicated, and time consuming, especially those that employ mesocosms. Furthermore, the 15 N tracer method has several problems when determining accurate nitrate uptake rates. For example, the usual 15 N tracer method does not include assimilated nitrogen released to dissolved organic-15 N (DO 15 N) during incubation within the estimated uptake rates, which results in the rates being underestimated (Slawyk et al., 1998). Additionally, incubation itself can also result in the production of artifacts by changing the physical/chemical environments. Finally, it is difficult to simulate nitrate uptake by periphyton or microbes on the lake floor through typical incubation in bottles (Axler and Reuter, 1996).
The gross nitrate uptake rate estimated using 17 O values of NO − 3 ( 17 O method) overcomes the aforementioned problems inherent in the conventional 15 N-labelled tracer methods. Accordingly, the 17 O method can be an alternative to standard techniques for accurate determination of the gross nitrate uptake rates in lakes that contain detectable quantities of atmospheric nitrate within the total nitrate.
In addition to being used to determine the gross nitrate uptake rate, the 17 O method can be applied to determine the gross nitrification rate in a hydrosphere. Although recent progress in the use of 15 N-labelled tracer methods to determine the gross nitrification rate were remarkable (e.g. Santoro et al., 2010), the 17 O method can be an alternative technique to determination of the gross nitrification rate.
This study clearly demonstrated that 17 O can be a powerful tracer describing the fate of NO − 3 atm deposited onto an oligotrophic hydrosphere, even if it has only a small fixednitrogen input. By measuring the 17 O data describing nitrate in various hydrospheres, we can increase our understanding of the fixed-nitrogen processing and fixed-nitrogen retention efficiencies in hydrospheric ecosystems that are subjected to the input of atmospheric fixed-nitrogen.

Conclusions
Nitrification is the major source of nitrate in Lake Mashu. The average mixing ratio of atmospheric nitrate to total nitrate was only 9.7 ± 0.8% in the lake. Moreover, there is low potential for denitrification in and around the lake. The lake water dissolved nitrate was characterized by rapid removal through assimilation during summer until it was almost completely removed from the euphotic layer, as well as continuous feeding into the lake through nitrification and deposition, regardless of the seasons. Thus, atmospheric nitrate deposited into the lake will be assimilated quickly and have a mean residence time of 1.2 ± 0.1 yr. Additionally, more than 90% of the assimilated nitrate will be remineralized to nitrate and assimilated again via active nitrogen cycling in the lake, as schematically shown in Fig. 6.