Quantifying nitrate dynamics in a mesotrophic lake using triple oxygen isotopes as tracers

Vertical distributions of both concentrations and stable isotopic compositions of nitrate, including the 17O‐excesses (Δ17O), were determined four times during 1 yr within the mesotrophic water column of Lake Biwa in Japan. By using both the deposition rate of atmospheric nitrate onto the entire surface of the lake and the influx/efflux of both atmospheric and remineralized nitrate via streams reported in the literature, we quantified the annual dynamics of nitrate (gross production rate of nitrate through nitrification and gross metabolic rate of nitrate through assimilation and denitrification), together with their seasonal variations, based on the Δ17O method. The results revealed that 642 ± 113 Mmol (Mmol = 106 mol) of the remineralized nitrate was supplied into the water column through nitrification in the lake on an annual basis, while 810 ± 120 Mmol of nitrate was metabolized in the lake through assimilation and denitrification. In addition, it turns out that nitrification was active, not only in the hypolimnion, but also in the epilimnion and upper thermocline in this lake. Furthermore, the total metabolic rates of nitrate varied seasonally, with the highest rates in summer and the lowest in winter. Because the difference between the annual metabolic rate of nitrate estimated based on the Δ17O method and the annual assimilation rate of nitrate estimated based on the traditional 15N incubation method was only 20%, we concluded that the Δ17O method reliably estimates the dynamics of nitrate in mesotrophic lakes.


Nitrate (NO 2
3 ) is a key nutrient in aquatic environments that often limits primary production. Nitrate dynamics in an aquatic environment, i.e., gross production rate of nitrate through nitrification (F nit ), gross metabolic rate of nitrate through assimilation (F assim ), and gross metabolic rate of nitrate through denitrification (F denit ), are important parameters to be quantified when evaluating both the present and future state of the aquatic environment. In most studies that have been conducted to date, nitrate dynamics has been estimated via incubation experiments using 15 N tracer techniques. To quantify F assim , for instance, 15 N-labeled NO 2 3 is added into bottles that simulate in situ conditions of the aquatic environment studied, 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 (Dugdale and Goering 1967;Knap et al. 1996). The PO 15 N is then gathered and quantified using mass spectrometry.
The experimental procedures using 15 N tracer, however, are generally costly and complicated. Besides, while the obtained nitrate dynamics is an instantaneous assimilation rate at the point of observation, such a value may be temporally variable in response to various factors such as changes in temperature, light intensity, nutrients, and community structure. As a result, tedious and time-consuming time series observations are needed to estimate long-term nitrate dynamics (such as annual nitrate dynamics). Furthermore, nitrate dynamics estimated based on bottle incubations often can be inaccurate, because the incubation itself can result in the production of artifacts by changing the physical/chemical environment from that in situ. It is difficult to simulate nitrate dynamics via periphyton or microbes on the lake bottom using bottle incubations (Axler and Reuter 1996). Additionally, the usual 15 N tracer methods do not include assimilated nitrogen released to dissolved organic-15 N (DO 15 N) during incubation within the estimated assimilation rates (Slawyk et al. 1998).
To estimate both the gross nitrification rate (F nit ) and gross metabolic rate of nitrate (F assim 1 F denit ) in a lake more *Correspondence: urumu@nagoya-u.jp accurately, we proposed a new method using the 17 O-excess (D 17 O) of dissolved NO 2 3 in the water column of the lake as a tracer   [VSMOW] for oxygen). The atmospheric nitrate (NO 2 3 atm ) that is produced from atmospheric NO through photochemical reactions can be characterized by the anomalous enrichment in 17 O from the other usual nitrate (remineralized nitrate: NO 2 3 re ) that is produced from organic nitrogen through general chemical reactions including microbial nitrification in the biosphere (Michalski et al. 2004). Because the oxygen atoms of NO 2 3 re are derived from either terrestrial O 2 or H 2 O via usual chemical reactions such as microbial nitrification (Aleem et al. 1965;Andersson and Hooper 1983;Kumar et al. 1983), NO 2 3 re shows mass-dependent relative variations between 17 O/ 16 O and 18 O/ 16 O ratios. On the other hand, only unprocessed NO 2 3 atm displays an anomalous enrichment in 17 O from the mass-dependent relative variations, reflecting oxygen atom transfers from anomalously 17 O enriched ozone (O 3 ) during the conversion of NO x to NO 2 3 atm (Michalski et al. 2003;Morin et al. 2008;Tsunogai et al. 2010). By using the D 17 O signature (the magnitude of 17 O excess) defined by the following equation (Miller 2002;Kaiser et al. 2007), we can distinguish unprocessed NO 2 3 atm (showing D 17 O around 126& in mid-latitude: Tsunogai et al. 2016) where the constant b is 0.5279 (Miller 2002;Kaiser et al. 2007). Continuous monitoring of the D 17 O value of NO 2 3 atm deposited at mid-latitudes has clarified that the annual averages of D 17 O values of NO 2 3 atm are relatively the same every year (Michalski et al. 2003;Kaiser et al. 2007;Alexander et al. 2009;Tsunogai et al. 2010Tsunogai et al. , 2016. In addition, D 17 O is nearly stable during the mass-dependent isotope fractionation processes within surface ecosystems (Miller 2002;Michalski et al. 2004;Nakagawa et al. 2013). Therefore, although the d 15 N or d 18 O signature of NO 2 3 atm can be overprinted by biogeochemical processes subsequent to deposition, D 17 O can be used as a robust tracer of unprocessed NO 2 3 atm to reflect the mole fraction of unprocessed NO 2 3 atm within total NO 2 3 , regardless of partial metabolism through denitrification and assimilation subsequent to deposition (Michalski et al. 2004;Tsunogai et al. 2011Tsunogai et al. , 2014. As a result, the average D 17 O value of nitrate in a lake's water column (D 17 O lake ) should reflect the long-range average relative supply rate between NO 2 3 atm and NO 2 3 re prior to the observation . That is to say, by determining D 17 O lake in a lake where we can omit the influence of influx/efflux of nitrate via rivers, we can express the average supply rate of NO 2 3 re through nitrification in the lake's water column (F nit ) as a function of the average supply rate of nitrate through atmospheric deposition (F atm ). In addition, assuming steady-state conditions in the lake, we can express the total metabolic rate of nitrate through assimilation and denitrification (F assim 1 F denit ) as a function of the average supply rate of nitrate through atmospheric deposition (F atm ) as well.
The deposition rate of NO 2 3 atm (F atm ) has been monitored extensively at many observation sites worldwide because of the problem of transboundary air pollution (EANET 2014;Vet et al. 2014), and the data generated from such can be employed to estimate the precise deposition rate of NO 2 3 atm onto individual aquatic environments (F atm ), at least in eastern Asia (EANET 2014). Using both the D 17 O lake value determined for Lake Mashu, an oligotrophic lake in northern Japan (Fig. 1a), and the rate at which NO 2 3 atm is deposited into the lake (F atm ), Tsunogai et al. (2011) estimated both the average nitrification rate (F nit ) and average assimilation rate of nitrate (F assim ) in the lake successfully, assuming that the metabolic rate of nitrate through denitrification (F denit ) was much less than F assim in the highly oxic lake. Recent progress in the use of 15 N tracer methods to determine the gross in vitro nitrification rate has been remarkable (Santoro et al. 2010). However, the D 17 O method represents a simple and accurate alternative technique to determine in situ values for both the gross nitrification rate and gross metabolic rate of nitrate in freshwater and marine environments that contain detectable quantities of NO 2 3 atm within the total nitrate pool in the water column .
Lake Mashu, however, is a subalpine, oligotrophic crater lake with no perennial inflows/outflows and a long residence time for the water of more than 100 yr. Most of the catchment is occupied by the lake surface so the influx/efflux of nitrate (not only total nitrate but also NO 2 3 atm ) via rivers can be omitted from the calculations. To apply the D 17 O method in lakes in general for the accurate determination of the nitrate dynamics where substantial quantities of nitrate could have been supplied/removed through inflows/outflows, additional corrections are needed.
Besides, to apply the D 17 O method in lakes, detectable quantities of NO 2 3 atm must be contained within the total nitrate pool. Whereas the water of oligotrophic Lake Mashu contained detectable quantities of NO 2 3 atm within the total nitrate pool (the average mixing ratio of NO 2 3 atm within total nitrate was 9.7% 6 0.8%; Tsunogai et al. 2011), a smaller mixing ratio can be anticipated for mesotrophic/eutrophic environments.
To confirm that we can quantify nitrate dynamics (F nit and F assim 1 F denit ) in lakes that are more general with inflows and outflows using the D 17 O method, the stable isotopic compositions of nitrate, including the D 17 O values, were determined four times during 1 yr in the water column of mesotrophic Lake Biwa, where influx/efflux via inflows/ outflows were already determined for both total nitrate and NO 2 3 atm (Table 1) (Tsunogai et al. 2016). In addition to determining the annual nitrate dynamics in the lake, we also deduced the seasonal variation in the dynamics. The quantified nitrate dynamics in the lake were applied to clarify the reasons for the remarkable biogeochemical features found in the lake, such as rapid removal of P nutrients to sediments (Tezuka 1986;Yoshimizu et al. 2002). The fate of NO 2 3 atm deposited onto the hydrosphere in general (Duce et al. 2008;Elser et al. 2009) were clarified through these studies as well. Furthermore, we also conducted traditional incubation experiments using the 15 N tracer method to obtain independent measurements of the gross assimilation rate (F assim ) to evaluate whether the D 17 O method could be used to obtain reliable nitrate dynamics.

Site description
Lake Biwa, located in the central part of the Japanese Islands, is the largest freshwater lake in Japan (Fig. 1). It has a surface area of 670.4 km 2 , a total catchment area of 3174 km 2 , and annual precipitation of around 2000 mm. More than 120 rivers flow into the lake, but the Seta River at the southern end of the lake, also known as the Yodo River, is the only natural outflow. The main basin of Lake Biwa is mesotrophic. Thermal stratification is present in the lake from May to December, and vertical water convection to the bottom of the lake occurs regularly from January to April. The average depth and water residence time of the basin are 43 m and 5.5 yr, respectively. The depth of the euphotic zone during the stratified season ranges from 10 m to 21 m, with an average of 15 m (Urabe et al. 1999).
Similar to many lakes worldwide, Lake Biwa has been experiencing eutrophication. The increase in nutrient loading, especially of P nutrients, due to urbanization around the lake started in the 1960s, and blooms of Uroglena americana have occurred since 1977 and blooms of cyanobacteria since 1983 (Hsieh et al. 2011). As a result of water treatment regulations in 1982, however, nutrient loading has been progressively reduced (Hsieh et al. 2011). Still, we can find many environmental problems related to eutrophication in the lake. To clarify the pathways and origins of the nitrate supplied into the lake, both concentrations and stable isotopic compositions (d 15 N, d 18 O, and D 17 O) of dissolved nitrate were determined in the major inflows/outflows of the lake (Tsunogai et al. 2016). Based on these values, Tsunogai et al. (2016) estimated the gross influx/efflux of total nitrate (DN) and NO 2 3 atm (DA) via inflows/outflows and groundwater during each observation interval, together with the average d 15 N, d 18 O, and D 17 O values of total nitrate in the inflows/ outflows (Table 1).

Sampling
Lake water was collected during four sampling campaigns in 2013, on 15 March, 17 June, 05 August, and 21 October, which are the same days river water sampling occurred as described by Tsunogai et al. (2016), from the research vessel HASU (Center for Ecological Research, Kyoto University). A 5 L Niskin sampler was used to collect the lake water samples every 5 m (shallow) to 20 m (deep) depth at locations nearby the Imazu central station (Sta. H1 in Fig. 1b; 35823 0 41 00 N, 13687 0 57 00 E; depth 5 85 m) and the Minami-hira central station (Sta. H3 in Fig. 1b; 35811 0 39 00 N, 135859 0 39 00 E; depth 5 65 m). Sta. H1 and H3 correspond to the monthly lake water monitoring Sta. 17B and 12B, respectively, of the Lake Biwa Environmental Research Institute (LBERI). Vertical profiles of temperature and conductivity were determined at the stations simultaneously by use of sensors (Sea-bird SBE911plus).
Each sample was transferred into a dark 250-500 mL polyethylene bottle that was prerinsed at least twice with sample water and subsequently stored under refrigeration (48C) on the boat. Then, the samples were filtered through a precombusted Whatman GF/F filter with a 0.7 lm pore size within 3 h after collection at a shore-based laboratory, and the filtrate was stored in a different dark polyethylene bottle under refrigeration until analysis. Additionally, the seston that was collected on each filter was washed with Milli-Q water, placed in a plastic case, and then stored in a deep freezer (2808C) for later analyses of the particulate organic nitrogen (PON).  (Tsunogai et al. 2016). † Total influx/efflux of N (NO 2 3 ) or A (NO 2 3 atm ) estimated from (1) flux-weighted average nitrate concentrations in the inflows/outflows determined by Tsunogai et al. (2016), (2) flux-weighted average D 17 O value of nitrate in the inflows/outflows determined by Tsunogai et al. (2016), and (3) total influx/efflux of water determined by other researchers and compiled by Tsunogai et al. (2016), in which both influx of water via streams and influx of water via groundwater were included.
In this study, we defined the sampling number n, where n 5 1, 2, 3, and 4, as representing the sampling in March, June, August, and October, respectively. In addition, we defined one more hypothetical sampling number (n 5 5) set exactly 1 yr later than the n 5 1 date. Please note that there are no data for sampling n 5 5. The sampling numbers were needed to calculate both annual average and seasonal variation of nitrate dynamics in the lake, by regarding the intervals between n 5 1 and n 5 2, n 5 2 and n 5 3, n 5 3 and n 5 4, n 5 4 and n 5 5, n 5 1 and n 5 5, as spring, summer, autumn, winter, and 1 yr, respectively, for the lake water in this study.

N tracer incubation
We also determined the gross assimilation rate of nitrate in the lake's water column based on traditional bottle incubation experiments using a 15 N tracer (Dugdale and Goering 1967;Knap et al. 1996;Konno et al. 2010). On the boat, lake water samples collected at the depths of 0 m and 10 m were transferred into 250 mL clear polycarbonate bottles with septum caps (samples were collected at least in duplicate for each depth). Then, 0.3-0.5 mL of 1 mmol L 21 K 15 NO 3 solution (10.4 atom%; Shoko, Tokyo, Japan) was added into each incubation bottle at the shore-based laboratory within a maximum of 3 h after collection. The bottles were gently shaken and then incubated in thermostatic baths (78C, 218C, 288C, and 208C in March, June, August, and October, respectively) on the shore for 24 h while covered with screens to simulate the in situ light intensity. In addition, water samples without 15 N tracer added were incubated in a similar manner. Immediately after the incubation period, the seston in each incubated water sample was collected and washed with Milli-Q water on a precombusted Whatman GF/F filter via gentle vacuum filtration (Konno et al. 2010). The obtained filters were then frozen in a deep freezer (2808C) until analysis.

Analysis
The concentrations of nitrate (NO 2 3 ) and nitrite (NO 2 2 ) in each filtrate sample were measured using ion chromatography (Prominence HIC-SP, Shimadzu, Japan) within a few days after each sampling event. The error (standard error of the mean) in the determined concentrations of nitrate was 6 3%. The d 18 O values of H 2 O in the samples were analyzed using the cavity ring-down spectroscopy method by employing an L2120-i instrument (Picarro, Santa Clara, California, U.S.A.) equipped with an A0211 vaporizer and autosampler; the error (standard error of the mean) in this method was 6 0.1&. Both the VSMOW and standard light Antarctic precipitation were used to calibrate the values to the international scale. Then, we determined the stable isotopic compositions of nitrate for the samples, except for the lake surface samples (0-10 m depths) that were taken in August and showed nitrate concentrations less than 1.0 lmol L 21 .
To determine the stable isotopic compositions, nitrate in each filtrate sample was chemically converted to N 2 O by using a method originally developed to determine the 15 N/ 14 N and 18 O/ 16 O ratios of seawater and freshwater nitrate (Mcilvin and Altabet 2005) that was later modified Konno et al. 2010;Yamazaki et al. 2011). In brief, the procedures were as follows. Approximately 10 mL of each sample solution was pipetted into a vial with a septum cap. Then, 0.5 g of spongy cadmium was added, followed by 150 lL of a 1 M NaHCO 3 solution. The sample was then shaken for 18-24 h at a rate of 2 cycles s 21 . Then, the sample solution was decanted into a different vial with a septum cap. After purging the solution using high purity helium, 0.4 mL of an azide/acetic acid buffer was added. After 45 min, the solution was alkalinized by adding 0.2 mL of 6 M NaOH.
Then, the stable isotopic compositions (d 15 N, d 18 O, and D 17 O) of the N 2 O in each vial were determined by using the continuous-flow isotope ratio mass spectrometry (CF-IRMS) system at Nagoya University. This system consists of an original helium purge and trap line, a gas chromatograph (Agilent 6890), a Finnigan MAT 252 mass spectrometer (Thermo Fisher Scientific, Waltham, Massachusetts, U.S.A.) with a modified Combustion III interface (Tsunogai et al. 2000(Tsunogai et al. , 2002(Tsunogai et al. , 2005Nakagawa et al. 2004), and a specially designed multicollector system . For each analysis, aliquots of N 2 O were introduced, purified using PoraPLOT-Q capillary column (50 m long, 0.32 mm i.d.) held at 308C, and carried continuously into the mass spectrometer via an open split interface, in which the isotopologues of N 2 O 1 at m/z ratios of 44, 45, and 46 were monitored to determine d 45 and d 46 Hirota et al. 2010). Each analysis was calibrated by using 99.999% N 2 O as a machine-working reference gas. This gas was introduced into the mass spectrometer via an open split interface according to a specific schedule to correct for subdaily temporal variations in the mass spectrometry process. In addition, a working-standard gas mixture containing a known concentration of N 2 O, ca. 1000 ppm N 2 O in air, was injected from a sampling loop and analyzed in the same manner as that of the samples at least once a day to correct for daily temporal variations in the mass spectrometry process.
Following the analyses based on N 2 O 1 monitoring, an additional aliquot of N 2 O was introduced to determine the D 17 O of N 2 O . By using the same procedures as those used in the N 2 O 1 monitoring mode, purified N 2 O was introduced into our original gold tube unit   Kaiser et al. 2007) to calibrate the values of the sample nitrate to an international scale and to correct for both isotope fractionation during the chemical conversion to N 2 O and the progress of oxygen isotope exchange between the nitrate-derived reaction intermediate and water (ca. 20%). In this study, we adopted the internal standard method (Nakagawa et al. 2013;Tsunogai et al. 2014) for the calibrations of sample NO 2 3 . To determine whether samples were deteriorated or contaminated during storage and whether the conversion rate from nitrate to N 2 O was sufficient, the concentrations of nitrate in the samples were determined each time we analyzed isotopic compositions using CF-IRMS based on the N 2 O 1 or O 1 2 outputs. We adopted the d 15 N, d 18 O, or D 17 O values only when concentrations measured via CF-IRMS correlated with those measured via ion chromatography just after the sampling within a difference of 10%. About 10% of the whole isotope analyses showed conversion efficiencies lower than this criterion. The nitrate in these samples was converted to N 2 O again and reanalyzed for the stable isotopic compositions. None of the samples showed significant nitrate deterioration or nitrate contamination during storage.
We repeated the analyses of the d 15 N, d 18 O, and D 17 O values of nitrate for each sample at least three times to attain better precision. Most of the samples had a nitrate concentration of more than 5.0 lmol L 21 , which corresponded to a nitrate quantity greater than 50 nmol in a 10 mL sample. This amount was sufficient for determining the d 15 N, d 18 O, and D 17 O values with the highest precision of our CF-IRMS system. For cases when the nitrate concentration was less than 5.0 lmol L 21 , the sample volume was increased to 30 mL and the number of analyses was also increased. Thus, all isotopic data presented in this study have an error (standard error of the mean) better than 6 0.2& for d 15 N, 6 0.3& for d 18 O, and 6 0.1& for D 17 O.
Nitrite (NO 2 2 ) in the samples interferes with the final N 2 O produced from NO 2 3 because the chemical method also converts NO 2 2 to N 2 O (Mcilvin and Altabet 2005). Therefore, it is sometimes necessary to remove NO 2 2 prior to converting NO 2 3 to N 2 O. However, in this study, all the lake water samples analyzed for stable isotopic compositions had NO 2 2 concentrations lower than the detection limit (0.05 lmol L 21 ). Thus, in this study, we skipped the processes for removing NO 2 2 . The concentrations and d 15 N values of PON on the GF/F filters were analyzed using the method developed by Tsunogai et al. (2008). In this method, the organic nitrogen on each filter is oxidized to NO 2 3 using persulfate. Subsequent processes to determine the d 15 N values of nitrate were generally the same as those used for the NO 2 3 analyses described above. To calibrate the value to the international scale, several local laboratory standards that had been calibrated using internationally distributed isotope reference materials (IAEA N1, USGS 25, and IAEA N2; B€ ohlke and Coplen 1995) were used for routine calibration purposes by measuring them in the same manner in which the samples were measured. The natural PON data presented in this study had an error of 6 0.3& for d 15 N.
Calculation for the nitrate dynamics using D 17 O First, the total inventory of nitrate in the lake water (N) and its d 15 N, d 18 O, and D 17 O values (d lake ) were calculated for each observation n (n 5 1, 2, 3, and 4) from the data describing their vertical distributions in the water column and the vertical distribution of the area in the lake using the following equations (Tsunogai et al. 2000: where C z , d z , and S z denote the nitrate concentration, each isotopic value (d 15 N, d 18 O, and D 17 O), and the area of the lake at depth z, respectively. In this study, we estimated S z from an electronic online map by the Geospatial Information Authority of Japan (http://maps.gsi.go.jp/). Because D 17 O can be used as a robust tracer of unprocessed NO 2 3 atm to reflect the accurate mole fraction of unprocessed NO 2 3 atm within total NO 2 3 regardless of partial metabolism through either denitrification and/or assimilation subsequent to deposition, we can relate D 17 O with the concentrations of NO 2 3 atm , NO 2 3 re , and NO 2 3 in each water sample by using the following equation: where C atm , C re , and C total denote the concentrations of NO 2 3 atm , NO 2 3 re , and NO 2 3 in each water sample, respectively; and D 17 O atm and D 17 O denote the D 17 O values of NO 2 3 atm and nitrate (total) in each water sample, respectively. Please note that all the NO 2 3 other than the unprocessed NO 2 3 atm can be classified into NO 2 3 re , including the NO 2 3 produced through natural/anthropogenic processes in the biosphere/ hydrosphere/geosphere and that stored in soil, fertilizer, manure, sewage, etc. The N nutrients that were originally supplied to the biosphere through atmospheric deposition but then became organic nitrogen through assimilation and eventually NO 2 3 via remineralization are classified into NO 2 3 re and not into NO 2 3 atm (Tsunogai et al. 2016). Because we used the power law (Eq. 1) for the definition of D 17 O, the D 17 O values are different from those based on the linear definition (Michalski et al. 2002 3 as always stable irrespective of any partial metabolism subsequent to deposition, such as assimilation or denitrification. On the other hand, D 17 O values based on the power law definition are not conserved during mixing processes between fractions having different D 17 O values, so the C atm /C total ratios estimated using Eq. 4 are somewhat deviated from the actual C atm /C total ratios in the samples (Tsunogai et al. 2016). However, in this study, the extent of the deviations of the C atm /C total ratios of the lake water NO 2 3 was less than 0.15%, therefore, we disregarded this effect in the discussion.
By substituting D 17 O lake estimated from Eq. 3 for D 17 O in Eq. 4, the inventory of NO 2 3 atm in the lake water (A) at the initial (t 5 0) and final (t 5 t) observation times can be estimated from the inventory of NO 2 3 in the lake (N) using the following equations: where A 0 and A t denote the initial and final inventory of NO 2 3 atm in the lake, respectively; N 0 and N t denote the initial and final inventory of NO 2 3 in the lake, respectively; and (D 17 O lake ) 0 and (D 17 O lake ) t denote the initial and final D 17 O lake , respectively. The relationships between A 0 , A t , N 0 , and N t are schematically shown in Fig. 2, in which we divide the supply/removal processes into river input/output, atmospheric deposition, in-lake nitrification, and in-lake metabolism through assimilation and denitrification.
Because the D 17 O value of NO 2 3 is nearly stable during the partial metabolism of NO 2 3 through assimilation and denitrification, the left-hand side of Eq. 6 can be replaced by using the gross amount of NO 2 3 supplied/removed through inflows/outflows, atmospheric deposition (DN atm ), and nitrification in the lake (DN nit ), as well as the initial inventories of NO 2 3 atm (A 0 ) and NO 2 3 (N 0 ) in the lake, as shown in the following equations: where D 17 O in and D 17 O out denote the flux-weighted average D 17 O values of NO 2 3 in the inflows and outflows, respectively; DN in and DA in denote the gross amount of NO 2 3 and NO 2 3 atm being supplied via inflows, respectively; and DN out and DA out denote the gross amount of NO 2 3 and NO 2 3 atm being removed via outflows, respectively, during the interval between the initial (t 5 0) and final (t 5 t) observation periods.
In estimating the inventories of NO 2 3 atm (A) and thus nitrate dynamics in the Lake Biwa, we used the 3-yr average By using Eqs. 7-9, we can obtain DN nit for the interval between the initial (t 5 0) and final (t 5 t) time as follows: Then, the gross amount of NO 2 3 metabolized totally through assimilation and denitrification in the water column (DN assim 1 DN denit ) can be obtained from DN nit using the following equation (Fig. 2): By using Eqs. 10, 11, we can estimate both DN nit and DN assim 1 DN denit for each interval between the observations, i.e., spring (interval between n 5 1 and 2), summer (interval between n 5 2 and 3), autumn (interval between n 5 3 and 4), and winter (interval between n 5 4 and 5). Additionally, we can estimate the annual supply rate of NO 2 3 re through nitrification (F nit ) by integrating the whole DN nit estimated for each season. We can estimate the annual metabolic rate of NO 2 through assimilation and denitrification (F assim 1 F denit ) as well, by integrating the whole DN assim 1 DN denit estimated for each season.
To estimate DN atm for each interval, we used the areal deposition rate of NO 2 3 (wet deposition 1 dry deposition) determined at the Ohtsu Observatory (Mitamura 2014; Environmental Laboratories Association in Japan 2015), which is located on the southeastern shore of the lake (3581 0 35 00 N, 135852 0 2 00 E; Fig. 1b), for the entire surface area of the lake (670.4 km 2 ). The dry deposition is about 30% of the total deposition (Mitamura 2014). The obtained DN atm was 9.5 6 1.7 Mmol, 4.9 6 0.9 Mmol, 7.8 6 1.4 Mmol, and 14.6 6 2.6 Mmol (Mmol 5 10 6 mol) for the spring, summer, autumn, and winter, respectively. The error ranges (about 20%) were estimated from the deviation in the wet deposition rates over a decade at the Ohtsu Observatory from those determined for the Takashima Observatory, located on the northeastern shore of the lake (35824 0 21 00 N, 136802 0 24 00 E; Fig. 1b), where only the wet deposition rates were determined for NO 2 3 (Shiga Prefecture 2015). As for the values of DN in , DN out , D 17 O in , and D 17 O out in each interval, we used those already determined through actual observations of the inflows/outflows (Table 1) (Tsunogai et al. 2016).
Calculation for gross assimilation rates using the 15 N tracer method The gross assimilation rate of NO 2 3 in a volume of lake water (V assim ) was calculated for each incubation bottle with 15 NO 2 3 addition through comparisons with that without 15 NO 2 3 addition using the following equation: 3 addition (in atom%), and t denotes the duration of the incubation (24 h). Then, each assimilation rate at a particular depth was estimated as the average value of duplicate bottles sampled and incubated simultaneously. . The data were obtained by dividing the supply/removal processes into river input (DN in ), river output (DN out ), atmospheric deposition (DN atm ), inlake nitrification (DN nit ), and total metabolism through assimilation and denitrification (DN assim 1 DN denit ). The values represented are those that were obtained in March (initial) and June (final) 2013.
Next, we calculated the areal gross assimilation rate for each observation by integrating the assimilation rates based on volume, whereby we assumed that the data obtained at 0 m and 10 m represented the average values from 0 m to 5 m and from 5 m to 15 m, respectively, and the gross assimilation rates below 15 m were always 0.

Results and discussion
Nitrate in the lake's water column Our samplings of the lake water were done at two different stations: H1 (depth 5 85 m) and H3 (depth 5 65 m), which are shown in Fig. 1b 2015). Moreover, the observed vertical and temporal variations in concentrations were typical of those observed during the past 30 yr (Hayakawa et al. 2012).
Whereas the data showed large variations, the differences between the stations for samples taken at the same depth and observation time were small, i.e., 0.6 lmol L 21 for concentrations, 0.7& for d 15 N, 0.5& for d 18 O, and 0.2& for D 17 O, on average. We concluded that a major part of the lake's water column was horizontally homogeneous. As a result, we used the average values as those representing each depth between 0 m and 60 m and to obtain a single profile for each observation for the depths from 0 m to 80 m in the lake. The obtained profiles are presented in Fig. 3b-e, and these data will be used in further discussions as values representing the whole water column.
In March, the concentrations of NO 2 3 were homogenous throughout the water column, at 15.4 lmol L 21 (Fig. 3b), which suggests that the water was well mixed vertically in winter. This finding is also supported by the values of d 15 N, d 18 O, and D 17 O, which were almost uniform in March. Subsequently, the NO 2 3 in the surface 10 m decreased to less than 8 lmol L 21 in June and to less than 1 lmol L 21 in August (Fig. 3b), thus suggesting that active metabolism of NO 2 3 occurred, probably through assimilation by phytoplankton during stratification. These results were supported by the 15 N and 18 O enrichment in the d 15 N and d 18 O values of NO 2 3 in the surface 10 m in June when compared with the values in March (Fig. 3d,e), because partial assimilation of NO 2 3 by phytoplankton results in residual NO 2 3 being enriched with 15 N and 18 O (Granger et al. 2010).
Although assimilation must have been one of the major processes that controlled both the concentration and isotopic compositions of NO 2 3 in the surface layer, we found definite evidence of a trace contribution of new NO 2 3 from internal/external sources as well. The maximum D 17 O value (around 12.3&) found at the surface in June implied that deposition and accumulation of NO 2 3 atm from the atmosphere at the lake surface occurred during stratification. Meanwhile, the gradual decrease in the D 17 O value from March to October for the bottom layer (60-80 m) implied that NO 2 3 re remineralized from sinking PON via nitrification had accumulated at the bottom. Thus, while NO 2 3 assimilation was the major process that controlled the distribution and temporal variation of NO 2 3 in the lake, deposition of NO 2 3 atm on the surface and accumulation of NO 2 3 re through nitrification, at least at the bottom, were also responsible for the distribution and temporal variation of NO 2 3 in the lake.
By applying the obtained data to Eqs. 2, 3, we ascertained the values of N, d 15 N lake , d 18 O lake , and D 17 O lake for each observation in Table 2 Because the amount of NO 2 3 in the surface layers was small in August (about 1.2% of the whole NO 2 3 pool in the water column), this assumption had little influence on the final obtained values (d 15 N lake , d 18 O lake , and D 17 O lake ) in August, especially for D 17 O lake , which was an important value for subsequent calculations on the NO 2 3 dynamics. The estimated average D 17 O values of NO 2 3 in the lake (D 17 O lake ) were 11.6& in March, 11.6& in June, 11.2& in August, and 11.2& in October (Table 2), which corresponded to values for the average mixing ratio of NO 2 3 atm to the inventory of nitrate in the lake of 6.0%, 6.2%, 4.8%, and 4.7%, respectively, using Eq. 5. We concluded that 5.4% 6 0.8% of the inventory of nitrate in the lake originates directly from the atmosphere in the lake's water column; therefore, the remainder of nitrate was of remineralized origin (NO 2 3 re ) and was produced through nitrification in and around the lake.
The estimated average mixing ratio of NO 2 3 atm to the inventory of NO 2 3 in Lake Biwa (5.4% 6 0.8%) was smaller Tsunogai et al. Quantifying nitrate dynamics in a mesotrophic lake than the value determined for the oligotrophic Lake Mashu (9.7% 6 0.8%), which was estimated from D 17 O values as well . Because the deposition rate of NO 2 3 atm per unit area of the lake surface must be higher in Lake Biwa than in Lake Mashu (EANET 2014), the lower mixing ratios in Lake Biwa imply that there is a larger supply rate of NO 2 3 re to the Lake Biwa water column than that of Lake Mashu. These findings are quantitatively discussed in "Quantifying nitrate dynamics between each observation" section.

Quantifying nitrate dynamics between each observation
By using the values of N and D 17 O lake for each observation in Table 2, we calculated the gross amount of NO 2 3 supplied through nitrification (DN nit ) as well as that being metabolized through assimilation and denitrification (DN assim 1 DN denit ) in the lake by using Eqs. 10, 11 for each interval between the observation times. For the spring season (between 15 March and 17 June sampling), we found that 166 6 26 Mmol (Mmol 5 10 6 mol) of NO 2 3 re had been supplied into the lake water through nitrification, while 297 6 27 Mmol of NO 2 3 had been metabolized in the lake (Table 3). In a similar manner, we also estimated that 216 6 18 Mmol and 166 6 29 Mmol of NO 2 3 re had been supplied into the lake water through nitrification during summer season (between 17 June and 05 August sampling) and autumn season (between 05 August and 21 October sampling), respectively, while 245 6 19 Mmol and 111 6 30 Mmol of the NO 2 3 had been metabolized in the lake. Furthermore, by assuming that the lake returned back to its initial state 1 yr after the first observation in March, we estimated 92 6 41 Mmol of the NO 2 3 re had been supplied into the lake water through nitrification, while 156 6 44 Mmol of the NO 2 3 had been metabolized in the lake in winter season (between 21 October and 15 March sampling). On a whole year basis, 641 6 113 Mmol of the NO 2 3 re had been supplied into the lake's water column through nitrification, while 809 6 120 Mmol of the NO 2 3 had been metabolized in the lake through assimilation and denitrification (Table 3; Fig.  4). By dividing each estimated amount by the duration between the observations, we found that the average nitrification rates (F nit ) and average metabolic rates of nitrate (F assim 1 F denit ) were 1. Similar seasonal variation in F assim 1 F denit of showing a maximum value in summer and a minimum value in winter was detected in Lake Mashu as well . Past observations on primary production rates in Lake Biwa (F assim ) also displayed similar seasonal variation (Yoshimizu et al. 2002;Urabe et al. 2005;Ota et al. 2013). Thus, the observed seasonal variation in F assim 1 F denit , showing a maximum in summer and a minimum in winter, is a highly reasonable estimate for this lake.
Notably, however, the seasonal F nit variation in Lake Biwa was different from that in Lake Mashu. Whereas F nit in Lake Mashu was almost stable regardless of the season , F nit in Lake Biwa showed significant seasonal variation, with the maximum in summer, and the minimum in winter (Fig. 5). Moreover, F nit in Lake Biwa showed normal correlation with F assim 1 F denit , with a slope close to 1 Tsunogai et al.
Quantifying nitrate dynamics in a mesotrophic lake S468 (Fig. 5). This normal correlation between F assim 1 F denit and F nit implies that F nit in the lake increased in response to the F assim 1 F denit increase and decreased in response to the F assim 1 F denit decrease, which corresponds to rapid remineralization of organic nitrogen to NO 2 3 in the lake. That is to say, organic nitrogen produced from NO 2 3 via assimilation had a short lifetime in the lake's water column, remineralizing to NO 2 3 shortly after assimilation. We also detected a gradual increasing trend in the F nit / (F assim 1 F denit ) ratios from spring to autumn (Fig. 5).
Whereas the F nit /(F assim 1 F denit ) ratio was 0.6 in spring, the F nit /(F assim 1 F denit ) ratio increased to 0.9 in summer, and 1.5 in autumn. The gradual increasing trend can be explained well by assuming the average time lag between production of new organic nitrogen through assimilation (5 assimilation of NO 2 3 ) and remineralization to NO 2 3 through nitrification was around 1 month, on average, in the lake's water Table 3. Estimated gross variation in the inventories of atmospheric nitrate (DA), remineralized nitrate (DR), and total nitrate (DN) in the lake divided into each supply/removal process, i.e., (1) atmospheric deposition (Dep), (2) influx via inflows (In) and efflux via outflows (Out), and (3) in-lake nitrification (Nit) and nitrate metabolism through assimilation and denitrification (Metab), in the lake during the observation period. All units are in Mmol N (5 10 6 mol N).   column. While F nit /(F assim 1 F denit ) increased because of blooming in spring, F nit was still low because of the time lag, so that the F nit /(F assim 1 F denit ) ratio was low in spring. In summer, when F assim was at the maximum for the year, F nit increased and became comparable with F assim , therefore the F nit /(F assim 1 F denit ) ratio was close to 1. While F assim decreased in autumn, F nit remained at a high level because of the time lag, and thus the F nit /(F assim 1 F denit ) ratio became higher in autumn. This average time lag was highly reasonable given the residence time of PON in freshwater environments. For instance, Islam et al. (2013) determined the average decomposition rates for the reactions from natural PON to NO 2 3 in rivers under dark conditions and found that the rate-limiting step (from PON to dissolved organic nitrogen) was 0.028 d 21 . We concluded that the seasonal variations in F nit and F assim 1 F denit estimated in this study were highly reliable estimates for the lake.

Spring
The total amount of NO 2 3 metabolized in the water column for the year (809 6 120 Mmol; Table 3) was much larger than the total inventory of NO 2 3 in the lake's water column in March (447 Mmol; Table 2), as well as the annual influx of NO 2 3 via inflows (199 6 40 Mmol; Table 3) or atmospheric deposition (36.9 6 6.7 Mmol; Table 3). We concluded that the rapid remineralization (nitrification) in the lake played a major role in sustaining the primary production using NO 2 3 within the lake, rather than that from influx via inflows or atmospheric deposition. Dividing the total inventory of NO 2 3 in March by the integrated annual removal rates (annual gross metabolic rate in the lake and annual efflux rate via outflows) yielded an approximate residence time of NO 2 3 in the lake of 0.5 yr. This residence time corresponds to less than 1/10 of that for the water in the lake.

Comparison with the 15 N tracer method
To see if the estimated total metabolic rates of NO 2 3 (F assim 1 F denit ) using the D 17 O method were reasonable, we also determined the assimilation rates of NO 2 3 (F assim ) using the 15 N tracer method simultaneously and compared the results between the two. Clear 15 N enrichment of more than 1200& was always observed in the PON samples incubated for 24 h under 15 NO 2 3 addition. The determined gross NO 2 3 assimilation rates in the bottles ranged from 90 mmol N L 21 d 21 to 709 mmol N L 21 d 21 , and the depth integrated areal gross rates ranged from 4.0 mmol N L 21 d 21 to 5.2 mmol N d 21 m 22 (Fig. 6). These values coincided well with those determined using the 15 N tracer incubation method in the same lake in past studies (Frenette et al. 1996(Frenette et al. , 1998. The estimated annual assimilation rate using the 15 N tracer method was 978 Mmol yr 21 (5 4.6 mmolNO 2 3 m 22 d 21 ), which almost corresponds with the annual metabolic rates using the D 17 O method (809 6 120 Mmol yr 21 5 3.3 6 0.5 mmolNO 2 3 m 22 d 21 ; Table 3 and Fig. 6), implying that the estimated gross metabolic rates of NO 2 3 obtained through the use of the D 17 O method were highly reliable as for the NO 2 3 dynamics in the lake. Whereas the metabolic rates of NO 2 3 estimated based on the D 17 O method were the total metabolic rates of NO 2 3 (F assim 1 F denit ), in which not only those through assimilation (F assim ) but also those through denitrification (F denit ) were included ), the assimilation rates estimated based on the 15 N tracer method corresponded to those through assimilation only (F assim ). If denitrification was significant in the lake, the metabolic rates estimated based on the D 17 O method would have been higher than those estimated based on the 15 N tracer method. However, the actual total metabolic rates estimated based on the D 17 O method showed the opposite trend; smaller than the assimilation rates estimated based on the 15 N tracer method by 20% on the annual average. Consequently, the present results also implied that the metabolic rates of NO 2 3 through denitrification were much lower than those through assimilation in the lake (i.e., F denit F assim ). Furthermore, several problems inherent in the two different methods could be responsible for the discrepancies between the results.
These problems include the (1) NO 2 3 assimilation by periphyton that had been excluded from the assimilation rates estimated based on the 15 N method using bottles (Axler and Reuter 1996), (2) NO 2 3 metabolism in the littoral zone of the lake that had been excluded from the assimilation rates estimated based on the 15 N method using bottles (Slawyk et al. 1998), (3) production of DO 15 N during incubation in the bottles using the 15 N tracer method, and (4) occurrence of photoinhibition during water sample handling shipboard for the incubation using the 15 N tracer method. However, all of these problems were likely minor because they would have induced higher total metabolic rates in the D 17 O method than in the 15 N tracer method, whereas the results showed the opposite trend (Fig. 6). More likely causes for the discrepancies are (5) artificial stimulation of NO 2 3 assimilation rates using the 15 N tracer method from possible contamination by trace nutrients (including trace metals) in the bottles and (6) poor representativeness of the determined assimilation rates based on the 15 N tracer method for the values representing each season. Because the assimilation rate estimated by using the 15 N tracer method was based on the instantaneous assimilation rate at each sampling point, the potential problem described in (6) was most likely responsible for the discrepancies, especially for those in summer and winter.
Because NO 2 3 was almost exhausted from the surface 10 m in August (Fig. 3b), the instantaneous assimilation rate determined was inevitably low. The observed NO 2 3 depletion in August, however, implies that active NO 2 3 assimilation occurred prior to the sampling. As a result, if we take into account the active NO 2 3 assimilation prior to the sampling date (i.e., prior to the NO 2 3 being exhausted), the actual assimilation rate in summer should be larger than that determined in August based on the 15 N tracer method.
In contrast, the instantaneous assimilation rate determined on the sampling days in winter (15 March and 21 October) might be larger than that of the other days in winter. Whereas the solar irradiance levels were lowest in winter, e.g., less than 10 MJ m 22 at the surface in general, they were high on the sampling days, e.g., at around 15 MJ m 22 and 20 MJ m 22 , respectively. In addition, the surface was enriched in nutrients owing to deep convection. Because assimilation rates of NO 2 3 are a function of photosynthetically available radiation under low irradiance/high nutrient conditions (Frenette et al. 2003), the NO 2 3 assimilation rates might have been higher during sampling in October and March than the typical values for winter. This was partly a result of our attempts to avoid windy or rainy days during lake water sampling to ensure safe boat operations; hence, the solar irradiance levels were higher than normal.
Whatever the specific reasons were, however, all of the possible problems described above are problems inherent in the 15 N tracer method and not problems associated with the D 17 O method. The findings for both the total metabolic rates using the D 17 O method was higher than the assimilation rates using the 15 N tracer incubation method in summer and the total metabolic rates using the D 17 O method was lower than the assimilation rates using the 15 N tracer incubation method in winter also support the notion that the total metabolic rates of NO 2 3 based on the D 17 O method are highly reliable for the studied lake. Thus, we concluded that the estimated total metabolic rates of NO 2 3 that were obtained using the D 17 O method represented accurate values for the lake.
Comparison with the denitrification rates reported in the literatures As shown in "Comparison with the 15 N tracer method" section, the results of the present study implied that, in the lake, the metabolic rates of NO 2 3 through denitrification were much lower than those through assimilation (F denit F assim ). To verify this hypothesis, we compared the total metabolic rates of NO 2 3 (F assim 1 F denit ) determined for the lake in this study with those through denitrification (F denit ) determined for the lake in past studies. Miyajima (1994) estimated the denitrification rate in the lake as 159 6 13 Mmol yr 21 , based on areal denitrification rates determined directly at the surface of offshore sediments (ranged from 0.08 mmol m 22 d 21 to 0.16 mmol m 22 d 21 ). Similar areal denitrification rates have been obtained during recent surveys as well (Morita and Maegawa 2006). These denitrification rates correspond to only 20% 6 5% of the total metabolic rates of NO 2 3 (F assim 1 F denit ) estimated based on the D 17 O method in this study (809 6 120 Mmol yr 21 ). We concluded that denitrification was minor within the whole NO 2 3 metabolism in the lake, and thus more than 75% of the NO 2 3 metabolism (F assim 1 F denit ) was through assimilation (F assim ).
Whereas dissolved oxygen in the hypolimnion of the lake shows a gradual decreasing trend every year (Kalff 2002), oxygen is still enriched in most of the lake's water column (Shiga Prefecture 2015). The minimum concentration of dissolved oxygen in 2013, for instance, was 39% of the saturation level within the whole monthly monitoring data set collected at offshore stations by Shiga Prefecture (Shiga Prefecture 2015). The relatively slower denitrification rates than the assimilation rates in the lake should be reasonable as the NO 2 3 dynamics in the lake. As presented in the previous section, the estimated assimilation rates (F assim ) based on the 15 N tracer method were less reliable in this study (as well as in past studies) than the total metabolic rates of NO 2 3 (F assim 1 F denit ) estimated based on the D 17 O method, probably because the number of sampling events was insufficient to obtain accurate and precise F assim using the 15 N tracer method. If we were to estimate F assim that was more precise and accurate based on the 15 N tracer method by increasing the number of sampling events throughout the year, we would be able to estimate denitrification rates (F denit ) that were more precise from the difference between F assim obtained through the highly precise 15 N