The subtropical Feitsui Reservoir, located in northern Taiwan, is the country's second largest reservoir by volume (first is Tsengwen Dam in the south), serving as the main water source for over 5 million people in the Taipei metropolitan area. The domestic demand is supplied by water releases from the Feitsui Reservoir and unregulated flow from Nanshin Creek downstream of the watershed. The upstream watershed encompasses the Beishi stream basin a branch of Xindian River, one of the three major tributaries of Tamsui River. The total catchment area of the reservoir is 303 km2 and storage volume at normal maximum water level is 406 million m3. The mean depth of the watershed is 40 m with maximum depth of 113 m near the dam site. The mean daily inflow to Feitsui Reservoir is ∼ 30 m3 s-1 and the amount of water released depends on the reservoir's storage capacity and whether flow from Nanshin Creek is sufficient to supply domestic demand (Shiau and Wu, 2010). In the past the reservoir was found to alternate between mesotrophic and oligotrophic states (Kuo et al., 2003), although more recent studies (Kuo et al., 2006) observed a trend towards eutrophication. In 2012 the reservoir was in a mesotrophic state according to Carlson's Trophic State Index (CTSI). In order to prevent deterioration of water quality, the watershed is protected by the Feitsui Reservoir Administration with restricted access to the water as well as adjacent areas and any commercial and recreational activities are prohibited. In addition, since January 1988 the Feitsui Reservoir Administration operates a meteorological station that provided direct wind speed measurements 10 m above the water level and rainfall data used in this study. Typhoon information was obtained from a typhoon database (http://rdc28.cwb.gov.tw/TDB/ctrl_typhoon_range_search).

Current assessments of PP rates rely on steady-state assumption. Whether the approximation is valid requires careful assessment and can be verified by studying the physical structure of the water body. Feitsui Reservoir is a typical monomictic system (characteristic of subtropical lakes) that stays thermally stratified throughout the greater part of the year, with changing intensity of winter vertical mixing depending on the meteorological conditions. The topographic characteristics of the reservoir, a large water mass located in a valley, make its physical structure (i.e. water temperature) fairly simple and stable over the seasonal scale (Itoh et al., 2015). The residence time of water in the reservoir tends to be rather long; throughout our study we estimated it to be about 150 days, comparable to durations reported in the past (150 days reported by Kuo et al., 2003, and 115 days reported by Chen et al., 2006), sufficiently long to mix horizontally well. Field measurements as well as model simulation by Kuo et al. (2003) reported similar trends in dissolved oxygen concentration throughout a period of 12 months, recorded at the Dam Site (S1) and at the Wu-Tan station situated on the other side of the reservoir upstream of the Beishi Creek. A comparison between the top, middle, and bottom layers of the water column showed that the reservoir is horizontally rather uniform and is not affected significantly by horizontal water advection (Kuo et al., 2003).

Sampling was carried out at station S1 (24.9∘ E, 121.566667∘ N; Fig. 1) in the Feitsui Reservoir in the upper 100 m, located in the deepest region of the lake (∼ 113 m). Water samples were collected using 5 L GO-FLO samplers with a manual messenger. For dissolved oxygen analysis, we collected waters at 9 depths (1, 5, 10, 15, 20, 30, 50, 70, and 90 m) during 13 separate trips to the reservoir, covering 1 full year from June 2014 to July 2015. Sampling for isotope analysis of water started later in September 2014.

Vertical profiles of temperature, chlorophyll a, and dissolved oxygen concentration were recorded routinely using Ocean Seven 316 CTD (IDRONAUT, Italy) multiparameter probe. A PAR sensor (BioTech) was used to measure photic irradiance. The casts were typically carried out on weekly basis during the summer and every 2 weeks during the winter. The accuracy of dissolved oxygen measurements was verified against in vitro measurements; water samples collected from 10 depths (0, 2, 5, 10, 15, 20, 30, 50, 70, and 90 m) were siphoned intro triplicate 60 mL bottles (Wheaton) and a colorimetric method of Pai et al. (1993) was adopted for in vitro dissolved O2 determination with precision of 0.2 % r.s.d. (full scale). We used a conservative approach for determining the mixed-layer depth based on visual inspections of vertical temperature and dissolved oxygen profiles to ensure the well-mixed layer only is described, without influences from the thermocline. For visualization and analysis of the profile data, we used Ocean Data View (ODV; Schlitzer, 2015).

Dissolved gasses were extracted from water following Emerson et al. (1995) and Luz et al. (2002). In summary, 300 mL flasks with LouwersHapert^© O-ring stopcock, containing 50 µL of saturated HgCl2 solution, were evacuated prior to sampling and closed with a water lock. Approximately 150 mL of water sample was collected in the flask, leaving 150 mL of headspace for gases to exsolve. Once stopcock closed, the port was filled with the same water as sampled and sealed with a rubber cap to avoid air contamination. All samples were equilibrated for 24 h in a shaker at room temperature. After equilibration, water was removed from the samples and the flasks were subsequently connected to a preparation system for removal of water vapour, CO2, and other condensable molecules at liquid nitrogen temperature. The extracted gases were then either stored in a sealed glass tube or directly introduced to a GC system (Thermo Scientific TRACE gas chromatograph) for complete removal of N2, after which only O2 and Ar remained the main components in the gas mixture. The separation was done using a chromatographic column (3 m long, 1/8 in. SS tube, packed with molecular sieve 5A at mesh 60/100), modified from Barkan and Luz (2003). During the separation the chromatographic column was kept at room temperature, and the yielded oxygen–argon mixture was absorbed onto two pellets of molecular sieve (1.6 mm, 5A, manufactured by SUPELCO) for subsequent isotopic analysis, following Abe (2008) with slight modifications.

In summary, water samples were incubated for approximately 2∼ 3 h and a chlorophyll-normalized photosynthesis rate versus light intensity (i.e. PB vs. I) model without the photoinhibition term, proposed by Jassby and Platt (1976), was used to calculate primary production over 24 h performed using an artificial light source to mimic the solar spectrum at an intensity controlled according to the solar irradiance measured in situ. The 14C rates reflect gross C production and are integrated for the entire euphotic zone. Detailed description of methodology for 14C incubation experiments is provided in Shiah et al. (1996).

δ17O and δ18O in O2 from the purified oxygen–argon mixture (as explained in Sect. 2.3) were determined by dual inlet mass spectrometry (Thermo Scientific Finnigan MAT 253 Stable Isotope Ratio Mass Spectrometer). Each sample was run for 3 acquisitions, 12 changeover cycles each, and thus the reported δ values represent the average of 36 cycles. The analytical errors (1-σ standard error of the mean n=36 multiplied by Student's t factor for a 95 % confidence limits, reported following Barkan and Luz, 2003) for δ17O and δ18O were 0.013 and 0.006 ‰, respectively. Our actual and long-term precision (1-σ standard deviation) established from routine measurements (n= 36) of atmospheric O2 for δ17O, δ18O, and 17Δ was 0.017, 0.030 ‰, and 6 per meg, respectively (see Supplement Table S1). Our current O2 scale, reported in Liang and Mahata (2015), is in agreement with that of Luz and Barkan (2011).

The O2 / Ar ratio was obtained by peak jumping; a sequential measurement of m/z “32” and “40” in the same collector (with the idle and integration times 20 and 4 s, respectively, following Barkan and Luz, 2003) prior to isotopic ratio analysis. The O2 / Ar ratio is expressed in the standard δ notations and calculated as δO2 / Ar (‰) = [(32/40)sample/(32/40)standard-1]103. The long-term precision (1-σ standard deviation) of routine measurements of atmospheric air was better than 5 ‰. For all water samples the final δO2 / Ar values were corrected for the distribution of gases between the headspace and water in the sampling flasks, following Luz et al. (2002) and normalized to air. To verify the purity of the collected oxygen–argon mixture after the GC separation, we have also included regular monitoring of m/z “28” signal during peak jumping. We did not detect any significant presence of N2 during the course of the study, either in atmospheric air or water samples for dissolved oxygen analysis. For all analysed samples the N2 / O2 signal ratio was lower than 0.001.

Similar to Barkan and Luz (2003) and Abe and Yoshida (2003), we found that the values of δ17O, δ18O, and 17Δ are affected by the O2 / Ar ratio, presumably due to interference with the ion source of the mass spectrometer. Although this effect on the δ17O and the δ18O values is minor, it may significantly affect the 17Δ. We have calculated the dependencies of the δ17O, δ18O, and 17Δ on the δO2 / Ar, derived from measurements of aliquots of pure O2 with added different amounts of Ar and applied the correction to the reported final isotopic values. The regression slopes for δ17O, δ18O, and 17Δ were 0.00001‰/‰(R2=0.66), -0.00002‰/‰(R2=0.79), and 0.0217 per meg / ‰  (R2=0.99), respectively.

To minimize the influence of Ar, and for obtaining more precise results, we used a working O2–Ar reference mixture from pure gases (> 99.999 %) with the proportion of O2 / Ar ∼ 20:1, similar to the O2–Ar solubility ratio in surface water (Benson and Krause, 1984; Krause and Benson, 1989; Barkan and Luz, 2003). The integrity of the standard was checked regularly by measuring aliquots of atmospheric O2. For every set of samples for dissolved O2 analysis from Feitsui Reservoir (one set representing one trip to the reservoir) three aliquots of atmospheric O2 were prepared and measured against the same aliquot of working reference gas mixture as used for the water sample set.

To evaluate the reproducibility and performance of sample preparation, we prepared air–equilibrated water. The equilibration was achieved by continuous stirring of 8 L of deionized water with added HgCl2 in a circulator with temperature control at 25 ∘C over a period of 72 h. Dissolved gases were extracted following the same procedure as applied for the reservoir samples (see Sect. 2.2). The reproducibility (1-σ standard deviation) for the analysis of equilibrated water samples (n = 3) was 0.020, 0.037 ‰, and 3 per meg for δ17O, δ18O, and 17Δ, respectively, and 4.6 ‰ for δO2 / Ar (Table 1).

To identify the source of water in the reservoir, we carried out additional analyses of δD and δ18O in the H2O molecule of reservoir water. For this, water samples were collected in 15 mL centrifuged vials and sealed with Parafilm M^® to prevent any isotopic alteration due to evaporation. Prior to analysis, water was transferred to 2 mL vials with the aid of a pipette and analysed in a Picarro L2130-I Isotopic H2O Analyser, following Laskar et al. (2014). δD and δ18O values are expressed with respect to VSMOW (‰). The 17Δ was determined using CoF3 fluorination method following Barkan and Luz (2005). Briefly, an aliquot of 5 µL of water was converted to O2 by injecting it to a CoF3-containing reaction tube heated at 370∘ under helium flow. The evolved oxygen gas was collected in a 13X molecular sieve U-trap at liquid nitrogen temperature and then determined by dual-inlet mass spectrometry (Thermo Scientific Delta Plus). Each sample was run for 80 changeover valve cycles, i.e. 80 sample–standard combinations. Mean standard deviations (1-σ) of multiple duplicate analyses for various waters (including VSMOW2, GISP, and SLAP) for δ17O, δ18O, and 17Δ, were 0.086 ‰, 0.168 ‰, and 11 per meg, respectively.

Aquatic PP, the synthesis of organic compounds from aqueous carbon-containing species, in a steady-state system may be distinguished as GP and NP. The GP represents the total carbon fixed by primary producers, and the NP represents the carbon available to the heterotrophic community. The NP is therefore the difference between GP and community respiration and corresponds to the overall metabolic balance of an ecosystem. NP can be positive or negative. NP is positive when GP exceeds respiration and the ecosystem may export or store organic C. The value is negative when respiration exceeds GP and the ecosystem respires more organic C than was able to produce. Both GP and NP are terms of fundamental interest in carbon cycle studies.

To quantify GP rates from 17Δ values, a simple box model may be applied; mixed-layer gross oxygen production (GOP) is assumed at steady state with respect to 17Δ and O2 concentrations, and vertical mixing is neglected, following Luz and Barkan (2000). GOP=KCo(17Δ-17Δeq)/(17Δbio-17Δ), where Co is the O2 concentration at saturation using solubility coefficients from Benson and Krause (1984) and K is piston velocity (the coefficient for gas exchange; Crusius and Wanninkhof, 2003; Wanninkhof et al., 2009). Here the 17Δeq is the air–water equilibrium, deviating from zero due to isotopic fractionation during O2 invasion and the 17Δbio represents the value of purely biologically produced O2. We calculated K (the piston velocity) from daily wind speeds at Feitsui Reservoir according to Wanninkhof et al. (1987) and Vachon and Prairie (2013), based on studies of gas transfer velocities in lakes of comparable sizes to Feitsui Reservoir. Because the gas concentrations in the mixed layer depend on the recent history of wind speeds, we averaged K over the residence time of O2 in the mixed-layer preceding sampling, based on the mixed-layer depth and gas transfer coefficient.

Equation (2), however, represents a mathematical approximation to provide a first order realization of processes and sources that affect the GP. This simplified formulation may introduce large errors, in particular in ecosystems with elevated export ratios. Prokopenko et al. (2011) and Kaiser (2011) derived an improved “dual-delta approach”, which we applied for estimating GP rates in the Feitsui Reservoir, where the GOP may be directly calculated from the measured δ17O and δ18O values, as follows: GOP=KCo1-δ17Oeq+1δ17O+1-0.5181-δ18Oeq+1δ18O+1δ17Op+1δ17O+1-1-0.518δ18Op+1δ18O+1-1 where δ∗O is the measured value in a sample, δ∗Oeq is the air–water equilibrium, and δ∗Op represents the photosynthetic O2.

To estimate the net oxygen production (NOP) rates, we have used the O2 / Ar measurements, following the biological O2 supersaturation concept for net photosynthetic production. Because the physical properties of O2 and Ar are similar, and Ar has no biological sources and sinks, measurements of Ar concentration in water may be used to remove physical contributions to O2 supersaturation. The biological oxygen supersaturation Δ(O2 / Ar) is defined as the relative deviation of the O2 / Ar in a sample to the O2 / Ar at equilibrium with the atmosphere (Craig and Hayward, 1987; Spitzer and Jenkins, 1989; Emerson et al., 1995; Kaiser et al., 2005) and may be calculated as follows: Δ(O2/Ar)=1+(δO2/Ar)sample1+δO2/Areq-1. Assuming the mixed layer is at steady state, NOP can be calculated following Luz et al. (2002): NOP =KCoΔ(O2/Ar). A shortcoming associated with the calculation of PP rates from dissolved O2 isotopes is that the rates are in O2 units, instead of C-based units, and the conversion between them is not straightforward. To convert between O2 and C-based rates, we follow the common approach presented earlier (e.g. Hendricks et al., 2014; Juranek et al., 2012). GOP from 17Δ is greater than gross C production because it measures total oxygen produced regardless of its fate, such as the fraction of O2 produced which is linked to Mehler reaction and photorespiration. To scale GOP to gross C production, we account for this fraction following Laws et al. (2000) and apply a photosynthetic quotient (PQ) of 1.2. We convert NOP to a comparable C flux using a PQ of 1.4, for new production (Laws, 1991).

We refer to our monthly sampling dates as MMMYY for convenience. The subtropical Feitsui Reservoir was thermally stratified for the great part of the year, with a distinct seasonal thermocline (Fig. 2a). In spring, seasonal stratification developed (APR15), and the lake remained well stratified with a shallow epilimnion with temperature above ∼ 30 ∘C throughout the warmer months in the top 10 m layer. In summer, the reservoir was strongly stratified as the result of continued heating of the surface water and the mixed layer remained shallow, typically about 3–5 m deep, as observed in JUN14, AUG14, APR15, MAY15, and JUL15. Although the thermal structure of the reservoir controls the gas exchange during the warm months, processes such as rainfall and windstorms may entrain atmospheric air to the thermocline, as indicated from dissolved O2 and Δ(O2 / Ar) vertical profiles (Figs. 2c and 4c), playing a critical role in influencing the conditions in the mixed layer. From SEP14 and OCT14, as a result of decreasing ambient temperature and gradual cooling of surface water, the mixed layer deepened and reached 11 and 23 m, respectively. In DEC14 the thermal stratification became weaker, initiating the winter overturn and resulting in well-mixed epilimnion of ∼ 22 ∘C to 34 m depth and a decreasing temperature gradient in the metalimnion. In JAN15 the mixed layer was deepest at 51 m. The mixed layer remained deep throughout FEB15 (40 m) when the reservoir was coolest and nearly homothermal ∼ 17 ∘C in the epilimnion and ∼ 16 ∘C in the hypolimnion.

The chlorophyll a (Chl a) (Fig. 2b) in the reservoir was predominantly restricted to the epilimnion and the upper thermocline. The distribution and concentration varied with seasons and with the occurrence of stochastic events (such as storms, strong rainfall, or typhoons) that enhanced the photosynthetic activity in the phytoplankton. Chl a concentration was high from JUN14 to SEP14, with a subsurface maximum below the mixed layer at ∼ 10 m, averaging to 15 mg m-3 and occasionally above 20 mg m-3. In late SEP14, the Chl a maximum shifted to the surface. No apparent maximum was observed in OCT14 when Chl a concentration was rather uniform throughout the mixed layer of average ∼ 8 mg m-3 in the upper 23 m. From DEC14 to FEB15, Chl a remained low at ∼ 3 mg m-3. In spring, Chl a concentration started to increase at the surface averaging ∼ 5 mg m-3, followed by later appearance of a subsurface maximum at 12 m of ∼ 8 mg m-3. A short episodic decrease in Chl a was recorded in APR15, a likely result of cooler ambient temperature than normal and frequent precipitation. In MAY15, Chl a concentration increased again and high subsurface maximum of > 10 mg m-3 formed at 15 m.

The dissolved oxygen (DO) concentration and saturation levels (Fig. 2c) varied in association with O2–Ar ratios measured, indicating the availability of dissolved O2 supplied by primary production, aeration, or mixing processes. The epilimnion remained saturated throughout the year, and in the thermocline DO varied greatly; DO was undersaturated from AUG14 to DEC14 (< 50 %), reached near-saturation levels during the winter, and remained supersaturated from APR15 to JUN15 (> 100 %). In spring and summer the DO reached the hypolimnion where the saturation was typically above 50 %. Conversely, from early AUG14, throughout autumn and winter the hypolimnion was undersaturated (< 50 %) with minimal DO content.

In addition to dissolved O2, we have measured the isotopic composition of water in the Feitsui Reservoir throughout the different seasons. The isotopic composition of water varied in both δ18O (Fig. 3a) and δD (Fig. 3b) seasonally and vertically. Overall, the variation of δ18O was smaller than that of δD, varying between -29.73 and -28.18 ‰ (-6.5 and -5.3 ‰ vs. VSMOW) in δ18O and between -37.1 and -25.4 ‰ in δD. The general pattern for both δD and δ18O showed more depleted values during autumn, followed by gradual enrichment throughout the winter, spring, and early summer. No statistically significant (within errors) seasonal variation was found in 17Δ values. We therefore averaged the 17Δ over the year, with the resultant 17Δ of 257 ± 14 per meg, representing the 17Δ of water in the Feitsui Reservoir. The insignificance in 17Δ seasonality is consistent with the small overall variation in δ18O and also with the long residence of water in the reservoir.

The 17Δ signal of dissolved O2 varied with depth and seasons (Fig. 4b). The overall range of the 17Δ values measured varied between the maximum of 205 per meg in late AUG14 and JUL15 and minimum of 26 per meg in JUN14. The annual mean 17Δ at the surface (1 m) was 65 ± 13 per meg and remained constant throughout the year, with the exception of late SEP14 and JUL15, when the surface values were higher, recording 97 and 76 per meg, respectively, and coinciding with an episodic shift of Chl a maximum towards the surface (Fig. 2b). During months with persistent thermal stratification in the reservoir, the 17Δ followed a similar vertical pattern, with distinct 17Δ values. From JUN14 to early SEP14, when the mixed layer was very shallow (∼ 3–5 m), the 17Δ signal accumulated below, in the upper thermocline, with a peak exceeding 150 per meg observed typically at ∼ 10–20 m depth. Below the thermocline at ∼ 50 m depth in AUG14 and SEP14 the 17Δ was low, showing signals characteristic of surface water. In late SEP14 and OCT14 as the mixed layer deepened gradually, we observed a corresponding trend for the 17Δ, with the peak in the signal deepening (205 and 156 per meg at ∼ 20 and 30 m, respectively) following the mixed-layer boundary. In DEC14 the deep mixed layer and decreasing importance of the thermal stratification facilitated increased gas exchange throughout the water column resulting in low and rather uniform 17Δ values in the water column of 63 ± 6 per meg. This trend continued throughout the winter period, during which the 17Δ values stayed comparatively low and less variable. The onset of thermal stratification during the spring allowed for 17Δ to increase below the mixed layer; in APR15 we observed a developing peak in the 17Δ signal of 105 per meg at 10 m. The 17Δ increased throughout MAY15, and in JUN15 and JUL15 the accumulated 17Δ signal at 10–30 m, reached up to 193 per meg, coinciding with the observed DO supersaturation (Fig. 2c) and elevated Δ(O2 / Ar) (Fig. 4c). In contrast to the trend from JUL14, in JUL15 the 17Δ signal was high below the mixed layer and throughout the whole water column. Although samples from regions below 50 and 70 m were limited due to insufficient amount of gas for isotope analysis, overall the 17Δ values tend to increase towards the bottom of the hypolimnion, in particular high 17Δ was measured at 70 m in late AUG14, SEP14, and JUL15 of 152, 157, and 174 per meg, respectively.

Following Prokopenko et al. (2011) and Kaiser (2011), we estimated PP rates using the dual-delta approach in the Feitsui Reservoir from JUN14 to JUL15.

The GP rates, NP rates and the NP / GP ratio obtained by the dual-delta approach are summarized in Table 2. Overall, the GP rates varied between 187 and 1372 mg C m-2 d-1. The general pattern showed higher values during the cooler months and in winter, averaging to 702 ± 107 mg C m-2 d-1 between OCT14 and APR15. This may be considered as maximum production because the mixed layer is deeper than the euphotic zone in winter. A decrease in the GP was observed in summer, averaging to 303 ± 66 mg C m-2 d-1 throughout JUN14, AUG14, MAY15 and JUN14. This represents the minimum GP for this period, because the mixed layer is shallower than the euphotic zone and therefore some production also took place below the mixed layer, which may not be evaluated by the present model. Production was highest in late SEP14 and in JUL15, 1372 and 1162 mg C m-2 d-1, respectively, coinciding with typhoon events affecting the area of the Feitsui Reservoir.

Overall, the NP ranged between -311 and 228 mg C m-2 d-1. The NP was negative from OCT14 to FEB15, averaging -198 ± 78 mg C m-2 d-1, indicating the reservoir was net heterotrophic in the mixed layer during the winter. Positive NP rates dominated in the warmer months with values typically averaging 57 ± 26 mg C m-2 d-1, implying the reservoir remained net autotrophic during the greater part of the year. Highest NP rates were observed in JUL15 measuring 228 mg C m-2 d-1. The NP / GP ratio varied between -0.44 and 0.30.

Using the GP and NP rates measured in our study, we estimated the annual C production in the Feitsui Reservoir. Excluding the measurements obtained during typhoons (late SEP14 and JUL15), the average annual GP amounted to 177 g C m-2 yr-1 and the average annual NP was -12 g C m-2 yr-1. Taking into consideration typhoon events, the average annual GP increases to 220 g C m-2 yr-1, and the average annual NP to -3 g C m-2 yr-1. For comparison, a model study by Lewis (2011) estimates the global average annual production per unit area for a lake 200 g C m-2 yr-1 for GP and 160 g C m-2 yr-1 for NP. While our GP estimates agree well with this projection, in particular when the production rates take into account typhoon events, our NP rates lie at the lower end of the global average. The measured NP rates in the Feitsui Reservoir thus indicate that over the year the respiration exceeds gross primary production in the reservoir, affecting the net balance of carbon. Episodic events such as typhoon events seem to play a key role in the metabolism of Feitsui Reservoir, and it is plausible that during years with frequent typhoon events the annual balance of the reservoir may shift to net autotrophy. Although some carbon storage is expected in the form of accumulation of organic matter to the sediments (Dean and Gorham, 1988), our results indicate that from 2014 to 2015 the Feitsui Reservoir acted as a positive though minor carbon source to the atmosphere.

The schematics of 17Δ transport and variation are summarized in Fig. 5. The near-surface 17Δ value represents a balance between O2 produced photosynthetically, which tends to increase the 17Δ, and that from gaseous exchange with atmospheric O2, which reduces the 17Δ value. The nearly constant surface 17Δ values measured in the Feitsui Reservoir throughout the year (65 ± 13 per meg) suggest that the balance of these processes does not typically vary with seasons. In late SEP14 and in JUL15, the surface 17Δ values were 32 and 10 per meg higher, respectively, than the annual mean, indicating additional input from photosynthesis. Further analysis showed that in both cases, the samples were taken within a few days after typhoon occurrences. Thus the resulting elevated 17Δ is likely to be a consequence of nutrient enrichment caused by typhoons, mediating enhanced vertical mixing and hence photosynthesis (see Sect. 4.5 for further details). Previous studies showed that in the Feitsui Reservoir phosphate plays a key role as the limiting nutrient, restricting the microbial production. The key processes that determine its availability are vertical mixing from changes in the mixed-layer depth in the spring and typhoon intensity in summer and autumn (Tseng et al., 2010; Itoh et al., 2012). These processes therefore likely play a role in the distribution of the 17Δ signal in the water column as well as increase photosynthetic activity as a result of intensified production after nutrient enrichment.

High subsurface 17Δ may be primarily attributed to the decreasing importance of gas exchange with depth. This is particularly characteristic of the warmer months during which strong thermal stratification developed, confining the primary producers to the thermocline (also shown by Chl a, Fig. 2b) where the conditions are optimal for phytoplankton growth, representing a compromise between light, temperature, and nutrient availability. From AUG14 to OCT14 we recorded high 17Δ (often above 150 per meg) values below the thermocline (5–30 m). It is likely that the local primary production was initially high, a possible result of a phytoplankton bloom influencing the observed 17Δ composition. However, the measured low Δ(O2 / Ar) values (about -30 %) and undersaturation of DO indicate O2 consumption from AUG14 to OCT14 in the upper thermocline. In the absence of photosynthesis, the residual 17Δ signal thus points towards the lack of vertical mixing in the reservoir during this period as well as no influence from atmospheric air. At 50 m depth, we recorded 17Δ values, typical of near-surface water. Here, the 17Δ shows an inverse relationship to Δ(O2 / Ar) as well as DO, with lower 17Δ and higher Δ(O2 / Ar) and DO observed in AUG14 and SEP14 and increasing 17Δ and decreasing Δ(O2 / Ar) DO saturation observed in OCT14. Additionally, the signal also follows the thermal structure of the reservoir; from July to about November 2014 we observe well-mixed epilimnion in the upper ∼ 10 to 20 m and an extensive metalimnion to about 50–60 m, with strong thermal gradient before reaching hypolimnion below. It is likely that the low 17Δ origins from atmospheric air entrainment during early summer (June and July, DO profile, Fig. 2c).

Intrusion of surface water below the metalimnion has been observed in previous studies and may also be supported by dust loading, which results in an increase in total suspended material at depth (Tseng et al., 2010). Strong vertical mixing of air–saturated water down the water column in JUN15, indicated by the low 17Δ values, increased Δ(O2 / Ar), and DO, as a result of heavy rainfall (∼ 700 mm accumulated precipitations during JUN14 compared to ∼ 340 and ∼ 200 mm measured in JUL14 and AUG14, respectively; Fig. 6) may have supplied atmospheric O2 to the metalimnion and the hypolimnion. As of early AUG14 at 50 m, the observed 17Δ signal possibly traces the remaining 17Δ signal from JUN15, locally confined due to the strong thermal gradient and unaltered by photosynthesis due to the lack of primary producers at this depth. The breaking down of both the high 17Δ from ∼ 20 to 30 m and the low 17Δ from 50 m throughout autumn is controlled by decreasing air temperatures and the consequent weakening thermal stratification in the reservoir, also observed in other years (Itoh et al., 2012). Apart from storms and typhoons causing wind stress at the air–water interface or heavy precipitation, lake processes such as seiches may contribute to vertical mixing. Seiches were never evaluated in the Feitsui Reservoir, but they may play an important role in affecting the vertical transfer of the water masses, dissolved gases, and nutrients in the Feitsui Reservoir and should be considered in future studies.

An increase in the 17Δ towards the bottom of the lake (90 m samples) was observed during all seasons, likely originating from the transport of enhanced 17Δ values from the upper part of the water column and any photosynthetically induced changes to the signal before it reached the bottom. These samples, however, contained only small amounts of O2 (saturation less than ∼ 50 %), and therefore it is possible that minor photosynthetic contributions could significantly increase the 17Δ values as a result of vertical entrainment mentioned previously.

Although the improved dual-delta method presents a mathematically more accurate approximation than the previous 17Δ model, a number of uncertainties associated with both methods for estimating PP rates remain, which need closer attention. Luz and Barkan (2000), Prokopeno et al. (2011), and Kaiser (2011) demonstrated that GP in the mixed layer could be determined from the measurements of 17Δ or the δ values in dissolved O2 using a steady-state mixed-layer oxygen budget model which allows for estimation of integrated gross productivity in the mixed layer over the residence time of mixed-layer O2. It is important to note that this approach may underestimate GP on occasions when the euphotic zone is deeper than the mixed layer since the calculation accounts for GP in the mixed layer only. This may particularly affect PP estimates during summer months, when the photic layer is typically deeper than the mixed layer in subtropical reservoirs in general, and about 4 times deeper in the Feitsui Reservoir. Furthermore, this model lacks terms for advection and vertical mixing. While the effect of these simplifications may be negligible in the open ocean (Emerson et al., 1997), lakes and reservoirs often feature a complex vertical and horizontal structure, the effect of which needs to be considered. Fortunately, given the rather simple physical structure of the Feitsui Reservoir (see Sect. 2.2), horizontal inhomogeneities may be neglected. The column inventory approach presented below (Sect. 4.3) provides a robust technique for assessing the contributions of vertical mixing and to estimate the production below the mixed layer.

The key parameter to constrain the GP and NP rates is the gas exchange rate between the mixed layer and the atmosphere. Presently this is best achieved by parameterization of wind speeds, which is commonly used in models with several empirical relationships between the wind speed and gas exchange rate (e.g. Clark et al., 1995; Ho et al., 2006; Wanninkhof et al., 2009). However, parameterization of wind speeds does not come without inaccuracies. In most of the oceanic studies, the error associated with the parameterization is attributed to the accuracy of wind speed measurements and the relationship between the wind speed and gas exchange rate at very high or low wind speed conditions (Wanninkhof, 1992). In freshwater systems, factors such as lake size and ecosystem heterogeneity present another important factor (Vachon and Prairie, 2013) and should be taken into consideration when choosing an appropriate parameterization.

Apart from δ values measured in samples, δ∗Oeq and δ∗Op or 17Δeq and 17Δbio are important constituents of this method. δ∗Oeq or 17Δeq is rather well established and can be determined experimentally by air–water equilibrations, usually achieved by bubbling or stirring (Keedakkadan et al., 2015). The δ∗Op or 17Δbio represents the photosynthetic O2 composition, with controversy on these values discussed in the literature (e.g. Kaiser 2011; Luz and Barkan, 2011; Nicholson, 2011). The major problem lies in proper quantification of the value for 17Δbio. Being closely dependent on the 17Δ of substrate water and less straightforward to measure, the 17Δbio value was previously often assumed to be the same as that of water. Recently, Luz and Barkan (2011) showed that a small difference exists between the substrate water values and the average composition of photosynthetic O2 produced by phytoplankton. This potential bias has to be considered in order to improve the accuracy of primary production estimates. Furthermore, whereas a uniform value for 17Δ of seawater may be applied to study PP in the ocean, 17Δ for a freshwater system of interest has to be determined because the isotopic composition of freshwater tends to vary geographically and among different water sources (Luz and Barkan, 2010). For Feitsui Reservoir we determined 257 ± 14 per meg for 17Δ of water based on measurements of water samples collected throughout the year. The difference between the isotopic composition of Feitsui Reservoir water and that of photosynthetic O2 provided by Luz and Barkan (2011) therefore reflects the associated fractionation between the substrate water and the photosynthetic O2. To obtain the representative δ∗Op and 17Δbio values for the Feitsui Reservoir, we consider these additional fractionations of 26 per meg and 3.306 ‰ for 17Δbio and δ18O, respectively, to our measured values of water and retrospectively calculate the δ17OP. The resulting annual mean values for δ17OP, δ18OP and 17Δbio were -13.156 ± 0.192 ‰, -25.975 ± 0.370 ‰, and 283 ± 9 per meg, respectively.

Compared to the GP, estimating the NP is less complicated, since the model only requires the coefficient for gas exchange and a term describing the biological supersaturation. The second term can be constrained by the Δ(O2 / Ar) based on measurements from flask samples or determined in situ using a sensor for dissolved O2 supersaturation, although the accuracy of the latter is inferior and may be less suitable for this purpose. Combining 17Δ and Δ(O2 / Ar) measurements we can get the NP / GP ratio, which is equivalent to an export ratio (Laws et al., 2000) describing the capacity of an ecosystem to export C. The NP / GP ratio can be far better constrained than the GP on its own, since it is independent of the gas exchange rate and the uncertainty in the ratio only depends on the error in the measurement of 17Δ and Δ(O2 / Ar).

As discussed previously (Sect. 4.1), in case of fast changing physical dynamics in a reservoir, a mixed-layer budget by isotope mass balance calculation may not be applicable for the assessment of PP rates. To assess the relevance of this method for the Feitsui Reservoir, we tested an alternative mass balance model based on a whole column inventory approach (onwards referred to as column inventory approach or CI-GP). Unlike isotope mass balance limited to the mixed layer, the column inventory model requires time-series data of full profiles from the surface to the bottom of the lake, and it is able to obtain the GP rates below the mixed layer without steady-state assumptions.

Calculating the GP by the column inventory model is done by solving the following simultaneous equations: 16Ot-16Ot-1=16P-16C+16I-16E,17Ot-17Ot-1=17P-17C+17I-17E,18Ot-18Ot-1=18P-18C+18I,-18E where nOt and nOt-1 are the total amount of oxygen isotope n in the water column from the surface to the bottom of lake at the time slice t and t-1 (a step before time t), respectively; nP, nC, nI, and nE are GP, consumption rate for entire water column, influx from the atmosphere, and efflux to the atmosphere, respectively, for oxygen isotope n. Equation (6) can be substituted by column inventory or rates of total dissolved oxygen in Eq. (9). Ot-Ot-1=P-C+I-E Equations (7) and (8) can be obtained by multiplying isotopic composition (1+δnO) and/or isotope fractionation factor (1+nε) in Eq. (9).

While a non-steady-state model is beyond the scope of this paper, the column inventory approach enables us to introduce dynamics into the calculations of GP and evaluate the feasibility of the mixed-layer approach for estimating PP rates in the Feitsui Reservoir. Because the purpose of this model is to compare two different approaches rather than produce accurate estimates, and for simplicity, we calculated the mixed-layer approach GP rates using Eq. (2) and present the 17Δ-GP / CI–GP ratio (Fig. 7). Overall, the GP rates obtained from 17Δ-GP and CI–GP model showed a good agreement with each other, indicating the calculation of GP rates using a mixed-layer model may be valid for the Feitsui Reservoir, not only for open oceans. A better fit between the respective rates may be obtained using lambda slope 0.520, although the reasons for this remain presently unclear. Further adjustments of 17Δeq and 17Δbio could also improve the fit.

While both methods aim to evaluate the natural GP rates, direct comparisons between estimates from the dual-delta method and from the 14C bottle incubation are impractical because of the principal differences in the methodologies (in situ vs. in vitro). Each method provides rates integrated over different spatial and temporal scales, and clearly methodological biases are associated with each. A number of studies have addressed the dual-delta GP / 14C–GP in the ocean, but the ratios were found to vary significantly from 2.2 (Quay et al., 2010) to 8.2 ± 4.0 (Stanley et al., 2010; see also Juranek and Quay, 2013, for an extensive review). The variability in the ratios remains a conundrum. Overall, the dual-delta GP method showed a tendency to yield higher production rates. The factors responsible for the variability in the GP / 14C–GP are, however, yet to be properly identified, before the gross O2 production and C fixation can be properly linked and compared.

Contrasting the GP rates from dual-delta approach and the 14C–GP rates (Table 2 and Fig. 6) we note that both estimates show a very similar trend. Moreover the production rates are on the same order of magnitude, with an average GP / 14C–GP ratio of 1.2 ± 1.1. Although, due to the reasons mentioned above, it is unclear why the respective GP rates may agree or disagree, our results support the findings from an earlier study by Luz and Barkan (2000) who demonstrated near equivalence of GP rates obtained from incubation-dependent and incubation-independent methods from Lake Kinneret. Presumably, near 1 GP / 14C–GP ratios are characteristic of systems with shallow mixed-layer and rapid O2 turnover, such as subtropical reservoirs in general, including the Feitsui Reservoir. The disparity between the 17Δ GP and 14C–GP rates from AUG14 and early SEP14 could be explained by the shallow summer mixed layer, which would provide minimal GP rates due to the limitations of this approach. Conversely, it could also be that the 14C–GP is overestimating the production rates particularly during this period, when algal blooms are more likely to occur. This highlights one of the key assets of the GP method, which in principle is not significantly affected by small-scale short-term events. From DEC14 onwards the dual-delta GP rates and 14C–GP show a close fit. Throughout the winter months, both methods showed rather invariable GP rates, though the dual-delta results were by approximately a factor of 2 higher than the 14C–GP rates, a possible attribute of the integration on which each method operates. A similar, but reverse, trend was also observed in MAY15, but onwards in JUN15 and JUL15 both methods showed a close fit.

Passing of tropical cyclones has been documented to cause entrainment and upwelling or “atmospheric pumping”, i.e. injecting nutrients into the mixed layer which may significantly elevate PP. In the South China Sea, Lin et al. (2003) reported that the occurrence of only a moderate cyclone led to a 30-fold increase in the concentration of surface Chl a. Ko et al. (2015) studied the phytoplankton responses to typhoons in the Feitsui Reservoir and found a 2-fold increase in the phytoplankton level during typhoon periods. Conversely, in regions with deep mixed layer and nutricline, typhoon events may not be sufficient to increase PP or induce phytoplankton blooms (Lin, 2012). The effect of typhoon events on ecosystems is, however, complex and difficult to document properly because of their sporadic occurrence. Although our data are too limited to draw solid conclusions, we briefly discuss our results in context of typhoon events.

Two typhoons closely affected the north-eastern Taiwan and the Feitsui Reservoir during our study period. Typhoon Fung Wong hit Taiwan on 22 September 2014 and typhoon Chan Hom on 10 July 2015, 1 and 4 days before the sample collection, respectively. Post-typhoon sampling occasions are indicated in Table 2. On both occasions, we found a considerable increase in the GP in the mixed layer (to 1372 and 1162 mg C m-2 d-1), representing approximately a 3-fold increase in the GP rates to those obtained on previous sampling days (Fig. 6), suggesting a critical role of typhoons in modifying the seasonal metabolic balance of the reservoir. This corresponds to 32 and 10 per meg increase in surface 17Δ. However, short episodic events of high production are normally expected to average out by the lower background 17Δ of the mixed layer due to elevated gas exchange with air. It is plausible that if the mixed layer is very shallow and the photosynthetic O2 production is high, the elevated 17Δ signal would remain for an extended period of time. Alternatively, increased 17Δ values could arise from ventilation from water below the mixed layer or enhanced vertical mixing. Greater K caused by higher wind speeds during a typhoon event could explain the higher GP rates; however, it does not explain the increase in 17Δ signal. Nevertheless it is important to note that these GP rates should be considered as minimum values because on both occasions the thermocline was situated in the photic zone and therefore some of the production also took place below the mixed layer.