Frequency Dynamics of Dissolved Oxygen and Chlorophyll Widens the Scope of Lake Metabolism Studies

LIMNOLOGY

and Limnol. Oceanogr. 63, 2018, 72–90 VC 2017 The Authors Limnology and Oceanography published by Wiley Periodicals, Inc. OCEANOGRAPHY on behalf of Association for the Sciences of Limnology and Oceanography doi: 10.1002/lno.10615

Coupled simulation of high-frequency dynamics of dissolved oxygen and chlorophyll widens the scope of lake metabolism studies

Vera Istvanovics ,* Mark Honti MTA-BME Water Research Group, Budapest, Hungary Abstract High frequency time series of dissolved oxygen (DO), delayed chlorophyll fluorescence (Chl) and relevant background variables were recorded on nearly 900 d during 7 yr in large, shallow, meso-eutrophic Lake Bala- ton (Hungary). Novel models were developed for coupled simulation of diel dynamics of DO and Chl using sequential learning and uncertainty assessment in a Bayesian framework. Despite the generally good model fit for both variables, the uncertainty of the metabolic estimates was high, due primarily to the identification problem of individual metabolic processes. Deviations between observed and simulated DO concentrations suggested that neglect of transient stratification might be responsible for the bulk of the systematic model errors. Net ecosystem production (NEP) was uncertain. Unless air-water oxygen exchange can be estimated from direct measurements, the free-water DO method cannot reliably estimate NEP. Gross primary production (GPP) could satisfactorily be hindcasted assuming non-linear multiplicative dependence on Chl, water temperature and light. Hindcast of community respiration (CR) was less successful, possibly due to the impact of local benthic respiration. Results suggested a major shift in lake metabolism at about 168C. Below and above this temperature, 70% and 90% of net primary production could be utilized by heterotrophs within a day, respectively. Indirect evidence suggested that biomass-specific net primary production was determined by phosphorus. The large difference between reproductive rates and net growth rates estimated from GPP and Chl and from daily change in Chl, respectively indicated that loss rates of phytoplankton were as important determinants of algal dynamics as reproductive rates.

In a carbon-based biosphere, every single individual and Vollenweider et al. 1974), because it is easier to measure DO each ecosystem take part in the global biogeochemical cycle than inorganic carbon, and because dissolution of O2 in water of carbon (C). There is a considerable interest in understand- is a pure physical process in contrast to the complicated ing dynamics of C cycling in various types of lakes (also chemical equilibrium of CO2 (Stumm and Morgan 1981; Han- called “lake metabolism”), because it reﬂects overall ecosys- son et al. 2003). With the spread of relatively cheap, auto- tem functioning (Odum 1956; Batt et al. 2013). Studies of mated, reliable DO sensors, an increasing number of lake lake metabolism have recently gained momentum in the con- metabolism studies are based on the free-water DO method text of climate change that brought into question whether (Staehr et al. 2010a). The relationship between C and DO lakes are sinks or sources of CO2 at regional and global scales metabolism, however, is not straightforward. (Cole et al. 2007; Tranvik et al. 2009). Since oxygenic photo- An approximate stoichiometric coupling between CO2 and synthesis and aerobic respiration dominate the biological car- O2 exists only in oxygenic photosynthesis and aerobic respira- bon cycle (Holland and Turekian 2011), cycles of carbon and tion. Anoxygenic photosynthesis, anaerobic respiration and

O2 are inherently associated in most aquatic ecosystems. Free- fermentation tend to decouple C and O2 cycles in aquatic eco- water assessment of lake metabolism on the basis of dissolved systems. Photo-oxidation of organic carbon further modiﬁes

O2 concentration (DO) has a long tradition (Odum 1956; the C : O2 stoichiometry of metabolism in humic lakes (Graneli et al. 1996). Besides these complications, molar quo-

tients of both photosynthesis and respiration (O2 : C and *Correspondence: [email protected] C:O2, respectively) exhibit taxon-speciﬁc and physiological Additional Supporting Information may be found in the online version variability (Falkowski and Raven 1997). While inputs and of this article. outputs of DO other than gas exchange with the atmosphere This is an open access article under the terms of the Creative Commons are usually negligible, catchment-borne inputs of organic Attribution License, which permits use, distribution and reproduction in carbon may profoundly inﬂuence lake metabolism (Hanson any medium, provided the original work is properly cited. et al. 2003; Tranvik et al. 2009; Staehr et al. 2010b).

72 Istvanovics and Honti Coupled simulation of DO and Chl dynamics

Odum (1956) has developed a simple method to estimate could only be identified at the cost of poorly supported gross primary production (GPP) and community respiration assumptions (“bookkeeping” method) or a set of poorly recog- (CR) from diel DO curves measured in streams: nizable parameters (mechanistic models). Although the respiration of both autotrophic and heterotrophic organisms DDO 5GPP2CR2X1INl;w (1) depends on organisms’ physiological status and environmen- Dt tal conditions (Geider and Osborne1989; Pringault et al. 23 21 where rates are expressed as g O2 m d . X is the atmo- 2009), the “bookkeeping” approach assumed that CR was spheric exchange rate (positive when O2 escapes from the identical in the dark and in the light (Staehr et al. 2010a). water). Inflow and outflow of DO via advection have been Dynamic models linked GPP and CR to one or more drivers neglected. Local input from the watershed, INl;w, has also (light, temperature, and algal biomass), usually without been neglected because it was small and did not show diel constraining any of the parameters by direct observations variability. Odum (1956) solved his equation using the (for a review, see McNair et al. 2015). “bookkeeping” method – the only option when DO data are A better identification of the underlying processes in a sparse (hourly or less frequent). Although nowadays high fre- dynamic system can be achieved by developing tighter quency DO measurements (order of minutes) are common, theories, and/or collecting richer data (Manski 1993). most studies adopted Odum’s method to estimate metabolic Nowadays phytoplankton and/or dissolved organic matter rates (Cole et al. 2000; Hanson et al. 2003; Lopez-Archilla fluorescence is measured at high frequency in many lakes, et al. 2004; Staehr et al. 2010a). Dynamic models with vari- simultaneously with DO (http://www.gleon.org; http://www. ous levels of complexity have also been developed that allow dkit.ie/networking-lake-observatories-europe). Combining these assessment of the uncertainty in metabolic estimates (Han- datasets within an appropriate modeling framework may par- son et al. 2008; Solomon et al. 2013; Honti et al. 2016). tially solve the identification problem and promote under- Uncertainties that showed up in modeling were most often standing of details of lake metabolism that have not been explained by neglected physical processes, primarily vertical explored by existing models. and horizontal transport (Hanson et al. 2008; Staehr et al. The present study aimed at coupling dynamics of DO and 2010a; Solomon et al. 2013; Rose et al. 2014). Indeed, a sig- phytoplankton by mechanistic models of various complexity nificant effect of transport on single point DO measurements using high frequency records from nearly 900 d in a 7-yr long has repeatedly been demonstrated (Lauster et al. 2006; Sadro period from large, shallow, meso-eutrophic Lake Balaton (sur- 2 et al. 2011; Staehr et al. 2012b; Antenucci et al. 2013; face area is 594 km , mean depth is 3.1 m), Hungary. Our McNair et al. 2015). objective was to explore whether these complex models could Surprisingly, the major source of uncertainty, the identifi- provide a consistent and deeper insight into lake metabolism cation problem has been overlooked in nearly every study of than models aiming at capturing only DO dynamics. We lake metabolism (but see Hanson et al. 2008; Honti et al. adopted the modeling approach of Honti et al. (2016), which 2016), while it has attracted much attention in other disci- is based on sequential learning and uncertainty assessment in plines, such as economics and hydrology (Manski 1993; Beven a Bayesian framework. The long dataset allowed us to statisti- 2001). The identification problem means that quite different cally analyze metabolic rates as a function of environmental model structures and/or more than one set of parameters of drivers at various time scales. the same model generate observationally equivalent distributions and therefore there is no way to decide which model is Materials and methods the “best” one and which parameter set is the “true” one. Study site

According to Eq. 1 (assuming INl,w 5 0), observed changes in In shallow, elongated Lake Balaton strong, steady north, DO should first be split into two unknown components: net north-west winds generate relatively closed large-scale water cir- ecosystem production (NEP; NEP 5 GPP–CR) and atmospheric culations in the four basins (Shanahan et al. 1986; Fig. 1). Large gas exchange (X). To cope with the identification problem, longitudinal and transverse seiches are characteristic of the lake metabolic studies applied empirical or semi-empirical func- (Muszkalay 1973; Shanahan et al. 1986). Wind-induced waves tions to estimate X (Odum 1956; Cole and Caraco 1998; Staehr cause frequent sediment resuspension (Luettich et al. 1990; et al. 2010a). The choice of X, however, predetermined NEP Istvanovics et al. 2004). The main inflow (the Zala River) drains and error in X propagated directly into uncertainty in NEP about half (2750 km2) of the total watershed into the smallest (Vollenweider et al. 1974; Gelda and Effler 2002; Dugan et al. and shallowest Basin 1 (surface area is 38 km2; mean depth is 2016). A second identification problem emerges when NEP is 2.3 m, maximum depth is 3 m, mean water residence time is 3 decomposed into GPP and CR. Since night-time GPP is zero, months), where we operate our monitoring station (Fig. 1). CR (more precisely, CR-X) can be recognized with relatively Balaton is a calcareous lake (in Basin 1, mean pH is high confidence when transport does not interfere seriously 8.4, alkalinity is 4 mEq L21, calcium concentration is (Hanson et al. 2008). During the day, however, GPP and CR 46 g Ca m23, magnesium concentration is 57 g Mg m23).

73 Istvanovics and Honti Coupled simulation of DO and Chl dynamics

Sió Canal

Depth (m) B3 0 - 1.5 1.5 - 2.5 2.5 - 4.0 4.0 - 5.0 1 5.0 - 9.0 B1 B2

Shoreline 0 5 10 km Settlements Zala River

Fig. 1. Bathymetric map of Lake Balaton. Open star indicates the monitoring site. B1–B4 are the four basins of the lake. Insertion shows the watershed.

The water is always turbid due to intense calcite precipita- aquatic macrophytes had low abundance during the study tion and sediment resuspension. Secchi depth averages period. Water depth at the station varied between 0.9 m and 0.5 m in Basin 1 during the ice-free period. Macrophyte 1.9 m as estimated from a reference depth – water level and growth is restricted to about 5% of surface area by low light daily mean water levels of the lake (http://www.hydroinfo. availability and high wave exposure (Entz and Sebestyen hu). Measurements were carried out between 2009 and 2015, 1946; Virag 1998; Istvanovics et al. 2008). usually from early April to late October. Sensors were Rapid eutrophication during the 1970s (Herodek 1986) inspected and cleaned manually twice a week according to a has successfully been managed by measures taken from the maintenance protocol. We kept strict electronic record of late 1980s. Although N2-ﬁxing ﬁlamentous cyanobacteria every intervention and event that might concern the quality still dominate summer phytoplankton in Basin 1 in most of measurements. years (Padisak et al. 2006), recovery from eutrophication has In April 2009, we deployed an electrochemical DO sensor been observed from the late 1990s (Istvanovics and (WTW Oxi, Germany) in the middle of the water column. Somlyody 2001). In the early 2000s, the climate sensitivity This sensor was replaced with an optical sensor (Hach HQD, of the lake has unexpectedly come into the focus of manage- U.S.A.) in May 2009. From 2010, two optical DO sensors ment. After several decades of maintaining water level in a were positioned at known depths (0.3–0.6 m and 0.8–1.2 m gradually narrowing range prescribed on socio-economic from the bottom depending on water level). Sensors were rather than ecological grounds, the lake lost one third of its calibrated in water-saturated air. DO concentration and volume during the severe drought in 2000–2004. Climate water temperature were recorded every minute, taking a 30 s change has been predicted to increase the frequency of low average. water levels (Honti and Somlyody 2009). Wind speed and direction, as well as global radiation (400–1100 nm) were recorded at 6.1 m from the bottom High frequency measurements every minute (Mettech Ltd., Hungary). The height of the Our monitoring station was situated in the muddy north- anemometer above the water surface was calculated ern littoral (4384501400N and 1781405900E; Fig. 1), where from mean daily water depth. Wind speed was corrected for

74 Istvanovics and Honti Coupled simulation of DO and Chl dynamics

21 10 m (U10,ms ) according to the logarithmic rule (Smith (1962). Carbon-based cell quota was estimated by assuming 1988). Turbidity was recorded every 6 s with light- a C/Chl ratio of 50. backscattering sensors (Wetlabs, U.S.A.) facing downwards. Daily mean discharge (Q,m3 s21), daily loads of SRP The number of turbidity sensors decreased from 5 to 2 dur- (molybdenum blue method), total P (measured as SRP after ing the study period due to technical reasons. H2SO4–H2O2 digestion), nitrate (the salicylate method) and The concentration of chlorophyll (Chl) and photosyn- weekly load of dissolved organic C (DOC; CHN autoanalyser) thetic properties of phytoplankton were estimated every were obtained from the West Transdanubian Water Director- 35–45 min by the delayed fluorescence (DF) technique, ate at the inlet gauge of the Zala River that transports about which detects only living, actively photosynthesizing algae 90% of total loads to Basin 1. (Gerhardt and Bodemer 1998; Istvanovics et al. 2005). The Metabolic models fully automated DF equipment (Tett Ltd., Hungary) sampled The most parsimonious model for simulating coupled water from the middle of the water column into a dark dynamics of DO and phytoplankton biomass requires three chamber. After 5–10 min of dark adaptation, algae were illu- state variables: DO, autotrophic biomass (B , mg Chl m23) minated with white LEDs at saturating light intensity. DF a and heterotrophic biomass (B ,gCm23): decay kinetics was measured in the dark for 100 s. To mea- h sure light-dependence of DF, dark-adapted algae were sub- dDO 5GPPi2Ri 2Ri 2Xi; (2a) jected to 9–18 light levels up to 400 lmol photon m22 s21 dt a h before their DF signal was measured for 1 s (dimension: dBa 1 i i i 5 3 GPP 2Ra2GHP ; (2b) Nominal DF Unit, NDFU; Honti and Istvanovics 2011). The dt qðÞO2 : Chl hyperbolic tangent function of Jassby and Platt (1976) was dBh i i 5qðÞC : O2 3 GHP 2Rh ; (2c) fitted to the data using Solver in Microsoft Excel to estimate dt aB (NDFU [mg Chl]21 [lmol photon m22 s21]21), the where the superscript i denotes instantaneous rates. Each biomass-specific initial slope that reflects efficiency of light 23 21 B 21 rate is expressed as g O2 m d . Community respiration utilization and Pmax (NDFU [mg Chl] ), the biomass-specific i i was split into its autotrophic (Ra) and heterotrophic (Rh) maximal rate of photosynthesis. i i i components (CR 5 Ra 1 Rh). The quotient of photosynthesis Manual measurements and the reciprocal of the quotient of autotrophic respiration To convert vertically averaged turbidity (NTU) to the coef- were assumed to be equal [qðÞO2 : Chl ] and were expressed 21 21 ficient of diffuse light attenuation (Kd,m ), underwater in terms of chlorophyll (g O2 [mg Chl] ). Respiratory quo- light profiles were measured manually each week at 0.1 m tient of heterotrophic organisms qðÞC : O2 had the dimen- 21 i depth intervals using a 4p quantum sensor (LiCor, U.S.A.). sion g C (g O2) . GHP was gross heterotrophic production.

Kd and mean turbidity were linearly related (Kd5 A metabolic model cannot fully reflect the diversity of tro- 0:078 NTU 1 0:612, r2 5 0.89, n 5 92). phic interactions. Equation 2 was based on two simplifying The concentration of Chl was estimated from DF data using assumptions. First, the contribution of higher than second- conversion factors obtained from linear regressions between ary trophic levels to community metabolism was negligible DF kinetic integral and weekly manual measurements of Chl. and thus, heterotrophic organisms included only bacteria, Water samples were filtered onto Whatman GF/F glass fiber fil- grazers, and detritivores. Second, net sedimentation of ters. Chlorophyll a was extracted for 24 h in cold acetone in phytoplankton was zero. the dark, and measured with a TD700 fluorimeter (Turner To address the lack of high frequency information on Bh Designs, U.S.A.) using the non-acidification optical kit (EPA and GHPi, two solutions were possible. The first option was Method 445). Conversion factors were different from year to to further simplify Eq. 2 by assuming that sub-diel changes year because of major upgrades of the DF equipment. The in Bh were negligible (Model 1; Table 1, Supporting Informa- determination coefficient of linear regressions exceeded 0.85 tion Table S1). This assumption did not preclude day-to-day in each year (n 5 20–25). and seasonal variability in Bh, since the rate of heterotrophic 20 Potential phosphorus (P) limitation of GPP was assessed respiration at 208C(Rh ) was calibrated and its changes 21 using cell quota of surplus phosphorus (QSP, mg P [g C] ). should reflect changes in Bh at scales over a day. The second Since surplus P has not been measured in the present study, option was to simulate daily change in heterotrophic bio- we used weekly data obtained between 2000 and 2004 at our mass (Model 2; Supporting Information Table S1). While monitoring site (Istvanovics et al. 2004). Triplicate water Model 1 decreased the power of the identification problem samples were filtered onto pre-washed cellulose acetate compared to Odum’s model (Eq. 1), Model 2 provided a more membrane filters (0.2 lm pore diameter; Whatman) and detailed description of lake metabolism than the models pub- extracted in boiling distilled water for 1 h (Fitzgerald and lished so far on free-water DO dynamics (McNair et al. 2015). Nelsson 1966). Concentration of soluble reactive P (SRP) was GPPi was a hyperbolic tangent function of mean photosyn- determined in the extracts according to Murphy and Riley thetically active radiation (PAR) in the mixed water column

75 Istvanovics and Honti Coupled simulation of DO and Chl dynamics

Table 1. Definition of state variables, processes, and parame- (Garcia and Gordon 1992). The Schmidt number (Sci)wascalcu- ters used to model lake metabolism. lated from Ti according to Wanninkhof (1992). Piston velocity i 21 (k600,md at Sc 5 600) should depend on both wind speed and Symbol Definition convective currents (MacIntyre et al. 2010; Dugan et al. 2016). 23 DO Concentration of dissolved oxygen (g O2 m ) Since no direct measurements were available on atmospheric gas 23 Ba Biomass (mg Chl m ) exchange in Lake Balaton to choose the proper empirical func- 23 i Bh Heterotrophic biomass (g C m ) tion for k600, we used an iterative approach. First we ran Model 1 i GPP , GPP Instantaneous rate and daily integral of gross on the whole data set with k600 as an adjustable parameter. 23 21 i primary production (g O2 m d ) Thereafter we examined the relationship between estimated k600 CRi, CR Instantaneous rate and daily integral of community and wind speed during periods of cooling, warming and constant 23 21 i i respiration (g O2 m d ) temperature. The k600 5 f(U10) relations were similar in these i Ra; Ra Instantaneous rate and daily integral of three periods. Therefore, the final lake-specific function used in 23 21 autotrophic respiration (g O2 m d ) both Models 1 and 2 was based on wind speed only: Ri ; R Instantaneous rate and daily integral of ( h h 1:44 if Ui < 6 heterotrophic respiration (g O m23 d21) i i 10 2 k600 U10 5 : (3) i i GHP , GHP Instantaneous rate and daily integral of gross 0:413U1020:99; otherwise 23 21 heterotrophic production (g O2 m d ) i X ,X Instantaneous rate and daily integral of Processing of input variables 23 21 atmospheric O2 exchange (g O2 m d ) The measured time series were preprocessed before using q(O2 : Chl) Photosynthetic quotient, reciprocal of autotrophic them as inputs to the models. A day was defined as the 21 respiratory quotient (g O2 [mg Chl] ) period between two successive sunrises. We selected days 21 q(C : O2) Heterotrophic respiratory quotient (g C [g O2] ) when each input variable, as well as DO and Chl data were B; 20 Pmax Biomass-specific maximum rate of photosynthesis available during the whole day. The number of such days 21 21 at T 5 208C(gO2 [mg Chl] d ) was 887. Four additional days were also accepted when DO B a Biomass-specific light utilization efficiency measurements ceased during the night, but at least half of 21 21 22 21 21 (g O2 [mg Chl] d [lmol photon m s ] ) the dark period was covered by data. Of the input variables, hP Temperature coefficient of photosynthesis (–) Ti, Ui , incident PAR (PARi ) and Ki were averaged for 10 20 23 21 10 0 d CR Community respiration at T 5 208C(gO2 m d ) i B B min. T was also averaged vertically. DF data (Pmax and a ) f 20 Fraction of autotrophic biomass respired a were averaged for a day and converted from their original 21 in a day at T 5 208C(d ) dimensions to their dimensions used in the model. Based on R20 Heterotrophic respiration at T 5 208C(gO m23 d21) h 2 previous results (Honti and Istvanovics 2011), a conversion hR Temperature coefficient of respiration (–) 21 21 factor of 0.004 mg O2 NDFU d was adopted. Consider- 21 kGHP Rate constant of gross heterotrophic production (d ) ing that mean measured PB was in the order of 105 NDFU 21 max k600 Piston velocity of O2 at Sc 5 600 (m d ) 21 21 21 [mg Chl] , this corresponded to 0.4 g O2 [mg Chl] d ,a i Sc Schmidt number (–) realistic value (Stefan and Fang 1994). PAR was estimated Zmix Mixing depth (m) according to Reynolds (1997): DOsat Temperature-dependent concentration of qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 23 i DO at 100% saturation (g O2 m ) i i PAR 5PAR0 3 exp 2Kd3 Zmix : (4)

We assumed that PAR was 47% of global radiation (J m22 21 21 i s ) and mean energy of photons was 218 kJ mol in the (PAR , lmol photon m22 s21; Jassby and Platt 1976) with a visible range (400–700 nm). Mixing depth (Z ) was taken van’t Hoff–Arrhenius type dependence on water temperature mix equal to the depth of the water column in spite of frequent (Ti, 8C; Talling 1966; Supporting Information Table S1). Respi- but transient stratification that usually lasted for a few hours ration was also temperature-dependent. GHPi was proportion- (Vor€ os€ et al. 2010). ate to Ba and independent of Bh. We chose this description because in Lake Balaton the most important consumers of Parameters and model calibration algae and algal detritus were chironomid larvae besides bacte- The number of adjustable parameters was reduced before ria (Specziar and Vor€ os€ 2001). Since maximum clearance rate fitting the models by finding constant values for certain of filter feeding zooplankton did not exceed 10% of water vol- parameters. We assumed that the molar respiratory quotient 21 ume per day (G.-Toth et al. 1986), grazing was omitted. of heterotrophs was 1, that is qðÞC : O2 5 0.375 g C (g O2) . Xi was a linear function of saturation deficit and piston veloc- Similarly, molar quotients of both photosynthesis and auto- i ity (Supporting Information Table S1). DOsat was approximated trophic respiration were assumed to equal 1. Since these lat- from water temperature by a 5th order polynomial function ter quotients were expressed in terms of Chl, a C/Chl ratio

76 Istvanovics and Honti Coupled simulation of DO and Chl dynamics

Table 2. Coefﬁcients of autocorrelations (in the diagonal) and Sperman’s rank correlations (below the diagonal) among drivers of metabolism and daily integrals of metabolic estimates.*

Variable ADO T PAR DTU10 Ba GPP CR NPP X NEP Bh NHP

ADO 0.67 T 0.42 0.96 PAR 0.50 0.42 0.64 DT 0.40 0.33 0.64 0.45

U10 20.37 20.14 20.44 20.44 0.43

Ba 0.56 0.18 0.12 0.10 20.16 0.96 GPP 0.76 0.59 0.51 0.34 20.31 0.71 0.93 CR 0.65 0.49 0.29 0.12 20.22 0.67 0.83 0.92 NPP 0.76 0.56 0.52 0.35 20.32 0.68 1.00 0.82 0.92 X 20.28 20.36 20.46 20.51 0.18 20.15 20.40 0.07 20.41 0.90 NEP 0.29 0.28 0.42 0.45 20.17 0.17 0.39 20.12 0.40 –0.92 0.84

Bh 0.35 20.02 0.25 0.04 20.22 0.42 0.42 0.53 0.43 0.09 20.14 0.80 NHP 0.25 0.21 0.36 0.41 20.17 0.13 0.28 20.17 0.28 –0.81 0.84 20.12 0.70

23 * ADO, amplitude of daily change in DO concentration (g O2 m ); T, daily mean water temperature (8C); PAR; daily mean photosynthetically active radia- 22 21 21 tion in the mixed water column ([lmol photon m s ); DT , daily mean temperature difference between the two DO sensors (8Cm ); U10, daily mean 21 23 21 23 21 wind speed at 10 m above water surface (m s ); NPP, net primary production (g O2 m d ); NEP, net ecosystem production (g O2 m d ); NHP, 23 21 net heterotrophic production (g O2 m d ). Other deﬁnitions are listed in Table 1. For numbers in bold, Nclass 2; 762 n 891.

was needed to find the value of qðÞO2 : Chl . Although C/Chl Bayesian parameter inference and uncertainty analysis were B B ratios of phytoplankton might vary in a wide range depend- performed. Measured daily mean values of Pmax and a with ing primarily on resource availability and temperature a prescribed coefficient of variation (CV; CV 5 standard devi- (Geider et al. 1998), we found a good agreement between ation/mean) of 20% were taken as prior distributions in each phytoplankton biomass and daily mean DO amplitude (A , 20 20 DO calibration unit. Non-measured parameters (CR , Rh and 23 21 gO2 m ) assuming a C/Chl ratio of 50 mg C (mg Chl) kGHP) were estimated by a sequential Bayesian learning pro- (Supporting Information Fig. S1). ADO was defined as the dif- cedure, in which posterior distributions obtained in the pre- th st ference between the 99 and 1 percentiles of DO concen- ceding day became prior distributions in the actual day (for trations measured during a day. Using this C/Chl ratio, the philosophy of this approach, see Honti et al. 2016). 21 qðÞO2 : Chl equaled 0.133 g O2 (mg Chl) . Structural errors of the metabolic model were described by a To determine the temperature coefficients of photosyn- first-order autoregressive error model for DO (Reichert and thesis and respiration (hP and hR, respectively) we ran Model Schuwirth 2012). A single likelihood function incorporated 1 on a sample of days with different parameter values. With fit to both the diel DO curve and daily mean algal biomass B; 20 20 “wrong” temperature coefficients, Pmax and CR strongly (Honti et al. 2016). Posterior distribution of parameters was h 5 h 5 co-varied with T. The final choice was P 1.06 and R 1.09. sampled for each calibration window with Markov chain With these values, Spearman’s rank correlation coefficients Monte Carlo sampling using the Metropolis algorithm between daily mean T and T-dependent parameters of both (Gamerman 1997). The differential equations of the model models (PB; 20,CR20 and R20) were low (0 > r > 20.1; max h s (Eq. 2, Supporting Information Table S1) were solved with n 5 891). Daily respiration of algae was taken as 10% of auto- the LSODA solver (Hindmarsh 1983; Petzold 1983). Instanta- trophic biomass (f 2050.1 d21; Reynolds 1997). In the a neous rates were integrated over the day; in the following observed range of daily mean water temperatures (10.6– only daily integrals are presented and analyzed. 31.68C), 4–27% of biomass could be respired in a day. Daily

Ra represented 4 to over 100% of daily GPP (average was 11%). The final number of adjustable model parameters was Statistical methods B; 20 B 20 B; 20 three in Model 1 (Pmax , a ,CR ) and four in Model 2 (Pmax , A locally weighted regression/smoothing technique B 20 (LOWESS; Cleveland 1979) was used to visualize non-linear a , Rh , kGHP; cf. Supporting Information Table S1). Models were calibrated to DO data that were averaged relationships between daily rates of metabolism and their both vertically and for 10 min time steps and to daily mean drivers. Multivariate non-linear regression models were fitted Chl using the method of Honti et al. (2016). Calibration was to square root transformed area-specific daily GPP and CR 22 21 done in a sliding window of 3 d. In each calibration unit, (Y,gO2 m d ):

77 Istvanovics and Honti Coupled simulation of DO and Chl dynamics

Y5Ymax3 fj; (5) ) a 1 j − s

2 where Y was the maximum transformed daily rate, j − max )

Q m 3 denoted driver variables and j fj reﬂected the assumption − m

that the effect of various drivers (fj) was independent and 2 multiplicative. For the sake of simplicity, each fj was O

expressed by the same function: photon

( 0 if x50 fjðÞx 5 (6) mol DO μ

a 3 2a ; otherwise (

expðÞ 1 6 8 10 12

i 0 50 100 150 where

8 PAR x 2x > crit > < if x xopt ) xcrit2xopt b 1 a5 (7) − > s :> xopt2x 11b 3 ; otherwise 2 xopt2xmin − m

In Eq. 7, b 5 5 was used to force fjðÞx to attain a near-zero value at x . Regression was calculated by using a conven- min C) ° tional likelihood function assuming independent, normally (

photon i

20 30 distributed errors. Square root transformation of data before T model ﬁtting was needed to improve the normality of model mol residuals. μ (

Autocorrelations of variables were measured by Pearson i 0 50 100 150 product-moment correlation coefﬁcients, whereas correla- 10

tions between variables were characterized by Spearman’s PAR rank correlation coefficients. Due to the large number of data (n > 730), correlations and linear regressions were highly c significant even at diminutive r. Instead of using statistical significance, we considered a correlation or regression useful

if the resolution power index (Nclass) of Prairie (1996) ) 1 exceeded a threshold value of 2. − s

C) ° ( (m

Results T i Raw data 10 There was a considerable year-to-year variability in both U Chl and external nutrient loads to Basin 1 (Supporting Infor-

mation Fig. S2). Although N2-ﬁxing cyanobacteria occasion- 02468 ally made up more than half of phytoplankton biomass in 20 21 22 23 most years (L. Vor€ os,€ unpubl.; Supporting Information Fig. 00:00 09:00 18:00 S2), large summer blooms developed only in 2010 and 2015. The highest Chl concentrations coincided with low external nutrient loads. Concentration of DOC was relatively con- Time 22 stant in the Zala River and thus, DOC load (LDOC;gCm month21) was primarily dependent on discharge. Fig. 2. Diel patterns of dissolved oxygen concentration (DO) and its To characterize the typical diel course of DO and its driv- drivers. Median (line) and 95% uncertainty range (2.5–97.5% quantiles; ers, we pooled data from each day (n 5 891) and calculated gray area) of 10 min values were calculated from pooled daily data (n 5 891). PARi - photosynthetically active radiation in the mixed water the median and 95% uncertainty range (2.5–97.5% quan- i i column, T - water temperature, U10 - wind speed at 10 m above water sur- tiles) of variables every 10 min (Fig. 2). Median DO ranged face. (a) DO (solid [black] line and range) and PARi (dashed [orange] line). 23 i i i between 8.1 and 9.7 g O2 m during this “average” day. (b) T (solid [black] line and range) and PAR (dashed [orange] line). (c) U10 i As expected, peak DO coincided with maximum T and was (solid [black] line and range) and T (dashed [orange] line). delayed behind the highest PAR by 4 h. DO saturation

78 Istvanovics and Honti Coupled simulation of DO and Chl dynamics

a b ) 3 − 1.10 m

2 O

) 1 1.08 − (g

d (

f DO k − sat DO −4 −2 0 2 1.04 1.06 1.08 1.1 1.04 1.06

00:00 09:00 18:00 −1.0 0.0 0.5 1.0 − −3 Time DOsat DO (g O2 m )

Fig. 3. Diel patterns of oxygen saturation deficit (DOsat-DO) and atmospheric gas exchange coefficient (kf). Median (line) and 95% uncertainty range (2.5–97.5% quantiles; gray area) of 10 min values were calculated from pooled daily data (n 5 891). (a) Saturation deficit (solid [black] line and range) and kf (dashed [orange] line). (b) Phase shift in the diel cycles of median saturation deficit and kf. Open circle indicates 00:00, arrows show evolution with time. ranged from 40% to 210%; oversaturation occurred in about average and a bad fit of Model 2 by selecting days when fre- half of the daytime period and in 40% during the night. quency of relative error was 0.025, 0.5, and 0.975 (Supporting

Median saturation deficit (DOsat-DO) ranged from 20.8 g O2 Information Fig. S3). Since the two models performed similarly 23 23 m to 0.9 g O2 m . Median atmosphericpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gas exchange well and yielded similar estimates for shared metabolic rates, 21 coefficient (kf,[d ]; kf5k600=Zmix3 600=Sc) had its mini- only results obtained with Model 2 will be presented in detail. mum before dawn and rose up to about 1.1 d21 by sunset To assess the influence of neglected transport, we deter- (Fig. 3), following the course of median water temperature mined the distribution of the DO error (DDO 5 DOobs-DOsim) and wind speed (Figs. 2, 3). Thus, gas exchange tended to be for every 10 min time step (n 5 128,172). Mean wind speed higher during the day than during the night (Fig. 3). Conse- and mean temperature difference between the two DO sen- 21 quently, an error in X might more strongly influence the sors (DT, 8Cm ) were calculated for each bin of DDO (Fig. estimates of GPP than CR. During the “average” day, there 4b,c). In the range, where 100 or more DDO values were 23 21 was a net oxygen release of 64 mg O2 m d from the available, the error tended to increase with decreasing wind lake. speed and increasing strength of stratification. The same pat- Of the environmental drivers of metabolism, water tem- tern emerged by integrating the area between observed and perature was strongly autocorrelated (Table 2). Autocorrela- modeled DO curves (not shown). However, integration tions of, and correlations between other drivers were too resulted in a relatively small sample size (n 8500) due to weak (r < 0.75) to reach the resolution power of Nclass 2. strong autocorrelation of deviations. Considering the “average” day, the peak in DDO coincided with maximal DT Simulation results (Fig. 4d). There was a good agreement between simulated and Despite their wide ranges, GPP and CR showed relatively observed time series of Chl (Model 1: Chlsim5 smooth seasonal variations (Supporting Information Fig. S4). 2 ðÞ5:34 6 0:19 1ðÞ0:91 6 0:01 3Chlobs, r 5 0.94, n 5 891, Nclass 5 This resulted in high autocorrelation of GPP and CR, that

5.24; Model 2: Chlsim5ðÞ2:74 6 0:15 1ðÞ0:94 6 0:01 3Chlobs, partly reflected the autocorrelation of ADO and partly that of 2 r 5 0.96, n 5 891, Nclass 5 6.48). In general, both models fitted the main drivers (Table 2). Net primary production (NPP, 23 21 reasonably to the DO time series. Measurement noise was an NPP 5 GPP - Ra;[gO2 m d ]) exceeded net heterotrophic 23 21 order of magnitude higher in the first 18 d of the study when production (NHP, NHP 5 GHP-Rh;gO2 m d ) by an order DO was measured with an electrochemical sensor than later of magnitude (Supporting Information Fig. S4). Uncertainties on when we used optical sensors. In the latter period, the stan- of metabolic estimates were compared by their mean daily 23 dard error of fit ranged between 0.05 g O2 m and 0.62 g O2 CVs calculated from posterior parameter distributions. Both m23. Relative error was obtained by dividing standard error model structure and the success of recognizing metabolic with the amplitude of diel DO change. Relative error remained processes influenced the CVs (Table 3). Community respira- below 10% in 59 and 66% of days fitting Models 1 and 2, tion could be identified with the highest confidence, respectively (Fig. 4). We exemplified a particularly good, an whereas uncertainty of net ecosystem production exceeded

79 Istvanovics and Honti Coupled simulation of DO and Chl dynamics

a b 0 10 ) 1 − ) (−) 2 − x ≤ (m s 10 X i 10 ( U P 4 − Prob. density (−) Prob. 10 01234567 0.0 0.4 0.8

0.0 0.1 0.2 0.3 0.4 −6 −2 2 4 6

−3 Relative Error (−) ΔDO (g O2 m )

c d 2.5 0.6 0 ) 10 3 − ) ) 1 1 m − − 0.5 1.5 2 2 − Cm Cm ° ° 10 ( ( T T Δ Δ −0.5 DO (g O 4 − Δ Prob. density (−) Prob. 10 00.511.52 0 0.2 0.4 −1.5 −6 −2 2 4 6 00:00 09:00 18:00 Δ −3 DO (g O2 m ) Time

Fig. 4. Model performance and the impact of physical processes on the error in dissolved oxygen concentrations (DDO, the difference between observed and modeled DO). (a) Distribution function of daily relative error (RE; n 5 869) in Model 1 (black line) and Model 2 (gray [orange] line). To obtain RE, DDO was divided by the daily amplitude of DO. Probability density of DDO (solid line; n 5 128,172) and (b) wind speed at 10 m above water i surface (U10; open circle) and (c) temperature difference between the two DO sensors (DT; open circle). In the semitransparent areas, less than 100 DDO data fell in a bin. (d) Diel patterns of DDO (solid [black] line and range) and DT (dashed [orange] line). Median (line) and 95% uncertainty range (2.5– 97.5% quantiles; gray area) of 10 min values were calculated from pooled daily data (n 5 891).

processes than Model 1 because of the higher level of the Table 3. Average and range of coefﬁcients of variation of daily identiﬁcation problem. integrals of metabolic estimates (n 5 891).* There was a strong linear relationship between ADO and Model 1 Model 2 GPP that slightly exceeded the Nclass 5 2 threshold, whereas the relationship between ADO and CR had weaker resolution Variable Mean Range Mean Range power (Fig. 5a). This was reasonable, since ADO approxi- GPP 1.24 0.82–4.68 1.24 0.85–3.37 mately equaled the sum of GPP and half of CR. As expected, CR 0.13 0.06–0.75 0.22 0.08–1.10 GPP and CR as well as NPP and GHP were linearly related

Ba 0.35 0.08–2.22 0.33 0.06–1.23 (Fig. 5). According to Model 1, 79% of GPP was respired

NEP 22.48 23225, 14036 219.85 215276, 1740 within 1 d (Nclass 5 2.88). Model 2 resulted in a somewhat

X 0.59 292, 1164 1.40 2778, 11074 lower CR relative to GPP (74.5%, Nclass 5 2.38). Of net pri- GHP NA NA 0.34 0.12–1.37 mary production, 92% could be channeled to gross hetero-

Bh NA NA 0.24 0.03–1.05 trophic production in the day of production (Fig. 4c;

23 21 Nclass 5 4.07). Heterotrophic respiration contributed by 6.7– NEP, net ecosystem production (g O2 m d ); NA, not applicable. * Deﬁnitions of state variables and processes are listed in Table 1. 99% to CR, its mean share was 88%. Rh peaked at an inter- mediate phytoplankton biomass of 20–40 mg Chl m23. After the most likely value by up to several orders of magnitude. an initial increase with heterotrophic biomass, GHP leveled 23 Although Model 2 had one more parameter than Model 1, off at Bh 5–10 g C m . Most of the variability in NEP it generally yielded less certain estimates for metabolic (88%) was explained by gas exchange (Fig. 5f).

80 Istvanovics and Honti Coupled simulation of DO and Chl dynamics

Fig. 5. Relationships between daily metabolic rates. (a) Gross primary production (GPP, closed circle) and community respiration (CR, open [orange] diamond) 2 as a function of the diel amplitude of dissolved oxygen concentration (ADO). (Linear regression models: GPP 5 ð0:55 6 0:08Þ 1 ð1:12 6 0:03Þ 3 ADO; r 5 0.61, 2 n 5 887, Nclass 5 2.09 and CR 5 ð1:14 6 0:09Þ 1 ð0:84 6 0:03Þ 3 ADO; r 5 0.42, n 5 887, Nclass 5 1.72). (b) CR as a function of GPP. (Linear regression model: 2 CR 5 ð0:73 6 0:06Þ 1 ð0:75 6 0:02Þ 3 GPP; r 5 0.70, n 5 891, Nclass 5 2.38). (c) Gross heterotrophic production (GHP) as a function of net primary production 2 (NPP). (Linear regression model: GHP 5 ð0:37 6 0:03Þ 1 ð0:92 6 0:01Þ 3 NPP; r 5 0.90, n 5 891, Nclass 5 4.07). (d) GHP as a function of heterotrophic biomass (Bh). (e) Heterotrophic (Rh, closed circle) and autotrophic respiration (Ra, open [orange] diamond) as a function of Ba.(f) Net ecosystem production (NEP) as a 2 function of gas exchange between air and water (X). (Linear regression model: NEP 5 ð0:02 6 0:01Þ 2 ð0:92 6 0:01Þ 3 X; r 5 0.88, n 5 891, Nclass 5 3.74).

Drivers of metabolism beyond sub-diel scales drivers captured 80% and 58% of variability in GPP and CR, We related GPP and CR with daily mean values of several respectively. Temperature limitation caused most of the vari- potential drivers including wind speed, signiﬁcant wave ability in both GPP and CR. GPP was limited moderately by height, temperature, DT, buoyancy frequency, etc. using PAR (Fig. 6). LOWESS smoothing for visualization. Highly scattered, non- Biomass-speciﬁc NPP declined with increasing algal bio- linear patterns emerged with algal biomass, temperature and mass (Fig. 7a). A similar pattern was observed in the phos-

PAR as independent variables (Supporting Information Fig. phorus limitation factor (fP) that was calculated from cell S5). Multivariate non-linear regressions ﬁtted with these quota of surplus P according to the Droop model (Droop

81 Istvanovics and Honti Coupled simulation of DO and Chl dynamics

Fig. 6. (a) Observed vs. modeled gross primary production (GPP; closed circle)ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi and community respiration (CR, open [orange]ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi diamond) for Model p p 2 2. Note the squareffiffiffiffiffiffiffiffiffiffiffiffiffiffi root transformed axes. Linear regressionffiffiffiffiffiffiffiffiffiffiffiffi models: GPPmod 5 ðÞ0:42 6 0:03 1ðÞ0:80 6 0:01 GPPobs, r 5 0.80, n 5 891, p p 2 Nclass 5 2.92 and CRmod 5 ðÞ0:87 6 0:04 1ðÞ0:58 6 0:02 CRobs, r 5 0.58, n 5 891, Nclass 5 2.02. (b) Limitation factors (fj) of GPP and CR as a function of normalized drivers. Biomass limitation factor of GPP (solid black line) and CR (dashed black line); temperature limitation factor of GPP (solid gray [orange] line) and CR (dashed gray [orange] line); light limitation factor of GPP (dotted [blue] line).

Fig. 7. (a) Biomass-speciﬁc net primary production (NPP/Ba; closed [orange] circle) and phosphorus limitation factor (fP; open diamond) as a function of phytoplankton biomass (Ba). (b) Area-speciﬁc NPP and (c) replication rate of phytoplankton (l) averaged for the weeks of the year. (d) Monthly mean gross heterotrophic production (GHP) as a function of monthly mean ratio of NPP to external load of dissolved organic carbon (LDOC).

82 Istvanovics and Honti Coupled simulation of DO and Chl dynamics

1973; fP5 QSP2QSP;0 =QSP), assuming a maintenance cell Antenucci et al. 2013; McNair et al. 2015). Further research, 21 quota, QSP;0 of 6 mg P [g C] . Daily NPP was averaged for however, is needed before this coupling will be generally fea- weeks. Weekly mean NPP ranged between 0.05 g C m22 d21 sible. In Lake Balaton, hydrodynamic modeling has a long and 4.8 g C m22 d21 during the study period (Fig. 7b). Its tradition (Muszkalay 1973; Shanahan et al. 1986; Kramer seasonal trend was remarkably similar from early May until et al. 2004). Lake-specific 1D–3D models reasonably capture late July (weeks 18–30) in each year, followed by rapid differ- water movements (basin-wide circulations, seiches, wind- entiation across years. The lowest late summer productivity induced waves) but they lack the required accuracy to be was observed in 2014 when summer was relatively cold and meaningfully coupled with a local heat budget (Torma and cyanobacteria failed to dominate (cf. Supporting Information Kramer 2017) or DO model. Fig. S2). The highest productivity occurred in the hot sum- Goodness of fit to observed data is an important albeit mers of 2010 and 2015 when cyanobacteria made up 80– not an absolute measure of usefulness of a model. In con- 94% of phytoplankton biomass (Supporting Information Fig. trast to classical calibration methods, where the single objec- S2; L. Vor€ os,€ unpubl.). Using the exponential growth equa- tive is to minimize fit error, the Bayesian parameter tion, the reproductive rate of phytoplankton (l,d21) was inference makes a formal statistical compromise in fit to match a priori expectations that reflect independent knowl- approximated as l 5 ln(1 1 NPP/Ba). Mean weekly l was as high as 0.76 d21 during the study period (Fig. 7c). At the edge on the examined system. We had three basic expecta- same time, 96% of net growth rates calculated from daily tions. First, recognizing that a metabolic model without a change in phytoplankton biomass were between 20.5 d21 transport term was structurally imperfect (Lauster et al. and 10.5 d21 (not shown). 2006; Van de Bogert et al. 2007; Hanson et al. 2008; Sadro Weekly, monthly and seasonal mean NPP were unrelated et al. 2011; Staehr et al. 2012b; Antenucci et al. 2013; McNair et al. 2015), we assumed that model errors were to external nutrient loads. Rh was not related to DOC load. significantly autocorrelated. Although 60% of modeled DO Monthly mean NPP exceeded the respective LDOC by a mean 23 factor of 25 (the range was from 1.3 to 139). Gross heterotro- values (n 5 128,172) deviated by no more than 0.2 g O2 m phic production tended to increase with the increasing NPP/ from measured DO, autocorrelation of errors occasionally resulted in large departures from measured DO curves and in LDOC ratio (Fig. 7d). high parameter uncertainty (Fig. 4, Supporting Information Discussion Fig. S4; Table 3). Second, we expected that day-to-day variability in community respiration and photosynthetic param- Alternative metabolic models – is there a superior model? eters should be smooth in a resilient ecosystem. Applying A few studies have compared performance of various met- sequential Bayesian learning and model calibration in a 3 d abolic models over short periods. Assuming that transport sliding window (Honti et al. 2016), no irreversible shifts could be neglected, both Hanson et al. (2008) and McNair occurred in estimated metabolic rates during the 7 yr long et al. (2015) found that the simplest DO model (Odum study period to falsify the resilience hypothesis. This could 1956) fitted nearly as well to the data as models that incor- be seen from smooth seasonal changes (Supporting Informa- porated more biological complexity when the basic assumption Fig. S4) and high autocorrelation of estimated metabolic tion on transport was met and vice versa, even complex rates (Table 2). Third, acknowledging that productivity and models failed when the impact of transport was significant. biomass of phytoplankton were closely coupled, we expected In line with these studies, our more complex Model 2 that diel DO curves and biomass dynamics of algae could yielded marginally better fits than Model 1, and both models simultaneously be modeled when daily biomass data were performed poorly in certain days (Fig. 4, Supporting Infor- available for calibration. This could successfully be done mation Fig. S3). Deviations between observed and modeled both in this study and in other lakes (Honti et al. 2016). DO tended to increase with decreasing wind speed and We agree with Hanson et al. (2008) that multiple meta- increasing strength of stratification (Fig. 4), indicating that bolic models can be equivalent in terms of fit quality, mak- the lack of full mixing was the primary source of systematic ing the simplest good performing model the best for error. Strong radiative forcing could build up relatively stable practical applications. At the same time, too simple models thermal stratification in calm days; the temperature differ- hide a series of scientifically important information. Heuris- ence between surface and bottom waters occasionally tic values, such as insight into the consistency of metabolic reached 58C(Vor€ os€ et al. 2010). Sea and land breezes were estimates do distinguish between models that fit similarly strong enough to result in a periodic daily wind pattern on well to the data. In published models, mass balance of DO is the background of much stronger synoptic winds (Fig. 2) but open, giving no chance to check consistency of model out- they could not prevent development of transient stratifica- puts. In contrast, both of our models showed that metabolic tion, the mean duration of which was 5.1 h per day (Vor€ os€ rates were consistent with observed changes in phytoplank- et al. 2010). Coupling hydrodynamical and metabolic mod- ton biomass. Additionally, the biologically more complex els might reduce systematic error (Staehr et al. 2012b; Model 2 allowed us to discriminate between autotrophic and

83 Istvanovics and Honti Coupled simulation of DO and Chl dynamics

23 21 heterotrophic production and respiration (Supporting Infor- (0.075 g O2 m d ). Similarly, Cremona et al. (2014) mation Table S1). In this abstract sense, Model 2 was supe- observed that various models resulted in either net heterotro- rior to Model 1 and to published metabolic models. phy or in net autotrophy in Lake Vortsj~ arv€ (Estonia). In agree- Complexity of models should only be increased if additional ment with our modeling results, low organic content of information was available to keep the identification problem sediments (1–4%; Mat e 1987) indicated that primary produc- under control. Developing Model 2, we intended to include tion was closely balanced by mineralization at long time grazing into GHP besides bacterial decomposition and detri- scales (years, decades) in Lake Balaton. NEP is a small differ- tivory. Grazing should depend on both autotrophic and het- ence between two large, uncertain metabolic rates (GPP and erotrophic biomass, whereas the supply of exudates and CR) that does not have its own constraining drivers (Eq. 1, algal detritus can be thought of as a function of only Ba Supporting Information Table S1), therefore its calculated (Supporting Information Table S1). In Lake Balaton, where value is incidental. filter feeding zooplankton were insignificant (G.-Toth et al. Besides its high uncertainty, NEP strongly depended on 1986), the impact of grazing could not be recognized from the choice of the gas exchange function in a recent ensem- DO and Chl data. In lakes where zooplankton are important, ble modeling study (Dugan et al. 2016). This is not surpris- grazing may leave its signature in the DO and Chl time ing, since from a decomposition perspective, NEP equals the series and may potentially be identified in a metabolic difference between observed changes in DO concentration model. In scientific applications, complexity of metabolic and X (Eq. 1). Accordingly, in the present study X explained models should be driven by data availability and basic 88% of the variability in NEP (Nclass 5 3.74, n 5 891; Fig. 5). limnological knowledge on the study lake. Proper description of gas exchange is crucial to reliably esti- Uncertainty of metabolic estimates – can NEP mate NEP and to assess the role of lakes as sources or sinks reliably be estimated from diel DO curves? of carbon. In the present study, we aimed at iteratively deriv- In spite of the reasonable fit of our models (Fig. 3), uncer- ing a lake-specific function for atmospheric gas exchange tainty of metabolic estimates was high for several reasons coefficient from diel DO curves. Since atmospheric exchange (Table 3; Supporting Information Fig. S4). Uncertainty aris- rates have not been measured in Lake Balaton to verify our ing from neglect of transient stratification burdened each kf estimates, we cannot offer this approach as a well-tried metabolic rate, as explained by Coloso et al. (2011). In most recipe. Nevertheless, it seems worth developing indepen- cases, Model 1 yielded rate estimates with lower CV than dently verified methods to estimate gas flux from high fre- Model 2 because of better identification of processes. For quency DO curves in lakes of different sizes, morphometry, shared rates, CVs followed the order CR < GPP < NEP (Table and wind exposure. 3). Unlike NEP, CR and particularly GPP were strongly asso- In spite of the uncertain and incidental nature of NEP, ciated with, and therefore constrained by the diel amplitude comparative studies have revealed meaningful patterns in of DO (ADO; Table 2; Fig. 5). NEP along broad gradients of nutrient and DOC availability Community respiration could be identified with the high- (Hanson et al. 2003; Staehr et al. 2010b; Solomon et al. est confidence, because nighttime decrease in DO depended 2013). The possible explanation for the emergence of these primarily on CR and thus, about one third of the observa- patterns is that dependence of NEP on gas flux cannot fully tions supported the identification of this single process. mask the large differences in diel changes in DO saturation Uncertainty was introduced by gas exchange and transport, and concentration among lakes that cover a spectrum of tro- the latter being most evident when the DO signal increased phic types and states. This, however, does not make the during the night (also observed by Hanson et al. 2008). GPP absolute values of NEP estimates less incidental or more was more uncertain than CR, because its magnitude was credible. Consequently, ranges of TP and DOC concentra- partly dependent on uncertain CR and because it was more tions where lakes are predicted to be net autotrophic or het- strongly affected by gas exchange than respiration (Table 2; erotrophic need revision when these ranges have been Fig. 2). Moreover, similar uncertainty of GPP in the two derived from high frequency DO measurements. models suggested that measurement error might also contribute: time series of mean underwater PAR might occasionally Ecological observations beyond the autotrophic- be inconsistent with measured photosynthetic parameters heterotrophic dichotomy B B (Pmax and a ) that were used in our models as prior parameter The interannual stability of weekly NPP between late distributions. Uncertainty of NEP was disappointingly large spring and late July (Fig. 7c, Week 15–30) was consistent considering either its CV (Table 3) or standard deviation (in with the observation of Honti et al. (2007) that in the lack 23 21 Model 2, mean SD was 3.7 g O2 m d , range was from of a sufficiently long-lasting unidirectional selective pressure, 23 21 23 21 0.1 g O2 m d to 11.8 g O2 m d ). According to Model phytoplankton were in a “ground state” characterized by 23 21 1, NEP averaged at 20.03 g O2 m d during the study low biomass and hectic compositional changes. In contrast, period, whereas in Model 2, the balance was slightly positive variability of weekly NPP from late July reflected year-to-year

84 Istvanovics and Honti Coupled simulation of DO and Chl dynamics variability of growth conditions in blooming sub-spaces of explanatory variables overlapped with the most powerful phytoplankton identified by Honti et al. (2007). predictors of GPP and CR in other productive lakes (Harris Reproductive rates of algae estimated from NPP often 1978; Staehr and Sand-Jensen 2007; Staehr et al. 2010b). reached 1–1.2 d21, the average was 0.76 d21 during the Of the predictor variables, water temperature explained the study period (Fig. 7). These rates reasonably agreed with largest variability in both GPP and CR. The temperature limita- reproductive rates obtained under natural conditions using tion factor increased more steeply with T for CR than for GPP different methods (Schnoor and Di Toro 1980; Reynolds and (Fig. 6) as also noted by Staehr et al. (2010b). The fT values of Irish 1997). Net growth rates estimated from daily change in these to processes were equal at about 168C, suggesting a major 21 21 Ba (20.5 d to 10.5 d ) also agreed with commonly shift in lake metabolism below and above this temperature. reported values (Sommer 1981; Reynolds and Irish 1997; Indeed, splitting the dataset at T 5 16.08C, parameters of Istvanovics et al. 2005). The large difference in the rates of the linear regression between volumetric GPP and CR in the reproduction and net growth indicated substantial mortal- warm season (CR5ðÞ0:38 6 0:08 1ðÞ0:91 6 0:02 3GPP, r2 5 0.67, ities of phytoplankton implying that algal dynamics n 5 811, Nclass 5 2.29) became nearly identical to those of the depended as much on loss processes (exudation of excess NPP vs. GHP relationship (Fig. 5). Although the regression photosynthates, sedimentation, grazing, physiological mor- between GPP and CR did not reach the resolution power index tality) than on growth (Schnoor and Di Toro 1980; Crump- of 2 in the cold season (r2 5 0.39, n 5 80), the slope was signifi- ton and Wetzel 1982; Reynolds and Irish 1997). Strong cantly lower (0.71 6 0.10) whereas the intercept was signifi- linear regression between NPP and GHP (Fig. 5) suggested cantly higher (0.59 6 0.14) than in the summer. Thus, about that in Lake Balaton heterotrophs utilized on average, 90% 90% and 70% of GPP might immediately be respired in the of NPP in the same day when biomass was produced. summer and spring/autumn, respectively, and a higher fraction There was no relationship between external nutrient loads of CR might be supported by allochthonous DOC when produc- and phytoplankton biomass or metabolic rates in this study tivity was low in the cold season. Since we usually failed to cap- (Supporting Information Figs. S2, S4). Similar exponential ture the spring diatom bloom (Supporting Information Fig. S2) decrease in the upper bounds of both biomass-specific NPP that might have developed prior to the start of our monitoring and P limitation factor with increasing algal biomass (Fig. 7) program, phytoplankton biomass was low in the 80 d colder was an indirect indication that growth rates might be than 168C. This left open the question, how much increased increasingly P-determined (fP < 0.5) when biomass exceeded availability of autochthonous carbon sources might trigger 2gCm23 (40 mg Chl m23). These observations were sup- community respiration at low temperature. ported by findings that P desorption from resuspended sedi- The temperature limitation factors of GPP and CR ments was the prime source of P supply of seriously attained a value of fT 5 0.99 at 308C and 268C, respectively. phosphorus deficient summer phytoplankton in Lake Bala- The high temperature, at which GPP was fully released from ton (Lijklema et al. 1986; Istvanovics and Herodek 1995; T-limitation might be explained by the high optimum tem- Istvanovics et al. 2004). perature for growth of Cylindrospermopsis raciborskii (around When both NPP and NHP were positive (503 d out of 318C; Shafik et al. 2001; Briand et al. 2004; Kovacs et al. 891), NHP averaged at 30% of NPP. This value agreed well 2016), the dominant summer species in years when cyano- with the estimate of Cole et al. (1988) who found that bacte- bacteria blooms have developed in Lake Balaton (Padisak rial and zooplankton production made up a mean 20% and and Reynolds 1998). During the study period, 17% and 2% 12% of NPP, respectively in a broad selection of fresh and of days were warmer than 268C and 308C, respectively. In a saltwater ecosystems. Since high concentrations of fine- changing climate, both frequencies are expected to increase. grained particles make Lake Balaton into a stressful habitat A disproportionately larger increase in the frequency of days for filter-feeding zooplankton (G.-Toth et al. 1986), the con- above 268C than 308C might potentially increase gross pro- tribution of these two groups of heterotrophs to NHP might ductivity and reduce net productivity in Lake Balaton, differ from the estimate of Cole et al. (1988). increasing the chance of net C release. This prediction may Daily area-specific GPP could reasonably be hindcasted by hold true in other lakes dominated by cyanobacteria. multivariate non-linear regression using daily mean area- In contrast to the considerable increase in daily GPP with specific biomass of phytoplankton, T, and PAR as indepen- T and autotrophic biomass, the impact of PAR was modest dent variables (Fig. 6, Supporting Information Fig. S5). Hind- (Fig. 6). Moreover, GPP showed an unexpected increase cast of area-specific CR was considerably weaker using either when underwater light exceeded about 120–130 lmol pho- 22 21 Ba, and T (Fig. 6, Supporting Information Fig. S5) or Ba1Bh, ton m s (Supporting Information Fig. S5). This was sur- and T. The pragmatic consequence was that CR could be pre- prising because GPPi was a hyperbolic tangent function of i dicted with a roughly similar uncertainty from either Ba and PAR in our models (Supporting Information Table S1). The T or from the multivariate non-linear regression model of lack of a strong light limitation might be due to the low GPP combined with the linear regression between GPP and light requirement of species selected by the generally poor CR (cf. Fig. 5, Supporting Information Fig. S5). Our underwater light climate that prevailed in Lake Balaton

85 Istvanovics and Honti Coupled simulation of DO and Chl dynamics

(Reynolds 1997). PAR tended to exceed 125 lmol photon the same in shallow, turbid lakes as in deep ones (Lauster m22 s21 for several days only in July and August, during the et al. 2006; Van de Bogert et al. 2007; Sadro et al. 2011). potential blooming period of C. raciborskii. This cyanobacte- Unlike local benthic photosynthesis, local benthic respira- rium has low light requirement (Ik is 15–30 lmol photon tion might significantly influence our CR estimates. This 2 2 m 2 s 1) and it is tolerant to light intensities up to several may partly explain that the deviation between observed and 22 21 hundreds of lmol photon m s (Shafik et al. 2001; Briand modeled 10 min DO values tended to increase with transient et al. 2004; Kovacs et al. 2016). The coincidence of high tem- stratification (Fig. 4), and could be one of the reasons why perature, physical stability and relatively good light condi- the multivariate hindcast of CR was less successful than that tions might enhance photosynthesis and growth of C. of GPP (Fig. 6). raciborskii and this could lead to the unexpected increase in GPP in the range of the highest PAR values (Supporting Metabolism in Lake Balaton Information Fig. S5). Benthic primary production might also Weekly area-specific net primary production averaged at contribute to this upward trend in GPP (see below). 1.5 g C m22 d21 during the study period and typically varied Several studies have demonstrated a significant contribu- between 2 and 4 g C m22 d21 during the summer (Fig. 7). tion of benthic/littoral metabolism in both seasonally strati- These values were similar to those estimated at around the fied and shallow lakes, even though availability of benthic turn of the century (Presing et al. 2001; Istvanovics et al. habitats was limited in some of these lakes (Lauster et al. 2004) and lower by a factor of 2–3 than those estimated dur- 2006; Van de Bogert et al. 2007; Sadro et al. 2011; Idrizaj ing the eutrophication in the 1970s (Herodek 1986) using et al. 2016). A rich and abundant algal flora inhabits the different variants of the 14C technique. Compared to other sediments of Lake Balaton (Uherkovich and Lantos 1987). lakes where metabolic rates have been estimated from high Typically, Fragilaria construens dominate the phytobenthos frequency DO measurements, Basin 1 of Lake Balaton ranked (Vor€ os€ et al. 2000). Benthic primary production was compa- among the most productive third of systems (Laas et al. rable under clear ice to pelagic production in summer in 2012; Staehr et al. 2012a; Solomon et al. 2013). mesotrophic Basin 4 of the lake (Herodek and Olah 1973). Monthly mean NPP exceeded monthly external load of PB of benthic algae collected at shallow (< 1 m) sites in max DOC by a mean factor of 25. Considering that biological summer varied between 10 and 20 mg C [mg Chl]21 h21 in availability of DOC ranged from 9% to 15% at the mouth laboratory incubations (Uveges€ et al. 2011). Assuming a 10 h of the Zala River irrespective of the season (Toth et al. photoperiod, these rates translated into 270–540 mg O [mg 2 2007), bacterial production should have been fueled almost Chl]21 d21. For comparison, biomass-specific GPP averaged 21 21 exclusively by NPP. Nevertheless, the tendency of increas- at 175 mg O2 [mg Chl] d and ranged between 0 and 21 21 ing GHP with NPP/LDOC ratios (Fig. 7) suggested that micro- 400 mg O2 [mg Chl] d in our study. Thus, light- bial utilization of allochthonous DOC might occasionally saturated benthic photosynthesis had a high potential to be important in Basin 1 of Lake Balaton. The intercept of influence measured DO time series. Ik values of phytobenthos were estimated to range between 240 lmol photon m22 the GPP vs. CR regression (Fig. 5) suggested that a daily 23 21 s21 and 940 lmol photon m22 s21 (Uveges€ et al. 2011). The mean respiration of 0.73 g O2 m d might be supported maximum, 97.5th percentile and median 10 min light inten- by DOC. sities that reached the sediment surface were 222 lmol photon m22 s21,40lmol photon m22 s21, and 3.4 lmol photon Implications for high frequency lake metabolism studies m22 s21, respectively, at our monitoring site during the The role of lakes as sinks or sources or CO2 is a focal ques- study period (n 5 78,424). Thus, local benthic photosynthesis tion in most contemporary studies of lake metabolism. We was unlikely to influence DO concentrations significantly argue that lake metabolism studies that use the free-water DO technique cannot reliably estimate net ecosystem pro- even after taking into consideration that Ik estimates of phytobenthos by Uveges€ et al. (2011) might be too high. (Sam- duction unless independent lake-specific information is ples were illuminated with daylight fluorescent tubes, the available on gas exchange between the air and water. emission spectrum of which is different from the underwater Transient stratification and full mixing may cause as light spectrum in a turbid lake.) Halving the depth range much uncertainty in metabolic estimates in shallow lakes as observed at our site (0.9–1.9 m), the lowest laboratory- in deep ones. Therefore, vertical DO profiles may bear impor- 22 21 derived Ik value of 240 lmol photon m s occurred at the tant information on mixing processes in shallow lakes, too. bottom for a shorter or longer period nearly each day. In Complex models of lake metabolism that incorporate rele- this way horizontal currents associated with transverse vant biological, chemical, and/or physical data (e.g., algal seiches might transport oxygen-rich water masses from the biomass, DOC concentration, velocity field) may help to vicinity of the shore to the monitoring site about 100 m off- assess consistency of metabolic estimates and may reveal shore. Conclusively, the mechanism how benthic photosyn- details of lake metabolism that are beyond the scope of thesis might influence offshore DO concentrations might be simple models.

86 Istvanovics and Honti Coupled simulation of DO and Chl dynamics

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