Seasonal Nutrient and Plankton Dynamics in a Physical-Biological Model of Crater Lake

Hydrobiologia (2007) 574:265–280 DOI 10.1007/s10750-006-2615-5

CRATER LAKE, OREGON

Seasonal nutrient and plankton dynamics in a physical-biological model of Crater Lake

Katja Fennel Æ Robert Collier Æ Gary Larson Æ Greg Crawford Æ Emmanuel Boss

Springer Science+Business Media B.V. 2007

Abstract A coupled 1D physical-biological fall the model displays a marked vertical structure: model of Crater Lake is presented. The model the phytoplankton biomass of the functional group simulates the seasonal evolution of two functional 1, which represents diatoms and dinoflagellates, phytoplankton groups, total chlorophyll, and zoo- has its highest concentration in the upper 40 m; the plankton in good quantitative agreement with phytoplankton biomass of group 2, which repre- observations from a 10-year monitoring study. sents chlorophyta, chrysophyta, cryptomonads and During the stratified period in summer and early cyanobacteria, has its highest concentrations between 50 and 80 m, and phytoplankton chlorophyll Guest Editors: Gary L. Larson, Robert Collier, and Mark has its maximum at 120 m depth. A similar vertical W. Buktenica structure is a reoccurring feature in the available Long-term Limnological Research and Monitoring at data. In the model the key process allowing a Crater Lake, Oregon vertical separation between biomass and chlorophyll is photoacclimation. Vertical light attenua- K. Fennel (&) Institute of Marine and Coastal Sciences and tion (i.e., water clarity) and the physiological Department of Geological Science, Rutgers ability of phytoplankton to increase their cellular University, New Brunswick 08901, New Jersey, USA chlorophyll-to-biomass ratio are ultimately deter- e-mail: [email protected] mining the location of the chlorophyll maximum. R. Collier The location of the particle maxima on the other College of Oceanic and Atmospheric Sciences, hand is determined by the balance between growth Oregon State University, Corvallis 97331, Oregon, and losses and occurs where growth and losses USA equal.The vertical particle flux simulated by our G. Larson model agrees well with flux measurements from a USGS Forest and Rangeland Ecosystems Center, sediment trap. This motivated us to revisit a pre- Forest Science Laboratory Oregon State University, viously published study by Dymond et al. (1996). Corvallis 97331, Oregon, USA Dymond et al. used a box model to estimate the G. Crawford vertical particle flux and found a discrepancy by a Department of Oceanography, Humboldt State factor 2.5–10 between their model-derived flux and University, Arcata 95521, California, USA measured fluxes from a sediment trap. Their box model neglected the exchange flux of dissolved E. Boss School of Marine Sciences, University of Maine, and suspended organic matter, which, as our model Orono 04473, Maine, USA and available data suggests is significant for the

123 266 Hydrobiologia (2007) 574:265–280 vertical exchange of nitrogen. Adjustment of Dy- box-model considerations and measurements of mond et al.’s assumptions to account for dissolved vertical particle fluxes from sediment traps reveal and suspended nitrogen yields a flux estimate that large discrepancies, i.e. the particle flux falls short is consistent with sediment trap measurements and of balancing the estimated upwelled nitrogen our model. (Dymond et al., 1996). The populations of microorganisms show dis- Keywords Physical-biological model Æ Deep tinct vertical maxima during stratified conditions chlorophyll maximum Æ Photoacclimation Æ (McIntire et al., 1996; Larson et al., 1996b; Crater Lake Urbach et al., 2001). In July and August, diatoms and dinoflagellates reach their maximum biomass in the upper 20 m of the water column, isolated Introduction from below by a pronounced thermocline. Chlo- rophyta, chrysophyta and cryptophyta dominate Crater Lake is an ultra-oligotrophic, isolated cal- below the thermocline with biomass maxima dera lake in the Cascade Mountains, Oregon. between 80 and 100 m (Fig. 1) coincident with With a maximum depth of 590 m it is the deepest the vertical maximum of primary production lake in the US and one of the clearest bodies of (McIntire et al., 1996). The chlorophyll concen- water on Earth. Crater Lake is surrounded by tration has a deep maximum at a depth of 120 m, steep caldera walls, has a very small watershed separated from the phytoplankton biomass max- and only small inputs of allochthonous matter. imum by about 50 m (Fig. 2). The vertical sepa- Most of the water entering the lake is direct pre- ration of the maxima in phytoplankton biomass cipitation onto its surface, which makes up 78% of (in units of carbon or nitrogen) and chlorophyll is its watershed. The remainder enters as run off mainly due to photoacclimation (Fennel & Boss, from the caldera walls and as hydrothermal influx 2003) which results in dramatic vertical changes in from the bottom (Collier et al. 1991). Despite its the chlorophyll to biomass ratio (Fig. 2) and im- great depth, Crater Lake is relatively well-mixed. plies that the chlorophyll concentration does not The upper portion of the lake (upper 200 m) is represent phytoplankton biomass. homogenized twice a year in early winter and late We developed a coupled physical-biological spring by free convection and wind-mixing model of Crater Lake that captures the processes (McManus et al. 1993). Partial ventilation of the thought to determine nutrient cycling and phy- deep lake occurs during these mixing periods toplankton production at first-order in a simpli- when the upper water column is nearly isothermal fied description of the food-web. We consider the (McManus et al., 1993) and during sporadic deep- simplicity as valuable since it allows us to keep mixing events (Crawford & Collier, 1997). Inde- the number of poorly known model parameters at pendent estimates of the lake ventilation time a minimum, but can elucidate dependencies and agree that the lake is ventilated on timescales of 1 regulating mechanisms not easily seen in the to 5 years (Simpson, 1970; McManus et al., 1993; observations alone. The model allows us to test Crawford & Collier, 1997). Depletion of inorganic hypotheses about the factors determining spatial nitrogen species in the upper 200 m of the lake in and temporal patterns in species distribution, summer implies nitrogen-limitation of phyto- chlorophyll concentration, and primary produc- plankton growth, although bioassays suggest tion in relation to physical circulation processes. co-limitation by trace metals (Lane & Goldmann, Here we present results of a 1-year model simu- 1984). Concentrations of inorganic phosphorus lation in comparison with measurements obtained and silicic acid are relatively high and nearly uni- during a 10-year monitoring study (Larson, this form throughout the water column (Larson et al., issue), integrating the available data in a biomass- 1996a). Vertical mixing is the most important based framework. We discuss factors leading to source of new nutrients for primary production in the observed vertical distribution of phytoplank- the euphotic zone (Dymond et al., 1996). ton populations and compare model-simulated Comparisons of upward nutrient fluxes based on vertical fluxes with particle flux measurements

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August

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Fig. 1 Available August data from 1989 to 2001 (gray plankton group 1. Chlorophyta, chrysophyta, cryptomo- bullets) and median with 25- and 75-percentiles (black nads and cyanobacteria comprise phytoplankton group 2 bullets). Diatoms and dinoﬂagellates comprise phyto- and box-model estimates (Dymond et al., 1996) nitrogen-limited (Lane & Goldman, 1984; Larsen reconciling a previously reported mismatch. et al., 1996a). Note that the nutrient variable N also includes dissolved organic nitrogen in addition to inorganic nitrogen. Technically detritus Materials & methods includes both, particulate and dissolved pools of organic nitrogen. However, the detritus variable The biological model D in our model is subject to vertical sinking. Hence, the dissolved organic nitrogen is more We formulated a relatively simple biological realistically treated as part of the nutrient pool N. model containing the following 7 state variables: The phytoplankton group P1 represents diatoms dissolved nitrogen N, two phytoplankton groups and dinoﬂagellates, i.e. the phytoplankton domi-

P1 and P2, one group of zooplankton Z, one nating in the upper 20 m of the water column. P2 detrital pool D, and the chlorophyll concentrations comprises the remaining phytoplankton divisions

C1 and C2 of P1 and P2, respectively (Fig. 3). All (chlorophyta, chrysophyta, cryptomonads and variables are expressed in units of mmol N m–3 cyanobacteria). The chlorophyll concentrations except the chlorophyll variables, which are C1 and C2 of P1 and P2 are included as dynamical in mg chl m–3. Nitrogen was chosen as the nutri- variables, to allow an explicit inclusion of photo- ent currency since Crater Lake is considered acclimation.

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All data August 0 All data August 50 50 50

100 100 100

Depth [m] 150 150 150

200 200 200 biomass [mg C m–3] biomass [mg C m –3] chlorophyll [mg m–3 ] chlorophyll [mg m –3] 250 250 250 0 0.5 1 1.5 0 0.5 1 1.5 0 0.2 0.4 0.6 0.8 1 Chl/biomass [g chl (g C) –1]

Fig. 2 Median and 25- and 75-percentiles of chlorophyll and phytoplankton biomass. All data (left panel), August data (middle panel), and chlorophyll to biomass ratio (right panel) are shown The dynamics of the biological state variables EzðÞ¼E0 par exp zkW þ kChlchljz ; ð4Þ are determined by the following set of equations. The corresponding parameter values are where z is the water depth, E0 is the incoming given in Table 1. The biological sources minus shortwave radiation just below the lake surface, sinks (sms) of the phytoplankton groups are and par is the fraction of this radiation that is defined as active in photosynthesis and assumed to be equal –1 –1 to 43%. kW = 0.04 m and kChl = 0.03 m (mg –3 –1 smsðÞ¼ Pi li Pi ðÞLiN þ LiD Pi gi Z; ð1Þ chl m ) are the light attenuation coefficients for water and chlorophyll, respectively. chl|z is the with i = 1,2, where li is the phytoplankton growth rate, LiN and LiD are phytoplankton loss rates representing fluxes due to respiration and natural mortality, and gi is the zooplankton grazing rate. The phytoplankton growth rates li depend on the nutrient concentration N, following the Michaelis–Menten response, the photosynthetically available radiation E and the chlorophyll concentration Ci as m max aiECi li ¼ li 1 exp max ; ð2Þ li Pi

m N li ¼ li with i ¼ 1; 2: ð3Þ kiN þ N

max Here li is the maximum phytoplankton growth rate, ai is the chlorophyll-speciﬁc initial slope of the photosynthesis-irradiance curve, and kiN is the half-saturation concentration for nutrient uptake. Note that we assume a tight coupling of nutrient uptake, growth and photosynthesis. E represents the light that is available for photosynthesis, which is determined for a given depth as Fig. 3 Schematic of the biological model component

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Table 1 Biological model parameters used in this study and range of published parameter values. N.D. denotes non- dimensional parameter Symbol Description Value Unit Range

max –1 a b l1 maximum growth rate of P1 1.50 d 0.62 –3.0 max –1 a b l2 maximum growth rate of P2 0.85 d 0.62 –3.0 –3 c k1N half-saturation concentration for nutrient-uptake of P1 0.01 mmol N m 0.0005–3.86 –3 c k2N half-saturation concentration for nutrient-uptake of P2 0.01 mmol N m 0.0005–3.86 –1 –2 –1 d a1 chlorophyll-speciﬁc initial slope of the photosynthesis- 0.05 mol N (g chl) (W m ) 0.007–0.13 irradiance curve of P1 –1 –2 –1 d a2 chlorophyll-speciﬁc initial slope of the photosynthesis- 0.7 mol N (g chl) (W m ) 0.007–0.13 irradiance curve of P2 max –1 e Q 1 maximum ratio of chlorophyll to biomass of P1 0.5 g chl (mol N) maximum 5.6 max –1 e Q 2 maximum ratio of chlorophyll to biomass of P2 6.0 g chl (mol N) maximum 5.6 –1 i g L1N loss rate from P1 to N 0.13 d 0.02 –0.1 –1 f L1D loss rate from P1 to D 0.06 d 0.05–0.2 –1 i g L2N loss rate from P2 to N 0.15 d 0.02 –0.1 –1 f L2D loss rate from P2 to D 0.15 d 0.05–0.2 –1 g h gmax maximum grazing rate 0.25 d 0.5 –1.0 –3 i j K3 half-saturation concentration for grazing 0.1 mmol N m 0.75 –1.89 P1 grazing preference for P1 0.2 N.D. P2 grazing preference for P2 0.8 N.D. –1 g j LZN loss rate from Z to N 0.1 d 0.04 –15.0 –1 g j LZD loss rate from Z to D 0.1 d 0.04 –15.0 –1 k l wD sinking rate of D 0.5 m d 0.009 –10 r remineralization rate for D 0.3 d–1 0.05k–0.18m a Taylor, 1988 b Anderson et al., 1987 c Moloney & Field, 1991 d Geider et al., 1997 e Geider et al., 1998 f Taylor et al., 1991 g Wroblewski, 1989 h Fasham, 1995 i Palmer & Totterdell, 2001 j Ross et al., 1994 k Moskilde, 1996 l Fasham, 1993 m Jones & Henderson, 1986

C mean chlorophyll concentration above the actual smsðC Þ¼q l P L C g Z i ; ð6Þ i i i i iD i i P depth z and is determined by integrating over i

C1 and C2 as with Zz max liPi 1 0 qi ¼ Hi : ð7Þ chlj ¼ ðÞC1 þ C2 dz : ð5Þ a EC z z i i 0 max Qi is the maximum ratio of chlorophyll to The chlorophyll concentrations are determined biomass (in units of nitrogen) of phytoplankton following the photoacclimation model of Geider group i. qi represents the fraction of growth of et al. (1996, 1997) phytoplankton i that is devoted to chlorophyll

123 270 Hydrobiologia (2007) 574:265–280 synthesis and is regulated by the ratio of freshwater, the model predicts the evolution of achieved-to-maximum potential photosynthesis the surface boundary layer depth, the vertical

(liPi)/(aiECi) (Geider et al., 1997). eddy diffusivity profile kz(z), and the vertical The zooplankton dynamics are determined by profiles of temperature T and salinity S. The turbulent mixing of T, S and biological scalars in smsðÞ¼ Z ðÞg1 þ g2 Z ðÞLZN þ LZD Z; ð8Þ the surface boundary layer is controlled by finite eddy diffusivities which decrease below the p P g ¼ g i i ð9Þ boundary layer. The boundary layer depth rep- i max k þ p P þ p P 3 1 1 2 2 resents the penetration depth of surface-generated turbulence and does not resemble a surface where i = 1,2. g is the maximum grazing rate, max mixed layer a priori. pi are the grazing preferences (note that 0 < p1, p <1andp +p = 1), k is the half-saturation 2 1 2 3 Model set up and forcing concentration of grazing, and LZN and LZD are the zooplankton excretion and mortality rates. The physical model is set up on an equidistant The sources and sinks of the detrital pool are grid with 150 vertical levels of 4 m thickness. The given by model is forced with hourly values of the surface smsðÞ¼ D L1DP1 þ L2DP2 þ LZDZ wind stress, the net shortwave radiation, the net @D ð10Þ longwave radiation, and sensible and latent heat rD wD ; fluxes. No evaporation or precipitation is @z included. Wind stress and heat fluxes were either where r is the remineralization rate of detrital measured directly or estimated from continuous matter and wD is the sinking rate. measurements at one of the two meteorological The nutrient equation follows as stations located on a tower at the southwest caldera rim and on a buoy in the North Basin of the smsðNÞ¼l1P1 l2P2 þ L1NP1 lake. The u and v components of the wind stress ð11Þ were determined from hourly averages of wind þ L2NP2 þ LZNZ þ rD: speed and direction. The net shortwave radiation was estimated from measurements of the downwelling shortwave radiation at the rim station and The physical model a parameterization of albedo following Payne (1972). The downwelling radiation at the rim was The biological model is coupled to a one-dimen- corrected to account for the shading effect of the sional physical model such that the evolution of caldera walls on the lake surface by a simple any biological scalar X is given by geometric argument. The net longwave heat flux is given by the downwelling longwave heat flux @X @ @X minus the longwave back radiation which was ¼ k þsmsðXÞ; ð12Þ @t @z z @z determined assuming the lake radiates like a grey body. The downwelling longwave heat flux was where t is time and z is water depth. The first determined by a bulk parameterization depend- term on the right-hand side is the turbulent flux ing on air temperature, water vapor pressure of X, and the second term represents the bio- (determined from measurements of air tempera- logical sources minus sinks of X, including the ture and relative humidity) and a cloudiness sinking of particles defined in the previous sec- parameterization. The sensible heat flux was tion. The physical model component is an determined from the difference between the lake implementation of the turbulent mixing scheme surface and air temperatures based on the bulk developed by Large et al. (1994) to simulate the formula of Large & Pond (1982). The latent heat planetary boundary layer in oceanic applications. flux was determined from the evaporation rate Given surface fluxes of wind stress, heat and following Large & Pond (1982).

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Note that our model does not include the et al., 1996b). Zooplankton weight conversion atmospheric precipitation of nitrogen and the factors were estimated for each taxon from dried nitrogen loss due to burial in the sediment and animals and used to convert organism densities to seepage. However, as the input from precipitation dry weight biomass (Larson et al., 1993). Here we and the loss by burial and seepage balance converted from dry weight to biomass in units of (Dymond et al., 1996), this does not affect the carbon and nitrogen assuming that carbon overall nitrogen inventory of the lake. The initial constituted 48\% and nitrogen 10% of dry weight conditions for the biological variables were ob- respectively (Andersen & Hessen 1991; Brett tained as follows: N was defined by interpolating et al., 2000). the mean profile all available nitrate and ammonium data onto the model grid, while all other biological variables were set to 0.01 mmol N m–3. Results The model was then started on January 1 and run for 3 year to allow an adjustment to the initial We present model results of a simulation for 1995 conditions. All the results discussed here are from in comparison with observations. The simulated the third year of the simulation. annual evolution of vertical distributions of the phytoplankton groups, total chlorophyll and zooplankton are shown in Fig. 4. Quantitative Limnological data comparisons of the simulated concentrations with mean observations are given in Figs. 5–7. Water samples were collected from the RV The simulated total phytoplankton biomass is Neuston at station 13 (4256¢ N 12206¢ W, located low from January through March. The biomass of at the deepest part of Crater Lake) between June phytoplankton group 2 (comprised of chlorophyta, 1988 and September 2001. Nitrate and ammonia chrysophyta, cryptomonads and cyanobacteria) were measured by automated cadmium reduction starts to increase in April with increasing solar and phenate calorimetric methods, respectively, radiation before the upper water column stratifies and a Technicon autoanalyzer (Larson et al., thermally. Phytoplankton group 1 (diatoms and 1996a). Chlorophyll concentrations were deter- dinoflagellates) does not increase until thermal mined by fluorometry after filtration of samples stratification is established in late May/early June onto 0.45-lm pore-size filters and extraction with (Fig. 4). During the stratified period in summer 90% acetone. Phytoplankton were preserved with and early fall a marked vertical structure persists. Lugol’s solution and concentrated by gravity set- The phytoplankton groups 1 and 2 express pro- tling (96 h). Cells > 1 lm were identified and nounced vertical maxima in the upper 40 m, and counted by means of inverted microscopy. Biovo- between 50 and 80 m, respectively (Figs. 4, 5). The lume conversion factors were determined for each low biomass in January and the vertical distribu- taxon by geometric approximation (McIntire et al., tion of P1 and P2 compare well with the observed 1996). We converted biovolume to biomass (in biomass of the ‘‘surface’’ and ‘‘deep’’ groups units of carbon) by applying the following formula: (Fig. 5). In particular, the profiles of phytoplank- cell C = 0.142 volume0.996 [pg C lm–3] for each ton group 2 agree remarkably well with the ob- taxon. The conversion formula has been obtained served mean profiles of the ‘‘deep group’’ from by Rocha & Duncan (1985) by fitting 47 determi- June through September. The simulated vertical nations of cell carbon and cell volume for 25 structure of phytoplankton group 1 agrees quali- freshwater algal species. tatively with mean profiles of the ‘‘shallow group,’’ Zooplankton samples were obtained by verti- but the absolute surface concentrations are over- cal towing of a 64-lm mesh-size tow net. Zoo- estimated by our model in June and July. plankton were diluted with pre-filtered lake The simulated chlorophyll profiles have a ver- water, preserved with 4% formaldehyde/4% su- tical maximum at about 120 m from June through crose, concentrated by gravity settling (24 h), and August, about 50 m below the vertical maximum counted by means of inverted microscopy (Larson of phytoplankton group 2 (Figs. 4–6). The vertical

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Phytoplankton group1 mmol N m–3 Phytoplankton group2 mmol N m –3 0.7 0.7

40 0.6 40 0.6

80 0.5 80 0.5 0.4 0.4 120 120 0.3 0.3

Depth [m] 160 Depth [m] 160 0.2 0.2 200 200 0.1 0.1 240 240 0 0 J F M A M J J A S O N D J F M A M J J A S O N D

Chlorophyll mg m –3 Zooplankton mmol N m –3 1 0.15

40 40 0.8 80 80 0.1 0.6 120 120 0.4 Depth [m] 160 Depth [m] 160 0.05 200 0.2 200

240 240 0 0 J F M A M J J A S O N D J F M A M J J A S O N D

Fig. 4 Simulated evolution of phytoplankton groups 1 and 2, total chlorophyll and zooplankton concentrations in the upper 250 m of the water column. The white line represents the depth of the simulated surface boundary layer distribution of the simulated chlorophyll concen- Discussion trations, which are low at the surface and increase monotonically to the deep maximum, agrees well We now discuss the seasonal evolution of vertical with mean profiles of extracted chlorophyll mixing and thermal stratification and its (Fig. 6), but the absolute chlorophyll values are implications for the distribution of nutrients and overestimated by the model. plankton (section Physical controls of nutrient The zooplankton concentrations are highest and plankton dynamics); suggest biochemical and between 40 and 80 m and increase over the bio-optical factors that contribute to the vertical course of the growing season (Fig. 4). The mag- structure of phytoplankton during the stable nitude of zooplankton biomass compares well period in summer and early fall (section Biologi- with observed values, but a discrepancy in the cal factors for the vertical distribution of biomass vertical structure is apparent (Fig. 7). Some zoo- and chlorophyll); and discuss a nitrogen budget plankton species in Crater Lake exhibit diel ver- for the watercolumn of Crater Lake (section tical migrations with displacements between 20 Nitrogen budget). and 40 m (Larson et al. 1993, 1996b). This behavior is not easily accounted for in the model Physical controls of nutrient and plankton but may explain the apparent discrepancy in dynamics vertical structure between simulated and observed zooplankton. Vertical mixing exerts important controls on the In summary, the model captures essential fea- biological system, i.e., it affects nutrient supply to tures of the system. Quantitative discrepancies the euphotic zone, phytoplankton spatial distri- exist and may stem from unresolved and/or butions and light levels received by the phyto- poorly quantified processes. plankton community. We briefly describe the

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Fig. 5 Simulated phytoplankton concentrations given as diatoms and dinoflagellates. P2 (filled diamonds and monthly means (solid and dashed lines) in comparison dashed lines) includes chlorophyta, chrysophyta, crypto- with medians of observed phytoplankton biomass (dia- monads and cyanobacteria monds). P1 (open diamonds and solid lines) includes annual evolution of vertical mixing and stratifi- fall decreasing solar radiation and surface cooling cation. erode the summer thermocline and produce cool, In winter and early spring the upper portion of dense surface water that is convected. Convective Crater Lake (upper 200–250 m) is relatively well mixing continues until the temperature of mixed. The water column is isothermal at two maximum density (about 4 C) is reached. At this distinct events—once in early winter and once in point the upper part of the water column is iso- early spring (McManus et al., 1993; Crawford & thermal and a direct exchange of water between Collier 1997). The timing of these isothermal the upper and deep portions of the lake is possi- events and the intensity of mixing at a given time ble. Continued cooling of surface water below the are determined by the current thermal structure temperature of maximum density leads to inverse and the surface wind stresses and heat fluxes. In thermal stratification. Heating in early spring

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0 0 June July 50 50

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250 250 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

Fig. 6 Simulated chlorophyll concentrations given as monthly means (solid lines) in comparison with observed chlorophyll data plotted as median with 25- and 75-percentiles (squares) results in convective mixing until the temperature depth-integrated respiration). In other words, net of maximum density is reached again—the second phytoplankton growth in spring can only occur in isothermal event. Subsequent heating leads to Crater Lake after the temperature of maximum pronounced thermal stratification in summer. density is exceeded and convective mixing This evolution of convection and inverse thermal ceases—a link that has been demonstrated for the stratification is typical for high latitude systems spring bloom in the Baltic Sea (Fennel, 1999). below 20 PSU (e.g., Fennel, 1999; Botte & Kay, Consistent with this concept phytoplankton bio- 2000). mass increases in our simulation only in April The history of winter mixing affects processes after the temperature of maximum density is ex- in the euphotic zone in two important ways:(i) the ceeded in late March. most significant input of inorganic nutrients from In summer a strong seasonal thermocline is the deep lake occurs during the isothermal peri- established between 20 and 30 m depth and ods (Dymond et al., 1996; Crawford & Collier, effectively limits vertical exchange. The vertical 1997); and (ii) as microorganisms are mixed ver- transport of nutrients is at a minimum and parti- tically the photosynthetically active radiation cles are not displaced vertically by advective (PAR) received by the phytoplankton community forcings other than their own buoyancy forcing. is strongly determined by mixing depth (Sverd- The vertical transport of nitrate is restricted to rup, 1953). According to Sverdrup (1953) net turbulent diffusion. Since nitrate concentrations phytoplankton growth in spring can only occur in the upper 100 m are low without a notable when the depth of vertical mixing is shallower vertical gradient, a significant diffusive input to than the critical depth (the depth at which the the euphotic zone can only occur below 100 m. depth-integrated phytoplankton growth equals Due to the stable stratification, microorganisms

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0 0

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Fig. 7 Stimulated zooplankton concentrations given as monthly means (solid lines) in comparison with observed zooplankton biomass plotted as median with 25- and 75-percentiles (squares) can maintain their vertical position allowing for stable conditions in summer and early fall, this the observed and simulated dominance of distinct vertical separation is pronounced in Crater Lake. species groups at different depths (McIntire et al., The inclusion of photoacclimation in our model this issue: Fig. 5). results in a vertical separation similar to the one observed. The location of the chlorophyll maximum is ultimately determined by light Biological factors for the vertical distribution attenuation and the physiological ability of phy- of biomass and chlorophyll toplankton to increase their cellular chlorophyll- to-biomass ratio. The particle maximum on the Our model captures a separation between the other hand, is determined by the balance between vertical maxima of phytoplankton biomass and biomass growth and losses including respiration, chlorophyll (by up to 50 m) and the vertical dif- grazing, mortality, and divergence in sinking ferentiation between the phytoplankton func- velocity. tional groups 1 and 2 in agreement with Under steady-state conditions the biomass observations. General criteria that determine the maximum is located at the depth where growth vertical structure of phytoplankton biomass and and losses equal (Riley et al., 1949; Fennel & chlorophyll in stable, oligotrophic environments Boss, 2003). This criterion can be derived as fol- were discussed recently in Fennel & Boss (2003). lows. Assuming that growth, biological losses We suggested that the particle maximum and the (due to respiration, mortality and grazing), sink- chlorophyll maximum are generated by funda- ing and vertical mixing are the main processes mentally different processes. Photoacclimation determining the distribution of phytoplankton, a results in a deep chlorophyll maximum vertically general 1D phytoplankton equation can be separated from the biomass maximum. During written as

123 276 Hydrobiologia (2007) 574:265–280 @P @ðÞwP @ @P 0 0 þ ¼ ðÞl R P þ k : ð13Þ @t @z @z z @z 20 20 Here P represents the phytoplankton biomass, w the phytoplankton settling velocity, l the growth 40 40 rate, R the rate of biological losses including res- 60 60 piration, mortality and grazing, and kz the eddy diffusion coefficient. We want to solve Eq. 13 for Depth [m] 80 80 steady state conditions, in which case the first term can be neglected and the equation simplifies to 100 100 dðÞwP d dP 120 ¼ ðÞl R P þ k : ð14Þ 120 dz dz z dz –2 0 2 4 6 8 –5 0 5 10 P1 [mmol N m–3 ] P2 [mmol N m–3 ]

The condition for the location of a vertical Fig. 8 Mean July biomass of phytoplankton groups 1 and 2 (solid lines) and sum of their growth, respiration, grazing, phytoplankton maximum P(zmax) then follows as mortality and diffusion terms on an arbitrary scale (dashed lines). The vertical biomass maxima occur where sources @P and sinks are equal as indicated by the circles ¼ 0 ð15Þ @z zmax present in Crater Lake. Data from oceanic algae, 2 however, are consistent with our parameter dw d PzðÞmax ) l R þ k ¼ 0: ð16Þ choices for a and l . Geider et al. (1997) dz z dz2 chl max collected photo-physiological parameters of 15 Since the particle maximum is usually located in a different marine algae from a wide range of region with low diffusivity we neglect the diffu- environments (obtained from a total of 19 stud- sive flux term in Eq. 16 and obtain ies). We calculated the mean values of lmax and achl for the 8 bacillariophyta and 11 chrysophyta dw included in this collection. The mean lmax equals l R ¼ 0: ð17Þ –1 –1 dz 3.6 ± 1.3 d and 1.3 ± 0.9 d for bacillariophyta and chrysophyta, respectively, and the mean achl In other words, at the particle maximum the equals 0.05 ± 0.36 mol N (g chl W m–2)–1 and community growth rate l equals the sum of the 0.054 ± 0.34 mol N (g chl W m–2)–1 for bacilla- biological losses R and the divergence of particles riophyta and chrysophyta, respectively. Consis- due to changes in the settling velocity. This cri- tent with our parameter choices the mean terion can be applied to the phytoplankton groups maximum growth rate is significantly higher for 1 and 2 to predict the location of their vertical the bacillariophyta. There is no significant dif- maxima (Fig. 8). ference in achl between both divisions, due to In our model the growth and loss term profiles large variations between different taxa. Moore & of both phytoplankton groups differ mainly due Chisholm (1999) have shown that different iso- to different parameter choices for the initial slope lates of Prochlorochoccus express distinct photo- of the PI-curve achl and the maximum growth rate physiological parameters. Comparing 10 different lmax (see Table 1), although grazing and respira- isolates they found two clusters: a high-light tive losses differ as well. The higher maximum adapted group that had higher maximum light- growth rate of group 1 results in an advantage at saturated growth rates (corresponding to lmax) high light levels near the surface, while the larger and lower growth efficiencies under sub-saturat- initial slope of phytoplankton group 2 is advan- ing light intensities (corresponding to achl) than tageous at lower light levels deeper in the water the low-light adapted group. These distinct eco- column. Unfortunately, no data are available on types have been found to coexist in the same the light-physiological parameters of the algae water column.

123 Hydrobiologia (2007) 574:265–280 277

A potentially strong selective factor in the a sediment trap at 200 m measured between 1984 epilimnion in Crater Lake, not considered in our and 2002 (Dymond et al., 1996; Collier, R.W., model is ultra-violet (UV) radiation. UV unpublished data). The sediment trap data vary radiation is a significant stressor in aquatic between 40 and 260 mg N m–2 yr–1 with a mean of environments. In Crater Lake, UV levels are 130 ± 67 mg N m–2 yr–1. Note that our estimate is particularly high. Incident UV radiation is ele- conservative as our model does not account for vated due to the high altitude and attenuation in atmospheric inputs of nitrogen. the water column is small because concentrations This agreement between simulated and of colored dissolved organic matter are low (Boss observed fluxes stands in contrast to box-model et al., this issue). Widely observed deleterious estimates of vertical particle flux by Dymond effects of UV on planktonic microorganisms in- et al. (1996), who found a significant discrepancy clude inhibition of photosynthesis (Lorenzen, between estimated vertical particle fluxes and the 1979; Cullen et al., 1992; Smith et al., 1992) and sediment trap data. The authors derived an bacterial heterotrophic potential (Herndl et al., internal nitrogen budget, dividing Crater Lake 1993), and damage of DNA (Karentz et al., 1991). into an upper and deep box (at 200 m) and for- Two physiological acclimation mechanisms that mulating the nitrogen mass balance equations for decrease algal sensitivity to UV are efficient re- both boxes as pair of photodamage, and the synthesis of photoprotective pigments (Litchman et al., 2002). Fp ¼ Fa þ Fr þ Fu Fd Fsp;upper ð18Þ In Crater Lake, the efficiency of both of these and acclimation mechanisms is likely compromised by nitrogen limitation which has been observed to 1 F ¼ F F þ F : ð19Þ significantly depress the potential to repair p 1 a u d sp;deep photodamage and, to a lesser extent, the synthesis of photoprotective pigments (Litchman et al., Fp is the vertical flux of nitrogen due to settling 2002). particles. Fa and Fr are nitrogen sources to the Despite the nitrogen limitation in Crater Lake, upper box due to atmospheric inputs and runoff, microorganisms in the epilimnion contain photo- respectively. Fu and Fd represent the nitrogen protective pigments (Lisa Eisner, personal exchange between the upper and deep box due to comm.). The usefulness of these pigments in upward mixing of deep-lake nutrients and down- decreasing sensitivity to UV radiation is strongly ward mixing of surface nitrate pools, respectively. linked to organism size: for picoplankters (ra- Fsp is the seepage loss of nitrogen through the dii < 1 lm) pigment sunscreens are not of any lake floor, split into seepage losses from the upper relevance for photoprotection, but for micro- and deep portions, Fsp,upper and Fsp,deep. The plankter (cell radii > 10 lm) these sunscreens can sediment burial term Fb is assumed to relate be very effective (Garcia-Pichel, 1994). Conse- proportionally to the settling of particles Fp with a quently, cell size represents a selective criterion, representing the fraction of settling particles favoring larger cells in the epilimnion. This is buried in the sediments (Fb = aFp). consistent with optical measurements of the slope By inserting their best estimates of atmospheric, of the beam attenuation spectrum which point to runoff and seepage inputs and losses, and a rea- the dominance of larger cells near the surface sonable range of values for the burial fraction of than at the deeper biomass maximum (Boss et al., settling particles into the right-hand-sides of Eqs. this issue). (18) and (19), Dymond et al. obtained model estimates for the vertical particle flux that were 2.5–10 Nitrogen budget times larger than the measured sediment trap fluxes. In their discussion the authors state that this The simulated sinking flux of detritus at 200 m in discrepancy could be due to errors in the direct our model is 92 mg N m–2 yr–1. This value agrees measurements, errors in their box-model assump- well with vertical particulate nitrogen fluxes from tions, or unaccounted processes. They suggested a

123 278 Hydrobiologia (2007) 574:265–280 combination of sediment focusing and significantly (Fig. 9). With these nitrogen concentrations in higher productivity at the edges of Crater Lake to the upper and deep boxes we obtain a DNof explain the mismatch. Both of these processes are 0.2 lM and an exchange flux (Fu–Fd) of 0.4– hard to quantify with the available data. 0.8 · 106 mol yr–1. This flux estimate compares An analysis of our model results suggests a well with our simulated flux of 0.57 · 106 mol yr–1. different explanation. We calculated the simu- Iterating Dymond et al.’s box-model calculation lated exchange of nitrogen between the upper and with our estimate of Fu–Fd, we obtain vertical deep box due to winter mixing as 0.57 · 106 mo- particle fluxes of 0.69–1.38 · 106 mol yr–1 from lyr–1. This value is significantly smaller than the Eq. (18) and 0.5–1.1 · 106 mol yr–1 from Eq. (19). flux assumed by Dymond et al. (2.0– These revised box-model estimates are consistent 4.0 · 106 mol yr–1). The authors obtained this with the sediment trap fluxes of 0.49 ± 0.25 · exchange flux of nitrogen between the upper and 106 mol N yr–1, our model estimates, and the deep deep boxes assuming (i) that winter mixing re- lake’s oxygen budget (McManus et al., 1996). places 2–4 · 1012 liters of water between both boxes and (ii) a nitrate inventory of 0 and 1 lM for the upper and deep boxes, respectively. They Conclusions neglected the possibility of dissolved and suspended organic matter being exchanged between We developed a simple physical-biological model the upper and deep portions in addition to the of Crater Lake that captures the observed vertical exchange of nitrate. A flux of organic dissolved structure of two distinct phytoplankton groups and suspended nitrogen could counterbalance an and chlorophyll, and predicts the biomass of exchange of inorganic nitrogen. Interestingly, the phytoplankton and zooplankton in good quanti- simulated exchange of DIN in our model equals tative agreement with observations from a 1.13 · 106 mol yr–1, a value closer to Dymond 10-year monitoring study. Our model suggests et al.’s estimate, while the simulated exchange of organic matter is –0.56 · 106 mol yr–1, reducing 0 the net exchange to 0.57 · 106 mol yr–1. In order to revisit the box-model calculations we estimate a ‘‘corrected’’ exchange flux (F –F ) u d 100 based on the following arguments. Dymond et al. assumed a DN (defined as the difference between NO 3 TKN nitrogen in the upper and deep portions of the 200 lake) of 1 lM neglecting dissolved and suspended nitrogen. We suggest a reduction of DN to 0.2 lM. We obtain this value assuming that the nitrate 300

concentrations in the upper box equals 0 in Depth [m] agreement with Dymond et al., but reduce the assumed nitrate concentration in the deep box from 400 total N 1 to 0.6 lM. Our value is more representative of nitrate concentrations between 200 and 400 m depth—a water mass more likely to be mixed up 500 above 200 m than water from below 400 m depth (Fig. 9). For estimates of dissolved and organic 600 nitrogen we compare total Kjeldahl nitrogen 0 0.5 1 1.5 2 2.5 NO , TKN, and total nitrogen [mmol N m–3] (TKN) values between the upper and deep por- 3 tions of the lake. TKN represents nitrogen in the ammonium, dissolved and particulate organic Fig. 9 Mean proﬁles of nitrate and Kjeldahl nitrogen (represents the sum of ammonia, and particulate and matter pools. TKN in the upper box is typically dissolved nitrogen) with standard deviation, and total 1.4 lM and TKN in the deep box is about 1 lM nitrogen

123 Hydrobiologia (2007) 574:265–280 279 that phytoplankton production starts in spring Andersen, V., P. Nival & R. Harris, 1987. Modelling of a only after the temperature of maximum density planktonic ecosystem in an enclosed water column. Journal of the Marine Biological Association of the (about 4C) is exceeded. That is, the onset of U.K. 67: 407–430. phytoplankton production is dependent on the Boss, E., R. Collier, G. Larson, K. Fennel & W. S. Pegau, evolution of vertical mixing in winter. Stable this issue. Measurements of spectral optical properties stratification in summer allows a pronounced and their relation to biogeochemical variables and processes in Crater Lake. vertical structure of phytoplankton distributions Botte, V. & A. Kay, 2000. A numerical study of plankton to emerge. The vertical separation of the deep population dynamics in a deep lake during the pas- chlorophyll maximum (at about 120 m) and the sage of the spring thermal bar. Journal of Marine biomass maximum (between 50 and 80 m) results Systems 26: 367–386. Brett, M. T., D. C. Mueller-Navarra & S.-K. Park, 2000. from photoacclimation. In our model the biomass Empirical analysis of the effect of phosphorus limi- maximum of both functional phytoplankton tation on algal food quality for freshwater zooplank- groups during stable conditions in summer is ton. Limnology and Oceanography 45: 1564–1575. located where their respective growth and loss Collier, R. W., J. Dymond & J. McManus, 1991. Studies of hydrothermal processes in Crater Lake, Oregon. rates are equal. The differences in the vertical College of Oceanography Report, 90. Oregon State position of the biomass maximum of phyto- University. plankton groups 1 and 2 at 20 m and 50–80 m, Crawford, G. B. & R. W. Collier, 1997. Observations of a respectively, result mainly from parametric dif- deep-mixing event in Crater Lake, Oregon. Limnol- ogy and Oceanography 42: 299–306. ferences in the initial slope of the PI-curve and Cullen, J. J., P. J. Neale & M. P. Lesser, 1992. Biological the maximum growth rate. While no experimental weighting functions for the inhibition of phytoplank- data on the growth and light-response parameters ton photosynthesis by ultraviolet radiation. Science are available for the specific species present in 258: 646–650. Dymond, J., R. Collier & J. McManus, 1996. Unbalanced Crater Lake, parameters determined for oceanic particle flux budgets in Crater Lake, Oregon: Impli- species are consistent with our choices. Sensitivity cations for edge effects and sediment focusing in to UV radiation is likely to be an important lakes. Limnology and Oceanography 41: 732–743. selective factor as well, but is not included in our Fasham M. J. R., 1993. Modelling marine biota. In Hei- mann M. (ed.), The Global Carbon Cycle. Springer model since quantitative information on its effect Verlag, New York, 457–504. is lacking. The average annual vertical flux of Fasham M. J. R., 1995. Variations in the seasonal cycle of particles in our model compares well with the biological production in subarctic oceans: A model average annual flux measured in sediment traps at sensitivity analysis. Deep-Sea Research I 42: 1111–1149. Fennel K., 1999. Convection and the timing of the phyto- a depth of 200 m. We suggest correcting previous plankton spring bloom in the Western Baltic Sea. model estimates of vertical exchange by Dymond Estuarine, Coastal and Shelf Sciences 49: 113–128. et al. (1996), who found a mismatch between Fennel K. & E. Boss, 2003. Subsurface maxima of phyto- model-estimated and observed vertical fluxes. plankton and chlorophyll: Steady state solutions from a simple model. Limnology and Oceanography 48: Our model simulation pointed to a significant 1521–1534. downward flux of suspended and dissolved or- Garcia-Pichel F., 1994. A model for internal self-shading in ganic matter which had been neglected by planktonic organisms and its implications for the Dymond et al. Inclusion of this flux reconciles the usefulness of ultraviolet sunscreens. Limnology and Oceanography 39: 1704–1717. box-model estimates and the trap measurements. Geider R. J., H. L. McIntyre & T. M. Kana, 1996. A dynamic model of photoadaptation in phytoplankton. Acknowledgements We wish to thank Leon Tovey for Limnology and Oceanography 41: 1–15. reviewing the manuscript and three anonymous reviewers Geider R. J., H. L. McIntyre & T. M. Kana, 1997. Dynamic for helpful comments. Funding for KF was provided by model of phytoplankton growth and acclimation: USGS. Responses of the balanced growth rate and the chlorophyll a:carbon ratio to light, nutrient-limitation and temperature. Marine Ecology Progress Series 148: References 187–200. Geider R. J., H. L. McIntyre & T. M. Kana, 1998. A dy- Andersen, T. & D. O. Hessen, 1991. Carbon, nitrogen and namic regulatory model of phytoplanktonic acclima- phosphorus content of freshwater zooplankton. Lim- tion to light, nutrients and temperature. Limnology nology and Oceanography 36: 807–814. and Oceanography 43: 679–694.

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