Untangling the uncertainties about combined effects of temperature and concentration on nutrient uptake rates in the ocean

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1 Click Here for Full Article GEOPHYSICAL RESEARCH LETTERS, VOL. 37,, doi: /2010gl043617, 2010 Untangling the uncertainties about combined effects of temperature and concentration on nutrient uptake rates in the ocean S. Lan Smith 1 Received 15 April 2010; accepted 10 May 2010; published 9 June [1] I show that assumptions about how uptake rates depend on concentration strongly impact the interpretation of field observations, specifically with respect to the combined effects of temperature, T, and nitrate concentration, [NO 3 ], on nitrate uptake. The standard assumption that maximum uptake rate, V max, is independent of ambient nutrient concentration, S a, contrasts with the prediction of the recently developed Optimal Uptake kinetics that V max should increase hyperbolically with S a. Assuming Arrhenius T dependence, I fit the respective equations to field observations of chlorophyll specific V max, T and [NO 3 ]. The inferred sensitivity to T differs by a factor of two. Considerable uncertainty therefore remains about the T dependence of uptake rates, and therefore about biological production and biogeochemical cycles. Given that both climate change and anthropogenic nutrient inputs are altering the relationship between T and nutrients in the ocean, these uncertainties limit our understanding of the direct effects and associated feedbacks. Citation: Smith, S. L. (2010), Untangling the uncertainties about combined effects of temperature and concentration on nutrient uptake rates in the ocean, Geophys. Res. Lett., 37,, doi: /2010gl Introduction [2] Smith et al. [2009] found that the observed pattern in Michaelis Menten (MM) half saturation constants, K NO3, as determined by shipboard experiments for uptake of the important nutrient nitrate, agrees with the prediction of the recently developed Optimal Uptake (OU) kinetics, based on physiological acclimation by phytoplankton to optimize uptake rate. Maximum uptake rates, V max, as fit to the MM equation, vary more widely with environmental conditions [Kanda et al., 1985; Harrison et al., 1996; Collos et al., 2005] and are more difficult to interpret. Therefore, both Collos et al. [2005] and Smith et al. [2009] chose to examine only the pattern for K NO3. Yet understanding and quantitatively modeling the large scale pattern of nutrient uptake in the ocean requires consistently addressing the dependencies of both V max and half saturation constants (or more generally, affinities). [3] Field experiments observe the combined effects of temperature (T), ambient nutrient concentration, S a, and potentially light. In the surface ocean, T and S a are strongly negatively correlated [e.g., Silio Calzada et al., 2008]; cold, 1 Environmental Biogeochemical Cycles Research Program, RIGC, JAMSTEC, Yokohama, Japan. Copyright 2010 by the American Geophysical Union /10/2010GL nutrient rich water is up welled, then warmed as nutrients are depleted. Therefore, interpretation of the data (i.e., untangling the effects) depends on assumptions about how uptake rates depend on each factor, respectively. [4] Arrhenius type T dependence of chemical reaction rates is well established, as is a similar exponential T dependence for phytoplankton growth rates [Eppley,1972;Bissinger et al., 2008]. However, Moisan et al. [2002] present an alternative T dependence, based on simulations of the dynamic response of a diverse assemblage of phytoplankton. Two competing assumptions exist about how uptake rates depend on concentration. The most common assumption for decades has been that V max (as fit to the MM equation) is independent of S a. However, the recently developed OU kinetics makes the rather different prediction [Smith et al., 2009] that typical short term incubation experiments should observe a saturating increase in V max as a function of S a, to which phytoplankton were pre acclimated upon sampling. Given that compared to MM, OU kinetics has been found to better describe uptake in chemostat experiments under limitation by N, P and vitamin B 12 [Smith and Yamanaka, 2007], the dependence of K NO3 on ambient nitrate concentration ([NO 3 ] a ) in seawater [Smith et al., 2009], and changes in Si and N uptake rates during an oceanic iron fertilization experiment [Smith et al., 2010], its prediction about V max should be considered as an alternative. [5] Here I examine the consequences of these different assumptions about the nutrient and T dependence of V max for interpreting field observations of uptake rates, specifically with respect to the combined effects of T and [NO 3 ]on nitrate uptake. Furthermore, I seek to evaluate whether the predictions of OU kinetics are consistent with field observations of both V max and K s. 2. Methods 2.1. Data [6] I analyzed data for chlorophyll (chl) specific V max for nitrate from the short term (1 3 h), shipboard incubation experiments (at ambient T) of Kanda et al. [1985] (North Pacific, n = 17) and Harrison et al. [1996] (North Atlantic, n = 60). G. W. Harrison (personal communication) provided the latter data set as a digital file, from which I matched the observed uptake rates to the ambient T and [NO 3 ], by crossreferencing the cruise numbers, dates and T from that file with the uptake rates and [NO 3 ] as digitized from Harrison et al. [1996]. Both data sets provide values of V max and K NO3, with corresponding ambient T and [NO 3 ]. However, for Kanda et al. [1985], K NO3 must be estimated by subtracting the observed [NO 3 ] from the reported estimate of 1of5

2 where V max, r is the V max at reference temperature T r, E a is the activation energy, R is the gas constant, T is temperature in K, S is the nutrient concentration, and K s is the MM half saturation constant for nutrient S. This is a multiplicative combination of Arrhenius type T dependence and the Monod (or MM) kinetics for growth (or uptake) as applied by Dugdale [1967]. Thus the MM based the expression for dependence of V max on T is: V max; MM ¼ V max;r e Ea=RTr e Ea=RT ð2þ In contrast, OU kinetics [Smith et al., 2009] predicts that apparent values of both V max and K s, as obtained by fitting the MM equation to data from short term experiments, should depend on S a, the ambient nutrient concentration (in seawater) to which the phytoplankton were pre acclimated before the experiments: max ¼ V app ð3þ K app s rffiffiffiffiffiffiffiffiffi S a ¼ A 0 ð4þ where and A 0 are, respectively, the potential maximum values of V max and affinity [Smith and Yamanaka, 2007]. Analogous to the equation of Goldman and Carpenter [1974], combining Arrhenius type T dependence with OU kinetics yields for uptake rate: v OU ¼ ; re Ea=RTr e Ea=RT S þ S S a A 0 ð5þ where S is the concentration in the incubation flasks. This gives the OU based equation for V max as a function of T: Figure 1. Schematic of the implications of combining multiplicatively an exponential dependence of maximum uptake rate, V max,ontwith either Michaelis Menten or Optimal Uptake kinetics, respectively, to describe the dependence on ambient nutrient concentration S a. Because of the negative relationship between T and S a in the nearsurface ocean, the dependencies counteract one another in the case of Optimal Uptake kinetics. (K NO3 + [NO 3 ]), whereas Harrison et al. [1996] report values of K NO3 directly from nonlinear fits of the MM equation to their data, which includes more precise measurements down to nanomolar [NO 3 ] Equations [7] The equation most commonly applied to describe the combined effects of nutrient concentration and T is that of Goldman and Carpenter [1974], originally applied to growth, but here written (as often applied) for uptake rate: v MM ¼ V max; r e Ea=RTr e Ea=RT S K s þ S ð1þ V max; OU ¼ ; re Ea=RTr e Ea=RT I similarly tested MM and OU based equations using the T dependence of Moisan et al. [2002, equation 9] for the effective population response in a fluctuating environment Fitting [8] Log transformations of equations (2) and (6) were fit, respectively, to values of logv max, using observed ambient T and [NO 3 ] to calculate the fitted values of V max for each data set, respectively. For the OU case, the ratio /A 0, which determines how the apparent values of MM constants depend on nutrient concentration (equations (3) and (4)), was determined from fits of logk NO3 versus log[no 3 ] as by Smith et al. [2009] for each data set, respectively. This left two adjustable parameters to be fit in either case: for MM (equation (2)), V max, r and E a, and for OU (equation (6)),, r and E a. The nls algorithm in Splus software (v. 8) was used for nonlinear fitting. 3. Results [9] Qualitatively, the most striking difference between the MM and OU based assumptions is that the latter implies that the greatest value of V max should occur at intermediate values of both T and S a (Figure 1), because the latter two are ð6þ 2of5

3 [10] With Arrhenius T dependence, the fits (Table 1) of the OU based equations to the data were nominally better than those of the MM based equations. However, neither model reproduces the wide variability in the data, and these observed chl specific rates are not ideal for testing the OU predictions for biomass specific rates (see section 4). Therefore, these results alone are not sufficient to draw conclusions about which model is better. Still, with OU kinetics the nutrient dependence of V max was modeled according to equation (3), using values of the ratio /A 0 obtained from separate fits of logk NO3 vs. log[no 3 ], based on equation (4). No inconsistency was found in these inextricably linked predictions of OU kinetics about the respective patterns of variation in V max and K NO3 as a function of S a. Compared to the exponential T dependence, fits to the data of Harrison et al. [1996] using the T dependence of Moisan et al. [2002], which adds one extra parameter, were worse for MM and only slightly better for OU kinetics (Figure 3). Figure 2. Observed (circles) V max of nitrate from the shortterm (1 2 h) incubation experiments of Harrison et al. [1996] in the North Atlantic Ocean plotted versus (a, b) ambient ocean T and (c, d) ambient nitrate concentration, [NO 3 ] a at time of sampling. Fits (crosses and lines) of two different models, based respectively on MIchaelis Menten (Figures 2a and 2c) and Optimal Uptake (Figures 2b and 2d) kinetics for uptake as a function of concentration. Crosses are best fits of each model, respectively, using the observed T and [NO 3 ] a. Lines are model fits using best fit parameters, but assuming that T and [NO 3 ] a follow exactly the log log correlation from this data set. strongly and negatively correlated in the near surface ocean. For the data set of Harrison et al. [1996] the inferred T dependence, Q 10 (the factor by which rates increase for a 10 C increase in T), was approximately twice as strong assuming OU versus MM kinetics (Table 1). This is because of the counteracting effects of the two dependencies, as can be seen by comparing the effects of each separately (Figures 2a and 2b). Results were similar for the data of Kanda et al. [1985] (not shown) with less difference between the MMand OU based estimates of Q 10 (Table 1) because of the lower estimate of /A 0 for this data set. However, given that the values of both K NO3 and [NO 3 ] a were less precise for this data set, which contains fewer data, I have more confidence in the results based on the data of Harrison et al. [1996]. Using that value, /A 0 = , to fit the OU model to the data of Kanda et al. [1985] yields a Q 10 of 3.8, with very little difference in quality of fit (results not shown). Even for the data set of Harrison et al. [1996], there pffiffiffiffiffiffiffiffiffiffiffiffi is considerable uncertainty in the estimate of /A 0 : log( =A 0 )= with 90% confidence intervals of ±0.118, equivalent to a 90% confidence range from to 0.14 for /A 0, which results in a range of inferred Q 10 from 3.17 to 3.74 (with little difference in the quality of fit, results not shown). 4. Discussion 4.1. Comparison With Growth Kinetics [11] The finding that phytoplankton maximum growth rates, m max, increase exponentially with T, with Q 10 = 1.8 [Eppley, 1972; Bissinger et al., 2008], is an idealization of the inter species variation in m max based on fitting through the top of the data (maximum value of m max at each ambient temperature, T a ). In controlled laboratory experiments growth rates of individual species decrease above some speciesspecific optimal temperature, T opt. Application of exponential T dependence to model large scale growth (or uptake) rests on the assumption of a continuum of species, such that the dominant species at any time and place is the one having T opt = T a. Species specific T opt are also observed for nutrient uptake [Dauta, 1982; Tilman et al., 1981], and an analogous idealization is possible for V max. However, that approach cannot examine the combined effects of T and nutrients, nor do I expect that it would yield meaningful results for the data sets considered here, which contain far fewer values than those analyzed for m max. [12] The Q 10 estimated herein based on MM kinetics is essentially the same as that reported for growth, but that based on OU kinetics is twice as large. Furthermore, Lomas and Gilbert [1999] have hypothesized that nitrate uptake rates may decrease with T if cool water diatoms are reducing nitrate in order to dissipate excess energy under high light conditions. Their hypothesis implies a distinctly different pattern of variation for MM constants for nitrate than for other nutrients and would impact the interpretation of field observations, because diatoms dominate phytoplankton biomass in many nitrate rich areas of the ocean. [13] Moisan et al. [2002] present an alternative theoretical argument that the greatest values of m max should occur at intermediate T, which if applied to V max could potentially explain the wide variability observed. In their simulations of assemblages in a fluctuating environment, the dominant species at any given time did not have T opt = T a, because of the dynamics of competition. However, they made no quantitative comparison to observations, and the specific shape of their population response depended both on the assumed species specific shape of T dependence and on the fluctuations (e.g., on seasonality, which varies with latitude). 3of5

4 Table 1. Best Fit Parameter Values and Statistics for Fits of the Respective Equations for V max to the Data Sets From Field Experiments a Fit to Data Set Kanda et al. [1985] Harrison et al. [1996] MM OU MM OU Arrhenius T Dependence Parameter (units) V max, r (nmol h 1 (mg Chl) (0.030) 10.1 (1.08), r (nmol h 1 (mg Chl) (0.049) 40.3 (4.92) E a /R (K 1 ) 3570 (1540) 8110 (1300) 4410 (1090) (1240) T Sensitivity (Q 10 ) Residual Square Error (RSE) degrees of freedom (df) Significance Level of fit for E a /R p < Moisan et al. [2002] T Dependence Parameter (units) V max, r (nmol h 1 (mg Chl) (0.72), r (nmol h 1 (mg Chl) (7.14) T opt (K) 285 (0.52) 299 (12.8) T scale (K) 1402 (272) 9326 (14700) Residual Square Error (RSE) degrees of freedom (df) a SE, standard errors, in parentheses. Values of rate coefficients are for a reference T of 293 K. For fitting the OU based equation, a value of /A 0 = was applied for the data set of Kanda et al. [1985], and for that of Harrison et al. [1996], based on separate fits of logk NO3 vs. logno 3 as by Smith et al. [2009], for each data set, respectively. Fits of the equation of Moisan et al. [2002] to the data of Kanda et al. [1985] did not converge, and for Harrison et al. [1996] in OU case the value of T scale is less than its SE. Therefore, their relatively more complex equation is not a compelling alternative for quantitative large scale modeling Caveat [14] The data analyzed here were for chl specific V max, whereas the predictions of OU kinetics are strictly valid on a cell specific basis and should ideally be compared to cellspecific, or at least biomass specific, observations. Chl:C ratio varies by a factor of from 5 to 10 depending on light and nutrient environment [Flynn, 2003], and chl:n by at least a factor of two to three [Geider et al., 1998]. Chl:N ratios tend to be higher in nutrient rich areas, which tend to have deeper mixed layers and therefore darker conditions, compared to nutrient poor areas with shallow mixed layers. Therefore, relative to the data analyzed herein, N specific rates would tend to be faster at high [NO 3 ] (low T) and slower at low [NO 3 ] (high T), which would yield lower estimates of Q 10 based on either uptake kinetics. [15] Still, given the lack of field observations of biomassspecific V max, the data sets analyzed herein are the best that I know. Furthermore, OU kinetics will consistently result in greater values of Q 10 than MM kinetics, even for biomassspecific V max, because the nutrient dependence in OU kinetics counteracts the T dependence. This is an inescapable result of the negative correlation between T and S a in the near surface ocean. Although the data and quality of fits in this study alone are insufficient to determine which model is superior, these results together with those of Smith et al. [2009] do show that OU kinetics provides a consistent interpretation for the observed patterns of both V max and K NO3. 5. Conclusions [16] Significant uncertainty remains about the T dependence of nutrient uptake rates, and therefore also in our understanding of large scale marine biogeochemistry, most acutely for our ability to quantitatively model nutrient cycles. Although three recent studies [Smith and Yamanaka, 2007; Smith et al., 2009, 2010] have shown OU kinetics to be a Figure 3. Same as Figure 2, but with fits using the equation of Moisan et al. [2002] for T dependence, with the assumption of symmetry about the effective optimal temperature for the assemblage, T opt, implying a single value of T scale. 4of5

5 superior alternative to MM kinetics, the predictions of the former specifically for V max have yet to be tested against controlled experiments. This means that in addition to the quantitative uncertainty about Q 10, there is also structural uncertainty about the correct form of the equations for describing uptake rates. This study has shown that structure to be important for untangling combined effects in field observations. If we are to understand the direct effects and associated feedbacks, given that both climate change and anthropogenic nutrient inputs [Duce et al., 2008] are altering the relationship between nutrients and T in the ocean, these uncertainties need to be reduced. This will require controlled laboratory experiments examining the combined effects of T and pre conditioning to S a, field observations of biomassspecific uptake rates, and data assimilation studies. [17] Acknowledgments. I thank G. W. Harrison for providing the data set, J. D. Annan, J. C. Hargreaves, J. Kanda, M. Kishi, A. Oschlies, M. Pahlow, Y Yamanaka and N. Yoshie for helpful discussions, and the anonymous reviewers. References Bissinger, J. E., D. J. S. Montagnes, J. Sharples, and D. Atkinson (2008), Predicting marine phytoplankton maximum growth rates from temperature: Improving on the eppley curve using quantile regression, Limnol. Oceanogr., 53, Collos, Y., A. Vaquer, and P. Souchu (2005), Acclimation of nitrate uptake by phytoplankton to high substrate levels, J. Phycol., 41, Dauta, A. (1982), Conditions for phytoplankton development, comparative study of the behaviour of eight species in culture. II. Role of nutrients: Assimilation and intracellular storage, Ann. Limnol., 18, Duce, R. A., et al. (2008), Impacts of atmospheric anthropogenic nitrogen on the open ocean, Science, 320, , doi: /science Dugdale, R. C. (1967), Nutrient limitation in the sea: Dynamics, identification, and significance, Limnol. Oceanogr., 12, Eppley, R. W. (1972), Temperature and phytoplankton growth in the sea, Fish. Bull., 70, Flynn, K. J. (2003), Modeling multi nutrient interactions in phytoplankton: Balancing simplicity and realism, Prog. Oceanogr., 56, Geider, R. J., H. L. MacIntyre, and T. M. Kana (1998), A dynamic regulatory model of phytoplankton acclimation to light, nutrients, and temperature, Limnol. Oceanogr., 43, Goldman, J. C., and E. J. Carpenter (1974), A kinetic approach to the effect of temperature on algal growth, Limnol. Oceanogr., 19, Harrison, W. G., L. R. Harris, and D. B. Irwin (1996), The kinetics of nitrogen utilization in the oceanic mixed layer: Nitrate and ammonium interactions at nanomolar concentrations, Limnol. Oceanogr., 41, Kanda, J., T. Saino, and A. Hattori (1985), Nitrogen uptake by natural populations of phytoplankton and primary production in the Pacific Ocean: Regional variability of uptake capacity, Limnol. Oceanogr., 30, Lomas, M. W., and P. M. Gilbert (1999), Temperature regulation of nitrate uptake: A novel hypothesis about nitrate uptake and reduction in coolwater diatoms, Limnol. Oceanogr., 44, Moisan, J. R., T. A. Moisan, and M. R. Abbott (2002), Modelling the effect of temperature on the maximum growth rates of phytoplankton populations, Ecol. Modell., 153, Silio Calzada, A., A. Bricaud, and B. Gentili (2008), Estimates of sea surface nitrate concentrations from sea surface temperature and chlorophyll concentration in upwelling areas: A case study for the benguela system, Remote Sens. Environ., 112, Smith, S. L., and Y. Yamanaka (2007), Optimization based model of multinutrient uptake kinetics, Limnol. Oceanogr., 52, Smith, S. L., Y. Yamanaka, M. Pahlow, and A. Oschlies (2009), Optimal uptake kinetics: Physiological acclimation explains the pattern of nitrate uptake by phytoplankton in the ocean, Mar. Ecol. Prog. Ser., 384, Smith, S. L., N. Yoshie, and Y. Yamanaka (2010), Physiological acclimation by phytoplankton explains observed changes in Si and N uptake rates during the SERIES iron enrichment experiment, Deep Sea Res., Part I, 57, , doi: /j.dsr Tilman, D., M. Mattson, and S. Langer (1981), Competition and nutrient kinetics along a temperature gradient: An experimental text of a mechanistic approach to niche theory, Limnol. Oceanogr., 26, S. L. Smith, Environmental Biogeochemical Cycles Research Program, RIGC, JAMSTEC, Showa machi, Kanazawa ku, Yokohama shi, Kanagawa ken , Japan. (lanimal@jamstec.go.jp) 5of5

Consistently modeling the combined effects of temperature and concentration on nitrate uptake in the ocean

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi:10.1029/2011jg001681, 2011 Consistently modeling the combined effects of temperature and concentration on nitrate uptake in the ocean S. Lan Smith 1 Received