A dynamic model of oceanic sulfur (DMOS) applied to the Sargasso Sea: Simulating the dimethylsulfide (DMS) summer paradox

A dynamic model of oceanic sulfur (DMOS) applied to the Sargasso Sea: Simulating the dimethylsulfide (DMS) summer paradox S. M. Vallina, 1,2 R. Simo´, 1 T. R. Anderson, 3 A. Gabric, 4 R. Cropp, 4 and J. M. Pacheco 5 Received 24 January 2007; revised 24 June 2007; accepted 31 October 2007; published 6 February 2008. [1]A new one-dimensional model of DMSP/DMS dynamics (DMOS) is developed and applied to the Sargasso Sea in order to explain what drives the observed dimethylsulfide (DMS) summer paradox: a summer DMS concentration maximum concurrent with a minimum in the biomass of phytoplankton, the producers of the DMS precursor dimethylsulfoniopropionate (DMSP). Several mechanisms have been postulated to explain this mismatch: a succession in phytoplankton species composition towards higher relative abundances of DMSP producers in summer; inhibition of bacterial DMS consumption by ultraviolet radiation (UVR); and direct DMS production by phytoplankton due to UVR-induced oxidative stress. None of these hypothetical mechanisms, except for the first one, has been tested with a dynamic model. We have coupled a new sulfur cycle model that incorporates the latest knowledge on DMSP/DMS dynamics to a preexisting nitrogen/carbon-based ecological model that explicitly simulates the microbial-loop. This allows the role of bacteria in DMS production and consumption to be represented and quantified. The main improvements of DMOS with respect to previous DMSP/DMS models are the explicit inclusion of: solar-radiation inhibition of bacterial sulfur uptakes; DMS exudation by phytoplankton caused by solar-radiation-induced stress; and uptake of dissolved DMSP by phytoplankton. We have conducted a series of modeling experiments where some of the DMOS sulfur paths are turned ‘‘off’’ or ‘‘on,’’ and the results on chlorophyll-a, bacteria, DMS, and DMSP (particulate and dissolved) concentrations have been compared with climatological data of these same variables. The simulated rate of sulfur cycling processes are also compared with the scarce data available from previous works. All processes seem to play a role in driving DMS seasonality. Among them, however, solar-radiation-induced DMS exudation by phytoplankton stands out as the process without which the model is unable to produce realistic DMS simulations and reproduce the DMS summer paradox. Citation: Vallina, S. M., R. Simo´, T. R. Anderson, A. Gabric, R. Cropp, and J. M. Pacheco (2008), A dynamic model of oceanic sulfur (DMOS) applied to the Sargasso Sea: Simulating the dimethylsulfide (DMS) summer paradox, J. Geophys. Res.,113, G01009, doi:10.1029/2007JG000415. 1. Introduction [2] The oceanic sulfur cycle, believed to be an important part of the Earth biogeochemical system because of its potential for climate regulation has received considerable attention in the last two decades. However, owing to the complexity of the cycle, in which the whole microbial food web is involved [Simo´, 2001], some important features regarding its seasonal dynamics remain largely unexplained. Phytoplankton are the primary producers of dimethylsulfoniopropionate (DMSP), the biochemical precursor of dimethylsulfide (DMS), a volatile compound that is ubiquitous in the global surface ocean. Emission of oceanic DMS to the atmosphere [Bates et al., 1992; Kettle and Andreae, 2000] is thought to contribute to non-sea-salt sulfate (nss-SO4) production and cloud condensation nuclei (CCN) formation [Charlson et al., 1987; Andreae and Crutzen, 1997; Vallina et al., 2007]. The amount of atmospheric CCN is linked to cloud albedo and therefore to the Earth radiative budget [Twomey, 1974; Albrecht, 1989; Kaufman et al., 2002]. In this regard, a negative feedback between oceanic DMS JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, G01009, doi:10.1029/2007JG000415, 2008 Click Here for Full A rticl e 1 Institut de Cie`ncies del Mar de Barcelona, Consejo Superior de Investigaciones Cientı´ficas (ICM - CSIC), Barcelona, Spain. 2 Now at School of Environmental Sciences, University of East Anglia (ENV - UEA), Norwich, UK. 3 National Oceanography Center (NOC), Southampton, UK. 4 Faculty of Environmental Sciences, Griffith University, Nathan, Queensland, Australia. 5 Departamento de Matema´ticas, Facultad de Ciencias del Mar, Universidad de Las Palmas de Gran Canaria (FCM - ULPGC), Islas Canarias, Spain. Copyright 2008 by the American Geophysical Union. 0148-0227/08/2007JG000415$09.00 G01009 1of23 production and Earth albedo has been postulated [Charlson et al., 1987]. [3] Intracellular DMSP (also called particulate DMSP or DMSPp) is released to the water as dissolved DMSP (DMSPd) during phytoplankton cell lysis by natural (nongrazing) mortality, zooplankton grazing and virus attacks [Groene, 1995; Yoch, 2002; Steinke et al., 2002a]. However, the amount of DMSPp varies among phytoplankton groups [Keller et al., 1989; Keller and Korjeff-Bellows, 1996] as well as with the physiological state of the cells within each group [Keller and Korjeff-Bellows, 1996; Stefels, 2000; Sunda et al., 2002; Bucciarelli and Sunda, 2003; Slezak and Herndl, 2003]. DMSP may also be exuded by phytoplankton living cells as an overflow of energy [Groene, 1995; Stefels, 2000]. The conversion of DMSP to DMS is mediated by DMSP-lyase, an enzyme that has been found in DMSP-producing phytoplankton groups as well as in numerous groups of DMSP-consuming bacteria [Groene, 1995; Yoch, 2002; Zubkov et al., 2002; Niki et al., 2000; Wolfe et al., 2002; Steinke et al., 2002b]. Until recently it was believed that the majority of DMS production was due to zooplankton grazing on phytoplankton and bacterial activity on DMSPd [Levasseur et al., 1996; Dacey et al., 1998; Gonza´lez et al., 1999]. However, recent studies suggest that the role of phytoplankton DMS production has been overlooked [Simo´ and Pedro´s-Alio´, 1999; Niki et al., 2000; Wolfe et al., 2002; Sunda et al., 2002; Toole and Siegel, 2004; Toole et al., 2006]. Under conditions of high UV radiation stress or severe nutrient limitation it seems that phytoplankton may be responsible of an important fraction of the total DMS production [Stefels and van Leeuwe, 1998; Wolfe et al., 2002; Sunda et al., 2002]. Most groups of oceanic bacteria are able to undertake DMSPd consumption (from which only a small fraction is cleaved to DMS plus acrylate, the rest being demethylated to other forms of sulfur [Groene, 1995; Yoch, 2002; Kiene and Linn, 2000]). DMS is consumed as a carbon source mostly by some methylotrophic bacteria [Kiene and Bates, 1990; Kiene, 1992, 1993; Bates et al., 1994; Wolfe et al., 1999; Simo´etal., 2000; Yoch, 2002; Zubkov et al., 2004; Vila-Costa et al., 2006a] or converted to dimethylsulfoxide (DMSO) with energy gain by unknown bacteria [Vila-Costa et al., 2006a; del Valle et al., 2007]. The other major sinks of DMS are photolysis by UV (a process mediated by photosynthesizer substances) [Brimblecombe and Shooter, 1986; Brugger et al., 1998; Toole et al., 2003; Kieber et al., 1996] and emission to the atmosphere [Kettle and Andreae, 2000]. Also, it has been recently discovered that non DMSP-producing phytoplankton are also able to take up DMSPd, potentially reducing the amount of DMSPd available for bacteria degradation and its conversion to DMS [Vila-Costa et al., 2006b]. [4] Both DMSP and DMS are an integral part of the dissolved organic matter (DOM) pool. The oceanic cycles of DOM and organic sulfur are therefore thought to be tightly coupled [Ve´zina, 2004]. DMSPd appears to be the main source of sulfur (S) for bacteria [Kiene et al., 1999; Kiene and Linn, 2000; Yoch, 2002; Zubkov et al., 2001, 2002], although it is also a source of carbon (C) [Yoch et al., 1997; Zubkov et al., 2001; Yoch, 2002]. On the other hand, DMS is mainly a source of carbon and energy, sulfate and DMSO being the primary fate of sulfur from bacterial consumption of DMS [Vila-Costa et al., 2006a; del Valle et al., 2007]. DMS dynamics are therefore regulated by a complex interplay of biotic and abiotic processes where phytoplankton, zooplankton and bacteria are believed to have a prominent role. [5] With the aim at gaining a better understanding on the processes governing the oceanic sulfur cycle, several dynamic (i.e. mechanistic) models of DMSP/DMS have been developed in the last decade or so [Gabric et al., 1993; Lawrence, 1993; van den Berg et al., 1996; Laroche et al., 1999; Jodwalis et al., 2000; Archer et al., 2002; Lefevre et al., 2002; Chu et al., 2004]. These models usually consist of two submodels: a nitrogen based one (N-cycle) characterizing the ecosystem, and a sulfur based one (S-cycle) of the DMSP/DMS dynamics [Ve´zina, 2004]. These two submodels are coupled but without feedbacks between them: the N-cycle affects the S-cycle, but not viceversa [Ve´zina, 2004]. Most of these models do not, however, include a characterization of the microbial loop, that is, an explicit representation of bacteria, bacterivory, and the DOM cycle. This is due to the fact that the first ecosystem models did not give sufficient relevance to the microbial loop. [6] However, in recent years, bacteria and DOM dynamics have gained relative importance in ecosystem models and it has been shown that their inclusion is fundamental in order to obtain realistic simulations of the seasonal cycles of the model state variables [Spitz et al., 2001]. In the Sargasso Sea, for example, most of the carbon cycling is through the microbial loop [Steinberg et al., 2001, and references therein]. The DMSP/DMS model of Archer et al. [2002] (which is based on the ERSEM ecosystem model [Baretta et al., 1995]) is the only ecosystem model to additionally incorporate bacteria and DOM dynamics. Although the model of Gabric et al. [1993] incorporated bacteria as part of the N-cycle, bacteria were not explicitly represented in the S-cycle. Rather, bacterial effects on DMSP and DMS concentrations were parameterized as constant rates, independently of their evolution in the N-cycle. This is probably due to the fact that the N-cycle of Gabric’s model (which is based on Moloney et al. [1986]) does not include DOM dynamics, such that predicted bacteria display ‘‘catastrophic behavior’’, being close to zero for much of the time [Cropp, 2002; Cropp et al., 2004]. Variations in bacterial sulfur demand have been suggested to affect DMS production, so that if DMSPd is in excess of bacterial requirements for sulfur, a larger proportion of the DMSPd taken up could be converted to DMS [Kiene et al., 1999]. Therefore, Cropp [2002] recommends that a priority for the next generation of DMSP/DMS models is the inclusion of a realistic microbial loop. Similar conclusions were reported by other authors [Lefevre et al., 2002; Le Clainche et al., 2004; Ve´zina, 2004]. [7] Another significant problem with most of the current DMSP/DMS models is the difficulty of decoupling DMS dynamics from that of phytoplankton. It has been observed that DMS peaks in summer at tropical, subtropical and low temperate latitudes, a time when chlorophyll-a (CHL, a common proxy for phytoplankton biomass) is at its annual minimum [Simo´ and Pedro´s-Alio´, 1999; Uher et al., 2000; Toole and Siegel, 2004; Vallina et al., 2006; Vila-Costa et al., 2008]. This finding has been dubbed the ‘‘DMS summer paradox’’ [Simo´ and Pedro´s-Alio´, 1999]. Several mechanisms have been proposed to explain it, such as a succession G01009 VALLINA ET AL.: A DYNAMIC MODEL OF OCEANIC SULFUR 2of23 G01009 in phytoplankton species composition towards high DMSPp producers, inhibition of bacterial DMS consumption by high UV, and a higher (direct) production of DMS from phytoplankton cells due to UV stress [Simo´ and Pedro´sAlio´, 1999; Sunda et al., 2002; Toole and Siegel, 2004]. Most of these potential explanations have not as yet been tested in models. The model of Lefevre et al. [2002] and the parameterization used by Gabric et al. [2005] are the sole examples of including a variable sulfur to nitrogen (S:N) phytoplankton internal quota as a function of light in order to account for a shift in species composition and/or a change in phytoplankton physiological state. This allowed a higher degree of decoupling between DMS and CHL in these models. It was, however, shown by Le Clainche et al. [2004] for the Sargasso Sea (using the same model as Lefevre et al. [2002] but coupled to a dynamic turbulent scheme) that the seasonality of modeled DMS was lower than that of DMS observations and the summer maximum was underestimated. [8] In this work we present a Dynamic Model of Oceanic Sulfur (DMOS) which is based on a modified version of the ecosystem model (N/C-cycles) developed by Anderson and Pondaven [2003] (hereafter AP’03). It has an explicit representation of bacteria and DOM dynamics, and is adapted for the Sargasso Sea using data collected during the Bermuda Atlantic Time-series Study (BATS) [Steinberg et al., 2001]. We have coupled a new S-cycle to it that incorporates the latest knowledge of DMSP/DMS dynamics. Model complexity was progressively increased in order to test several of the hypotheses generally used to explain the DMS summer paradox. The performance of the model in simulating annual cycles of concentrations, fluxes and turnover rates of the sulfur variables is analyzed. 2. Data and Methodology 2.1. Sargasso Sea Data [9] The Sargasso Sea is located in the subtropical West North Atlantic and represents an oligotrophic open ocean region where the DMS summer paradox is readily observable [Dacey et al., 1998; Toole and Siegel, 2004]. Phytoplankton seasonality is regulated by physical processes which drive the deep nutrient entrainment in the upper layers during winter and spring, followed by nutrient depletion in summer due to a strong stratification of the water column [Goericke, 1998; DuRand et al., 2001; Steinberg et al., 2001]. The dominant phytoplankton groups are prokariotic picophytoplankton (Prochlorococcus and Synechococcus) and eukariotic phytoplankton (Prymnesiophytes, Pelagophytes) [Goericke, 1998; DuRand et al., 2001; Steinberg et al.,2001].Diatomsarenota dominant group, although rare episodic blooms have been observed [Steinberg et al., 2001]. Dinoflagellates are also represented as a low percentage of the phytoplankton community [Goericke, 1998; Steinberg et al., 2001]. The mixed layer depth (MLD) has a marked seasonal cycle with values from 200 m to less than 10 m in summer [Steinberg et al., 2001; Spitz et al., 2001] and the sea surface temperature (SST) varies from 20°in winter to 28°in summer [Steinberg et al., 2001]. [10] During the Bermuda Atlantic Time-series Study, station BATS (31.75°N, 64.17°W) was sampled for vertically resolved profiles of CHL and bacteria (along with many other physical and biological variables) approximately monthly from 1989. Data are available at the BATS database (http://bats.bbsr.edu/). Hydrostation-S (32.17°N, 64.50°W) has been sampled for vertically resolved profiles of DMSPp, DMSPd and DMS approximately biweekly from 1992 to 1994 [Dacey et al., 1998; Toole and Siegel, 2004]. Using these depth resolved time series we have constructed two-dimensional (2-D; time and depth) climatologies of CHL and bacteria (more than 10 years of data, from 1989 to 2000) as well as DMSPp, DMSPd and DMS (three years of data, from 1992 to 1994). The methodology used for building the climatology was as follows. All measured profiles were merged by month. Then, for each month, a 6th degree polynomial regression was used to fit the cloud of data, obtaining a single depth-resolved profile per month. Finally the resulting monthly profiles were interpolated in time, generating 2-D (time, depth) plots with a resolution of 1 day 1 m. To be consistent, model results were also interpolated in depth and averaged in time to obtain the same 1 day 1 m resolution (see section 3. Results and Discussion). DMSPd did not display a clear seasonal pattern over the sampling period [Dacey et al., 1998] and therefore the obtained climatology has to be viewed with some caution. On the other hand, DMSPp and DMS showed a much clearer seasonal cycle. 2.2. Model Description [11] The AP’03 ecosystem model includes a detailed characterization of the microbial loop. It incorporates a complex description of the DOM cycle and explicitly includes heterotrophic bacteria as a state variable. The treatment of DOM includes dual currencies, nitrogen (DON) and carbon (DOC). Since DMSP and DMS are part of the DOM, and therefore they share many of their processes (such as bacterial uptake and degradation), a DMSP/DMS model including a detailed microbial loop is fundamental [Ve´zina, 2004]. We thus coupled our S-cycle model to the AP’03 N/C-cycles, calling this coupled ecosystem-DMSP/DMS model ‘‘DMOS’’ (Dynamic Model of Oceanic Sulfur). The new S-cycle model contains important improvements like the explicit representation of bacterial activity in the sulfur cycle (including for the first time UV inhibition of bacterial sulfur uptake), a time-varying DMS exudation term from phytoplankton (due to UV stress) as well as an uptake of DMSPd for phytoplankton. In a manner similar to Archer et al., 2002, we include nonlinear kinetics for sulfur uptake (other models use linear relationships [Ve´zina, 2004]). [12] One of the advantages of including bacteria explicitly in DMSP/DMS models is that it is then possible to evaluate the relative contributions of phytoplankton and bacteria to the DMS production, this being one of the important unanswered questions concerning the biogeochemistry of DMS [Yoch, 2002]. Further, the DMS-yield of the whole food web (total DMS production/total DMSP consumption), which is a very sensitive parameter in DMSP/DMS models [Lefevre et al., 2002; Ve´zina, 2004; Le Clainche et al., 2004; Cropp et al., 2004] is not prescribed as an a-priori parameter: it is now an output of the model (see section 3. Results and Discussion). The full set of DMOS equations is described in Appendix A. Model G01009 VALLINA ET AL.: A DYNAMIC MODEL OF OCEANIC SULFUR 3of23 G01009 Table 1. List of DMOS Parameters Parameter Symbol Value Unit Source Phyto. max. specific growth rate m P max 3.7 [d 1 ]Spitz et al. [2001] Phyto. saturating irradiance I s 60 [W m 2 ]Cropp et al. [2004] Phyto. half-sat. for NO 3 = uptake k P N 0.15 [mmolN m 3 ]Anderson and Pondaven [2003] Phyto. half-sat. for NH 4 + uptake k P A 0.05 [mmolN m 3 ]Anderson and Pondaven [2003] Phyto. NH 4 + inhibition parameter y1.5 [mmolN 1 ]Anderson and Pondaven [2003] Phyto. leakage fraction g 1 0.05 [adim]Anderson and Pondaven [2003] Phyto. DOC exudation parameter g 2 0.34 [adim]Anderson and Pondaven [2003] Phyto. specific mortality rate m P 0.045 [d 1 ]Anderson and Pondaven [2003] Phyto. mortality losses to DOM e0.34 [adim]Anderson and Pondaven [2003] Phyto. sinking rate j~ wpj0.05 [md 1 ] This study Phyto. C:N ratio q Pc:n 6.625 [mmolC mmolN 1 ]Anderson and Pondaven [2003] Phyto. CaCO 3 :C ratio q Ca 0.10 [mmolC mmolC 1 ]Anderson and Pondaven [2003] Phyto. max. CHL:C ratio q chl m 0.041 [mgCHL mgC1] Spitz et al. [2001] Phyto. initial slope of P-I curve a chl 1.0 [mgC mgCHL 1 (W m 2 ) 1 d 1 ] Spitz et al. [2001] Phyto. molecular weight of Carbon C mw 12 [mgC mmolC 1 ]Spitz et al. [2001] Phyto. min. S:N internal quota q Ps:n min 0.044 [mmolS mmolN 1 ]Lefevre et al. [2002] Phyto. max. S:N internal quota q Ps:n max 0.220 [mmolS mmolN 1 ]Lefevre et al. [2002] Phyto. max. DMS specific exudation rate g s max 0.25 [d 1 ] This study Phyto. fraction of DMSPd consumers a P 0.1 [adim] This study Phyto. free DMSP-lyase activity f0.01 [d 1 ] This study Zoo. max. specific ingestion rate g3.2 [d 1 ] This study Zoo. N assim. efficiency b n 0.75 [adim]Anderson and Pondaven [2003] Zoo. C assim. efficiency b c 0.65 [adim]Anderson and Pondaven [2003] Zoo. C net growth efficiency w Z 0.8 [adim]Anderson and Pondaven [2003] Zoo. half-sat. const. for N ingestion k g 0.75 [mmolN m 3 ]Anderson and Pondaven [2003] Zoo. grazing preference upon Phyto. p P 1/3 [adim]Anderson and Pondaven [2003] Zoo. grazing preference upon Bact. p B 1/3 [adim]Anderson and Pondaven [2003] Zoo. grazing preference upon Det. p D 1/3 [adim]Anderson and Pondaven [2003] Zoo. C:N ratio q Zc:n 5.5 [mmolC mmolN 1 ]Anderson and Pondaven [2003] Zoo. messy feeding losses to DOM f0.23 [adim]Anderson and Pondaven [2003] Zoo. max. specific mortality rate m Z 0.3 [d 1 ]Anderson and Pondaven [2003] Zoo. half-sat. const. for mortality k Z 0.2 [mmolN m 3 ]Anderson and Pondaven [2003] Zoo. mortality fraction going to DOM W dom 0.38 [adim]Anderson and Pondaven [2003] Zoo. mortality fraction going to NH 4 + W A 0.33 [adim]Anderson and Pondaven [2003] Zoo. mortality fraction going to Detritus-N W Dn 0.29 [adim]Anderson and Pondaven [2003] Zoo. mortality fraction going to Detritus-C W Dc 0.46 [adim]Anderson and Pondaven [2003] Zoo. mortality fraction going DIC W DIC 0.16 [adim]Anderson and Pondaven [2003] Zoo. DMSPp ingestion: fraction converted to DMSPd a 1 0.7 [adim]Simo´[2004] Bact. max. Lc/NH 4 + and sulfur uptake m B max 13.3 [d 1 ]Anderson and Pondaven [2003] Bact. max. Sc hydrolysis m Sc 4[d 1 ]Anderson and Pondaven [2003] Bact. half-sat. const. for NH 4 + uptake k A 0.5 [mmolN m 3 ]Anderson and Pondaven [2003] Bact. half-sat. const. for Lc uptake k Lc 25 [mmolC m 3 ]Anderson and Pondaven [2003] Bact. half-sat. const. for Sc hydrolysis k Sc 417 [mmolC m 3 ]Anderson and Pondaven [2003] Bact. max. inhibition by UV of nutrient uptake f inhib max 0.75 [adim] This study Bact. specific nitrification rate v0.03 [d 1 ]Anderson and Pondaven [2003] Bact. C gross growth efficiency w B 0.17 [adim]Anderson and Pondaven [2003] Bact. specific mortality rate m B 0.04 [d 1 ]Anderson and Pondaven [2003] Bact. C:N ratio q Bc:n 5.1 [mmolC mmolN 1 ]Anderson and Pondaven [2003] Bact. S:C ratio q Bs:c 1/250 [mmolS mmolC 1 ]del Valle et al. [2007] Bact. fraction of DMS consumers a B 0.20 [adim] This study Bact. half-sat. const. for DMSPd uptake k DMSPd 0.01 [mmolS m 3 ] This study Bact. half-sat. const. for DMS uptake k DMS 0.01 [mmolS m 3 ] This study Bact. DMSPd excess uptake: fraction converted to DMS a 2 0.1 [adim]Kiene and Linn [2000] Labile fraction of DOM produced d 1 0.7 [adim]Anderson and Pondaven [2003] Labile fraction of Phyto. extra-DOC exudation d 2 0.4 [adim]Anderson and Pondaven [2003] Detrital-N breakdown rate m Dn 0.055 [d 1 ]Anderson and Pondaven [2003] Detrital-C breakdown rate m Dc 0.04 [d 1 ]Anderson and Pondaven [2003] Detrital-CaCO 3 dissolution rate m Dh 0.05 [d 1 ]Anderson and Pondaven [2003] Detrital sinking rate j~ wDij0.05 [m d 1 ] This study Irradiance max. I max 150 [W m 2 ] This study Irradiance min. I min 45 [W m 2 ] This study Irradiance threshold I*25[Wm 2 ]Lefevre et al. [2002] Irradiance attenuation due to water k w 0.04 [m 1 ]Popova et al. [2002] Irradiance attenuation due to Phyto. self-sheding k p 0.03 [m 2 mmolN 1 ]Popova et al. [2002] Max. specific DMS photolysis rate k photo max 0.15 [d 1 ]Bailey et al. [2008] Max. turbulent diffusion kz max 250 [m 2 d 1 ]Cropp et al. [2004] Min. turbulent diffusion kz min 1[m 2 d 1 ]Cropp et al. [2004] Max. sea temperature (changes each day) st max SST [°C] This study Min. sea temperature st min 19 [°C] This study Steepness of the pycnocline r 20 [adim]Cropp et al. [2004] G01009 VALLINA ET AL.: A DYNAMIC MODEL OF OCEANIC SULFUR 4of23 G01009 parameters are listed in Table 1. An schematic diagram of DMOS model is shown in Figure 1. 2.3. N/C-Cycles [13] The model contains single state variables for phytoplankton (equation (A1)), zooplankton (equation (A2)) and heterotrophic bacteria (equation (A3)), two nutrient pools (nitrate (equation (A4)) and ammonium (equation (A5))), labile and semilabile DON and DOC (equations (A6 –A9)), detritus (equations (A10–A12)), dissolved inorganic carbon (DIC, equation (A13)) and alkalinity (equation (A14)). CHL (equation (A15)) is calculated for phytoplankton N at each time step based upon Geider et al. [1997] as in Spitz et al. [2001], permitting comparison with field data. Phytoplankton primary production (equation (A19)) is controlled by light (equation (A22)) [Walsh et al., 2001] and temperature (equation (A21)) [Eppley, 1972], affecting the specific growth rate (equation (A20)), as well as by nutrient availability (equation (A25)) [Spitz et al., 2001]. Phytoplankton losses are due to zooplankton grazing (equation (A29)), natural mortality (equation (A55)) and vertical sinking (equation (A80)). Zooplankton graze upon phytoplankton, bacteria and soft detritus (equations (A29–A32)). Zooplankton production (equation (A37) or equation (A39)), ammonium excretion (equation (A38) or equation (A40)), and respiration (equation (A41)) are calculated according to a stoichiometric model [Anderson and Hessen, 1995; Anderson and Pondaven, 2003]. Zooplankton mortality is assumed to occur in the form of a quadratic MichaelisMenten equation (equation (A56)). This is a classical way of parameterizing both natural mortality and grazing by higher predators (which are not explicitly modeled). Bacteria production, excretion and respiration (equations (A47– Figure 1. Schematic diagram of DMOS model. (left) Ecosystem submodel: (N/C-cycles; mmol m 3 )A, ammonium; N, nitrates; P, phytoplankton; B, bacteria; Z, zooplankton; DOM, dissolved organic matter (can be either nitrogen based or carbon based, and labile or semilabile); D, detritus (can be either nitrogen based or carbon based). Note that the modeled cycling of dissolved organic matter and detritus has been purposely simplified in this diagram as a generic DOM and D pools for clarity; a more detailed scheme of the ecosystem submodel can be found in the work of Anderson and Pondaven [2003]. (right) DMSP/ DMS submodel (S-cycle; mmol m 3 ): DMSPp, particulated dimethylsulfoniopropionate; DMSPd, dissolved dimethylsulfoniopropionate; DMS, dimethylsulfide. The red lines coming from the Sun refer to the S-cycle processes directly affected by solar radiation in DMOS model that has been tested by the five modeling experiments performed. G01009 VALLINA ET AL.: A DYNAMIC MODEL OF OCEANIC SULFUR 5of23 G01009 A52)) are calculated from elemental stoichiometry [Anderson, 1992; Anderson and Williams, 1998; Anderson and Pondaven, 2003]. Labile DOC and DON are the primary growth substrates, with ammonium supplementing DON when the ratio DOC/DON (C:N ratio of DOM) is high. Uptake of labile DOC and DON and the maximum potential uptake of ammonium are described in equations (A43)– (A45). Bacteria either take up or regenerate ammonium at any one time depending on the availability of DOC and DON (equation (A47)), an upper limit of ammonium uptake being given by equation (A44). The fraction of DOC taken up not used for balanced (C:N) growth is respired (equation (A49) or equation (A52)). Bacteria loss terms are zooplankton grazing (equation (A30)) and natural mortality (equation (A57)). [14] The main sink for nutrients is phytoplankton uptake (equation (A19)), ammonium also being lost to the nitrate pool via nitrification at constant rate (see second term on equation (A5)). The DOM pools are produced by phytoplankton leakage, excretion and exudation, zooplankton messy feeding, phytoplankton and bacterial natural mortality, and noncarbonate detrital breakdown (equations (A58–A59)). The semilabile DOM pool is converted to labile DOM due to the action of exoenzymes by bacterial (equations (A53– A54)). Phytoplankton exudation of DOC is directly proportional to primary production (see equation (A28)). Noncarbonate (or soft) detritus (equations (A10–A11)) arises from zooplankton egestion as well as phytoplankton and zooplankton mortality, and is lost by zooplankton grazing (equations (A31–A32)), breakdown, and vertical sinking (equation (A80)). The carbonate (or hard) detritus (equation (A12)) originates from the contribution of carbonate-forming (e.g. organisms such as coccolithophores to primary production). This is parameterized assuming a constant CaCO 3 :C ratio for phytoplankton (see Table 1). The carbonate fraction of total detritus is variable (for soft tissue and carbonate production, and also as additional carbon fixed as DOC), and returned by zooplankton and bacteria respiration as well as zooplankton mortality. Other return pathways, such as breakdown of carbonate detritus (equation (A60)), occur via cycling of DOC. Exchange of CO 2 with the atmosphere can also be estimated (F atm term in equation (A13)) although it is not necessary for our purposes. Parameterization of alkalinity (equation (A14)) is performed according to the stoichiometry described by Broecker and Peng [1982]. 2.4. S-Cycle [15] DMSPp (equation (A16)) production by phytoplankton is modeled by using a sulfur/nitrogen (S:N) internal quota (q Ps:n parameter, see Table 1). q Ps:n is allowed to vary as function of light intensity following Lefevre et al. [2002] (equations (A63–A64)). Since the model has only one generic phytoplankton group, this method permits an implicit simulation of a shift in species composition towards high DMSPp producers in summer and/or a shift in phytoplankton physiological state [Lefevre et al., 2002], one of the proposed explanations of the DMS summer paradox. DMSPp is released to the water as DMSPd (equation (A17)) due to phytoplankton leakage and natural mortality as well by zooplankton grazing. It is assumed that 70% of the grazed DMSPp is recovered in the dissolved phase [Levasseur et al., 2004; Simo´, 2004]. The DMSPd losses are bacterial (equation (A68)) and phytoplankton uptake (equation (A67)) as well as cleavage to DMS by free DMSP-lyases (as in Archer et al. [2002]). Bacterial uptake of DMSPd is a well known sink for DMSPd since this compound is a major source of reduced sulfur for apparently most of marine bacteria [Kiene and Linn, 2000; Yoch, 2002; Zubkov et al., 2002; Vila et al., 2004; Vila-Costa et al., 2007]. A close seasonal correlation between DMSP assimilation by bacteria and bacterial heterotrophic production (measured as leucine incorporation) has been observed recently in a Mediterranean coastal site [Vila-Costa, 2006]. We therefore assumed that DMSPd consumption is proportional to the total bacterial community in the model. On the other hand, various phytoplankton take up DMSPd such as diatoms, Synechococcus and Prochlorococcus, these all being low or non DMSP producers [Vila-Costa et al., 2006b; Malmstrom et al., 2004]. With current uncertainties regarding what fraction of total phytoplankton biomass is able to take up DMSPd and at what rates, we considered that this process is carried out by 10% of the phytoplankton (see parameter a P in Table 1). [16] In the model, DMS (equation (A18)) production has 3 sources: cleavage from DMSPd by bacteria (equations (A71– A72)) and free DMSP-lyases (3rd term in equation (A18)) as well as direct exudation by phytoplankton (equation (A65)). The total amount of sulfur required by bacteria for balanced (C:S) growth (also called bacterial sulfur demand) is given by equation (A70). If the DMSPd taken up is in excess of bacterial sulfur demand (no S-limitation), a fraction (a 2 , see Table 1) of this sulfur excess is cleaved to DMS (equation (A71)), the remainder being converted to other forms of sulfur (e.g. sulfates via the methanethiol pathway) [Kiene, 1996; Kiene and Linn, 2000; Kiene et al., 2000]. It has been observed experimentally that bacterial production of methanethiol dominates over DMS production [Kiene, 1996; Kiene and Linn, 2000; Zubkov et al., 2002]. Bacterial DMS-yield rarely goes beyond 10%. Recent works found a range between 2 and 12% (Slezak, personal communication). Similar values were reported by Kiene and Linn [2000] and [Zubkov et al., [2002] (6–12%). Therefore a 2 is assumed to be small (10%) [Kiene and Linn, 2000; Niki et al., 2000]. On the other hand, if the DMSPd taken up by bacteria is lower than the requirement for balanced (C:S) growth (S-limitation), DMS is not produced (equation (A72)) because sulfur is fixed exclusively into proteins. [17] Phytoplankton direct exudation of DMS has been assumed to be constant and very small in some models [e.g., Gabric et al., 1993; Chu et al., 2004], with many models not even including it as a process. Recent field research have however suggested that phytoplankton is likely an important source of DMS, mainly under high UV stress [Toole and Siegel, 2004; Toole et al., 2006; Vila-Costa et al., 2008]. In support of these findings, the work of Sunda et al. [2002] showed increases up to 3500% in the amount of DMS per unit cell volume in phytoplankton cultures exposed to high doses of UV-A. They proposed that DMS acts as an efficient hydroxyl radical scavenger, i.e. as an intracellular antioxidant under conditions of high UV exposure. In the model, therefore, direct exudation of DMS was made G01009 VALLINA ET AL.: A DYNAMIC MODEL OF OCEANIC SULFUR 6of23 G01009 a function of light intensity (first fraction in equation (A66)), although the level of phytoplankton activity is also taken into account (second fraction in equation (A66)). [18] There is only one biological loss for DMS, namely its uptake by bacteria (equation (A69)). The complete phylogeny of marine DMS-consuming bacteria is not known, but a recent study has shown that the use of DMS as a C source seems mostly restricted to some methylotrophic bacteria [Vila-Costa et al., 2006a], yet DMS consumption as a source of energy by unknown bacteria (conversion to DMSO without use of the C) might be more common [del Valle et al., 2007]. Therefore DMS consumption seems to be not as widespread a process among bacterioplankton as DMSPd utilisation [Vila-Costa et al., 2006a]. Thus, we assumed that only a fraction (20%, see parameter a B in Table 1) of the generic pool of modeled bacteria acts as a sink for DMS. The other two sinks for DMS in the model are photolysis and emission to the atmosphere. Photolysis is assumed to be solely a function of light intensity (equation (A73)) although in reality it is a process mediated by chromophoric DOM (or CDOM) [Brimblecombe and Shooter, 1986; Brugger et al., 1998; Toole et al., 2003], which is not modeled in the current version of DMOS. DMS emission to the atmosphere (equation (A75)) is parameterized with the gas transfer model of Nightingale et al. [2000] (equations (A76)–(A78)) using climatological (1992-1994) surface wind speed (U,ms 1 ) from the NCEP/ NCAR Reanalysis Project (provided by the NOAA-CIRES Climate Diagnostics Center). Monthly data were interpolated in time and smoothed to generate daily values. [19] Regarding the bacterial uptake of nutrients (either labile DON/DOC or NH 4 + ) and sulfur (either DMSPd or DMS), the model includes a light inhibition parameter that influences the specific rate of bacterial uptake (equation (A45)). This parameter accounts for the well known effect of UVR upon bacterial heterotrophic activity and bacterial DMSP/DMS consumption [Herndl et al., 1993; Slezak et al., 2001; Toole et al., 2006]. We assume a maximum inhibition of bacterial uptake of 75% (see f inhib max in Table 1) [Slezak et al., 2001; Toole et al., 2006]. 2.5. Physical Frame and Forcings [20] The biogeochemical model is embedded in a onedimensional (1-D) vertical physical frame. The model therefore neglects horizontal transport processes and takes into account only vertical processes, i.e. advection (equation (A80)) and diffusion (equation (A81)), which are considered the main driving forces of ecosystem dynamics in the upper ocean [Eigenheer et al., 1996; Denman and Pen˜a, 1999]. As in the models of Lefevre et al. [2002] and Cropp et al. [2004], vertical mixing in the current version of DMOS is parameterized using a prescribed turbulent diffusion coefficient (kz, Table 1) following the approach used by Cropp et al. [2004]. Coefficient kz is generated using a sigmoid equation (equation (A82)) and climatological MLD data [Levitus, 1982]. As a result the maximum diffusion (kz max ) occurs in the upper mixed layer (UML) and the minimum diffusion (kz min ) occurs below the UML. In between, kz decreases from kz max to kz min as dictated by the parameter r(Table 1) which defines the steepness of the pycnocline [Cropp et al., 2004]. The same sigmoid function (equation (A82)) is used to generate the vertical temperature profiles, the only difference being that the maximum value for temperature is the sea surface temperature (SST) which varies seasonally, instead of being constant as for diffusion. SST data for the Sargasso Sea were obtained from a climatology (1971-2000, NOAACIRES Climate Diagnostics Center). Monthly data were interpolated in time and smoothed to generate daily values. [21] Light in the model (I z ,Wm 2 ) is defined as daily averaged photosynthetic available radiation (PAR). Daily values of PAR at the surface (I 0 ) of the Sargasso Sea were obtained after interpolating in time and smoothing a SeaWiFS climatology (from years 2002 to 2004). Light decays with depth (z, in metres) following an exponential function (equation (A23)) that depends on water and phytoplankton. In the current version of DMOS we wanted to explore if the observed DMS seasonality could be simulated through the inclusion of light-driving processes, with the assumption that UVR is the forcing behind these processes (e.g. bacterial inhibition, phytoplankton stress), yet bacterial inhibition of sulfur uptakes has been also described to occur under PAR [Slezak et al., 2001]. PAR seasonality can be used as a proxy for UVR seasonality, UVR being a constant fraction of PAR. Given that all the parameterizations used to account for UVR-driven processes are based on the term Iz Imax, the constant fraction cancels out and we are just left with a nondimensional term representing UVR that varies between 0 and 1. While UVR attenuates faster in the water column than PAR, the UVR driving processes affecting DMS production may operate at higher depths. It has been described that organisms need some time for recovering after being exposed to high UVR doses [Toole et al., 2006]. Therefore when they escape from the UV zone (i.e. by sinking and/or turbulent diffusion) they may keep a ‘‘memory’’ of the stress deeper in the water column. Nevertheless, exploring the use of an explicit wavelengthresolved UVR formulation, with the inclusion of CDOM as a state variable, is desirable and will be object of future research. [22] The model domain is from 0 to 200 m with a vertical resolution of 2.5 m. Initial conditions (in mmol m 3 )are constant profiles for all variables: 0.1 for phytoplankton, zooplankton and bacteria; 2.0 for nitrates; 0.5 for ammonium and labile DON; 24 for labile DOC; 2100 for TIC; 2375 for alkalinity; 0.16 for chlorophyll-a; 0.013 for DMSPp; 0.1 for DMSPd and DMS; and zero for the remaining variables. The boundary conditions are zero-flux in order to conserve mass (with the exception of sulfur since DMS emission in the upper top grid is allowed). A mass-conservative ecosystem model is desirable so that the biotic pools do not eventually run out of nutrients [Spitz et al., 2001; Cropp et al., 2004]. An accumulation of dying phytoplankton and detritus in the bottom boundary due to vertical sinking occurs, which implies that DOM increases and finally that NH 4 + and NO 3 = (from NH 4 + nitrification) also accumulates. This simulates the observed presence of high NO 3 = levels deep in the water column at BATS [Steinberg et al., 2001]. During winter, the MLD reaches the bottom and the strong mixing carry some of this nutrients pool to the UML, generating the vernal phytoplankton bloom (see section 3. Results and Discussion). In order to reach an equilibrium state, the model was ran for 10 years (with a time step of 0.005 days) prior to the analysis of the results. Previous tests G01009 VALLINA ET AL.: A DYNAMIC MODEL OF OCEANIC SULFUR 7of23 G01009 Figure 2. Two-dimensional (time, depth) plots of bacteria (mmolN m 3 ) from climatological in situ data (left) and DMOS model results (right). Conversion from bacterial counts (10 8 cells kg 1 ,BATS data) to mmolN m 3 was done using a conversion factor of 0.0118 (mmolN m 3 /10 8 cells kg 1 ), which was obtained assuming that bacterial cells have 7.2 fgC cell 1 [Gundersen et al., 2002] and a C:N molar ratio of 5.1 (Table 1). Note that simulated bacteria are scaled up by a factor of 2 for the sake of visual comparison against data. Figure 3. Two-dimensional (time, depth) plots of chlorophyll-a, DMSP particulate, DMSP dissolved and DMS from climatological in situ data (upper-row panels) and DMOS model results for several modeling experiments (see Table 2): experiment A (second-row panels), experiment B (third-row panels), experiment C (fourth-row panels), experiment D (fifth-row panels), experiment E (sixth-row panels). Units: chlorophyll-a (mg m 3 ), DMSPp-DMSPd-DMS (mmolS m 3 ). G01009 VALLINA ET AL.: A DYNAMIC MODEL OF OCEANIC SULFUR 8of23 G01009 without seasonal forcings showed that the model reaches a ‘‘stable node’’ equilibrium, indicating that the model does not have unwanted internal dynamics (e.g. oscillations) and that the seasonal changes are driven by the seasonal forcings. 3. Results and Discussion [23] The model successfully reproduces bacteria (Figure 2) and CHL (Figure 3) distributions, capturing the winter/ spring phytoplankton bloom in surface and the deep chlorophyll maximum (DCM) during summer months (Figure 3) as well as the development of a subsurface maximum (40–60 m depth) of bacteria from late spring to early fall (Figure 2). Modeled values of bacteria concentrations are, however, about a half those of the data. This is because the model only simulates active bacteria, while the data includes both active and nonactive bacteria [Anderson and Pondaven, 2003]. The vernal phytoplankton bloom is triggered by the entrainment of deep nutrients. In contrast, nutrients are depleted in summer leading to lowest phytoplankton biomass in surface waters. Deeper in the water column, the presence of higher concentrations of nutrients along with light in sufficient quantity for primary production results in the formation of a DCM. Bacteria distributions mainly result from the interplay of DOM release by phytoplankton and the inhibition of bacterial DOM uptake by high solar radiation doses during summer. 3.1. Model Experiments [24] In order to gain some insight into the processes that are most relevant for explaining the observed seasonality of DMS in the Sargasso Sea, and therefore what drives the DMS summer paradox, we conducted several model experiments turning ‘‘off’’ or ‘‘on’’ various DMOS sulfur paths. This exercise was undertaken in a sequence of steps, starting from the simplest characterization of the S-cycle and increasing complexity in a stepwise fashion until realistic simulations were obtained. The first scenario excluded all of the processes usually cited in the literature to explain the DMS summer paradox, namely shift in the S:N ratio of phytoplankton, inhibition of bacterial uptake by UV light, phytoplankton uptake of DMSPd, and phytoplankton exudation of DMS under UV stress. Each of these processes was then added one after the other (see Table 2). Simulations for each of the experiments (A, B, C, D, E; Table 2) are compared with observations for the Sargasso Sea observations (0–140 m) in Figure 3. 3.1.1. Experiment A [25] In this experiment there is no seasonal increase in the S:N ratio of phytoplankton (therefore q Ps:n is constant and equal to 0.13 mmolS mmolN 1 , the middle value between q Ps:n min and q Ps:n max ), UV induces neither bacterial inhibition of semilabile-DOM/NH 4 + and sulfur uptake (DMSPd and DMS) nor phytoplankton stress-driven DMS production, and phytoplankton does not to take up DMSPd. Modeled DMSPp, DMSPd and DMS closely follow the predicted CHL distribution, all displaying maximum values in winter/ spring and minima in summer/fall (Figure 3). The main differences between DMSPp and CHL are due to the variability of CHL as a response of the levels of light intensity. This constancy between sulfur species and CHL is not observed in the data. Further, DMSPp maximum values are slightly underestimated while DMS values are highly underestimated. We must conclude that this experiment is not capturing at all the main processes controlling oceanic sulfur dynamics. 3.1.2. Experiment B [26] In contrast to the previous experiment, a variable S:N internal quota in phytoplankton was now added in order to parameterize a seasonal change in species composition towards high DMSPp producers and/or a change in phytoplankton physiological state due to higher UV doses [Sunda et al., 2002; Slezak and Herndl, 2003]. Results are shown in Figure 3. The simulations for DMSPp are improved in comparison to the first experiment. However, the modeled DMSPp maximum in spring takes place earlier than observed (by about one month, similar to what was observed by [Le Clainche et al., 2004]) and DMSPd distributions correlate too closely with DMSPp, a feature not observed in the field [Dacey et al., 1998]. DMSPp simulations are also clearly overestimated during summer. Therefore, the parameterization of the S:N ratio as a function of light, although better than using a constant value, is far from being perfect. There is a need to explore other ways of modeling DMSPp concentrations, e.g., by including in the model several phytoplankton groups with specific S:N internal quotas. On the other hand, DMS values are again severely underestimated and, although a summer maximum is now predicted, it is deeper in the water column and smaller in magnitude than seen in the observations. Furthermore, predicted DMS in surface waters does not display the summer maximum seen in the observations, but rather shows a spring maximum. It therefore appears that inclusion of a variable the S:N ratio of phytoplankton in the model can not on its own account for the observed seasonality of DMS nor explain the DMS summer paradox. 3.1.3. Experiment C [27] Next, the inhibition of bacterial uptake of nutrients (semilabile-DOM/NH 4 + ) and sulfur (DMSPd and DMS) by solar radiation was added to the model [Herndl et al., 1993; Slezak et al., 2001; Toole et al., 2006]. This fact has been also cited as a potential explanation for the DMS summer paradox since a reduction in a major sink may cause DMS to accumulate [Simo´ and Pedro´s-Alio´, 1999; Simo´, 2001, 2004]. Model results (see Figure 3) indicate that inhibition of bacterial sulfur uptake by UV could partly explain the Table 2. Model Experiments Process Affecting S-Cycle ExpA ExpB ExpC ExpD ExpE Phyto. S:N ratio shift by UV: NO YES YES YES YES Bact. inhibition by UV: NO NO YES YES YES Phyto. DMSPd consumption: NO NO NO YES YES Phyto. DMS production by UV: NO NO NO NO YES G01009 VALLINA ET AL.: A DYNAMIC MODEL OF OCEANIC SULFUR 9of23 G01009 where X kcontrol ,X kmax and X kmin are the annual budgets of DMSPp, DMSPd and DMS integrated over the upper 50m obtained for the 3 simulations: control (reference value of the parameter k), 50% increase in the parameter k(k max = 1.5k), and 50% decrease in the parameter k(k min =0.5k)[Le Clainche et al., 2004]. Only those parameters which gave SA indices greater than 10% are plotted in Figure 12. Black bars indicate that an increase of the parameter results in an increase in the state variable, while grey bars indicate that an increase in the parameter produced a decrease in the state variable. [43] For DMSPp (Figure 12a) we observe that parameters related to zooplankton grazing have the largest effects, mainly the maximum zooplankton specific ingestion rate. This is not surprising since they directly affect the phytoplankton biomass. Another important parameter is the labile fraction of DOM produced. Other SA tests (not shown) revealed that this parameter is a key one for the nutrient pools due to the bacterial microbial loop; an increase of DOM concentrations is associated to a rise of NO 3 = and NH 4 + in the model, and thus to an increase of modeled phytoplankton. Bacterial hydrolysis of semilabile DOM and gross growth efficiency are also very important because they affect the amount of labile DOM (and then again the nutrient pools and phytoplankton biomass). Parameters related to zooplankton mortality are associated to DMSPp through the levels of grazing activity upon phytoplankton, while the zooplankton C:N ratio affects the DOC pool (and again the microbial loop). Interestingly, the maximum S:N internal quota of phytoplankton is not the most important parameter contrary to the results of Lefevre et al. [2002] and Le Clainche et al. [2004]. This difference is in part attributable to the fact that in the SA carried out by these authors they increased/reduced by 50% the minimum and maximum S:N internal ratios at the same time, while we have increased/reduced them separately. Nevertheless, these results suggest that bottom-up (nutrient availability, regulated by the microbial loop) and top-down (zooplankton grazing) processes that control phytoplanktom biomass are more important for DMSPp concentrations than the internal sulfur quota. [44] For DMSPd (Figure 12b), the 10 most sensitive parameters are related to the microbial loop, except for the maximum phytoplankton internal S:N quota (4th position), the bacterial S:C ratio (5th position), the fraction of ingested DMSPp by zoo that is recovered as DMSPd (7th) and the phytoplankton maximum specific growth rate (8th). [45] Regarding DMS (Figure 12c), we observe a set of seven parameters that have a consistently high influence (from 90% to from 110%), clearly larger than the rest (<60%). With the exception of the maximum phytoplankton S:N internal quota (5th position) and the maximum phytoplankton DMS exudation specific rate (6th position), all were ranked already in the top five most sensitive parameters for DMSPp (Figure 12a). They are related to the bottom-up and top-down processes controlling phytoplankton biomass previously cited. The parameter for the fraction Figure 12. Sensitivity analysis indices of the DMOS model to changing parameters by ±50%. Black bars indicate that an increase of the parameter causes an increase of the variable, while grey bars indicate that an increase of the parameter causes a decrease of the variable. G01009 VALLINA ET AL.: A DYNAMIC MODEL OF OCEANIC SULFUR 16 of 23 G01009 of bacteria that is DMS consumers is ranked on the 10th position, which is significant since at present this is an uncertain parameter. It is followed by the bacterial S:C ratio. A higher S:C ratio implies higher sulfur requirements of bacteria (lower DMS production from DMSPd uptake) at the same time than higher DMS uptake. There is large variation in published values for the S:C molar ratio ranging from 1/ 50 to 1/250 [Zubkov et al., 2002, and references therein]. Further research is needed in order to better constrain this parameter. As expected, the light attenuation coefficient is also quite important (13th position) because any increase reduces the amount of DMS exudation by phytoplankton. On the other hand, increasing it also reduces the DMS photolysis. However, since DMS exudation by phytoplankton was about 3 times higher than DMS photolysis (see Figure 6), the reduction of the source term dominates. [46] In order to evaluate which parameters affect DMS concentrations in a way not directly related to changes in phytoplankton biomass (i.e., changes in DMSPp) the SA index was also calculated for the ratio DMS/DMSPp (Figure 12d). As expected the DMS/DMSPp ratio is very sensitive to the maximum phytoplankton DMS exudation rate. Significant increases of the DMS/DMSPp ratio are also observed for higher zooplankton grazing rates. On the other hand, parameters that increase bacteria concentrations (e.g., carbon gross growth efficiency, maximum DOM/NH 4 + uptake, the labile fraction of DOM produced, the phytoplankton DOC exudation parameter, etc.) are associated with a decrease in the ratio. An increase of the light attenuation coefficient also produces a decrease of the DMS/DMSPp ratio. 4. Conclusions [47] We have presented a state-of-the-art model of the oceanic sulfur cycle which includes the various processes currently thought to be important in DMSP/DMS dynamics and which resolves explicitly DOM and bacteria dynamics within the ecosystem. Sensitivity analyses have shown that parameters related to the microbial loop have a great impact on the N/C/S-cycles, in agreement with previous conclusions reached by both modeling and experimental studies [Spitz et al., 2001; Simo´etal., 2000]. The model is able to reproduce the seasonal DMS summer paradox observed in the Sargasso Sea and highlights that bacterial consumption of DMSPd to give DMS may not be the main process in the overall DMS budget. Field studies have also shown that DMS concentrations were not controlled by DMSPd uptake by bacteria [Dacey et al., 1998; Zubkov et al., 2002]. Rather it seems that the key process determining DMS concentrations in the upper ocean may be direct exudation from phytoplankton cells under high UV conditions, this providing an explanation for the strong seasonal decoupling observed between chlorophyll-a and DMS over most of the ocean’s surface [Vallina et al., 2006; Vallina and Simo´, 2007]. This mechanism is missing in all current models of the sulfur cycle, with the exception of the one presented here. [48] Our model results suggest that DMS production by phytoplankton, despite being only one among several processes that are relevant (such as light-induced increases in the S:N ratio of phytoplankton and light-induced inhibition of bacterial sulfur uptake), is a major contributor to the DMS summer paradox. This has been previously proposed from the analysis of field data in the Sargasso Sea [Toole and Siegel, 2004]. The fact that phytoplankton can directly produce DMS has been previously reported in the literature [Vairavamurthy et al., 1985; Niki et al., 2000, and references therein; Wolfe et al., 2002] and there is increasing experimental evidence in support of this claim [Toole et al., 2006]. The implication is that changes in UV levels due to shoaling of the MLD, as might occur in Global Warming scenarios, could have an impact on the oceanic DMS production, and therefore on its potential effect upon Earth climate through CCN formation. Global DMSP/DMS models should incorporate the light-mediated processes affecting DMS production included in DMOS if better estimates of surface DMS concentrations, and specially of its seasonality, are to be achieved. Appendix A A1. Model Equations [49] Phytoplankton [mmolN m 3 ] equation @P @t¼1g1 ðÞFPGPMPSPðÞþDPðÞ ðA1Þ Zooplankton [mmolN m 3 ] equation @Z @t¼FZMZþDZðÞ ðA2Þ Bacteria [mmolN m 3 ] equation @B @t¼FBGBMBþDB ðÞ ðA3Þ Nitrates [mmolN m 3 ] equation @N @t¼FN PþnAþDNðÞ ðA4Þ Ammonium [mmolN m 3 ] equation @A @t¼FA PnAþEBþEZþWAMZþDZðÞ ðA5Þ Labile DON [mmolN m 3 ] equation @Ln @t¼g1FPþd1fGnþeMPþMBþMDnþWdomMZ ½þUSn ULnþDL n ðÞ ðA6Þ Labile DOC [mmolC m 3 ] equation @Lc @t¼g1qPc:nFPþg1Edoc þd21g1 ðÞEdoc þd1fGcþeqPc:nMPþqBc:nMBþMDcþWdomqZc:nMZ ½ þUScqBc:nFBRBþDL c ðÞ ðA7Þ G01009 VALLINA ET AL.: A DYNAMIC MODEL OF OCEANIC SULFUR 17 of 23 G01009 Semilabile DON [mmolN m 3 ] equation @Sn @t¼1d1 ðÞfGnþeMPþMBþMDnþWdomMZ ½USn þDS n ðÞ ðA8Þ Semilabile DOC [mmolC m 3 ] equation @Sc @t¼1d2 ðÞ1g1 ðÞEdoc þ1d1 ðÞ fGcþeqPc:nMPþqBc:nMBþMDcþWdomqZc:nMZ ½ UScþDS c ðÞ ðA9Þ Detrital nitrogen [mmolN m 3 ] equation @Dn @t¼1bn ðÞ1fðÞGn þ1eðÞMPþWDnMZGDnMDn SD n ðÞþDD n ðÞ ðA10Þ Detrital carbon [mmolC m 3 ] equation @Dc @t¼1bc ðÞ1fðÞGc þ1eðÞqPc:nMPþWDcqZc:nMZ GDcMDcSD c ðÞþDD c ðÞ ðA11Þ Detrital CaCO 3 [mmolC m 3 ] equation @Dh @t¼qCaqPc:nGPþMP ðÞMDhSD h ðÞþDD h ðÞ ðA12Þ Dissolved inorganic carbon [mmolC m 3 ] equation @DIC @t¼1þqCa ðÞqPc:nFPEdoc þRBþRZþMDh þWDICqZc:nMZþFatm þDDIC ðÞ ðA13Þ Alkalinity [mmolC m 3 ] equation @ALK @t¼QNQA ðÞFP2qCaqPc:nFPþEBþEZþ2MDh þWAMZnAþD ALKðÞ ðA14Þ CHL [mg m 3 ] equation @CHL @t¼rchlCmwqPc:n ðÞFPGPþMP ðÞCHL=PðÞS CHLðÞ þD CHL ðÞ ðA15Þ DMSPp [mmolS m 3 ] equation @DMSPp @t¼qPs:n @P @t ¼qPs:n1g1 ðÞFPGPMPSPðÞþDPðÞ½ ðA16Þ DMSPd [mmolS m 3 ] equation @DMSPd @t¼qPs:ng1FPþa1GPþMP ½UDMSPd UP DMSPd fDMSPd þD DMSPdðÞ ðA17Þ DMS [mmolS m 3 ] equation @DMS @t¼RDMS þEDMS þfDMSPd UDMS DMSphoto DMSemiss * ðÞþD DMSðÞ ðA18Þ [50] (*) This term is applied only to the top model cell. A2. N/C-Cycles Model Terms [51] Phytoplankton production (F P ) FP¼FN PþFA P¼JQNPþJQAP¼JQP ðA19Þ J¼mPRðA20Þ mP¼mmax Pe0:063 TTmax ðÞðÞ ðA21Þ R¼Iz Is e1Iz Is ðÞ 1ðA22Þ Iz¼I0ekwþkp P ðÞ zðA23Þ  P¼1 zZz 0 Pdz ðA24Þ Q¼QNþQA1ðA25Þ QN¼ N kN P eyAðÞ 1þN kN P þA kA P ðA26Þ QA¼ A kA P 1þN kN P þA kA P ðA27Þ Phytoplankton extra-DOC exudation Edoc ¼g2qPc:nFPðA28Þ Zooplankton grazing on phytoplankton (G P ), bacteria (G B ), detrital nitrogen (G Dn ) and detrital carbon (G Dc ) GP¼gZpPP2 kgpPPþpBBþpDDn ðÞþpPP2þpBB2þpDD2 n ðA29Þ G01009 VALLINA ET AL.: A DYNAMIC MODEL OF OCEANIC SULFUR 18 of 23 G01009 GB¼gZpBB2 kgpPPþpBBþpDDn ðÞþpPP2þpBB2þpDD2 n ðA30Þ GDn¼gZpDD2 n kgpPPþpBBþpDDn ðÞ þpPP2þpBB2þpDD2 n ðA31Þ GDc¼Dc Dn  GDnðA32Þ Gn¼GPþGBþGDnðA33Þ Gc¼qPc:nGPþqBc:nGBþGDcðA34Þ Zooplankton production (F Z ) and excretion (E Z ) qf *¼bnqZc:n bcwZ ðA35Þ qf¼1fðÞGc 1fðÞGn ðA36Þ if q f >q* f (N-limitation): FZ¼bn1fðÞGnðA37Þ EZ¼0ðA38Þ if q f <q* f (C-limitation): FZ¼bcwZ qZc:n 1fðÞGcðA39Þ EZ¼bn qf bn qf *  1fðÞGcðA40Þ Zooplankton respiration RZ¼bc1fðÞGcqZc:nFZðA41Þ Bacterial uptake of labile DOC (U Lc ), labile DON (U Ln ) ULc¼mBqBc:nBLc kLc þLc ðA42Þ ULn¼Ln Lc  ULcðA43Þ Bacterial maximum potential uptake of ammonium U* A¼mBBA kAþAðA44Þ mB¼mmax B1finhib ðÞ ðA45Þ finhib ¼fmax inhib Iz Imax ðA46Þ Bacterial production (F B ), ammonium excretion or uptake (E B ) and respiration (R B ) EB¼ULnwB qBc:n  ULcðA47Þ if E B > 0 (ammonium excretion) if E B < 0 (ammonium uptake) if U* A E B (C-limitation): FB¼ULnEB¼wB qBc:n  ULcðA48Þ RB¼1wB ðÞULcðA49Þ if U* A <E B (N-limitation): EB¼U* AðA50Þ FB¼ULnEB¼ULnþU* AðA51Þ RB¼1 wB1  qBc:nFBðA52Þ Bacterial hydrolysis of semilabile DOC (U Sc ) and semilabile DON (U Sn ) USc¼mScqBc:nBSc kSc þSc ðA53Þ USn¼Sn Sc  UScðA54Þ Mortality of phytplankton (M P ), zooplankton (M Z ) and bacteria (M B ) MP¼mPPðA55Þ MZ¼mZZ2 kZþZðA56Þ MB¼mBBðA57Þ G01009 VALLINA ET AL.: A DYNAMIC MODEL OF OCEANIC SULFUR 19 of 23 G01009 Breakdown of detrital nitrogen (M Dn ), detrital carbon (M Dc ) and detrital CaCO 3 (M Dh ) MDn¼mDnDnðA58Þ MDc¼mDcDcðA59Þ MDh¼mDhDhðA60Þ Chlorophyll-a production rchl ¼qm chlJQ achlqchlIz ðA61Þ qchl ¼CHL CmwqPc:nPðA62Þ A3. S-Cycle Model Terms [52] S:N phytoplankton internal quota qPs:n¼qmin Ps:nþq0 Ps:nqmin Ps:n  min Iz;I*ðÞ I*ðA63Þ q0 Ps:n¼qmax Ps:nqmax Ps:nqmin Ps:n  Imax I0 Imax Imin ðA64Þ Phytoplankton DMS exudation EDMS ¼gsDMSPp ðA65Þ gs¼gmax s Iz Imax mP mmax P ðA66Þ Phytoplankton DMSPd uptake UP DMSPd ¼DMSPd AaPFA PþDMSPd NaPFN PðA67Þ Bacterial DMSPd and DMS uptake UDMSPd ¼mBqBs:cqBc:nBDMSPd kDMSPd þDMSPd ðA68Þ UDMS ¼mBqBs:cqBc:naBBDMS kDMS þDMS ðA69Þ Bacterial sulfur demand UDMSPd *¼qBs:cqBc:nFBðA70Þ Bacterial DMS production if U* DMSPd <U DMSPd (no S-limitation): RDMS ¼a2UDMSPd UDMSPd * ðÞðA71Þ if U* DMSPd U DMSPd (S-limitation): RDMS ¼0ðA72Þ DMS photolysis DMSphoto ¼kphotoDMS ðA73Þ kphoto ¼kmax photo Iz Imax ðA74Þ DMS emission to the atmosphere DMSemiss ¼kemissDMS ðA75Þ kemiss ¼kv24 100 DzðA76Þ kv¼0:24U2þ0:061U  Sc 600  0:5ðÞ ðA77Þ Sc ¼2674 147:12 SSTðÞþ3:726 SST2  0:038 SST3  ðA78Þ DMS yield DMSyield ¼DMSprod: DMSPcons: ¼EDMS þRDMS þfDMSPd EDMS þUDMSPd þUP DMSPd þfDMSPd ðA79Þ A4. Advection (Sinking) and Diffusion Terms [53] Phytoplankton and Detritus sinking SX i ðÞ¼j ~ wij@Xi @zðA80Þ for X i =P,D n ,D c ,D h and CHL. Turbulent diffusion DX i ðÞ¼ @ @zkz @Xi @z  ðA81Þ for X i =P,Z,B,N,A,L n ,L c ,S n ,S c ,D n ,D c ,D h ,DIC,ALK, CHL,DMSPp,DMSPd and DMS. A5. Turbulent Diffusion and Temperature Profiles [54] D¼D max þD minerD  minD max ðÞ 2zMLD ðÞ H 1þerD  minD max ðÞ 2zMLD ðÞ H ðA82Þ G01009 VALLINA ET AL.: A DYNAMIC MODEL OF OCEANIC SULFUR 20 of 23 G01009 where the asterisk symbol denotes normalized variables (values between 0 and 1): X*¼X=HðA83Þ Y*¼Y=Dmax ðA84Þ for X=z,MLD,H, and Y=D,D min ,D max .His the model vertical domain (200 m) and Dcan be either diffusion (kz) or sea temperature (st). A6. Numerical Scheme for Solving the 1-D Model [55] The general form of the model equations is: @Xi @t¼Jij~ wij@Xi @zþ@ @zkz @Xi @z  ¼fX i ðÞ ðA85Þ where J i are the biological source/sink terms for each variable ias defined above, j~ wij@Xi @zis the vertical sinking (only applies to phytoplankton and detritus), and @ @z(kz@Xi @z)is the vertical turbulent diffusion. The numerical scheme is implemented using a finite difference approximation. At each time step and for each vertical grid point j, all three terms are calculated independently to obtain f(X i ). The sinking term is calculated using a first-order upwind discretization: @Xj i @z¼Xj1 iXj i DzðA86Þ while the diffusion term is calculated using a second-order centered discretization: @ @zkz @Xi @z  ¼ kz jþ1=2Xjþ1 iXj i  kz j1=2Xj iXj1 i  DzðÞ 2 ðA87Þ where kz j+1/2 kz(z j+j/2 ). Finally, for each vertical grid point we then advance the solution in time from X i t to X i t+1 using a forward Euler method [Press et al., 1992]: Xtþ1 i¼Xt iþfX t i  DtðA88Þ [56]Acknowledgments. Our special thanks to E. E. Popova for her kindly assistance and advice during the computer coding of the model. The authors would also like to thank the two reviewers (Scott Elliott and Dierdre Toole) for their thorough and very constructive review. This work was supported by the Spanish Ministry of Education and Science (MEC) through the projects AMIGOS (contract REN2001-3462/CLI to R.S.) and MIMOSA (contract CTM2005-06513 to R.S.), and a Ph.D. studentship (to S.M.V.). T. R. Anderson is funded by the Natural Environment Research Council (NERC, U.K.). This work is a contribution to the objectives of the SOLAS project and the Eur-Oceans Network of Excellence of the 6th Framework Program of the EU. References Albrecht, B. A. 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