Skip to main content

Advertisement

SpringerLink
Log in

Seasonal dynamics and stoichiometry of the planktonic community in the NW Mediterranean Sea: a 3D modeling approach

  • Published:
Ocean Dynamics Aims and scope Submit manuscript

Abstract

The 3D hydrodynamic Model for Applications at Regional Scale (MARS3D) was coupled with a biogeochemical model developed with the Ecological Modular Mechanistic Modelling (Eco3M) numerical tool. The three-dimensional coupled model was applied to the NW Mediterranean Sea to study the dynamics of the key biogeochemical processes in the area in relation with hydrodynamic constraints. In particular, we focused on the temporal and spatial variability of intracellular contents of living and non-living compartments. The conceptual scheme of the biogeochemical model accounts for the complex food web of the NW Mediterranean Sea (34 state variables), using flexible plankton stoichiometry. We used mechanistic formulations to describe most of the biogeochemical processes involved in the dynamics of marine pelagic ecosystems. Simulations covered the period from September 1, 2009 to January 31, 2011 (17 months), which enabled comparison of model outputs with situ measurements made during two oceanographic cruises in the region (Costeau-4: April 27–May 2, 2010 and Costeau-6: January 23–January 27, 2011).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  • Aminot A, Kérouel R (2004) Hydrologie des écosystèmes marins. Paramètres et analyses. In: Ifremer (ed)

  • André G, Garreau P, Garnier V, Fraunié P (2005) Modeled variability of the sea surface circulation in the North-western Mediterranean Sea and in the Gulf of Lions. Ocean Dyn 55:294–308

    Article  Google Scholar 

  • André G, Garreau P, Fraune P (2009) Mesoscale slope current variability in the Gulf of Lions. Interpretation of in-situ measurements using a three-dimensional model. Cont Shelf Res 2:407–423

    Article  Google Scholar 

  • Auger PA, Diaz F, Ulses C, Estornel C, Neveux J, Joux F, Pujo-Pay M, Naudin JJ (2011) Functioning of the planktonic ecosystem on the Gulf of Lions shelf (NW Mediterranean) during spring and its impact on the carbon deposition: a field data and 3-D modeling combined approach. Biogeosciences 8:3231–3261

    Article  Google Scholar 

  • Avril B (2002) DOC dynamics in the northwestern Mediterranean Sea (DYFAMED site). Deep-Sea Res II 49:2163–2182

    Article  Google Scholar 

  • Baklouti M, Diaz F, Pinazo C, Faure V, Quequiner B (2006a) Investigation of mechanistic formulations depicting phytoplankton dynamics for models of marine pelagic ecosystems and description of a new model. Prog Oceanogr 71:1–33

    Article  Google Scholar 

  • Baklouti M, Faure V, Pawlowski L, Sciandra A (2006b) Investigation and sensitivity analysis of a mechanistic phytoplankton model implemented in a new modular tool (Eco3M) dedicated to biogeochemical modelling. Prog Oceanogr 71:34–58

    Article  Google Scholar 

  • Baklouti M, Chevalier C, Bouvy M, Corbin D, Pagano M, Troussellier M, Arfi R (2011) A study of plankton dynamics under osmotic stress in the Senegal River Estuary, West Africa, using a 3D mechanistic model. Ecol Model 222(15):2704–2721

    Article  Google Scholar 

  • Baretta-Bekker JG, Baretta JW, Ebenhoh W (1997) Microbial dynamics in the marine ecosystem model ERSEM II with decoupled carbon assimilation and nutrient uptake. J Sea Res 38:195–211

    Article  Google Scholar 

  • Barquero S, Cabal JA, Anadón R, Fernández E, Varela M, Bode A (1998) Ingestion rates of phytoplankton by copepod size-fractions on a bloom associated to an off-shelf front off NW Spain. J Plankton Res 20:957–972

    Google Scholar 

  • Bethoux JP, Gentili B, Morin P, Nicolas E, Pierre C, Ruiz-Pino D (1999) The Mediterranean Sea: a miniature ocean for climatic and environmental studies and a key for the climatic functioning of the North Atlantic. Prog Oceanogr 44(1–3):131–146

    Article  Google Scholar 

  • Bethoux JP, Durieu de Madron X, Nyffeler F, Tailliez D (2002) Deep water in the western Mediterranean: peculiar 1999 and 2000 characteristics, shelf formation hypothesis, variability since 1970 and geochemical inferences. J Mar Syst 33–34:117–131

    Article  Google Scholar 

  • Bissett WP, Walsh JJ, Dieterle DA, Carder KL (1999) Carbon cycling in the upper waters of the Sargasso Sea: I. Numerical simulation of differential carbon and nitrogen fluxes. Deep-Sea Res I 46:205–269

    Article  Google Scholar 

  • Bissett WP, Arnone R, DeBra S, Dieterle DA, Dye D, Kirkpatrick GJ, Schofield OM, Vargo GA (2005) Predicting the optical properties of the West Florida Shelf: Resolving the potential impacts of a terrestrial boundary condition on the distribution of colored dissolved and particulate matter. Mar Chem 95:199–233

    Article  Google Scholar 

  • Blumberg AF, Mellor GL (1987) A description of a three-dimensional coastal ocean circulation model. In: Heaps NS (ed) Three-dimensional coastal ocean models. Coastal and estuarine sciences. American Geophysical Union, Washington, pp 1–16

    Chapter  Google Scholar 

  • Brogueira MJ, Oliveira MR, Cabeçadas G (2007) Phytoplankton community structure defined by key environmental variables in Tagus estuary, Portugal. Mar Environ Res 64:616–628

    Article  Google Scholar 

  • Cauwet G, Miller A, Brasse S, Fengler G, Mantoura RFC, Spitzy A (1997) Dissolved and particulate organic carbon in the western Mediterranean Sea. Deep-Sea Res II 44:769–779

    Article  Google Scholar 

  • Chifflet M, Andersen V, Prieur L, Dekeyser I (2001) One-dimensional model of short-term dynamics of the pelagic ecosystem in the NW Mediterranean Sea: effects of wind events. J Mar Syst 20:89–114

    Article  Google Scholar 

  • Christaki U, Jacquet S, Dolan JR, Vaulot D, Rassoulzadegan F (1999) Growth and grazing on Prochlorococcus and Synechococcus by two marine ciliates. Limnol Oceanogr 44(1):52–61

    Google Scholar 

  • Christaki U, Courties C, Joux F, Jeffrey WH, Neveux J, Naudin JJ (2009) Community structure and trophic role of ciliates and heterotrophic nanoflagellates in Rhone River diluted mesoscale structures (NW Mediterranean Sea). Aquatic Microbial Ecology 57:263–277. doi:10.3354/ame01339

    Google Scholar 

  • Christaki U, Van Wambeke F, Lefevre D, Lagaria A, Prieur L, Pujo-Pay M, Grattepanche JD, Colombet J, Psarra S, Dolan J, Sime-Ngando T, Weinbauer M, Moutin T (2011a) Impact of anticyclonic mesoscale features on the Mediterranean Sea’s microbial food web. Biogeosciences 8:1–14

    Article  Google Scholar 

  • Christaki U, Courties C, Massana R, Catala P, Lebaron P, Gasol P, Zubkov MV (2011b) Optimized routine flow cytometric enumeration of heterotrophic flagellates using SYBR Green I. Limnol Oceanogr Methods 9:329–339

    Article  Google Scholar 

  • Christian JR (2005) Biogeochemical cycling in the oligotrophic ocean: Redfield and non-Redfield models. Limnol Oceanogr 50(2):646–657

    Google Scholar 

  • Coll M, Piroddi C, Steenbeek J, Kaschner K, Ben Rais Lasram F (2010) The biodiversity of the Mediterranean Sea: estimates, patterns, and threats. PLoS ONE 5(8):e11842. doi:10.1371/journal.pone.0011842

    Article  Google Scholar 

  • Crombet Y, Leblanc K, Quéguiner B, Moutin T, Rimmelin P, Ras J, Claustre H, Leblond N, Oriol L, Pujo-Pay M (2011) Deep silicon maxima in the stratified oligotrophic Mediterranean Sea. Biogeosciences 8:459–475

    Article  Google Scholar 

  • Diaz F, Raimbault P, Boudjellal B, Garcia N, Moutin T (2001) Early spring phosphorus limitation of primary productivity in a NW Mediterranean coastal zone (Gulf of Lions). Mar Ecol Prog Ser 211:51–62

    Article  Google Scholar 

  • Diaz F, Naudin J-J, Courties C, Rimmelin P, Oriol L (2008) Biogeochemical and ecological functioning of the low-salinity water lenses in the region of the Rhone River freshwater influence, NW Mediterranean Sea. Cont Shelf Res 28(12):1511–1526

    Article  Google Scholar 

  • Domingues RB, Anselmo TP, Barbosa AB, Sommer U, Galvão HM (2011) Nutrient limitation of phytoplankton growth in the freshwater tidal zone of a turbid, Mediterranean estuary. Estuar Coast Shelf Sci 91(2):282–297

    Article  Google Scholar 

  • Doney SC, Lindsay K, Caldeira K, Campin J-M, Drange H, Dutay J-C, Follows M, Gao Y, Gnanadesikan A, Gruber N, Ishida A, Joos F, Madec G, Maier-Reimer E, Marshall JC, Matear RJ, Monfray P, Mouchet A, Najjar R, Orr JC, Plattner G-K, Sarmiento J, Schlitzer R, Slater R, Totterdell IJ, Weirig M-F, Yamanaka Y, Yool A (2004) Evaluating global ocean carbon models: the importance of realistic physics. Glob Biogeochem Cycles 18, GB3017. doi:10.1029/2003GB002150

    Article  Google Scholar 

  • Droop MR (1968) Vitamin B12 and marine ecology. IV. The kinetics of uptake, growth and inhibition in Monochrysis lutheri. J Mar Biol Assoc U K 48:689–733

    Article  Google Scholar 

  • Droop MR (1970) Vitamin B12 and marine ecology. V. Continuous culture as an approach to nutritional kinetics. Heloglander wiss Meeresutners 20:629–636

    Article  Google Scholar 

  • Eisenhauer N, Milcu A, Nitschke N, Sabais ACW, Scherber C, Scheu S (2009) Earthworm and belowground competition effects on plant productivity. Oecologia 161:291–301

    Article  Google Scholar 

  • Faugeras B, Lévy M, Mémery L, Verron J, Blum J, Charpentier I (2003) Can biogeochemical fluxes be recovered from nitrate and chlorophyll data? A case study assimilating data in the Northwestern Mediterranean Sea at the JGOFS-DYFAMED station. J Mar Syst 40–44:99–125

    Article  Google Scholar 

  • Faugeras B, Bernard O, Sciandra A, Lévy M (2004) A mechanistic modelling and data assimilation approach to estimate the carbon/chlorophyll and carbon/nitrogen ratios in a coupled hydrodynamical–biological model. Nonlinear Proc Geoph 11:515–533

    Article  Google Scholar 

  • Fontana C, Grenz C, Pinazo C, Marsaleix P, Diaz F (2009) Assimilation of SeaWiFS chlorophyll data into a 3D-coupled physical–biogeochemical model applied to a freshwater-influenced coastal zone. Cont Shelf Res 29(11–12):1397–1409

    Article  Google Scholar 

  • Frost BW, Franzen NC (1992) Grazing and iron limitatioil in the control of phytoplankton stock and nutrient concentration: a chemostat analogue of the Pacific equatorial upwelling. Mar Ecol Prog Ser 83:291–303

    Google Scholar 

  • Geider RJ, La Roche J (2002) Redfield revisited: variability in the N:P ratio of phytoplankton and its biochemical basis. Eur J Phycol 37:1–17

    Article  Google Scholar 

  • Geider RJ, MacIntyre HL, Kana TM (1998) A dynamic regulatory model of phytoplankton acclimation to light, nutrients and temperature. Limnol Oceanogr 43:679–694

    Google Scholar 

  • Gentleman W, Leising A, Frost B, Strom S, Murray J (2003) Functional responses for zooplankton feeding on multiple resources: a review of assumptions and biological dynamics. Deep-Sea Res 50:2847–2875

    Article  Google Scholar 

  • Grell GA., Dudhia J, Stauffer DR (1993) A description of the fifth-generation Penn State / NCAR mesoscale model (MM5). NCAR Technical Note, NCAR/ TN-398+STR, pp 117

  • Han BP (2002) A mechanistic model of algal photoinhibition induced by photodamage to photosystem. J Theor Biol 214:519–527

    Article  Google Scholar 

  • Heldal M, Scanlan DJ, Norland S, Thingstad F, Mann NH (2003) Elemental composition of single cells of various strains of marine Prochlorococcus and Synechococcus using X-ray microanalysis. Limnol Oceanogr 48(5):1732–1743

    Google Scholar 

  • Holling CS (1965) The functional response of predator to prey density and its role in mimicry and population regulation. Mem Ent Sec Can 45:1–60

    Article  Google Scholar 

  • Janse JH, Aldenberg T (1991) Modelling the eutrophication of the shallow Loosdrecht Lakes. Verh Int Ver Limnol 24:751–757

    Google Scholar 

  • Kiorboe T (2008) Optimal swimming strategies in mate-searching pelagic copepods. Oecologia 155:179–192. doi:10.1007/s00442-007-0893-x

    Google Scholar 

  • Klausmeier CA, Litchman E, Daufresne T, Levin SA (2004) Optimal nitrogen-to-phosphorus stoichiometry of phytoplankton. Nature 429:171–174

    Article  Google Scholar 

  • Klausmeier CA, Litchman E, Daufresne T, Levin SA (2008) Phytoplankton stoichiometry. Ecol Res 23:479–485

    Article  Google Scholar 

  • Kooijman SALM (2000) Energy and mass budgets in biological systems. University Press, Cambridge

    Book  Google Scholar 

  • Krom MD, Herut B, Mantoura RFC (2000) Nutrient budget for the Eastern Mediterranean: implications for phosphorus limitation. Limnol Oceanogr 49(5):1582–1592

    Google Scholar 

  • Labrune C, Romero-Ramirez A, Amouroux JM, Duchêne JC, Desmalades M, Escoubeyrou K, Buscail R, Grémare A (2012) Comparison of ecological quality indices based on benthic macrofauna and sediment profile images: a case study along an organic enrichment gradient off the Rhône River. Ecol Indic 12(1):133–142

    Article  Google Scholar 

  • Lacroix G, Nival P (1998) Influence of meteorological variability on primary production dynamics in the Ligurian Sea (NW Mediterranean Sea) with a 1D hydrodynamic/biological model, in: Delhez, E.J.M. Modelling hydrodynamically dominated Manne ecosystems. J Mar Syst 16(Special Issue 1–2):23–50

    Article  Google Scholar 

  • Lazure P, Dumas F (2008) An external-internal mode coupling for a 3D hydrodynamical model for applications at regional scale (MARS). Adv Water Resour 31(2):233–250

    Article  Google Scholar 

  • Lazzari P, Solidoro C, Ibello V, Salon S, Teruzzi A, Beranger K, Colella S, Crise A (2012) Seasonal and inter-annual variability of plankton chlorophyll and primary production in the Mediterranean Sea: a modelling approach. Biogeosciences 9:217–233

    Article  Google Scholar 

  • Levy M (2003) Mesoscale variability of phytoplankton and of new production: Impact of the large-scale nutrient distribution. J Geophys Res 108(C11), doi:10.1029/2002JC001577

  • Li Y, Gal G, Waite AM, Hipsey MR (2011) Microbial loop processes shape the food web stoichiometry in Lake Kinneret. 19th International Congress on Modelling and Simulation, Perth, Australia, 12–16 December 2011

  • Ludwig W, Bouman AF, Dumont E, Lespinas F (2010) Water and nutrient fluxes from major Mediterranean and Black Sea rivers: past and future trends and their implications for the basin scale budgets. Glob Biogeochem Cycles 24:GB0A13. doi:10.1029/2009GB003594

    Article  Google Scholar 

  • Malanotte-Rizzoli P and the Pan-Med Group (2012) Physical forcing and physical/biochemical variability of the Mediterranean Sea: A review of unresolved issues and directions of future research. Report of the Workshop “Variability of the Eastern and Western Mediterranean circulation and thermohaline properties: similarities and differences” Rome, 7–9 November, 2011, 48pp

  • Marty JC, Garcia N, Raimbault P (2008) Phytoplankton dynamics and primary production under late summer conditions in the NW Mediterranean Sea. Deep-Sea Res I 55:1131–1149

    Article  Google Scholar 

  • Mauriac R, Moutin T, Baklouti M (2011) Accumulation of DOC in low phosphate low chlorophyll (LPLC) area: is it related to higher production under high N:P ratio? Biogeosciences 8:933–950. doi:10.5194/bg-8-933-2011

    Article  Google Scholar 

  • Mémery L, Levy M, Verant S, Merlivat L (2002) The relevant time scales in estimating the air–sea CO2 exchange in a mid-latitude region. Deep-Sea Res II 49:2067–2092

    Article  Google Scholar 

  • Millot C, Taupier-Letage I (2005) Circulation in the Mediterranean Sea, The Handbook of Environmental Chemistry, Vol. K: 29–66 doi: 10.1007/b107143

  • Moore JK, Doney SC, Kleypas JA, Glover DM, Fung IY (2002) An intermediate complexity marine ecosystem model for the global domain. Deep-Sea Res II 49:403–462

    Article  Google Scholar 

  • Moutin T, Raimbault P (2002) Primary production, carbon export and nutrients availability in western and eastern Mediterranean Sea in early summer 1996 (MINOS cruise). J Mar Syst 33–34:273–288

    Article  Google Scholar 

  • Nicolle A, Garreau P, Liorzou B (2009) Modelling for anchovy recruitment studies in the Gulf of Lions (Western Mediterranean Sea). Ocean Dyn 59(6):953–968

    Article  Google Scholar 

  • Oschlies A, Garçon V (1999) An eddy-permitting coupled physical-biological model of the North Atlantic 1. Sensitivity to advection numerics and mixed layer physics. Glob Biogeochem Cycles 13(1):135–160

    Article  Google Scholar 

  • Pairaud IL, Gatti J, Bensoussan N, Verney R, Garreau P (2011) Hydrology and circulation in a coastal area off Marseille: validation of a nested 3D model with observations. J Mar Syst 88:20–33

    Article  Google Scholar 

  • Perez MT, Dolan JR, Fukai W (1997) Planktonic oligotrich ciliates in the NW Mediterranean: growth rates and consumption by copepods. Mar Ecol Prog Ser 155:89–101

    Google Scholar 

  • Pinardi N, Allen I, De Mey P, Korres G, Lascaratos A, Le Traon PY, Maillard C, Manzella G, Tziavos C (2003) The Mediterranean Ocean Forecasting System: first phase of implementation (1998–2001). Ann Geophys 21(1):3–20

    Article  Google Scholar 

  • Polimene L, Pinardi N, Zavatarelli M, Allen JI, Giani M, Vichi M (2007) A numerical simulation study of dissolved organic carbon accumulation in the northern Adriatic Sea. J Geophys Res 112(C3): doi: 10.1029/2006JC003529. issn: 0148–0227

    Google Scholar 

  • Pujo-Pay M, Conan P, Oriol L, Cornet-Barthaux V, Falco C, Ghiglione J-F, Goyet C, Moutin T, Prieur L (2011) Integrated survey of elemental stoichiometry (C, N, P) from the western to eastern Mediterranean Sea. Biogeosciences 8:883–899

    Article  Google Scholar 

  • Raick C, Delhez EJM, Soetaert K, Grégoire M (2005) Study of the seasonal cycle of the biogeochemical processes in the Ligurian Sea using a 1D interdisciplinary model. J Mar Syst 55:177–203

    Article  Google Scholar 

  • Raick C, Soetaert K, Grégoire M (2006) Model complexity and performance: how far can we simplify. Prog Oceanogr 70:27–57

    Article  Google Scholar 

  • Raick C, Alvera-Azcarate A, Barth A, Brankart JM, Soetaert K, Grégoire M (2007) Application of a SEEK filter to a 1D biogeochemical model of the Ligurian Sea: twin experiments and real in-situ data assimilation. J Mar Syst 65:561–583

    Article  Google Scholar 

  • Raimbault P, Durrieu de Madron X (2003) Research activities in the Gulf of Lion (NW Mediterranean) within the 1997–2001 PNEC project. Oceanol Acta 26(4):291–298

    Article  Google Scholar 

  • Raybaud V, Nival P, Mousseau L, Gubanova A, Altukhov D, Khvorov S, Ibañez F, Andersen V (2008) Short term changes in zooplankton community during the summer–autumn transition in the open NW Mediterranean Sea: species composition, abundance and diversity. Biogeosciences 5:1573–1586

    Article  Google Scholar 

  • Raybaud V, Tunin-Ley A, Ritchie ME, Dolan JR (2009) Similar patterns of community organization characterize distinct groups of different trophic levels in the plankton of the NW Mediterranean Sea. Biogeosciences 6:431–438

    Article  Google Scholar 

  • Raybaud V, Nival P, Prieur L (2011) Short time-scale analysis of the NW Mediterranean ecosystem during summer–autumn transition: a 1D modelling approach. J Mar Syst 84:1–17

    Article  Google Scholar 

  • Redfield, A.C. (1934) On the proportions of organic derivations in sea water and their relation to the composition of plankton. In: Daniel, R.J. (Ed.), James Johnstone Memorial Volume. University Press of Liverpool, Liverpool, pp. 177–192

  • Ridame C, Moutin T, Guieu C (2003) Does phosphate adsorption onto Saharan dust explain the unusual N/P ratio in the Mediterranean Sea? Oceanol Acta 26:629–634

    Article  Google Scholar 

  • Romero E, Peters F, Marrasé C, Guadayol Ò, Gasol JM, Weinbauer MG (2011) Coastal Mediterranean plankton stimulation dynamics through a dust storm event: an experimental simulation. Estuar Coast Shelf Sci 93:27–39

    Article  Google Scholar 

  • Rubio A, Taillandier V, Garreau P (2009) Reconstruction of the Mediterranean northern current variability and associated cross-shelf transport in the Gulf of Lions from satellite-tracked drifters and model outputs. J Mar Syst 78:63–78

    Article  Google Scholar 

  • Schaeffer A, Molcard A, Forget P, Fraunie P, Garreau P (2011) Generation mechanisms for mesoscale eddies in the Gulf of Lions: radar observation and modeling. Ocean Dyn 61(10):1587–1609

    Article  Google Scholar 

  • Sempéré R, Charrière B, Van Wambeke F, Cauwet G (2000) Carbon inputs of the Rhône River to the Mediterranean Sea: biogeochemical implications. Glob Biogeochem Cycles 14:669–681

    Article  Google Scholar 

  • Sherr EB, Sherr BF, Sigmon CT (1999) Activity of marine bacteria under incubated and in situ conditions. Aquat Microb Ecol 20: 213–223. doi:10.3354/ame020213

    Google Scholar 

  • Sterner RW, Elser JJ (2002) Ecological stoichiometry: The Biology of Elements from Molecules to the Biosphere. Princeton University Press, Princeton, NJ., ISSN 0-691-07491-7

  • Tanaka T (2009) Structure and function of the mesopelagic microbial loop in the NW Mediterranean Sea. Aquat Microb Ecol 57:351–362

    Article  Google Scholar 

  • Tanaka T, Rassoulzadegan F (2002) Full-depth profile (0–2,000 m) of bacteria, heterotrophic nanoflagellates and ciliates in the NW Mediterranean Sea: vertical partitioning of microbial trophic structures. Deep-Sea Res II 49:2093–2107

    Article  Google Scholar 

  • Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J Geophys Res 106:7183–7192

    Google Scholar 

  • The MerMex Group, Durrieu de Madron X, Guieu C, Sempéré R, Conan P, Cossa D, D’Ortenzio F, Estournel C, Gazeau F, Rabouille C, Stemmann L, Bonnet S, Diaz F, Koubbi P, Radakovitch O, Babin M, Baklouti M, Bancon-Montigny C, Belviso S, Bensoussan N, Bonsang B, Bouloubassi I, Brunet C, Cadiou J-F, Carlotti F, Chami M, Charmasson S, Charrière B, Dachs J, Doxaran D, Dutay J-C, Elbaz-Poulichet F, Eléaume M, Eyrolles F, Fernandez C, Fowler S, Francour P, Gaertner JC, Galzin R, Gasparini S, Ghiglione J-F, Gonzalez J-L, Goyet C, Guidi L, Guizien K, Heimbürger L-E, Jacquet SHM, Jeffrey WH, Joux F, Le Hir P, Leblanc K, Lefèvre D, Lejeusne C, Lemé R, Loÿe-Pilot M-D, Mallet M, Méjanelle L, Mélin F, Mellon C, Mérigot B, Merle P-L, Migon C, Miller WL, Mortier L, Mostajir B, Mousseau L, Moutin T, Para J, Pérez T, Petrenko A, Poggiale J-C, Prieur L, Pujo-Pay M, Pulido-Villena, Raimbult P, Rees AP, Ridame C, Rontani J-F, Ruiz Pino D, Sicre MA, Taillandier V, Tamburini C, Tanaka T, Taupier-Letage I, Tedetti M, Testor P, Thébault H, Thouvenin B, Touratier F, Tronczynski J, Ulses C, Van Wambeke F, Vantrepotte V, Vaz S, Verney R (2011) Marine ecosystems’ responses to climatic and anthropogenic forcings in the Mediterranean. Prog Oceanogr 91:97–166

    Article  Google Scholar 

  • Thingstad TF (2005) Simulating the response to phosphate additions in the oligotrophic eastern Mediterranean using an idealized four-member microbial food web model. Deep-Sea Res II Top Stud Oceanogr 52:3074–3089

    Article  Google Scholar 

  • Thingstad TF, Skjoldal EF, Bohne RA (1993) Phosphorus cycling and algal–bacterial competition in Sandsfjord, Western Norway. Mar Ecol Progr Ser 99:239–259

    Article  Google Scholar 

  • Tusseau M-H, Lancelot C, Martin J-M, Tassin B (1997) 1D coupled physical–biological model of the north-western Mediterranean Sea. Deep Sea Res II 44(3–4):851–880

    Article  Google Scholar 

  • Vichi M, Pinardi N, Masina S (2007) A generalized model of pelagic biogeochemistry for the global ocean ecosystem. Part I: theory. J Mar Syst 64(1–4):89–109. doi:10.1016/j.jmarsys.2006.03.006

    Article  Google Scholar 

  • Vidussi F, Claustre H, Manca BB, Luchetta A, Marty JC (2001) Phytoplankton pigment distribution in relation to upper thermocline circulation in the eastern Mediterranean Sea during winter. J Geophys Res 106(19):939–956

    Google Scholar 

  • Vries I, Duin RMN, Peeters JCH, Los FJ, Bokhorst M, Laane RWPM (1998) Patterns and trends in nutrients and phytoplankton in Dutch coastal waters: comparison of time-series analysis, ecological model simulation, and mesocosm experiments. ICES J Mar Sci 55:620–634

    Article  Google Scholar 

Download references

Acknowledgments

The present research is part of the project COSTAS (“Trophic contaminants in the system: phytoplankton, zooplankton, anchovy, sardine”), funded by the French ANR/CES and IFREMER. One of the objectives of COSTAS was related to the model’s ability to replicate space-temporal dynamics of different functional groups of plankton and associated trophic fluxes. Part of this research is also a contribution to the Labex OT-Med (no. ANR-11-LABX-0061) funded by the French Government “Investissements d’Avenir” program of the French National Research Agency (ANR) through the A*MIDEX project (no ANR-11-IDEX-0001-02). We thank our anonymous reviewers for their helpful comments that allowed us to improve the manuscript.

Author information

Authors and Affiliations

  1. Aix-Marseille Université, Université de Toulon, CNRS/INSU, IRD, MIO, UM 110, 13288, Marseille, Cedex 09, France

    Elena Alekseenko, Boris Espinasse, François Carlotti, Bernard Queguiner & Melika Baklouti

  2. Aix-Marseille Université, Université de Toulon, CNRS/INSU, IRD, MIO, UM 110, 83957, La Garde Cedex, France

    Elena Alekseenko, Boris Espinasse, François Carlotti, Bernard Queguiner & Melika Baklouti

  3. Université Lille 1 - Sciences et Technologies (USTL), UMR 8187 LOG, Laboratoire d’Océanologie et de Géosciences, 28 Avenue Foch, F-62930, Wimereux, France

    Virginie Raybaud

  4. CNRS, UMR 8187 LOG, Laboratoire d’Océanologie et de Géosciences, 28 Avenue Foch, 62930, Wimereux, France

    Virginie Raybaud

  5. IFREMER, Centre de Brest, Plouzané, France

    Bénédicte Thouvenin & Pierre Garreau

Authors
  1. Elena Alekseenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Virginie Raybaud
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Boris Espinasse
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. François Carlotti
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Bernard Queguiner
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Bénédicte Thouvenin
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Pierre Garreau
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Melika Baklouti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elena Alekseenko.

Additional information

Responsible Editor: Martin Verlaan

This article is part of the Topical Collection on the 16th biennial workshop of the Joint Numerical Sea Modelling Group (JONSMOD) in Brest, France 21-23 May 2012

Appendices

Appendix A. Equations of the biogeochemical model

Mesozooplankton (adults).

$$ \frac{ dZ}{ dt}=\underset{\mathrm{growth}}{\underbrace{f_z^{\mu}\cdot Z}}-\underset{\mathrm{natural}\;\mathrm{mortality}}{\underbrace{f_z^m\cdot Z}}-\underset{\begin{array}{l}\mathrm{grazing}\;\mathrm{by}\;\\ {}\mathrm{higher}\kern0.36em \mathrm{trophic}\;\mathrm{levels}\end{array}}{\underbrace{f_z^{mq}\cdot {Z}^2}} $$
(1)
$$ \begin{array}{l}\frac{d{Z}_C}{ dt}=\underset{\mathrm{grazing}\;\mathrm{on}\kern0.48em \mathrm{CIL},\mathrm{HNF}\mathrm{and}\;\mathrm{PHYL}}{\underbrace{\left(1-{\in}_{sf}\right)\left({f}_z^{g_{\mathrm{CIL}}}\cdot {Q}_C^{\mathrm{CIL}}+{f}_z^{g_{\mathrm{HNF}}}\cdot {Q}_C^{\mathrm{HNF}}+{f}_z^{g_{\mathrm{PHYL}}}\cdot {Q}_C^{\mathrm{PHYL}}\right)\cdot {h}_Z^{Q_C}\cdot Z}}-\underset{\mathrm{resp}\mathrm{iration}}{\underbrace{f_z^{\mathrm{resp}}\cdot {Z}_C}}\hfill \\ {}-\underset{\mathrm{natural}\ \mathrm{mortality}}{\underbrace{f_z^m\cdot {Z}_C}}-\underset{\begin{array}{l}\mathrm{grazing}\;\mathrm{by}\;\\ {}\mathrm{high}.\mathrm{troph}.\kern0.36em \mathrm{lev}.\end{array}}{\underbrace{f_z^{mq}\cdot {Z}^2\cdot {Q}_C^Z}}+\underset{\begin{array}{l}\mathrm{grazing}\kern0.48em \mathrm{during}\kern0.36em \mathrm{juvenile}\\ {}\mathrm{stages}\kern0.36em \mathrm{on}\kern0.36em \mathrm{CIL},\mathrm{HNF}\kern0.36em \mathrm{and}\kern0.36em \mathrm{POM}\end{array}}{\underbrace{f_Z^{gjuv}\cdot Z}}\hfill \end{array} $$
(2)

Microzooplankton.

$$ \frac{ dCIL}{ dt}=\underset{\mathrm{growth}}{\underbrace{f_{\mathrm{CIL}}^{\mu}\cdot \mathrm{CIL}}}-\underset{\mathrm{natural}\;\mathrm{mortality}}{\underbrace{f_{\mathrm{CIL}}^m\cdot CIL}}-\underset{\mathrm{grazing}\;\mathrm{by}\kern0.36em \mathrm{meso}-\mathrm{Z}}{\underbrace{f_z^{g_{\mathrm{CIL}}}\cdot Z}}-\underset{\begin{array}{l}\mathrm{grazing}\kern0.24em \mathrm{by}\kern0.24em \mathrm{meso}-\mathrm{Z}\\ {}\mathrm{during}\kern0.36em \mathrm{juvenile}\kern0.24em \mathrm{stages}\end{array}}{\underbrace{\alpha_1\cdot {f}_Z^{\mathrm{gjuv}}\cdot \frac{Z}{Q_C^{\mathrm{CIL}}}}} $$
(3)
$$ \begin{array}{l}\frac{d{\mathrm{CIL}}_C}{ dt}=\underset{\mathrm{grazing}\;\mathrm{on}\;\mathrm{HNFand}\;\mathrm{PHYS}}{\underbrace{\left({f}_{\mathrm{CIL}}^{g_{\mathrm{HNF}}}\cdot {Q}_C^{\mathrm{HNF}}+{f}_{\mathrm{CIL}}^{g_{\mathrm{PHYS}}}\cdot {Q}_C^{\mathrm{PHYS}}\right)\cdot {h}_{\mathrm{CIL}}^{Q_C}\cdot CI L}}-\underset{\mathrm{resp}\mathrm{iration}}{\underbrace{f_{\mathrm{CIL}}^{\mathrm{resp}}\cdot CI{L}_C}}\hfill \\ {}-\underset{\mathrm{natural}\;\mathrm{mortality}}{\underbrace{f_{\mathrm{CIL}}^m\cdot {\mathrm{CIL}}_C}}-\underset{\mathrm{grazing}\;\mathrm{by}\;\mathrm{meso}-\mathrm{Z}}{\underbrace{f_z^{g_{\mathrm{CIL}}}\cdot {Q}_C^{\mathrm{CIL}}\cdot Z}}-\underset{\begin{array}{l}\mathrm{grazing}\kern0.24em \mathrm{by}\kern0.24em \mathrm{meso}-\mathrm{Z}\\ {}\mathrm{during}\kern0.36em \mathrm{juvenile}\kern0.24em \mathrm{stages}\end{array}}{\underbrace{\alpha_1\cdot {f}_Z^{\mathrm{gjuv}}\cdot Z}}\hfill \end{array} $$
(4)
$$ \begin{array}{l}\frac{d{\mathrm{CIL}}_N}{ dt}=\underset{\mathrm{grazing}\;\mathrm{on}\;\mathrm{HNFand}\;\mathrm{PHYS}}{\underbrace{\left({f}_{\mathrm{CIL}}^{g_{\mathrm{HNF}}}\cdot {Q}_N^{\mathrm{HNF}}+{f}_{\mathrm{CIL}}^{g_{\mathrm{PHYS}}}\cdot {Q}_N^{\mathrm{PHYS}}\right)\cdot {h}_{\mathrm{CIL}}^{Q_N}\cdot \mathrm{CIL}}}-\underset{\mathrm{natural}\;\mathrm{mortality}}{\underbrace{f_{\mathrm{CIL}}^m\cdot {\mathrm{CIL}}_N}}\hfill \\ {}-\underset{\mathrm{grazing}\;\mathrm{by}\;\mathrm{meso}-\mathrm{Z}}{\underbrace{f_z^{g_{\mathrm{CIL}}}\cdot {Q}_N^{\mathrm{CIL}}\cdot Z}}-\underset{\begin{array}{l}\mathrm{grazing}\kern0.24em \mathrm{by}\kern0.24em \mathrm{meso}-\mathrm{Z}\\ {}\mathrm{during}\kern0.36em \mathrm{juvenile}\kern0.24em \mathrm{stages}\end{array}}{\underbrace{\alpha_1\cdot {f}_Z^{\mathrm{gjuv}}\cdot Z\cdot \frac{Q_N^{CIL}}{Q_C^{CIL}}}}\hfill \end{array} $$
(5)
$$ \begin{array}{l}\frac{d{\mathrm{CIL}}_P}{ dt}=\underset{\mathrm{grazing}\;\mathrm{on}\;\mathrm{HNFand}\;\mathrm{PHYS}}{\underbrace{\left({f}_{\mathrm{CIL}}^{g_{\mathrm{HNF}}}\cdot {Q}_P^{\mathrm{HNF}}+{f}_{\mathrm{CIL}}^{g_{\mathrm{PHYS}}}\cdot {Q}_P^{\mathrm{PHYS}}\right)\cdot {h}_{\mathrm{CIL}}^{Q_P}\cdot \mathrm{CIL}}}-\underset{\mathrm{natural}\;\mathrm{mortality}}{\underbrace{f_{\mathrm{CIL}}^m\cdot {\mathrm{CIL}}_P}}\hfill \\ {}-\underset{\mathrm{grazing}\;\mathrm{by}\;\mathrm{meso}-\mathrm{Z}}{\underbrace{f_z^{g_{\mathrm{CIL}}}\cdot {Q}_P^{\mathrm{CIL}}\cdot Z}}-\underset{\begin{array}{l}\mathrm{grazing}\kern0.24em \mathrm{by}\kern0.24em \mathrm{meso}-\mathrm{Z}\\ {}\mathrm{during}\kern0.36em \mathrm{juvenile}\kern0.24em \mathrm{stages}\end{array}}{\underbrace{\alpha_1\cdot {f}_Z^{\mathrm{gjuv}}\cdot Z\cdot \frac{Q_P^{\mathrm{CIL}}}{Q_C^{\mathrm{CIL}}}}}\hfill \end{array} $$
(6)

Nanozooplankton.

$$ \begin{array}{l}\frac{ dHNF}{ dt}=\underset{\mathrm{growth}}{\underbrace{f_{\mathrm{HNF}}^{\mu}\cdot \mathrm{HNF}}}-\underset{\mathrm{natural}\kern0.36em \mathrm{mortality}}{\underbrace{f_{\mathrm{HNF}}^m\cdot \mathrm{HNF}}}-\underset{\mathrm{grazing}\;\mathrm{by}\;\mathrm{meso}-\mathrm{Z}}{\underbrace{f_z^{g_{\mathrm{HNF}}}\cdot Z}}\hfill \\ {}-\underset{\mathrm{grazing}\;\mathrm{by}\kern0.36em \mathrm{CIL}}{\underbrace{f_{\mathrm{CIL}}^{g_{\mathrm{HNF}}}\cdot \mathrm{CIL}}}-\underset{\begin{array}{l}\mathrm{grazing}\kern0.24em \mathrm{by}\kern0.24em \mathrm{meso}-\mathrm{Z}\\ {}\mathrm{during}\kern0.36em \mathrm{juvenile}\kern0.24em \mathrm{stages}\end{array}}{\underbrace{\alpha_2\cdot {f}_Z^{\mathrm{gjuv}}\cdot \frac{Z}{Q_C^{\mathrm{HNF}}}}}\hfill \end{array} $$
(7)
$$ \begin{array}{l}\frac{d{\mathrm{HNF}}_C}{ dt}=\underset{\mathrm{grazing}\;\mathrm{on}\kern0.48em \mathrm{PHYS}\;\mathrm{and}\kern0.36em \mathrm{BAC}}{\underbrace{\left({f}_{\mathrm{HNF}}^{g_{\mathrm{PHYS}}}\cdot {Q}_C^{\mathrm{PHYS}}+{f}_{\mathrm{HNF}}^{g_{\mathrm{BAC}}}\cdot {Q}_C^{\mathrm{BAC}}\right)\cdot {h}_{\mathrm{HNF}}^{Q_C}\cdot \mathrm{HNF}}}-\underset{\mathrm{resp}\mathrm{iration}}{\underbrace{f_{\mathrm{HNF}}^{\mathrm{resp}}\cdot {\mathrm{HNF}}_C}}-\underset{\mathrm{natural}\kern0.36em \mathrm{mortality}}{\underbrace{f_{\mathrm{HNF}}^m\cdot {\mathrm{HNF}}_C}}\hfill \\ {}-\underset{\mathrm{grazing}\;\mathrm{by}\kern0.36em \mathrm{meso}-\mathrm{Z}}{\underbrace{f_z^{g_{\mathrm{HNF}}}\cdot {Q}_C^{\mathrm{HNF}}\cdot Z}}-\underset{\mathrm{grazing}\;\mathrm{by}\kern0.36em \mathrm{CIL}}{\underbrace{f_{\mathrm{CIL}}^{g_{\mathrm{HNF}}}\cdot {Q}_C^{\mathrm{HNF}}\cdot \mathrm{CIL}}}-\underset{\begin{array}{l}\mathrm{grazing}\kern0.24em \mathrm{by}\kern0.24em \mathrm{meso}-\mathrm{Z}\\ {}\mathrm{during}\kern0.36em \mathrm{juvenile}\kern0.36em \mathrm{stages}\end{array}}{\underbrace{\alpha_2\cdot {f}_Z^{\mathrm{gjuv}}\cdot Z}}\hfill \end{array} $$
(8)
$$ \begin{array}{l}\frac{d{\mathrm{HNF}}_N}{ dt}=\underset{\mathrm{grazing}\kern0.36em \mathrm{on}\kern0.36em \mathrm{PHYS}\;\mathrm{and}\kern0.36em \mathrm{BAC}}{\underbrace{\left({f}_{\mathrm{HNF}}^{g_{\mathrm{PHYS}}}\cdot {Q}_N^{\mathrm{PHYS}}+{f}_{\mathrm{HNF}}^{g_{\mathrm{BAC}}}\cdot {Q}_N^{\mathrm{BAC}}\right)\cdot {h}_{\mathrm{HNF}}^{Q_N}\cdot \mathrm{HNF}}}-\underset{\mathrm{natural}\kern0.48em \mathrm{mortality}}{\underbrace{f_{\mathrm{HNF}}^m\cdot {\mathrm{HNF}}_N}}\hfill \\ {}-\underset{\mathrm{grazing}\kern0.36em \mathrm{by}\kern0.36em \mathrm{meso}-\mathrm{Z}\kern0.36em \mathrm{and}\kern0.36em \mathrm{CIL}}{\underbrace{\left({f}_z^{g_{\mathrm{HNF}}}\cdot Z+{f}_{\mathrm{CIL}}^{g_{\mathrm{HNF}}}\cdot \mathrm{CIL}\right)\cdot {Q}_N^{\mathrm{HNF}}}}-\underset{\begin{array}{l}\mathrm{grazing}\kern0.24em \mathrm{by}\kern0.24em \mathrm{meso}-\mathrm{Z}\\ {}\mathrm{during}\kern0.36em \mathrm{juvenile}\kern0.24em \mathrm{stages}\end{array}}{\underbrace{\alpha_2\cdot {f}_Z^{\mathrm{gjuv}}\cdot \frac{Q_N^{\mathrm{HNF}}}{Q_C^{\mathrm{HNF}}}}}\hfill \end{array} $$
(9)
$$ \begin{array}{l}\frac{d{\mathrm{HNF}}_P}{ dt}=\underset{\mathrm{grazing}\;\mathrm{on}\;\mathrm{PHYS}\;\mathrm{and}\;\mathrm{BAC}}{\underbrace{\left({f}_{\mathrm{HNF}}^{g_{\mathrm{PHYS}}}\cdot {Q}_P^{\mathrm{PHYS}}+{f}_{\mathrm{HNF}}^{g_{\mathrm{BAC}}}\cdot {Q}_P^{\mathrm{BAC}}\right)\cdot {h}_{\mathrm{HNF}}^{Q_P}\cdot \mathrm{HNF}}}-\underset{\mathrm{natural}\;\mathrm{mortality}}{\underbrace{f_{\mathrm{HNF}}^m\cdot {\mathrm{HNF}}_P}}\hfill \\ {}-\underset{\mathrm{grazing}\;\mathrm{by}\;\mathrm{meso}-\mathrm{Z}\;\mathrm{and}\kern0.48em \mathrm{CIL}}{\underbrace{\left({f}_z^{g_{\mathrm{HNF}}}\cdot Z+{f}_{\mathrm{CIL}}^{g_{\mathrm{HNF}}}\cdot \mathrm{CIL}\right)\cdot {Q}_P^{\mathrm{HNF}}}}-\underset{\begin{array}{l}\mathrm{grazing}\kern0.24em \mathrm{by}\kern0.24em \mathrm{meso}-\mathrm{Z}\\ {}\mathrm{during}\kern0.36em \mathrm{juvenile}\kern0.24em \mathrm{stages}\end{array}}{\underbrace{\alpha_2\cdot {f}_Z^{\mathrm{gjuv}}\cdot \frac{Q_P^{\mathrm{HNF}}}{Q_C^{\mathrm{HNF}}}}}\hfill \end{array} $$
(10)

Phytoplankton.

$$ \frac{ dPHYL}{ dt}=\underset{\mathrm{growth}}{\underbrace{f_{\mathrm{PHYL}}^{\mu}\cdot \mathrm{PHYL}}}-\underset{\mathrm{natural}\kern0.48em \mathrm{mortality}}{\underbrace{f_{\mathrm{PHYL}}^m\cdot \mathrm{PHYL}}}-\underset{\mathrm{grazing}\;\mathrm{by}\kern0.48em \mathrm{meso}-\mathrm{Z}}{\underbrace{f_z^{g_{\mathrm{PHYL}}}\cdot Z}}-\underset{\begin{array}{l}\mathrm{grazing}\;\mathrm{by}\kern0.48em \mathrm{higher}\\ {}\mathrm{troph}.\kern0.48em \mathrm{levels}\end{array}}{\underbrace{f_{\mathrm{PHYL}}^{mq}\cdot {\mathrm{PHYL}}^2}} $$
(11)
$$ \begin{array}{l}\frac{d{\mathrm{PHYL}}_C}{ dt}=\underset{ primary\; production}{\underbrace{f_{nr}^{\mathrm{PP}}\cdot {h}_{\mathrm{PHYL}}^{Q_C}\cdot \mathrm{PHYL}}}-\underset{\mathrm{resp}\mathrm{iration}}{\underbrace{f_{\mathrm{PHYL}}^{\mathrm{resp}}\cdot {\mathrm{PHYL}}_C}}-\underset{\mathrm{natural}\;\mathrm{mortality}}{\underbrace{f_{\mathrm{PHYL}}^m\cdot {\mathrm{PHYL}}_C}}\hfill \\ {}-\underset{\mathrm{grazing}\;\mathrm{by}\;\mathrm{meso}-\mathrm{Z}}{\underbrace{f_z^{g_{\mathrm{PHYL}}}\cdot {Q}_C^{\mathrm{PHYL}}\cdot Z}}-\underset{\begin{array}{l}\mathrm{grazing}\;\mathrm{by}\kern0.48em \mathrm{higher}\\ {}\mathrm{troph}.\kern0.48em \mathrm{levels}\end{array}}{\underbrace{f_{\mathrm{PHYL}}^{mq}\cdot {\mathrm{PHYL}}^2\cdot {Q}_C^{\mathrm{PHYL}}}}\hfill \end{array} $$
(12)
$$ \begin{array}{l}\frac{d{\mathrm{PHYL}}_N}{ dt}=\underset{\mathrm{primary}\;\mathrm{production}}{\underbrace{\left({f}_{\mathrm{PHYL}}^{{\mathrm{upt}}_N}+{f}_{\mathrm{PHYL}}^{{\mathrm{upt}}_{\mathrm{DON}}}\right)\cdot {h}_{\mathrm{PHYL}}^{Q_N}\cdot \mathrm{PHYL}}}-\underset{\mathrm{natural}\kern0.48em \mathrm{mortality}}{\underbrace{f_{\mathrm{PHYL}}^m\cdot {\mathrm{PHYL}}_N}}-\underset{\mathrm{grazing}\;\mathrm{by}\kern0.48em \mathrm{meso}-\mathrm{Z}}{\underbrace{f_z^{g_{\mathrm{PHYL}}}\cdot {Q}_N^{\mathrm{PHYL}}\cdot Z}}\hfill \\ {}-\underset{\begin{array}{l}\mathrm{grazing}\;\mathrm{by}\kern0.48em \mathrm{higher}\\ {}\mathrm{troph}.\kern0.48em \mathrm{levels}\end{array}}{\underbrace{f_{\mathrm{PHYL}}^{mq}\cdot {\mathrm{PHYL}}^2\cdot {Q}_N^{\mathrm{PHYL}}}}\hfill \end{array} $$
(13)
$$ \begin{array}{l}\frac{d{\mathrm{P}\mathrm{HYL}}_P}{ dt}=\underset{\mathrm{primary}\;\mathrm{production}}{\underbrace{\left({f}_{\mathrm{P}\mathrm{HYL}}^{{\mathrm{upt}}_{\mathrm{P}}}+{f}_{\mathrm{P}\mathrm{HYL}}^{{\mathrm{upt}}_{\mathrm{DOP}}}\right)\cdot {h}_{\mathrm{P}\mathrm{HYL}}^{Q_P}\cdot \mathrm{PHYL}}}-\underset{\mathrm{natural}\kern0.48em \mathrm{mortality}}{\underbrace{f_{\mathrm{P}\mathrm{HYL}}^m\cdot {\mathrm{P}\mathrm{HYL}}_P}}-\underset{\mathrm{grazing}\;\mathrm{by}\kern0.48em \mathrm{meso}-\mathrm{Z}}{\underbrace{f_z^{g_{\mathrm{P}\mathrm{HYL}}}\cdot {Q}_P^{\mathrm{P}\mathrm{HYL}}\cdot Z}}\hfill \\ {}-\underset{\begin{array}{l}\mathrm{grazing}\;\mathrm{by}\kern0.48em \mathrm{higher}\\ {}\mathrm{troph}.\kern0.48em \mathrm{levels}\end{array}}{\underbrace{f_{\mathrm{P}\mathrm{HYL}}^{mq}\cdot {\mathrm{P}\mathrm{HYL}}^2\cdot {Q}_P^{\mathrm{P}\mathrm{HYL}}}}\hfill \end{array} $$
(14)
$$ \begin{array}{l}\frac{d{\mathrm{PHYL}}_{\mathrm{chl}}}{ dt}=\underset{\mathrm{chl}\mathrm{orophyll}\kern0.48em \mathrm{synthesis}}{\underbrace{f^{PChl}\cdot {\mathrm{PHYL}}_N}}-\underset{\mathrm{natural}\kern0.48em \mathrm{mortality}}{\underbrace{f_{\mathrm{PHYL}}^m\cdot {\mathrm{PHYL}}_{chl}}}-\underset{\mathrm{grazing}\;\mathrm{by}\kern0.48em \mathrm{meso}-\mathrm{Z}}{\underbrace{f_z^{g_{\mathrm{PHYL}}}\cdot {Q}_{chl}^{\mathrm{PHYL}}\cdot Z}}\hfill \\ {}-\underset{\begin{array}{l}\mathrm{grazing}\;\mathrm{by}\kern0.48em \mathrm{higher}\\ {}\mathrm{troph}.\kern0.48em \mathrm{levels}\end{array}}{\underbrace{f_{\mathrm{PHYL}}^{mq}\cdot \mathrm{PHYL}\cdot {\mathrm{PHYL}}_{\mathrm{chl}}}}\hfill \end{array} $$
(15)
$$ \frac{ dPHYS}{ dt}=\underset{\mathrm{growth}}{\underbrace{f_{\mathrm{PHYS}}^{\mu}\cdot \mathrm{PHYS}}}-\underset{\mathrm{natural}\kern0.48em \mathrm{motrality}}{\underbrace{f_{\mathrm{PHYS}}^m\cdot \mathrm{PHYS}}}-\underset{\mathrm{grazing}\;\mathrm{by}\kern0.48em \mathrm{CIL}}{\underbrace{f_{\mathrm{CIL}}^{g_{\mathrm{PHYS}}}\cdot \mathrm{CIL}}}-\underset{\mathrm{grazing}\;\mathrm{by}\kern0.36em \mathrm{HNF}}{\underbrace{f_{\mathrm{HNF}}^{g_{\mathrm{PHYS}}}\cdot \mathrm{HNF}}} $$
(16)
$$ \begin{array}{l}\frac{d{\mathrm{PHYS}}_C}{ dt}=\underset{\mathrm{primary}\;\mathrm{production}}{\underbrace{f_{nr}^{\mathrm{PP}}\cdot {h}_{\mathrm{PHYS}}^{Q_C}\cdot \mathrm{PHYS}}}-\underset{\mathrm{resp}\mathrm{iration}}{\underbrace{f_{\mathrm{PHYS}}^{\mathrm{resp}}\cdot {\mathrm{PHYS}}_C}}-\underset{\mathrm{natural}\kern0.48em \mathrm{mortality}}{\underbrace{f_{\mathrm{PHYS}}^m\cdot {\mathrm{PHYS}}_C}}\hfill \\ {}-\underset{\mathrm{grazing}\kern0.48em \mathrm{by}\kern0.48em \mathrm{CIL}\kern0.48em \mathrm{and}\kern0.48em \mathrm{NHF}}{\underbrace{\left({f}_{\mathrm{CIL}}^{g_{\mathrm{PHYS}}}\cdot \mathrm{CIL}+{f}_{\mathrm{HNF}}^{g_{\mathrm{PHYS}}}\cdot \mathrm{HNF}\right)\cdot {Q}_C^{\mathrm{PHYS}}}}\hfill \end{array} $$
(17)
$$ \begin{array}{l}\frac{d{\mathrm{PHYS}}_N}{ dt}=\underset{\mathrm{net}\kern0.36em \mathrm{uptake}\kern0.36em \mathrm{of}\kern0.36em {\mathrm{N}\mathrm{O}}_3\mathrm{and}\ {\mathrm{N}\mathrm{H}}_4\kern0.36em \mathrm{and}\kern0.36em \mathrm{DON}}{\underbrace{\left({f}_{\mathrm{PHYS}}^{{\mathrm{upt}}_{\mathrm{N}}}+{f}_{\mathrm{PHYS}}^{{\mathrm{upt}}_{\mathrm{DON}}}\right)\cdot {h}_{\mathrm{PHYS}}^{Q_N}\cdot \mathrm{PHYS}}}-\underset{\mathrm{natural}\kern0.48em \mathrm{mortality}}{\underbrace{f_{\mathrm{PHYS}}^m\cdot {\mathrm{PHYS}}_N}}\hfill \\ {}-\underset{\mathrm{grazing}\kern0.48em \mathrm{by}\kern0.48em \mathrm{CIL}}{\underbrace{f_{\mathrm{CIL}}^{g_{\mathrm{PHYS}}}\cdot {Q}_N^{\mathrm{PHYS}}\cdot \mathrm{CIL}}}-\underset{\mathrm{grazing}\kern0.48em \mathrm{by}\kern0.48em \mathrm{H}\mathrm{NF}\;}{\underbrace{f_{\mathrm{HNF}}^{g_{\mathrm{PHYS}}}\cdot {Q}_N^{\mathrm{PHYS}}\cdot \mathrm{HNF}}}\hfill \end{array} $$
(18)
$$ \begin{array}{l}\frac{d{\mathrm{P}\mathrm{HYS}}_P}{ dt}=\underset{\mathrm{net}\kern0.36em \mathrm{uptake}\kern0.36em \mathrm{of}\kern0.36em {\mathrm{P}\mathrm{O}}_4\kern0.36em \mathrm{and}\kern0.36em \mathrm{DOP}}{\underbrace{\left({f}_{\mathrm{P}\mathrm{HYS}}^{{\mathrm{upt}}_{\mathrm{P}}}+{f}_{\mathrm{P}\mathrm{HYS}}^{{\mathrm{upt}}_{\mathrm{DOP}}}\right)\cdot {h}_{\mathrm{P}\mathrm{HYS}}^{Q_P}\cdot \mathrm{PHYS}}}-\underset{\mathrm{natural}\kern0.48em \mathrm{mortality}}{\underbrace{f_{\mathrm{P}\mathrm{HYS}}^m\cdot {\mathrm{P}\mathrm{HYS}}_P}}\hfill \\ {}-\underset{\mathrm{grazing}\kern0.36em \mathrm{by}\kern0.48em \mathrm{CIL}}{\underbrace{f_{\mathrm{CIL}}^{g_{\mathrm{P}\mathrm{HYS}}}\cdot {Q}_P^{\mathrm{P}\mathrm{HYS}}\cdot \mathrm{CIL}}}-\underset{\mathrm{grazing}\kern0.36em \mathrm{by}\kern0.48em \mathrm{HNF}\;}{\underbrace{f_{\mathrm{HNF}}^{g_{\mathrm{P}\mathrm{HYS}}}\cdot {Q}_P^{\mathrm{P}\mathrm{HYS}}\cdot \mathrm{HNF}}}\hfill \end{array} $$
(19)
$$ \begin{array}{l}\frac{d{\mathrm{PHYS}}_{\mathrm{chl}}}{ dt}=\underset{\mathrm{chl}\mathrm{orophyll}\kern0.48em \mathrm{synthesis}}{\underbrace{f^{PChl}\cdot {\mathrm{PHYS}}_N}}-\underset{\mathrm{natural}\kern0.48em \mathrm{mortality}}{\underbrace{f_{\mathrm{PHYS}}^m\cdot {\mathrm{PHYS}}_{\mathrm{chl}}}}-\underset{\mathrm{grazing}\kern0.36em \mathrm{by}\kern0.48em \mathrm{CIL}}{\underbrace{f_{\mathrm{CIL}}^{g_{\mathrm{PHYS}}}\cdot {Q}_{\mathrm{chl}}^{\mathrm{PHYS}}\cdot CIL}}\hfill \\ {}-\underset{\mathrm{grazing}\kern0.36em \mathrm{by}\kern0.48em \mathrm{HNF}}{\underbrace{f_{\mathrm{HNF}}^{g_{\mathrm{PHYS}}}\cdot {Q}_{chl}^{\mathrm{PHYS}}\cdot \mathrm{HNF}}}\hfill \end{array} $$
(20)

Bacteria.

$$ \frac{ dBAC}{ dt}=\underset{\mathrm{growth}}{\underbrace{f_{\mathrm{BAC}}^{\mu}\cdot \mathrm{BAC}}}-\underset{\mathrm{natural}\kern0.48em \mathrm{mortality}}{\underbrace{f_{\mathrm{BAC}}^m\cdot \mathrm{BAC}}}-\underset{\mathrm{grazing}\kern0.36em \mathrm{by}\kern0.48em \mathrm{HNF}}{\underbrace{f_{\mathrm{HNF}}^{g_{\mathrm{BAC}}}\cdot HNF}} $$
(21)
$$ \begin{array}{l}\frac{d{\mathrm{BAC}}_C}{ dt}=\underset{\mathrm{net}\kern0.36em \mathrm{uptake}\kern0.48em \mathrm{of}\kern0.36em \mathrm{LDOC}\kern0.36em \mathrm{and}\kern0.48em \mathrm{SLDOC}}{\underbrace{\left({f}_{\mathrm{BAC}}^{{\mathrm{upt}}_{\mathrm{LDOC}}}+{f}_{\mathrm{BAC}}^{up{t}_{\mathrm{SLDOC}}}\right)\cdot {h}_{\mathrm{BAC}}^{Q_C}\cdot \mathrm{BAC}}}-\underset{\mathrm{resp}\mathrm{iration}}{\underbrace{f_{\mathrm{BAC}}^{\mathrm{resp}}\cdot {\mathrm{BAC}}_C}}-\underset{\mathrm{natural}\kern0.6em \mathrm{mortality}}{\underbrace{f_{\mathrm{BAC}}^m\cdot {\mathrm{BAC}}_C}}\hfill \\ {}-\underset{\mathrm{grazing}\kern0.36em \mathrm{by}\kern0.48em \mathrm{HNF}}{\underbrace{f_{\mathrm{HNF}}^{g_{\mathrm{BAC}}}\cdot \mathrm{HNF}\cdot {Q}_C^{\mathrm{BAC}}}}\hfill \end{array} $$
(22)
$$ \frac{d{\mathrm{BAC}}_N}{ dt}=\underset{\mathrm{net}\kern0.36em \mathrm{uptake}\kern0.18em \mathrm{of}\kern0.18em \mathrm{N}}{\underbrace{\left({f}_{\mathrm{BAC}}^{{\mathrm{upt}}_{\mathrm{N}}}+{f}_{\mathrm{BAC}}^{{\mathrm{upt}}_{\mathrm{DON}}}\right)\cdot {h}_{\mathrm{BAC}}^{Q_N}\cdot \mathrm{BAC}}}-\underset{\mathrm{natural}\kern0.48em \mathrm{mortality}}{\underbrace{f_{\mathrm{BAC}}^m\cdot {\mathrm{BAC}}_N}}-\underset{\mathrm{grazing}\kern0.36em \mathrm{by}\kern0.48em \mathrm{N}\mathrm{HF}}{\underbrace{f_{\mathrm{HNF}}^{g_{\mathrm{BAC}}}\cdot \mathrm{HNF}\cdot {Q}_N^{\mathrm{BAC}}}} $$
(23)
$$ \frac{d{\mathrm{BAC}}_P}{ dt}=\underset{\mathrm{net}\kern0.28em \mathrm{uptake}\kern0.18em \mathrm{of}\kern0.18em \mathrm{P}}{\underbrace{\left({f}_{\mathrm{BAC}}^{{\mathrm{upt}}_{\mathrm{P}}}+{f}_{\mathrm{BAC}}^{{\mathrm{upt}}_{\mathrm{DOP}}}\right)\cdot {h}_{\mathrm{BAC}}^{Q_P}\cdot \mathrm{BAC}}}-\underset{\mathrm{natural}\kern0.48em \mathrm{mortality}}{\underbrace{f_{\mathrm{BAC}}^m\cdot {\mathrm{BAC}}_P}}-\underset{\mathrm{grazing}\kern0.36em \mathrm{by}\kern0.18em \mathrm{NHF}}{\underbrace{f_{\mathrm{HNF}}^{g_{\mathrm{BAC}}}\cdot \mathrm{HNF}\cdot {Q}_P^{\mathrm{BAC}}}} $$
(24)

Dissolved organic carbon material.

$$ \begin{array}{l}\frac{ dLDOC}{ dt}=-\underset{\mathrm{gross}\kern0.26em \mathrm{uptake}\kern0.18em \mathrm{by}\kern0.18em \mathrm{BAC}}{\underbrace{f_{\mathrm{BAC}}^{{\mathrm{upt}}_{\mathrm{LDOC}}}\cdot \mathrm{BAC}}}+\underset{\mathrm{BAC}\kern0.26em \mathrm{natural}\kern0.28em \mathrm{mortality}}{\underbrace{f_{\mathrm{BAC}}^m\cdot {\mathrm{BAC}}_C}}+\underset{\mathrm{PHYS}\kern0.36em \mathrm{natural}\kern0.48em \mathrm{mortality}}{\underbrace{f_{\mathrm{PHYS}}^m\cdot {\mathrm{PHYS}}_C}}\hfill \\ {}+\underset{\mathrm{HNF}\kern0.28em \mathrm{natural}\kern0.26em \mathrm{mortality}}{\underbrace{f_{\mathrm{HNF}}^m\cdot {\mathrm{HNF}}_C}}+\underset{\mathrm{POC}\;\mathrm{mineralization}}{\underbrace{f_{\mathrm{BAC}}^{\mathrm{rem}}\cdot {\mathrm{BAC}}_C}}\hfill \end{array} $$
(25)
$$ \begin{array}{l}\frac{ dSLDOC}{ dt}=-\underset{\mathrm{net}\kern0.28em \mathrm{uptake}\kern0.28em \mathrm{by}\kern0.28em \mathrm{BAC}}{\underbrace{f_{BAC}^{{\mathrm{upt}}_{\mathrm{SLDOC}}}\cdot {h}_{\mathrm{BAC}}^{Q_C}\cdot \mathrm{BAC}}}+\underset{\mathrm{exudation}\kern0.28em \mathrm{by}\kern0.28em \mathrm{BAC}}{\underbrace{f_{\mathrm{BAC}}^{{\mathrm{upt}}_{\mathrm{SLDOC}}}\cdot \left(1-{h}_{\mathrm{BAC}}^{Q_C}\right)\cdot \mathrm{BAC}}}+\underset{\mathrm{exudation}\kern0.28em \mathrm{by}\kern0.28em \mathrm{PHYL}}{\underbrace{f_{nr}^{\mathrm{PP}}\cdot \left(1-{h}_{\mathrm{PHYL}}^{Q_C}\right)\cdot \mathrm{PHYL}}}+\underset{\mathrm{exudation}\kern0.28em \mathrm{by}\kern0.4em \mathrm{PHYS}}{\underbrace{f_{nr}^{\mathrm{PP}}\cdot \left(1-{h}_{\mathrm{PHYS}}^{Q_C}\right)\cdot \mathrm{PHYS}}}+\\ {}+\underset{\mathrm{DOC}\kern0.26em \mathrm{release}\kern0.3em \mathrm{by}\kern0.28em \mathrm{meso}-\mathrm{Z}}{\underbrace{\varepsilon \left(1-{\in}_{sf}\right)\left({f}_Z^{g_{\mathrm{CIL}}}\cdot {Q}_C^{\mathrm{CIL}}+{f}_Z^{g_{\mathrm{HNF}}}\cdot {Q}_C^{\mathrm{HNF}}+{f}_Z^{g_{\mathrm{PHYL}}}\cdot {Q}_C^{\mathrm{PHYL}}\right)\cdot \left(1-{h}_Z^{Q_C}\right)\cdot Z}}+\underset{\mathrm{DOC}\kern0.28em \mathrm{release}\kern0.28em \mathrm{by}\kern0.28em \mathrm{CIL}}{\underbrace{\left({f}_{\mathrm{CIL}}^{g_{\mathrm{HNF}}}\cdot {Q}_C^{\mathrm{HNF}}+{f}_Z^{g_{\mathrm{PHYS}}}\cdot {Q}_C^{\mathrm{PHYS}}\right)\cdot \left(1-{h}_{\mathrm{CIL}}^{Q_C}\right)\cdot \mathrm{CIL}}}+\hfill \\ {}+\underset{\mathrm{DOC}\kern0.28em \mathrm{release}\kern0.28em \mathrm{by}\kern0.28em \mathrm{HNF}}{\underbrace{\left({f}_{\mathrm{HNF}}^{g_{\mathrm{PHYS}}}\cdot {Q}_C^{\mathrm{PHYS}}+{f}_{\mathrm{HNF}}^{g_{\mathrm{BAC}}}\cdot {Q}_C^{\mathrm{BAC}}\right)\cdot \left(1-{h}_{\mathrm{HNF}}^{Q_C}\right)\cdot \mathrm{HNF}}}\end{array} $$
(26)
$$ \begin{array}{l}\frac{ dDON}{ dt}=-\underset{\mathrm{gross}\kern0.26em \mathrm{uptake}\kern0.28em \mathrm{by}\kern0.248em \mathrm{BAC}}{\underbrace{f_{\mathrm{BAC}}^{{\mathrm{upt}}_{\mathrm{DON}}}\cdot \mathrm{BAC}}}+\underset{\mathrm{mineralization}\kern0.28em \mathrm{by}\kern0.28em \mathrm{BAC}}{\underbrace{f_{\mathrm{BAC}}^{\mathrm{rem}}\cdot BA{C}_N}}-\underset{\mathrm{net}\kern0.26em \mathrm{uptake}\kern0.26em \mathrm{of}\kern0.236em \mathrm{DON}\kern0.26em \mathrm{by}\kern0.26em \mathrm{PHYS}}{\underbrace{f_{\mathrm{PHYS}}^{{\mathrm{upt}}_{\mathrm{DON}}}\cdot {h}_{Q_N}^{\mathrm{PHYS}}\cdot \mathrm{PHYS}}}+\underset{\mathrm{BAC}\;\mathrm{mortality}}{\underbrace{f_{\mathrm{BAC}}^m\cdot {\mathrm{BAC}}_N}}+\underset{\mathrm{PHYS}\;\mathrm{mortality}}{\underbrace{f_{\mathrm{PHYS}}^m\cdot {\mathrm{PHYS}}_N}}+\underset{\mathrm{HNF}\;\mathrm{mortality}}{\underbrace{f_{\mathrm{HNF}}^m\cdot {\mathrm{HNF}}_N}}+\\ {}+\underset{\mathrm{exudation}\kern0.28em \mathrm{by}\kern0.28em \mathrm{PHYL}\kern0.28em \mathrm{and}\kern0.28em \mathrm{PHYS}}{\underbrace{\gamma \cdot \left({f}_{\mathrm{PHYL}}^{{\mathrm{upt}}_N}\cdot \left(1-{h}_{\mathrm{PHYL}}^{Q_N}\right)\cdot \mathrm{PHYL}+{f}_{\mathrm{PHYS}}^{{\mathrm{upt}}_N}\cdot \left(1-{h}_{\mathrm{PHYS}}^{Q_N}\right)\cdot \mathrm{PHYS}\right)}}\end{array} $$
(27)
$$ \begin{array}{l}\frac{ dDOP}{ dt}=-\underset{\mathrm{upt}\mathrm{ake}\kern0.28em \mathrm{by}\kern0.28em \mathrm{BAC}}{\underbrace{f_{\mathrm{BAC}}^{{\mathrm{upt}}_{\mathrm{DOP}}}\cdot \mathrm{BAC}}}+\underset{\mathrm{mineralization}\kern0.28em \mathrm{by}\kern0.28em \mathrm{BAC}}{\underbrace{f_{\mathrm{BAC}}^{\mathrm{rem}}\cdot {\mathrm{BAC}}_P}}-\underset{\mathrm{net}\kern0.36em \mathrm{uptake}\kern0.26em \mathrm{of}\kern0.26em \mathrm{DOP}\kern0.26em \mathrm{by}\kern0.26em \mathrm{PHYS}}{\underbrace{f_{\mathrm{PHYS}}^{{\mathrm{upt}}_{\mathrm{DOP}}}\cdot {h}_{Q_P}^{\mathrm{PHYS}}\cdot \mathrm{PHYS}}}+\underset{\mathrm{BAC}\kern0.28em \mathrm{mortality}}{\underbrace{f_{\mathrm{BAC}}^m\cdot {\mathrm{BAC}}_P}}+\underset{\mathrm{PHYS}\kern0.28em \mathrm{mortality}}{\underbrace{f_{\mathrm{PHYS}}^m\cdot {\mathrm{PHYS}}_P}}+\underset{\mathrm{HNF}\kern0.28em \mathrm{mortality}}{\underbrace{f_{\mathrm{HNF}}^m\cdot {\mathrm{HNF}}_P}}+\hfill \\ {}+\underset{\mathrm{exudation}\kern0.28em \mathrm{by}\kern0.28em \mathrm{PHYL}\kern0.28em \mathrm{and}\kern0.28em \mathrm{PHYS}}{\underbrace{\gamma \cdot \left({f}_{\mathrm{PHYL}}^{{\mathrm{upt}}_{{\mathrm{PO}}_4}}\cdot \left(1-{h}_{\mathrm{PHYL}}^{Q_P}\right)\cdot \mathrm{PHYL}+{f}_{\mathrm{PHYS}}^{{\mathrm{upt}}_{{\mathrm{PO}}_4}}\cdot \left(1-{h}_{\mathrm{PHYS}}^{Q_P}\right)\cdot \mathrm{PHYS}\right)}}\end{array} $$
(28)

Detrial material.

$$ \begin{array}{l}\frac{ dPOC}{ dt}=\underset{\mathrm{meso}-\mathrm{Z}\;\mathrm{mortality}}{\underbrace{f_Z^m\cdot {Z}_C}}-\underset{\begin{array}{l}\mathrm{meso}-\mathrm{Z}\;\mathrm{grazing}\;\mathrm{by}\;\\ {}\mathrm{higher}\kern0.48em \mathrm{trophic}\kern0.28em \mathrm{levels}\end{array}}{\underbrace{f_Z^{mq}\cdot {Q}_C^Z\cdot {Z}^2}}+\underset{\mathrm{CIL}\kern0.28em \mathrm{mortality}}{\underbrace{f_{CIL}^m\cdot CI{L}_C}}+\underset{\mathrm{PHYL}\kern0.28em \mathrm{mortality}}{\underbrace{f_{PHYL}^m\cdot PHY{L}_C}}-\underset{\mathrm{remineralization}}{\underbrace{f^{rem}\cdot BA{C}_C}}-\underset{\begin{array}{l}\mathrm{grazing}\kern0.26em \mathrm{during}\\ {}\mathrm{juvenile}\kern0.26em \mathrm{stages}\end{array}}{\underbrace{\alpha_3\cdot {f}_Z^{\mathrm{gjuv}}\cdot Z}}\hfill \\ {}+\underset{\mathrm{sloppy}\kern0.26em \mathrm{feeding}}{\underbrace{\in_{sf}\cdot \left({f}_Z^{g_{\mathrm{CIL}}}\cdot {Q}_C^{\mathrm{CIL}}+{f}_Z^{g_{\mathrm{HNF}}}\cdot {Q}_C^{\mathrm{HNF}}+{f}_Z^{g_{\mathrm{PHYL}}}\cdot {Q}_C^{\mathrm{PHYL}}\right)\cdot Z}}+\underset{\mathrm{fecal}\kern0.36em \mathrm{pellets}}{\underbrace{\left(1-\varepsilon \right)\left(1-{\in}_{sf}\right)\left({f}_Z^{g_{\mathrm{CIL}}}\cdot {Q}_C^{\mathrm{CIL}}+{f}_Z^{g_{\mathrm{HNF}}}\cdot {Q}_C^{\mathrm{HNF}}+{f}_Z^{g_{\mathrm{PHYL}}}\cdot {Q}_C^{\mathrm{PHYL}}\right)\left(1-{h}_Z^{Q_C}\right)\cdot Z}}\end{array} $$
(29)
$$ \begin{array}{l}\frac{ dPON}{ dt}=\underset{\mathrm{meso}-\mathrm{Z}\;\mathrm{mortality}}{\underbrace{f_Z^m\cdot {Z}_N}}+\underset{\begin{array}{l}\mathrm{meso}-\mathrm{Z}\kern0.26em \mathrm{grazing}\kern0.26em \mathrm{by}\;\\ {}\mathrm{higher}\kern0.28em \mathrm{trophic}\kern0.28em \mathrm{levels}\end{array}}{\underbrace{f_Z^{\mathrm{mq}}\cdot {Q}_N^Z\cdot {Z}^2}}+\underset{\mathrm{CIL}\kern0.28em \mathrm{mortality}}{\underbrace{f_{\mathrm{CIL}}^m\cdot {\mathrm{CIL}}_N}}+\underset{\mathrm{PHYL}\kern0.28em \mathrm{mortality}}{\underbrace{f_{\mathrm{PHYL}}^m\cdot {\mathrm{PHYL}}_N}}-\underset{\mathrm{rem}\mathrm{ineralization}}{\underbrace{f^{\mathrm{rem}}\cdot {\mathrm{BAC}}_N}}+\underset{\begin{array}{l}\mathrm{grazing}\kern0.26em \mathrm{by}\kern0.26em \mathrm{meso}\hbox{--} \mathrm{Z}\\ {}\mathrm{during}\kern0.26em \mathrm{juvenile}\kern0.26em \mathrm{stages}\end{array}}{\underbrace{\alpha_1\cdot {f}_Z^{\mathrm{gjuv}}\cdot Z\cdot \frac{Q_N^{\mathrm{CIL}}}{Q_C^{\mathrm{CIL}}}}}\hfill \\ {}+\underset{\begin{array}{l}\mathrm{grazing}\kern0.26em \mathrm{by}\kern0.26em \mathrm{meso}-\mathrm{Z}\\ {}\mathrm{during}\kern0.26em \mathrm{juvenile}\kern0.26em \mathrm{stages}\end{array}}{\underbrace{\alpha_2\cdot {f}_Z^{\mathrm{gjuv}}\cdot Z\cdot \frac{Q_N^{\mathrm{HNF}}}{Q_C^{\mathrm{HNF}}}}}+\underset{\mathrm{sloppy}\kern0.36em \mathrm{feeding}}{\underbrace{\in_{sf}\cdot \left({f}_Z^{g_{\mathrm{CIL}}}\cdot {Q}_N^{\mathrm{CIL}}+{f}_Z^{g_{\mathrm{HNF}}}\cdot {Q}_N^{\mathrm{HNF}}+{f}_Z^{g_{\mathrm{PHYL}}}\cdot {Q}_N^{\mathrm{PHYL}}\right)\cdot Z}}+\underset{\mathrm{implicit}\kern0.26em \mathrm{grazing}\kern0.26em \mathrm{by}\kern0.26em \mathrm{meso}-\mathrm{Z}}{\underbrace{\beta \cdot \left({f}_Z^{g_{\mathrm{PHYL}}}\cdot {Q}_N^{\mathrm{PHYL}}+{f}_Z^{g_{\mathrm{CIL}}}\cdot {Q}_N^{\mathrm{CIL}}+{f}_Z^{g_{\mathrm{HNF}}}\cdot {Q}_N^{\mathrm{HNF}}\right)\cdot Z}}\end{array} $$
(30)
$$ \begin{array}{l}\frac{ dPOP}{ dt}=\underset{\mathrm{meso}-\mathrm{Z}\;\mathrm{mortality}}{\underbrace{f_Z^m\cdot {Z}_P}}-\underset{\begin{array}{l}\mathrm{meso}-\mathrm{Z}\kern0.24em \mathrm{grazing}\kern0.26em \mathrm{by}\\ {}\;\mathrm{higher}\kern0.28em \mathrm{trophic}\kern0.28em \mathrm{levels}\end{array}}{\underbrace{f_Z^{\mathrm{mq}}\cdot {Q}_P^Z\cdot {Z}^2}}+\underset{\mathrm{CIL}\kern0.28em \mathrm{mortality}}{\underbrace{f_{\mathrm{CIL}}^m\cdot {\mathrm{CIL}}_P}}+\underset{\mathrm{PHYL}\kern0.26em \mathrm{mortality}}{\underbrace{f_{\mathrm{PHYL}}^m\cdot {\mathrm{PHYL}}_P}}-\underset{\mathrm{rem}\mathrm{ineralization}}{\underbrace{f^{\mathrm{rem}}\cdot {\mathrm{BAC}}_P}}+\underset{\begin{array}{l}\mathrm{grazing}\kern0.26em \mathrm{by}\kern0.26em \mathrm{meso}-\mathrm{Z}\\ {}\mathrm{during}\kern0.26em \mathrm{juvenile}\kern0.26em \mathrm{stages}\end{array}}{\underbrace{\alpha_1\cdot {f}_Z^{\mathrm{gjuv}}\cdot Z\cdot \frac{Q_P^{\mathrm{CIL}}}{Q_C^{\mathrm{CIL}}}}}+\underset{\begin{array}{l}\mathrm{grazing}\kern0.26em \mathrm{by}\kern0.26em \mathrm{meso}-\mathrm{Z}\\ {}\mathrm{during}\kern0.26em \mathrm{juvenile}\kern0.26em \mathrm{stages}\end{array}}{\underbrace{\alpha_2\cdot {f}_Z^{\mathrm{gjuv}}\cdot Z\cdot \frac{Q_P^{\mathrm{HNF}}}{Q_C^{\mathrm{HNF}}}}}\hfill \\ {}+\underset{\mathrm{sloppy}\kern0.26em \mathrm{feeding}}{\underbrace{\in_{\mathrm{sf}}\cdot \left({f}_Z^{g_{\mathrm{CIL}}}\cdot {Q}_P^{\mathrm{CIL}}+{f}_Z^{g_{\mathrm{HNF}}}\cdot {Q}_P^{\mathrm{HNF}}+{f}_Z^{g_{\mathrm{PHYL}}}\cdot {Q}_P^{\mathrm{PHYL}}\right)\cdot Z}}+\underset{\mathrm{implicit}\kern0.26em \mathrm{grazing}\kern0.26em \mathrm{by}\kern0.26em \mathrm{meso}-\mathrm{Z}}{\underbrace{\beta \cdot \left({f}_Z^{g_{\mathrm{PHYL}}}\cdot {Q}_P^{\mathrm{PHYL}}+{f}_Z^{g_{\mathrm{CIL}}}\cdot {Q}_P^{\mathrm{CIL}}+{f}_Z^{g_{\mathrm{HNF}}}\cdot {Q}_P^{\mathrm{HNF}}\right)\cdot Z}}\end{array} $$
(31)

Nutrients.

$$ \begin{array}{l}\frac{d{\mathrm{NH}}_4}{ dt}=-\underset{\mathrm{gross}\kern0.28em \mathrm{uptake}\kern0.28em \mathrm{by}\kern0.28em \mathrm{PHYL}}{\underbrace{f_{\mathrm{PHYL}}^{{\mathrm{upt}}_{{\mathrm{NH}}_4}}\cdot \mathrm{PHYL}}}-\underset{\mathrm{gross}\kern0.28em \mathrm{uptake}\kern0.28em \mathrm{by}\kern0.28em \mathrm{PHYS}}{\underbrace{f_{\mathrm{PHYS}}^{{\mathrm{upt}}_{{\mathrm{NH}}_4}}\cdot \mathrm{PHYS}}}-\underset{\mathrm{net}\kern0.26em \mathrm{uptake}\kern0.28em \mathrm{by}\kern0.28em \mathrm{BAC}}{\underbrace{f_{\mathrm{BAC}}^{{\mathrm{upt}}_{{\mathrm{NH}}_4}}\cdot \mathrm{BAC}\cdot {h}_{\mathrm{BAC}}^{Q_N}}}+\underset{\mathrm{mineralization}\kern0.28em \mathrm{by}\kern0.28em \mathrm{BAC}}{\underbrace{f_{\mathrm{BAC}}^{{\mathrm{upt}}_{\mathrm{DON}}}\cdot \left(1-{h}_{\mathrm{BAC}}^{Q_N}\right)\cdot \mathrm{BAC}}}\hfill \\ {}+\underset{\mathrm{exudation}\kern0.28em \mathrm{by}\kern0.28em \mathrm{PHYL}}{\underbrace{\left(1-\gamma \right)\cdot {f}_{\mathrm{PHYL}}^{{\mathrm{upt}}_N}\cdot \left(1-{h}_{\mathrm{PHYL}}^{Q_N}\right)\cdot \mathrm{PHYL}}}+\underset{\mathrm{exudation}\kern0.28em \mathrm{by}\kern0.28em \mathrm{PHYS}}{\underbrace{\left(1-\gamma \right)\cdot {f}_{\mathrm{PHYS}}^{up{t}_N}\cdot \left(1-{h}_{\mathrm{PHYS}}^{Q_N}\right)\cdot \mathrm{PHYS}}}+\underset{\mathrm{excretion}\kern0.28em \mathrm{by}\kern0.28em \mathrm{CIL}}{\underbrace{\left({f}_{\mathrm{CIL}}^{g_{HNF}}\cdot {Q}_N^{\mathrm{HNF}}+{f}_{\mathrm{CIL}}^{g_{\mathrm{PHYS}}}\cdot {Q}_N^{\mathrm{PHYS}}\right)\cdot \mathrm{CIL}\cdot \left(1-{h}_{\mathrm{CIL}}^{Q_N}\right)}}+\\ {}+\underset{\mathrm{excretion}\kern0.28em \mathrm{by}\kern0.28em \mathrm{HNF}}{\underbrace{\left({f}_{\mathrm{HNF}}^{g_{\mathrm{PHYS}}}\cdot {Q}_N^{\mathrm{PHYS}}+{f}_{\mathrm{HNF}}^{g_{BAC}}\cdot {Q}_N^{\mathrm{BAC}}\right)\cdot \mathrm{HNF}\cdot \left(1-{h}_{\mathrm{HNF}}^{Q_N}\right)}}-\underset{\mathrm{nitrif}\mathrm{ication}}{\underbrace{f_{{\mathrm{NH}}_4}^{\mathrm{nitrif}}\cdot {\mathrm{NH}}_4}}+\underset{\mathrm{grazing}\kern0.26em \mathrm{by}\kern0.26em \mathrm{meso}-\mathrm{Z}}{\underbrace{\left(1-\beta \right)\cdot \left({f}_Z^{g_{\mathrm{PHYL}}}\cdot {Q}_N^{\mathrm{PHYL}}+{f}_Z^{g_{\mathrm{CIL}}}\cdot {Q}_N^{\mathrm{CIL}}+{f}_Z^{g_{\mathrm{HNF}}}\cdot {Q}_N^{\mathrm{HNF}}\right)\cdot Z}}\end{array} $$
(32)
$$ \frac{d{\mathrm{NO}}_3}{ dt}=-\underset{\mathrm{gross}\kern0.28em \mathrm{uptake}\kern0.26em \mathrm{by}\kern0.28em \mathrm{PHYL}}{\underbrace{f_{\mathrm{PHYL}}^{{\mathrm{upt}}_{{\mathrm{NO}}_3}}\cdot \mathrm{PHYL}}}-\underset{\mathrm{gross}\kern0.28em \mathrm{uptake}\kern0.28em \mathrm{by}\kern0.26em \mathrm{PHYS}}{\underbrace{f_{\mathrm{PHYS}}^{{\mathrm{upt}}_{{\mathrm{NO}}_3}}\cdot \mathrm{PHYS}}}-\underset{\mathrm{net}\kern0.26em \mathrm{uptake}\kern0.24em \mathrm{by}\kern0.26em \mathrm{PHYL}}{\underbrace{f_{\mathrm{BAC}}^{{\mathrm{upt}}_{{\mathrm{NO}}_3}}\cdot \mathrm{BAC}\cdot {h}_{\mathrm{BAC}}^{Q_N}}}+\underset{\mathrm{nitrif}\mathrm{ication}}{\underbrace{f_{{\mathrm{NH}}_4}^{\mathrm{nitrif}}\cdot {\mathrm{NH}}_4}} $$
(33)
$$ \begin{array}{l}\frac{d{\mathrm{PO}}_4}{ dt}=-\underset{\mathrm{gross}\kern0.28em \mathrm{uptake}\kern0.28em \mathrm{by}\kern0.28em \mathrm{PHYL}}{\underbrace{f_{\mathrm{PHYL}}^{{\mathrm{upt}}_{{\mathrm{PO}}_4}}\cdot \mathrm{PHYL}}}-\underset{\mathrm{gross}\kern0.28em \mathrm{uptake}\kern0.28em \mathrm{by}\kern0.28em \mathrm{PHYS}}{\underbrace{f_{\mathrm{PHYS}}^{{\mathrm{upt}}_{{\mathrm{PO}}_4}}\cdot \mathrm{PHYS}}}-\underset{\mathrm{net}\kern0.28em \mathrm{uptake}\kern0.28em \mathrm{by}\kern0.28em \mathrm{PHYL}}{\underbrace{f_{\mathrm{BAC}}^{{\mathrm{upt}}_{{\mathrm{PO}}_4}}\cdot \mathrm{BAC}\cdot {h}_{\mathrm{BAC}}^{Q_P}}}+\underset{\mathrm{exudation}\kern0.28em \mathrm{by}\kern0.28em \mathrm{PHYL}}{\underbrace{\left(1-\gamma \right)\cdot {f}_{\mathrm{PHYL}}^{{\mathrm{upt}}_{{\mathrm{PO}}_4}}\cdot \left(1-{h}_{\mathrm{PHYL}}^{Q_P}\right)\cdot \mathrm{PHYL}}}\hfill \\ {}+\underset{\mathrm{exudation}\kern0.28em \mathrm{by}\kern0.28em \mathrm{PHYS}}{\underbrace{\left(1-\gamma \right)\cdot {f}_{\mathrm{PHYS}}^{{\mathrm{upt}}_{{\mathrm{PO}}_4}}\cdot \left(1-{h}_{\mathrm{PHYS}}^{Q_P}\right)\cdot \mathrm{PHYS}}}+\underset{\mathrm{mineralization}\kern0.28em \mathrm{by}\kern0.28em \mathrm{BAC}}{\underbrace{f_{\mathrm{BAC}}^{{\mathrm{upt}}_{\mathrm{DOP}}}\cdot \left(1-{h}_{\mathrm{BAC}}^{Q_P}\right)\cdot \mathrm{BAC}}}+\underset{\mathrm{excretion}\kern0.28em \mathrm{by}\kern0.28em \mathrm{CIL}}{\underbrace{\left({f}_{\mathrm{CIL}}^{g_{\mathrm{HNF}}}\cdot {Q}_P^{\mathrm{HNF}}+{f}_{\mathrm{CIL}}^{g_{\mathrm{PHYS}}}\cdot {Q}_P^{\mathrm{PHYS}}\right)\cdot \left(1-{h}_{\mathrm{CIL}}^{Q_P}\right)\cdot \mathrm{CIL}}}\\ {}+\underset{\mathrm{excretion}\kern0.28em \mathrm{by}\kern0.26em \mathrm{HNF}}{\underbrace{\left({f}_{\mathrm{HNF}}^{g_{\mathrm{PHYS}}}\cdot {Q}_P^{\mathrm{PHYS}}+{f}_{\mathrm{HNF}}^{g_{\mathrm{BAC}}}\cdot {Q}_P^{\mathrm{BAC}}\right)\cdot \left(1-{h}_{\mathrm{HNF}}^{Q_P}\right)\cdot \mathrm{HNF}}}+\underset{\mathrm{grazing}\kern0.26em \mathrm{by}\kern0.26em \mathrm{meso}-\mathrm{Z}}{\underbrace{\left(1-\beta \right)\cdot \left({f}_Z^{g_{\mathrm{PHYL}}}\cdot {Q}_P^{\mathrm{PHYL}}+{f}_Z^{g_{\mathrm{CIL}}}\cdot {Q}_P^{\mathrm{CIL}}+{f}_Z^{g_{\mathrm{HNF}}}\cdot {Q}_P^{\mathrm{HNF}}\right)}}\end{array} $$
(34)

Mortality

The natural mortality is represented through a first-order kinetic law:

$$ {f}_m={k}_m, $$
(35)

where k m in s − 1 is the specific mortality rate. The quadratic mortality function is used as a closure term for an implicit representation of the grazing of mesozooplankton by higher trophic levels:

$$ {f}_{mq}={k}_{mq}, $$
(36)

where  k mq in ind−1  s − 1 is the specific quadratic mortality rate.

Intracellular quota and growth

As usually done in flexible stoichiometry models, the model is based on the assumption that for each organism, intracellular X content (where X stands for C, N, P) must be comprised within a minimum (Q min X )  and maximum (Q max X )  value. Q min X can be interpreted as the amount of element X used in cellular structure and machinery and everything else can be seen as storage for future growth. Since Droop and his work on vitamin B12 (Droop 1968), this concept has been widely used, especially to simulate change in organism’s stoichiometry (Klausmeier et al. 2008). We therefore used the classical Droop formulation (Eq. 37) combined with the Leibig’s law of the minimum to describe the specific growth rate f μ:

$$ {f}^{\mu }=\overline{\mu}\cdot \underset{X}{ min}\left[1-\frac{Q_X^{min}}{Q_X}\right]. $$
(37)

In this formulation, Q X represents the actual cell (or individual) content for a given element X, and \( \overline{\mu} \)—the maximum theoretical growth rate of the organism.

Grazing

Grazing is represented by a Holling II formulation (Holling 1965) revised by Kooijman (2000)

$$ {f}^{g_{\mathrm{PREY}}}=\frac{I_m\left[\mathrm{PREY}\right]}{\frac{I_m}{F}+\left[\mathrm{PREY}\right]} $$
(38)

and generalized to several (here n PREY ) preys as follows (Gentleman et al. 2003):

$$ {f}^{g_{{\mathrm{PREY}}_i}}=\frac{\phi_i{F}_i\left[{\mathrm{PREY}}_i\right]}{1+{\displaystyle \sum_{k=1}^{n_{\mathrm{PREY}}}\frac{\phi_k{F}_k}{I_m^k}\left[{\mathrm{PREY}}_k\right]}}, $$
(39)

where I m is the maximum ingestion rate of the grazer, F either the clearance (for filter feeding organisms) or attack rate, ϕ i the preference of predator for the i th prey, and [PREY i ] the prey concentration of the ith prey in cell per liter.

Uptake of nutrients

To describe the gross uptake rate of nutrients, the Michaelis–Menten relationship was used (Eq. 42).

$$ {f}^{{\mathrm{upt}}_X}={V}_X^{max}\cdot \frac{\left[X\right]}{\left[X\right]+{K}_X} $$
(40)

[X] is the concentration for element X is the nutrient taken up by osmotrophs. V max X and K X are assumed constant in the model and represent the uptake parameters one would obtain from nutrient starved organisms (e.g., maximum potential uptake rate). Total inorganic N gross uptake rates by phytoplankton and bacteria are also used in the model equations:

$$ {f}_{\mathrm{PHY}}^{{\mathrm{upt}}_N}={f}_{\mathrm{PHY}}^{{\mathrm{upt}}_{{\mathrm{NO}}_3}}+{f}_{\mathrm{PHY}}^{{\mathrm{upt}}_{{\mathrm{NH}}_4}} $$
(41)
$$ {f}_{\mathrm{BAC}}^{{\mathrm{upt}}_N}={f}_{\mathrm{BAC}}^{{\mathrm{upt}}_{{\mathrm{NO}}_3}}+{f}_{\mathrm{BAC}}^{{\mathrm{upt}}_{{\mathrm{NH}}_4}} $$
(42)

Note that \( {f}^{{\mathrm{upt}}_{{\mathrm{NH}}_4}} \) is given by Eq. (45)

In addition, the model considers that ammonium inhibits nitrate uptake by phytoplankton and nitrate and DON uptake by bacteria and that phosphate inhibits DOP uptake by bacteria. This writes:

$$ {f}^{{\mathrm{upt}}_X}={V}_X^{max}\cdot \frac{\left[X\right]}{\left[X\right]+{K}_X}\cdot \frac{1}{1+\frac{\left[\mathrm{INH}\right]}{K_{\mathrm{INH}}}}, $$
(43)

where [INH] is the inhibitor concentration (NH4 or PO4) and K INH the inhibition constant (Frost and Franzen 1992).

Apart from this classical use of inhibition functions, we also added in the model a new function that acts as compensation. Otherwise, the inhibition as it is classically used in models amounts to reduce the total N (or P) uptaken by organisms for a given concentration of nutrients. We therefore deemed it necessary to allow organisms to uptake extra NH4 (PO4) to compensate the amounts of N and P that have not been uptaken as NO3 or DON (DOP) because of inhibition. The corresponding function writes:

$$ {f}^{{\mathrm{cpin}}_X}={V}_{{}_X}^{\max}\cdot \frac{\left[X\right]}{\left[X\right]+{K}_X}\cdot \frac{1}{1+\frac{K_{\mathrm{inh}}^X}{\left[\mathrm{INH}\right]}} $$
(44)

where X = NO3, DON or DOP.

The uptake rates of ammonium and phosphate by Y = PHYL, PHYS or BAC for a given organism among phytoplankton or bacteria are therefore given by:

$$ {f}^{up{t}_{NH4}}={V}_{NH4}^{\max}\cdot \frac{\left[{\mathrm{NH}}_4\right]}{\left[{\mathrm{NH}}_4\right]+{K}_{{\mathrm{NH}}_4}}+\left({V}_{{\mathrm{NO}}_3}^{\max}\cdot \frac{\left[{\mathrm{NO}}_3\right]}{\left[{\mathrm{NO}}_3\right]+{K}_{{\mathrm{NO}}_3}}+{V}_{\mathrm{DON}}^{\max}\cdot \frac{\left[\mathrm{DON}\right]}{\left[\mathrm{DON}\right]+{K}_{{\mathrm{NO}}_3}}\right)\cdot \frac{1}{1+\frac{K_{inh}^{P{O}_4}}{\left[P{O}_4\right]}} $$
(45)
$$ {f}^{{\mathrm{upt}}_{{\mathrm{PO}}_4}}={V}_{{\mathrm{PO}}_4}^{\max}\cdot \frac{\left[{\mathrm{PO}}_4\right]}{\left[{\mathrm{PO}}_4\right]+{K}_{{\mathrm{PO}}_4}}+{V}_{\mathrm{DOP}}^{\max}\cdot \frac{\left[\mathrm{DOP}\right]}{\left[\mathrm{DOP}\right]+{K}_{\mathrm{DOP}}}\cdot \frac{1}{1+\frac{K_{\mathrm{inh}}^{{\mathrm{PO}}_4}}{\left[{\mathrm{PO}}_4\right]}} $$
(46)

Photosynthesis and chlorophyll production

The model uses Han (2002) mechanistic formulation for photosynthesis (see Baklouti et al. 2006a for more details).

$$ {f}_{\mathrm{nr}}^{\mathrm{PP}}=\frac{\phi_{max}^C\cdot {\overline{a}}^{*}\cdot E\cdot \theta }{1+{\sigma}_{\mathrm{PSII}}\cdot E\cdot \tau +\left(\raisebox{1ex}{${k}_d^H$}\!\left/ \!\raisebox{-1ex}{${k}_r$}\right.\right)\cdot {\left({\sigma}_{\mathrm{PSII}}\cdot E\right)}^2\cdot \tau}\cdot {Q}_C^{\mathrm{PHY}} $$
(47)

Chlorophyll production is regulated by the N/Chl ratio of phytoplankton (θ N). The formulation used is extensively described in Baklouti et al. (2006a) and its adaptation to the model including cell densities in Mauriac et al. (2011).

$$ {f}^{\mathrm{PChl}}={\rho}_{\mathrm{chl}}\cdot {f}_{\mathrm{PHY}}^{{\mathrm{upt}}_{\mathrm{N}}}\cdot \frac{1-{\theta}_N/{\theta}_m^N}{\left(1-{\theta}_N/{\theta}_m^N\right)+0.05}, $$
(48)

where \( \theta =\frac{{\mathrm{PHY}}_{\mathrm{Chl}}}{{\mathrm{PHY}}_C} \), \( {\theta}^N=\frac{{\mathrm{PHY}}_{\mathrm{Chl}}}{{\mathrm{PHY}}_{\mathrm{N}}} \), \( {f}^{\mathrm{PP}}={f}_{\mathrm{nr}}^{\mathrm{PP}}\cdot {h}_{\mathrm{PHY}}^{Q_C} \) and \( {\rho}_{\mathrm{chl}}={\theta}_m^N\frac{f^{\mathrm{PP}}}{{\overline{a}}^{*}{\phi}_{max}^C\theta E} \).

In Eqs. (47) and (48), ϕ C max represents the maximum quantum yield for carbon fixation, \( {\overline{a}}^{\ast } \), the mean Chl a specific absorption coefficient, E, the irradiance, θ, the chlorophyll to carbon ratio, σ PSII, the PSII cross-section, τ, the electron turnover time, k H d , the PSII damage rate, k r , the PSII repair rate and θ N m the maximum chlorophyll to nitrogen ratio.

Feedback regulation

A feedback regulation from internal cellular status to mediate net primary production, net uptake rate as well as net grazing is in the form of a quota function given by Eq. (49) (Geider et al. 1998) as this is already done in Baklouti et al. (2006a):

$$ {h}^{Q_X}={\left(\frac{Q_X^{max}-{Q}_X}{Q_X^{max}-{Q}_X^{min}}\right)}^{0.06} $$
(49)

In the present version where organisms are represented through biomasses and cellular densities, a dual control is exercised, not only by intracellular quotas but by intracellular ratios. In substance, for the uptake of a given element X, if it happens that the Q X cellular quota is outside the [Q min X ;Q max X ] range, the quota function which is used for the uptake rate regulation is given by Eq. (49).

However, if Q X belongs to the [Q min X ;Q max X ] range, the regulation of the uptake rate is given by the minimum of quota functions similar to that of Eq. (49) in which the intracellular quotas are replaced by intracellular ratios \( {Q}_{X{Y}_i} \) (where Y i represents the biogenic elements apart from X that are handled by the model).

This can be summarized by the following equations:

$$ \mathrm{if}\kern0.5em \left({Q}_X\le {Q}_X^{\min}\right)\kern0.5em \mathrm{or}\kern0.5em \left(Q\ge {Q}_X^{\max}\right)\kern0.5em \mathrm{then} $$

\( {h}^{Q_X} \) is given by Eq. (49)else

$$ {h}_{Q_{X{Y}_i}}=\underset{Y_i}{ \min }{h}_{Q_{X{Y}_i}} $$

where \( {h}_{Q_{{\mathrm{XY}}_i}}=\frac{Q_{{\mathrm{XY}}_i}^{\max }-{Q}_{{\mathrm{XY}}_i}}{Q_{{\mathrm{XY}}_i}^{\max }-{Q}_{{\mathrm{XY}}_i}^{\min }} \)

Finally, the feedback regulation has been described here for the uptake process but the same method is used in the model for the other processes that are regulated through quota functions.

Autotrophic respiration

Several energetic costs associated with phytoplankton activities have been included as in Baklouti et al. (2006a):

$$ {f}_{\mathrm{PHY}}^{\mathrm{resp}}={r}_g{f}^{\mathrm{PP}}+{\displaystyle \sum_{\mathrm{NUT}}{r}_{u_{\mathrm{NUT}}}\cdot {f}^{{\mathrm{upt}}_{\mathrm{NUT}}}},\mathrm{where}\ \mathrm{NUT}\in \left\{{\mathrm{NO}}_3,{\mathrm{NH}}_4,{\mathrm{PO}}_4\right\} $$
(50)

r g and \( {r}_{u_{\mathrm{NUT}}} \) respectively represent the cost associated with growth and net uptake of nutrient NUT (see Table 1 for the units of these parameters).

Table 1 Model’s functions
Full size table

Bacteria respiration

Heterotrophic bacteria respiration rate is based on cost for DOC acquisition:

$$ {f}_{\mathrm{BAC}}^{\mathrm{resp}}=\left(1-{\omega}_1\right)\cdot {f}_{\mathrm{BAC}}^{{\mathrm{upt}}_{\mathrm{LDOC}}}+\left(1-{\omega}_2\right)\cdot {f}_{\mathrm{BAC}}^{{\mathrm{upt}}_{\mathrm{SLDOC}}} $$
(51)

ω 1 and ω 2 respectively refer to the efficiency of LDOC and SLDOC uptake and Eq. (51) conveys the fact that higher energetic costs are associated with the uptake of semi-labile DOC (SLDOC) than labile one (LDOC). In this way, bacteria are subject to two types of carbon limitation, either a limitation by availability (when DOC resource is scarce) or by lability (when DOC acquisition is costly), both cases resulting in a low bacterial growth rate.

Zooplankton respiration

Zooplankton respiration is proportional to the net growth rate through:

$$ {f}_{\mathrm{zoo}}^{\mathrm{resp}}={r}_g\cdot {Q}_C^{min}\cdot {f}^{\mu } $$
(52)

Carbon acquisition by juvenile stages

Before the adult stage, mesozooplankton (copepods) acquire carbon (and other elements but they are not explicitly represented in our model) through grazing. That means that the carbon which is affected to each new individual in the model does not come from the carbon pool of mesozooplankton but rather from the carbon pool of the different preys grazed by mesozoplankton during juvenile stages. This grazing during juvenile stages is implicitly represented in the model by:

$$ {f}_z^{\mathrm{gjuv}}=0.85\cdot {Q}_C^{\min}\cdot {f}_z^{\mu } $$
(53)

and distributed on three possible food, namely ciliates (arbitrarily 30 % of the food), HNF (50 %) and detrital material (20 %).

Appendix B. Model parameters

Most of the parameter values used in the model come from literature or have been derived from relationships that have been established between parameters. Only very few parameters (typically the mortality constants) have been chosen arbitrarily. The relationship (51) conveys the fact that at very low nutrient concentration, nutrient uptake is limited by molecular diffusion and the diffusion (Kiorboe 2008) and the Michaelis–Menten fluxes can be equalized through:

$$ \frac{V_{\max }}{K_s}=4\pi DR $$
(54)

Where D is the molecular diffusion coefficient and R—the mean equivalent disc radius of cells.

Table 2

Table 2 Model parameters for zooplankton. Parameters values have been taken from Perez et al. (1997); Sherr et al. (1999); Christaki et al. (1999) for ciliates, Christaki et al. (1999, 2009) for HNF and Barquero et al. (1998) for copepods
Full size table

Table 3

Table 3 Model parameters for phytoplankton. D NO3, \( {D}_{{\mathrm{NH}}_4} \), \( {D}_{{\mathrm{PO}}_4} \), D DON, D DOP are the diffusion coefficient of NO3, NH4, PO4, DON, and DOP, respectively equal to 1.7 · 10−9, 1.9 · 10−9, 7.5 · 10−10, 3 · 10−10, 3 · 10−10 m2s−1. Parameter values have been taken from Thingstad (2005); Baklouti et al. (2006b); Mauriac et al. (2011) and references herein
Full size table

Table 4

Table 4 Model parameters for heterotrophic bacteria. Parameter values have been taken from Thingstad (2005); Baklouti et al. (2006b); Mauriac et al. (2011)
Full size table

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alekseenko, E., Raybaud, V., Espinasse, B. et al. Seasonal dynamics and stoichiometry of the planktonic community in the NW Mediterranean Sea: a 3D modeling approach. Ocean Dynamics 64, 179–207 (2014). https://doi.org/10.1007/s10236-013-0669-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10236-013-0669-2

Keywords

Search

Navigation