1. SIMPLE COUPLED PHYSICAL-BIOGEOCHEMICAL MODELS OF MARINE ECOSYSTEMS

2. 2 Simple coupled physical-biogeochemical models of marine ecosystems Formulating quantitative mathematical models of conceptual ecosystems MS320: Wilkin 2011-Sep-12 SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

3. 3 Why use mathematical models? Conceptual models often characterize an ecosystem as a set of “boxes” linked by processes Processes e.g. photosynthesis, growth, grazing, and mortality link elements of the … State (“the boxes”) e.g. nutrient concentration, phytoplankton abundance, biomass, dissolved gases, of an ecosystem In the lab, field, or mesocosm, we can observe some of the complexity of an ecosystem and quantify these processes With quantitative rules for linking the boxes, we can attempt to simulate the changes over time of the ecosystem state SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

4. 4 What can we learn? Suppose a model can simulate the spring bloom chlorophyll concentration observed by satellite using: observed light, a climatology of winter nutrients, ocean temperature and mixed layer depth … Then the model rates of uptake of nutrients during the bloom and loss of particulates below the euphotic zone give us quantitative information on net primary production and carbon export – quantities we cannot easily observe directly SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

5. 5 Reality Model Individual plants and animals Many influences from nutrients and trace elements Continuous functions of space and time Varying behavior, choice, chance Unknown or incompletely understood interactions Lump similar individuals into groups –express in terms of biomass and C:N ratio Small number of state variables (one or two limiting nutrients) Discrete spatial points and time intervals Average behavior based on ad hoc assumptions Must parameterize unknowns SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

6. 6 The steps in constructing a model 1)Identify the scientific problem (e.g. seasonal cycle of nutrients and plankton in mid- latitudes; short-term blooms associated with coastal upwelling events; human-induced eutrophication and water quality; global climate change) 2)Determine relevant variables and processes that need to be considered 3)Develop mathematical formulation 4)Numerical implementation, provide forcing, parameters, etc. SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

7. 7 State variables and Processes “NPZD”: model named for and characterized by its state variables State variables are concentrations (in a common “currency”) that depend on space and time Processes link the state variable boxes SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

8. 8 Processes Biological: –Growth –Death –Photosynthesis –Grazing –Bacterial regeneration of nutrients Physical: –Mixing –Transport (by currents from tides, winds …) –Light –Air-sea interaction (winds, heat fluxes, precipitation) SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

9. 9 State variables and Processes Can use Redfield ratio to give e.g. carbon biomass from nitrogen equivalent Carbon-chlorophyll ratio Where is the physics? SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

10. 10 Examples of conceptual ecosystems that have been modeled A model of a food web might be relatively complex –Several nutrients –Different size/species classes of phytoplankton –Different size/species classes of zooplankton –Detritus (multiple size classes) –Predation (predators and their behavior) Multiple trophic levels –Pigments and bio-optical properties Photo-adaptation, self-shading –3 spatial dimensions in the physical environment, diurnal cycle of atmospheric forcing, tides SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

12. Silicic acid – important limiting nutrient in N. Pacific gelatinous zooplankton, euphausids, krill copepods ciliates particulate silicon Fig. 1 – Schematic view of the NEMURO lower trophic level ecosystem model. Solid black arrows indicate nitrogen flows and dashed blue arrows indicate silicon. Dotted black arrows represent the exchange or sinking of the materials between the modeled box below the mixed layer depth. Kishi, M., M. Kashiwai, and others, (2007), NEMURO - a lower trophic level model for the North Pacific marine ecosystem, Ecological Modelling, 202(1-2), 12-25.

13. 13 Fig. 1 – Schematic view of the NEMURO lower trophic level ecosystem model. Solid black arrows indicate nitrogen flows and dashed blue arrows indicate silicon. Dotted black arrows represent the exchange or sinking of the materials between the modeled box below the mixed layer depth. Kishi, M., M. Kashiwai, and others, (2007), NEMURO - a lower trophic level model for the North Pacific marine ecosystem, Ecological Modelling, 202(1-2), 12-25.

14. 14 SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

15. Soetaert K, Middelburg JJ, Herman PMJ, Buis K. 2000. On the coupling of benthic and pelagic bio- geochemical models. Earth-Sci. Rev. 51:173-201

16. Schematic of ROMS “Bio_Fennel” ecosystem model Phytoplankton concentration absorbs light Att(x,z) = AttSW + AttChl*Chlorophyll(x,z,t) SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

17. 17 ROMS fennel.h (carbon off, oxygen off, chl not shown) SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

18. 18 Examples of conceptual ecosystems that have been modeled In simpler models, elements of the state and processes can be combined if time and space scales justify this –e.g. bacterial regeneration can be treated as a flux from zooplankton mortality directly to nutrients A very simple model might be just: N – P – Z –Nutrients –Phytoplankton –Zooplankton … all expressed in terms of equivalent nitrogen concentration SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

19. 19 ROMS fennel.h (carbon off, oxygen off, chl not shown) SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

20. 20 Mathematical formulation Mass conservation –Mass M (kilograms) of e.g. carbon or nitrogen in the system Concentration C n (kg m -3 ) of state variable n is mass per unit volume V Source for one state variable will be a sink for another SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

21. 21 e.g. inputs of nutrients from rivers or sediments e.g. burial in sediments e.g. nutrient uptake by phytoplankton The key to model building is finding appropriate formulations for transfers, and not omitting important state variables Mathematical formulation SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

22. Slope of a continuous function of x is Some calculus SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

23. 23 Which comes from … Example: f = distance x = time df/dx = speed slope SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

24. 24 For example: State variables: Nutrient and Phytoplankton Process: Photosynthetic production of organic matter Large N Small N Michaelis and Menten (1913) v max is maximum growth rate (units are time -1 ) k n is “half-saturation” concentration; at N=k n f(k n )=0.5 SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

25. From Heidi’s lectures Average PP saturates at high PAR PP max 0.5 PP max SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

26. 26 Representative results from 32 Si kinetic experiments measuring the rate of Si uptake as a function of the silicic acid concentration (ambient+added). Four of the 26 multi- concentration experiments are shown, representing the main kinetic responses observed in this study (Southern Ocean). Nelson et al. 2001 Deep-Sea Research Volume 48, Issues 19- 20, 2001, Pages 3973-3995 SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

27. 27 Uptake expressions SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

28. 28 State variables: Nutrient and Phytoplankton Process: Photosynthetic production of organic matter The nitrogen consumed by the phytoplankton for growth must be lost from the Nutrients state variable SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

29. 29 Suppose there are ample nutrients so N is not limiting: then f(N) = 1 Growth of P will be exponential SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

30. 30 Suppose the plankton concentration held constant, and nutrients again are not limiting: f(N) = 1 N will decrease linearly with time as it is consumed to grow P SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

31. 31 Suppose the plankton concentration held constant, but nutrients become limiting: then f(N) = N/k n N will exponentially decay to zero until it is exhausted SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

32. 32 Can the right-hand-side of the P equation be negative? Can the right-hand-side of the N equation be positive? … So we need other processes to complete our model. SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

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36. 36 There are many possible parameterizations for processes: e.g. Zooplankton grazing Ivlev (1945) function Grazing parameter: Iv Zooplankton grazing rates might be parameterized as proportional to Z i.e. g = constant … or if P is small the grazing rate might be less because the Z have to find them or catch them first SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

37. 37 Light Irradiance: I Initial slope of the P-I curve: α SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

38. 38 Coupling to physical processes Advection-diffusion-equation: C is the concentration of any biological state variable advection turbulent mixing Biological dynamics physics SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

39. 39 winter springsummerfall I0I0 SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

40. 40 Simple 1-dimensional vertical model of mixed layer and N-P ecosystem Windows program and inputs files are at: http://marine.rutgers.edu/dmcs/ms320/Phyto1d/ http://marine.rutgers.edu/dmcs/ms320/Phyto1d/ –Run the program called Phyto_1d.exe using the default input files Sharples, J., Investigating the seasonal vertical structure of phytoplankton in shelf seas, Marine Models Online, vol 1, 1999, 3-38. SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

41. 41 winter springsummerfall I0I0 bloom SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

42. 42 winter springsummerfall I0I0 bloomsecondary bloom SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University

43. 43 winter springsummerfall I0I0 bloomsecondary bloom SUMBER: marine.rutgers.edu/.../2013-09-13-Coupled-physical-b...‎Rutgers University