MEECE Summer School on marine ecosystem models Ankara, Sept. 7 2011
Lecture (mostly) based on: W. Fennel and T. Neumann Introduction to the modelling of marine ecosystems Elsevier oceanography series 72
Biogeochemical models Tools to: describe, understand and quantify fluxes of matter trough the whole (or part of the) trophic web. In the “real world” fluxes of matter involve: many, many individuals of different “functional groups” (prducers, consumers.......) In the model: Differences among the individuals are ignored. Role of (say) phytoplanton reduced to a single state variable that carries (for any biogeochemical process) the summatory effect of all the individuals
State variables (and related processes))
Should be: Well defined observable However: Rates observation difficult for several processes (e.g. mortality) therefore process description based on: poorly constrained rates or adhoc reasonable assumptions
Differences with physical models In the “Physical world”: Model equations> mathematical formulations of basic (prime) principles. In the “ecosystem world” Model equations> derived from observations (an empirical or semiempirical process. However.....................
......some broad guiding principles are available: Redfield ratio: (C:N:P= 106:16:1) average molar ratio for the main chemical constituents of living matter. Liebig law: limiting factor for algal growth. Size considerations: “The big fish eats the small fish” Can provide some guidance in defining (conceptually) the model equations but:
no definition/indication about the mathematical formulation needed for modelling.
To proceed: Clearly identify the goal e. g.: Describe the seasonal cycle of phytoplankton: Quantify transfer of inorganic nutrients trough the lower trophic web. Estimate changes of biomass in response to external forcing
then: Determine the state variables and the process that must be included into the model. Achieve a mathematical formulation for the process definition.
STATE VARIABLES Concentrations (or abundances) that can be measured (numerical values with a physical dimension, mass/unit volume). Functions of space (x,y,z) and time (t)
THEIR DYNAMICS Governed by processes that are function of space, time and other state variables. For a generic state variable C:
Process = temporal rate of change =dC/dt=[state var. units]/t
MODEL FUNDAMENTAL CONSTRAINT: Conservation of mass. Model mass (M): Mass of (at least) one of the chemical elements (C, N, P.....) flowing trough the trophic web (the model “exchange currency”). Conservation in a closed system (no exchanges with the “rest of the universe”:
d M= 0 dt Conservation in an open system (exchanges with the “rest of the universe)”:
d M= ext_sources−ext_sinks dt ext_ sources: e.g. “model currency” inputs by river discharge (nutrients) Ext_sinks: e.g. burial of “model currency” into sediments
IMPORTANT !!!!!
d M= 0 dt
Differential equation
Implies that: State variables are treated as a continuous functions in space and time Nutrients: in situ (or average concentrations) Detritus, Phytoplankton, Zooplankton………. Particles(or individual number assumed to be high enough that their concentration behave like a continuous function)
Cn
Concentration of a generic state variable in a volume V
Total mass in the volume
M= ∑ C n V
hence
N
d V C n =ext_sources n −ext_sinks n ±transfersnupper trophic levels. The life cycle should be resolved.