Modelling of Aquatic Ecosystems

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Modelling of Aquatic Ecosystems

• Exercise 6
• 06.05.2009

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Exercise 5 additional constraints

• Calculation of stoichiometric coefficients for
  all substances j of process i with the help of k
  additional constraints
• Example ALG death exercise 5
• constraints list (c ( "C.ALG"
  paramY.ALG.death,
• "C.POMD" 1,
• "C.POMI" 1)
• (-1)YALG,death ((1-fi)YALG,death) 1
  (fiYALG,death)1 0

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Model exercise 6.1
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Model exercise 6.1
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Model exercise 6.1

• State variables
• phosphate (C.HPO4),
• O2 (C.O2),
• ammonium (C.NH4),
• nitrate (C.NO3), nitrite (C.NO2)
• constant values of benthic algae biomass (SALG
  (D.ALG)) and of sedimented organic particles
  (SPOM (D.POM))
• Considered processes
• growth of SALG on HPO4 and NH4 resp. NO3,
• respiration of SALG
• first (NH4 to NO2) and second (NO2 to NO3) step
  of nitrification,
• oxic mineralization of SPOM
• Considered interface fluxes
• oxygen exchange with the atmosphere,
• advection between the three river reaches

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Exercise 6.3 Identifiability

• Change in oxygen concentration due to change in
  oxygen exchange coefficient can be compensated by
  a change in the ALG and POM density
• ? Kinetic parameters of primary production and
  ecosystem respiration (mineralization, etc.) are
  not identifiable from oxygen concentration data
  if oxygen exchange coefficient is unknown

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Exercise 6.4 Simplifying assumptions

• Prismatic river reach, constant friction, wide
  rectangular river bed
• Constant flow velocity v in time and across river
  cross-section
• Constant vertical turbulent diffusion coefficient
  Kz
• Constant lateral diffusion and dispersion
  coefficient ey
• Vertical mixing substance enters the river
  homogeneously spread over the river width,
  lateral dimension and time dependence can be
  omitted
• Lateral mixing substance enters the river well
  mixed over the river depth, vertical dimension
  and time dependence can be ignored

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Exercise 6.4 Vertical/lateral mixing distance

• Vegetation in summer decreases flow velocity (v)
  and increases water depth (h) and vertical
  turbulent diffusion (Kz)
• higher Kz is partially compensated by difference
  in water depth resulting in similar vertical
  mixing distances (smix,z)
• For deeper rivers the coefficient of lateral
  turbulent diffusion and dispersion (ey) is higher
• Higher ey causes a smaller lateral mixing
  distance
• Vertical mixing is much faster than lateral
  because the width of the river is much larger
  than the depth

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Exercise 6.4 Longitudinal dispersion

• Significantly larger lateral mixing in summer
  reduces longitudinal dispersion
• Dispersion increases with increasing velocity
  differences across the river
• Dispersion increases with increasing width of the
  river, because of decreasing lateral mixing
• Dispersion decreases with lateral turbulent
  diffusivity (u h), as this increases mixing
  across the river

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Exercise 6.4 Numerical dispersion

• To avoid numerical dispersion being larger than
  longitudinal dispersion the length of the
  modelled river sections (mixed reactors) must
  fulfill
• ?x ltlt Ex 2wh / Q Ex 2 / v

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Exercise 6.4 Tracer experiment

• Mass of dye tracer needed for experiment, so that
  it fulfills Cmax m/hw 1/2v2Ext
• with Cmax 0.4 g/m3 and t 600 s