Algal growth (PhD Thesis, O. Fovet, 2010, p.101)

Definition

The biomass growth is calculated at time t, in each section x as follows :

\frac{\partial B}{\partial t}(x,t) = \mu(x,t) B(x,t) F_{lim}(B’(x,t))

where :

  • F_{lim}(B’(x,t)) = \left ( 1 - \frac{B’(x,t)}{B_{Max}} \right )
  •  \mu(x,t) = \mu_{0} \theta^{T(t)-T_{0}} \frac{I(x,t)}{I_{opt}} e^{1- \frac{I(x,t)}{I_{opt}}} \textup{min} \left ( \frac{N_{i}(x,t)}{N_{i}(x,t) + K_{N_{I}}} \right )
  •  I(x,t) = I_{s}(x,t) e^{-k_{ext} h(x,t)}
  •  I_{s}(x,t) = (1-C_m(x))(1-a)R_N(t)

Variables and parameters

  •  B(x,t) : fix biomass modified by the law (kg m-1)
  •  B’(x,t) : fix biomass parameter in the law (kg m-1)
  •  B_{Max} : maximum value of fix biomass (kg m-1)
  •  \mu_{0} : reference growth rate (s -1)
  •  \theta : growth coefficient
  •  T(x,t) : water temperature (°C)
  •  T_{0} : reference temperature (°C)
  •  I(x,t) : light intensity at the section’s bottom (W m-2)
  •  I_{s}(x,t) : solar light intensity (W m-2)
  •  C_{m}(x) : mask coefficient (cf. Temperature simulation)
  •  a : albedo (cf. Temperature simulation)
  •  R_{N}(t) solar radiation (W m-2) (cf. Temperature simulation)
  •  k_{ext} : extinction coefficient (due to turbidity)
  •  h(x,t) : mean water level (m)
  •  I_{opt}(x,t) : optimum light intensity (W m-2)
  •  N_{i}(x,t) : concentration of nutrient i (kg m-3)
  •  K_{N_{i}} : half-saturation constant of nutrient i (kg m-3)

Limiting nutrient

This law can take into account up to 3 nutrients for algae growth. If less than three nutrients are used,  K_{N_{i}} for unused nutrients should be set to 0.

Specifications

  • Law’s ID : 301
  • Number of acting classes: 6
  • Number of meteo parameters : 3
  • Number of parameters : 9

Acting classes :

  1.  B(x,t) :the class modified by the law
  2.  B’(x,t) : the parameter class of the law
  3.  T(x,t) :Water temperature
  4.  N_{1}(x,t) : Nutrient 1
  5.  N_{2}(x,t) : Nutrient 2
  6.  N_{3}(x,t) : Nutrient 3

Meteo parameters :

  •  C_{m}(x)
  •  a
  •  R_{N}(t)

Parameters

  1.  B_{Max} : maximum value of fix biomass
  2.  \mu_{0} : reference growth rate
  3.  \theta : growth coefficient
  4.  T_{0} : reference temperature
  5.  k_{ext} : extinction coefficient
  6.  I_{opt} : optimum light intensity
  7.  K_{N_{1}} : half-saturation constant of nutrient 1
  8.  K_{N_{2}} : half-saturation constant of nutrient 2
  9.  K_{N_{3}} : half-saturation constant of nutrient 3