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 : -# \(B(x,t)\) :the class modified by the law -# \(B'(x,t)\) : the parameter class of the law -# \(T(x,t)\) :Water temperature -# \(N_{1}(x,t)\) : Nutrient 1 -# \(N_{2}(x,t)\) : Nutrient 2 -# \(N_{3}(x,t)\) : Nutrient 3
Meteo parameters : - \(C_{m}(x)\) - \(a\) - \(R_{N}(t)\)
Parameters -# \(B_{Max}\) : maximum value of fix biomass -# \(\mu_{0}\) : reference growth rate -# \(\theta\) : growth coefficient -# \(T_{0}\) : reference temperature -# \(k_{ext}\) : extinction coefficient -# \(I_{opt}\) : optimum light intensity -# \(K_{N_{1}}\) : half-saturation constant of nutrient 1 -# \(K_{N_{2}}\) : half-saturation constant of nutrient 2 -# \(K_{N_{3}}\) : half-saturation constant of nutrient 3