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