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Light limitation on growth

I_lim.Rd

Calculates the relative limitation on growth rate due to light availability, via: $$I_{lim} = \frac{e}{K \cdot d_{top}} \times \Biggl[e^{-\frac{I_z e^{-K \cdot d_{top}}}{I_o}} - e^{-\frac{I_z}{I_o}} \Biggr]$$ where \(I_{z}=I e^{-k_W \cdot d_{top}}\) is the irradiance at the cultivation depth and \(K=k_{m}+kW\) is the total attenuation coefficient.

\(k_{m}\) is the additional attenuation coefficient from macroalgae biomass, calculated as: $$k_{m} = a_{cs} \times N_f \times \text{max} \Biggl( \frac{h_{m}}{d_{top}}, 1 \Biggr) \times \frac{1}{\text{min}(h_{m}, d_{top})}$$ where \(h_m\) is the macroalgae height.

Usage

I_lim(Nf, I, kW, spec_params, site_params)

Arguments

Nf

Fixed nitrogen (mg m\(^{-3}\))

I

the surface irradiance, PAR (\(\mu\)mol photons m\(^{-2}\) s\(^{-1}\))

kW

the light attenuation coefficient for open water (m\(^{-1}\))

spec_params

a vector of named numbers. Must include:

  • a_cs, the carbon-specific self-shading constant

  • I_o, the light saturation parameter

  • h_a, h_b and h_c, parameters governing height change with N_f

  • h_max, maximum species height

site_params

A vector of named numbers. Must include:

  • d_top, the below-surface depth (m) of the top of the macroalgae culture

Value

a scalar of relative light limitation on growth (between 0 and 1)

See also

height()

Examples

my_species <- c(I_o = 200, a_cs = 0.001, h_a = 750, h_b = 0.5, h_c = 0.01, h_max = 1)
my_site <- c(d_top = 1)
I <- seq(0, 2000, 10)
kW <- rnorm(length(I), 0.05, 0.01)

# Use purrr::map2 to calculate light limitation over a range of light and attenuation values, but fixed Nf
if (FALSE) { # \dontrun{
df <- purrr::map2_dfr(I, kW, function(Iz, kWz) {
  data.frame(
    I = Iz,
    kW = kWz,
    lim = I_lim(Nf = 1000, I = Iz, kW = kWz, spec_params = my_species, site_params = my_site)
  )
})
} # }