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8.7.3.2. Growth¶

Without DARWIN_ALLOW_GEIDER, the carbon-specific growth rate is

\[P^{\mathrm{C}}_j = P_{{\mathrm{C}},j}^{\max} \gamma^{\op{nut}}_j \gamma^{\op{light}}_j f^{{{\text{phy}}}}_j(T) \gamma_{\op{pCO2}}\]

where

\[\gamma^{\op{light}}_j = (1 - \mathrm{e}^{-k^{\op{sat}}_{\op{PAR}j} I}) \cdot \mathrm{e}^{-k^{\op{inh}}_{\op{PAR}j} I} \cdot n^{\op{light}}_j\]

and \(n^{\op{light}}_j\) normalizes the maximum of \(\gamma^{\op{light}}_j\) with respect to \(I\) to unity. For \(\gamma^{\op{nut}}_j\), see Section 8.7.3.6, for \(f^{\op{phy}}_j(T)\), see Section 8.7.3.19. \(\gamma_{\op{pCO2}}\) is currently set to 1 in the code.

With DARWIN_ALLOW_GEIDER,

\[P^{\mathrm{C}}_j = P^{{\mathrm{C}}{\op{m}}}_j \left( 1 - \exp\left\{ -\frac{\gamma^{\op{QFe}}_j \langle\alpha I\rangle_j \op{Chl\text{:}C}_j }{ P^{{\mathrm{C}}{\op{m}}}_j } \right\} \right) \gamma^{{{\text{inhib}}}}_j \qquad\text{if } I_{\op{tot}}>I_{\min}\]

where

\[\langle\alpha I\rangle_j = \sum_{l=1}^{\op{nlam}} \alpha^{\op{Chl}}_{j,l} I_l \quad\text{and}\quad I_{\op{tot}} = \sum_{l=1}^{\op{nlam}} I_l\]

and \(I_l\) is photosynthetically active radiation. The Chlorophyll a-specific initial slope of the photosynthesis-light curve is computed from the maximum quantum yield of carbon fixation and the coefficient of absorption by photosynthetically active pigments (see Section 8.7.3.5),

\[\alpha^{\op{Chl}}_{j,l} = \Phi_{\op{m}j} a^{\op{chl}}_{\op{ps}j,l} \;.\]

Without the radtrans package, spectral PAR, \(I_l\), is replaced by total PAR and the spectral absorption coefficient by an average one, aphy_chl_ave. The maximum growth rate is

\[P^{{\mathrm{C}}{\op{m}}}_j = P_{{\mathrm{C}},j}^{\max} \gamma^{\op{nut}}_j f^{{{\text{phy}}}}_j(T) \gamma_{\op{pCO2}} \;.\]

The iron limitation term, \(\gamma^{\op{QFe}}_j\), is discussed in Section 8.7.3.6.

With DARWIN_ALLOW_CHLQUOTA, \(\op{Chl\text{:}C}_j\) is computed from plankton Chlorophyll and carbon tracers. Without,

\[\op{Chl\text{:}C}_j = \op{Chl\text{:}C}_j^{\op{acclim}}\]

where

(8.55)¶\[\op{Chl\text{:}C}_j^{\op{acclim}} = \left[ \frac{\op{Chl\text{:}C}^{\max}_j} {1 + \op{Chl\text{:}C}^{\max}_j\langle\alpha I\rangle_j /(2P^{{\mathrm{C}}{\op{m}}}_j)} \right]_{\op{Chl\text{:}C}^{\min}_j}^{\op{Chl\text{:}C}^{\max}_j}\]

If \(P^{{\mathrm{C}}{\op{m}}}_j=0\), we set \(\op{Chl\text{:}C}_j^{\op{acclim}}=\op{Chl\text{:}C}^{\min}_j\). With the readtrans package,

\[\op{Chl\text{:}C}^{\min}_j = \frac{\op{Chl\text{:}C}^{\max}_j} { 1 + 2000 \op{Chl\text{:}C}^{\max}_j \overline\alpha_j /(2 P^{\max}_{\op{C},j}) } \;,\]

otherwise zero. Here,

\[\overline{\alpha}_j = \sum_l \Delta\lambda_l \alpha^{\op{Chl}}_{j,l} \Big/ \sum_l \Delta\lambda_l \;.\]

Photo inhibition is parameterized as

\[\begin{split}\gamma^{{{\text{inhib}}}}_j = \begin{cases} c^{\op{inhib}}_j \cdot \op{EkoverE} & \text{if } \op{EkoverE} \le 1 \\ 1 & \text{otherwise} \end{cases}\end{split}\]

where

\[\op{EkoverE} = \frac{P^{{\mathrm{C}}{\op{m}}}_j/(\op{Chl\text{:}C}_j\cdot\overline{\alpha}_j)} {\langle\alpha I\rangle_j/\overline{\alpha}_j} \;.\]

Table 8.29 summarized the parameters relevant for growth.

Table 8.29 Growth parameters¶
Trait	Param	Symbol	Default	Units	Description
ksatPAR	a_ksatPAR	\(k^{\op{sat}}_{\op{PAR}}\)	0.012	m² s μEin^-1	saturation coefficient for PAR
kinhPAR	a_kinhPAR	\(k^{\op{inh}}_{\op{PAR}}\)	0.006	m² s μEin^-1	inhibition coefficient for PAR
PCmax	a,b_PCmax	\(P^{\op{max}}_{\op{C}j}\)	(1/day) V^–0.15	1/s	maximum carbon-specific growth rate
	PARmin	\(I_{\min}\)	0.1	μEin/m²/s	minimum light for photosynthesis
mQyield	a_mQyield	\(\Phi_j\)	0.000075	mmol C (μEin)^-1	maximum quantum yield
chl2cmax	a_chl2cmax	\(\op{Chl\text{:}C}^{\op{max}}_j\)	0.3	mg Chl (mmol C)^-1	maximum Chlorophyll-carbon ratio
inhibGeider	a_inhibGeider	\(c^{\op{inhib}}_j\)	0.0		photo-inhibition coefficient for Geider growth
aphy_chl_ps	aphy_chl_ps_type	\(a^{\op{chl}}_{\op{ps}j,l}\)	read in	m² (mg Chl)^-1	absorption by PS active pigments

aphy_chl_ps is assigned from aphy_chl_ps_type via grp_aptype. The type-specific spectra are read in from darwin_phytoAbsorbFile and optionally scaled allometrically, see Allometric scaling of absorption and scattering spectra.