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a4f2018aab Oliv*0001 .. include:: ../defs.hrst
                0002 
                0003 .. _Growth:
                0004 
                0005 Growth
                0006 ^^^^^^
                0007 
                0008 Without :varlink:`DARWIN_ALLOW_GEIDER`, the carbon-specific growth rate is
                0009 
                0010 .. math::
                0011 
                0012    P^{\mathrm{C}}_j = P_{{\mathrm{C}},j}^{\max} \gamma^{\op{nut}}_j
                0013    \gamma^{\op{light}}_j f^{{{\text{phy}}}}_j(T) \gamma_{\op{pCO2}}
                0014 
                0015 where
                0016 
                0017 .. math::
                0018 
                0019    \gamma^{\op{light}}_j = (1 - \mathrm{e}^{-k^{\op{sat}}_{\op{PAR}j} I}) \cdot
                0020           \mathrm{e}^{-k^{\op{inh}}_{\op{PAR}j} I} \cdot n^{\op{light}}_j
                0021 
                0022 and :math:`n^{\op{light}}_j` normalizes the maximum of
                0023 :math:`\gamma^{\op{light}}_j` with respect to :math:`I` to unity.  For
                0024 :math:`\gamma^{\op{nut}}_j`, see :numref:`Uptake`, for
                0025 :math:`f^{\op{phy}}_j(T)`, see :numref:`Temperature`.
                0026 :math:`\gamma_{\op{pCO2}}` is currently set to 1 in the code.
                0027 
                0028 ..
                0029    n^{\op{light}}_j = \frac{k^{\op{sat}}_{\op{PAR}j}+k^{\op{inh}}_{\op{PAR}j}}
                0030                            {k^{\op{sat}}_{\op{PAR}j}}
                0031          \left( \frac{k^{\op{inh}}_{\op{PAR}j}}{k^{\op{sat}}_{\op{PAR}j}
                0032                 + k^{\op{inh}}_{\op{PAR}j}}
                0033          \right)^{-k^{\op{inh}}_{\op{PAR}j}/k^{\op{sat}}_{\op{PAR}j}}
                0034 
                0035 
                0036 With :varlink:`DARWIN_ALLOW_GEIDER`,
                0037 
                0038 .. math::
                0039 
                0040    P^{\mathrm{C}}_j = P^{{\mathrm{C}}{\op{m}}}_j \left(
                0041        1 - \exp\left\{ -\frac{\gamma^{\op{QFe}}_j
                0042                         \langle\alpha I\rangle_j
                0043                         \op{Chl\text{:}C}_j }{ P^{{\mathrm{C}}{\op{m}}}_j }
                0044                \right\}
                0045      \right) \gamma^{{{\text{inhib}}}}_j
                0046      \qquad\text{if } I_{\op{tot}}>I_{\min}
                0047 
                0048 where
                0049 
                0050 .. math::
                0051 
                0052    \langle\alpha I\rangle_j = \sum_{l=1}^{\op{nlam}} \alpha^{\op{Chl}}_{j,l} I_l
                0053    \quad\text{and}\quad
                0054    I_{\op{tot}} = \sum_{l=1}^{\op{nlam}} I_l
                0055 
                0056 and :math:`I_l` is photosynthetically active radiation.  The Chlorophyll
                0057 a-specific initial slope of the photosynthesis-light curve is computed from the
                0058 maximum quantum yield of carbon fixation and the coefficient of absorption by
faa67d1773 Oliv*0059 photosynthetically active pigments (see :numref:`Spectral`),
a4f2018aab Oliv*0060 
                0061 .. math::
                0062 
                0063    \alpha^{\op{Chl}}_{j,l} = \Phi_{\op{m}j} a^{\op{chl}}_{\op{ps}j,l}
                0064    \;.
                0065 
                0066 Without the radtrans package, spectral PAR, :math:`I_l`, is replaced by total
                0067 PAR and the spectral absorption coefficient by an average one,
                0068 :varlink:`aphy_chl_ave`.  The maximum growth rate is
                0069 
                0070 .. math::
                0071 
                0072    P^{{\mathrm{C}}{\op{m}}}_j = P_{{\mathrm{C}},j}^{\max} \gamma^{\op{nut}}_j
                0073                                 f^{{{\text{phy}}}}_j(T) \gamma_{\op{pCO2}}
                0074    \;.
                0075 
                0076 The iron limitation term, :math:`\gamma^{\op{QFe}}_j`, is discussed in
                0077 :numref:`Uptake`.
                0078 
                0079 With :varlink:`DARWIN_ALLOW_CHLQUOTA`, :math:`\op{Chl\text{:}C}_j` is computed
                0080 from plankton Chlorophyll and carbon tracers.  Without,
                0081 
                0082 .. math::
                0083 
                0084    \op{Chl\text{:}C}_j = \op{Chl\text{:}C}_j^{\op{acclim}}
                0085 
faa67d1773 Oliv*0086 where
                0087 
a4f2018aab Oliv*0088 .. math::
faa67d1773 Oliv*0089    :label: chl2cacclim
a4f2018aab Oliv*0090 
                0091    \op{Chl\text{:}C}_j^{\op{acclim}} = \left[
                0092          \frac{\op{Chl\text{:}C}^{\max}_j}
                0093               {1 + \op{Chl\text{:}C}^{\max}_j\langle\alpha I\rangle_j
                0094                    /(2P^{{\mathrm{C}}{\op{m}}}_j)}
                0095        \right]_{\op{Chl\text{:}C}^{\min}_j}^{\op{Chl\text{:}C}^{\max}_j}
                0096 
                0097 If :math:`P^{{\mathrm{C}}{\op{m}}}_j=0`, we set
                0098 :math:`\op{Chl\text{:}C}_j^{\op{acclim}}=\op{Chl\text{:}C}^{\min}_j`.  With the
                0099 readtrans package,
                0100 
                0101 .. math::
                0102 
                0103    \op{Chl\text{:}C}^{\min}_j = \frac{\op{Chl\text{:}C}^{\max}_j}
                0104       { 1 + 2000 \op{Chl\text{:}C}^{\max}_j \overline\alpha_j
                0105             /(2 P^{\max}_{\op{C},j}) }
                0106    \;,
                0107 
                0108 otherwise zero.  Here,
                0109 
                0110 .. math::
                0111 
                0112    \overline{\alpha}_j = \sum_l \Delta\lambda_l \alpha^{\op{Chl}}_{j,l} \Big/
                0113                            \sum_l \Delta\lambda_l
                0114      \;.
                0115 
                0116 Photo inhibition is parameterized as
                0117 
                0118 .. math::
                0119 
                0120    \gamma^{{{\text{inhib}}}}_j = \begin{cases}
                0121        c^{\op{inhib}}_j \cdot \op{EkoverE} & \text{if } \op{EkoverE} \le 1 \\
                0122        1                                   & \text{otherwise}
                0123      \end{cases}
                0124 
                0125 where
                0126 
                0127 .. math::
                0128 
                0129    \op{EkoverE} = \frac{P^{{\mathrm{C}}{\op{m}}}_j/(\op{Chl\text{:}C}_j\cdot\overline{\alpha}_j)}
                0130                   {\langle\alpha I\rangle_j/\overline{\alpha}_j}
                0131    \;.
                0132 
                0133 :numref:`tab_phys_pkgs_darwin_growth` summarized the parameters relevant for
                0134 growth.
                0135 
                0136 .. csv-table:: Growth parameters
                0137    :delim: &
                0138    :widths: auto
                0139    :class: longtable
                0140    :header: Trait, Param, Symbol, Default, Units, Description
                0141    :name: tab_phys_pkgs_darwin_growth
                0142 
                

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0143 :varlink:`ksatPAR` & :varlink:`a_ksatPAR` & :math:`k^{\op{sat}}_{\op{PAR}}` & 0.012 & m\ :sup:`2` s μEin\ :sup:`-1` & saturation coefficient for PAR

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0144 :varlink:`kinhPAR` & :varlink:`a_kinhPAR` & :math:`k^{\op{inh}}_{\op{PAR}}` & 0.006 & m\ :sup:`2` s μEin\ :sup:`-1` & inhibition coefficient for PAR faa67d1773 Oliv*0145 :varlink:`PCmax` & :varlink:`a <a_PCmax>`,\ :varlink:`b_PCmax` & :math:`P^{\op{max}}_{\op{C}j}` & (1/day) V\ :sup:`--0.15` & 1/s & maximum carbon-specific growth rate a4f2018aab Oliv*

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0146 & :varlink:`PARmin` & :math:`I_{\min}` & 0.1 & μEin/m\ :sup:`2`/s & minimum light for photosynthesis

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0147 :varlink:`mQyield` & :varlink:`a_mQyield` & :math:`\Phi_j` & 0.000075 & mmol C (μEin)\ :sup:`-1` & maximum quantum yield 0148 :varlink:`chl2cmax` & :varlink:`a_chl2cmax` & :math:`\op{Chl\text{:}C}^{\op{max}}_j` & 0.3 & mg Chl (mmol C)\ :sup:`-1` & maximum Chlorophyll-carbon ratio 0149 :varlink:`inhibGeider` & :varlink:`a_inhibGeider` & :math:`c^{\op{inhib}}_j` & 0.0 & & photo-inhibition coefficient for Geider growth 0150 :varlink:`aphy_chl_ps` & :varlink:`aphy_chl_ps_type` & :math:`a^{\op{chl}}_{\op{ps}j,l}` & read in & m\ :sup:`2` (mg Chl)\ :sup:`-1` & absorption by PS active pigments 0151 0152 :varlink:`aphy_chl_ps` is assigned from :varlink:`aphy_chl_ps_type` via 0153 :varlink:`grp_aptype`. The type-specific spectra are read in from 0154 :varlink:`darwin_phytoAbsorbFile` and optionally scaled allometrically, see 0155 :ref:`allomSpectra`. 0156