doc/phys_pkgs/darwin_resp.rst

81872c4188 Oliv*0001 .. include:: ../defs.hrst
                0002
                0003 .. _Respiration:
                0004
                0005 Respiration
                0006 ^^^^^^^^^^^
                0007
                0008 Carbon is respired with a temperature-dependent rate.
                0009 Respiration stops at :math:`{c}_j^{\min}`:
                0010
                0011 .. math::
                0012
                0013    R^{\mathrm{C}}_j = r^{{{\text{resp}}}}_j f^{{{\text{remin}}}}(T) ({c}_j - {c}_j^{\min})
                0014    \,.
                0015
                0016 For elements with fixed stochiometry, any excess is returned to the inorganic
                0017 pool, e.g.,
                0018
                0019 .. math::
                0020
                0021    R^{\mathrm{P}}_j = R^{\mathrm{P}:\mathrm{C}}_j R^{\mathrm{C}}_j
                0022    \qquad\text{(without P quota)}
                0023    \,.
                0024
                0025 For nitrogen, return fluxes to NH\ :sub:`4` and NO\ :sub:`2` are limited to not
                0026 exceed uptake.  If carbon respiration exceeds uptake, excess nitrogen goes to
                0027 NO\ :sub:`3`,
                0028
                0029 .. math::
                0030
                0031    R^{\mathrm{N,NH4}}_j &= U^{\op{NH4}}_j
                0032    \,,
                0033
                0034    R^{\op{N,NO2}}_j &= U^{\op{NO2}}_j
                0035    \,,
                0036
                0037    R^{\op{N,NO3}}_j &= R^{{\mathrm{N}}:{\mathrm{C}}}_j R^{\mathrm{C}}_j
                0038                        - U^{\op{NH4}}_j - U^{\op{NO2}}_j
                0039
                0040    \text{(if } R^{\mathrm{C}}_j &> U^{\op{DIC}}_j
                0041    \text{ without N quota).}
                0042
                0043 For non-phototrophs, all nitrogen goes to NO\ :sub:`3`.
                0044
                0045
                0046 Parameters
                0047 ''''''''''
                0048
                0049 .. csv-table:: Mortality and respiration parameters
                0050    :delim: &
                0051    :widths: 20,22,11,11,13,23
                0052    :class: longtable
                0053    :header: Trait, Param, Symbol, Default, Units, Description
                0054
                0055    :varlink:`respRate`        & :varlink:`a <a_respRate_c>`,\ :varlink:`b_respRate_c` [#]_ & :math:`r^{\op{resp}}_j`       & 0                & s\ :sup:`-1`            & respiration rate
                0056    :varlink:`qcarbon`         & :varlink:`a <a_qcarbon>`,\ :varlink:`b_qcarbon`         & :math:`Q^{\mathrm{c}}_j`      & 1.8E-11          & mmol C cell\ :sup:`--1` & cellular carbon content
                0057    :varlink:`Xmin`            & :varlink:`a_Xmin`                & :math:`c^{\min}_j`            & 0                & mmol C m\ :sup:`-3`     & minimum abundance for mortality, respiration and exudation
                0058
                0059 .. [#] the units of :varlink:`a_respRate_c` are mmol C cell\ :sup:`--1`, see discussion below.
                0060
                0061
                0062 The respiration rate follows a different scaling law from other traits: it
                0063 scales in terms of cellular carbon content,
                0064
                0065 .. math::
                0066
                0067     r^{\op{resp}}_j = \frac{\op{a\_respRate\_c(g)}}{Q^{\mathrm{c}}_j}
                0068     \left( 12\cdot10^9 \cdot Q^{\mathrm{c}}_j \right)^{\op{b\_respRate\_c(g)}}
                0069
                0070 where
                0071
                0072 .. math::
                0073
                0074    Q^{\mathrm{c}}_j = \op{a\_qcarbon(g)} \cdot V_j^{\op{b\_qcarbon(g)}}
                0075    \;.
                0076
                0077 .. So
                0078
                0079     .. math::
                0080
                0081         r^{\op{resp}}_j = 12\cdot10^9 \cdot \op{a\_respRate\_c}
                0082         \left( 12\cdot10^9 \cdot Q^{\mathrm{c}}_j \right)^{\op{b\_respRate\_c}-1}
                0083
                0084     .. math::
                0085
                0086        r^{\op{resp}}_j = 12\cdot10^9 \op{a\_respRate\_c}\cdot(12\cdot10^9 \cdot \op{a\_qcarbon})^{\op{b\_respRate\_c}-1}
                0087                    \cdot V^{(\op{b\_respRate\_c}-1)\cdot\op{b\_qcarbon}}
                0088
                0089 The units of a_respRate_c are mmol C cell\ :sup:`--1` s\ :sup:`--1`.  It
                0090 now defaults to zero.  In the quota model, the default was 3.21·10\
                0091 :sup:`--11`/86400.