\(\newcommand{\p}[1]{\frac{\partial }{\partial #1}}\) \(\newcommand{\pp}[2]{\frac{\partial #1}{\partial #2}}\) \(\newcommand{\dd}[2]{\frac{d #1}{d #2}}\) \(\newcommand{\h}{\frac{1}{2}}\) \(\newcommand{\op}[1]{\operatorname{#1}}\)

8.7.3.12. Mortality and Respiration

Respiration and mortality stop at \({c}_j^{\min}\) (maybe should not use \({c}_j^{\min}\) for respiration?)

\[R^{\mathrm{C}}_j = r^{{{\text{resp}}}}_j f^{{{\text{remin}}}}(T) ({c}_j - {c}_j^{\min})\]

\[M_j = m^{(1)}_j {f^{\op{mort}}(T)}^{e^{\op{m}}_j} ({c}_j - {c}_j^{\min}) + m^{(2)}_j {f^{\op{mort2}}(T)}^{e^{\op{m2}}_j} ({c}_j - {c}_j^{\min})^2\]

The released matter splits into dissolved and particulate organic pools,

\[\begin{split}M^{\op{DOM}}_j &= (1 - f_j^{\exp\op{m}}) m^{(1)}_j {f^{\op{mort}}(T)}^{e^{\op{m}}_j} ({c}_j - {c}_j^{\min}) \\ &+ (1 - f_j^{\exp\op{m2}}) m^{(2)}_j {f^{\op{mort2}}(T)}^{e^{\op{m2}}_j} ({c}_j - {c}_j^{\min})^2\end{split}\]

\[\begin{split}M^{\op{POM}}_j &= f_j^{\exp\op{m}} m^{(1)}_j {f^{\op{mort}}(T)}^{e^{\op{m}}_j} ({c}_j - {c}_j^{\min}) \\ &+ f_j^{\exp\op{m2}} m^{(2)}_j {f^{\op{mort2}}(T)}^{e^{\op{m2}}_j} ({c}_j - {c}_j^{\min})^2\end{split}\]

8.7.3.12.1. Parameters

Table 8.40 Mortality and respiration parameters

Trait	Param	Symbol	Default	Units	Description
respRate	a,b_respRate_c 1	\(r^{\op{resp}}_j\)	0	s-1	respiration rate
qcarbon	a,b_qcarbon	\(Q^{\mathrm{c}}_j\)	1.8E-11	mmol C cell–1	cellular carbon content
mort	a_mort	\(m^{(1)}_j\)	0.02 / day	s-1	linear mortality rate
mort2	a_mort2	\(m^{(2)}_j\)	0	m3 s / mmol C	quadratic mortality coefficient
Xmin	a_Xmin	\(c^{\min}_j\)	0	mmol C m-3	minimum abundance for mortality, respiration and exudation
tempMort	grp_tempMort	\(e^{\op{m}}_j\)	1		1: mortality is temp. dependent, 0: not
tempMort2	grp_tempMort2	\(e^{\op{m2}}_j\)	1		1: quadr.tic mortality is temperature dependent, 0: not
ExportFracMort	a_ExportFracMort	\(f^{\op{exp}\op{m}}_j\)	0.5		fraction of linear mortality to POM
ExportFracMort2	a_ExportFracMort2	\(f^{\op{exp}\op{m2}}_j\)	0.5		fraction of quadratic mortality to POM

1

the units of a_respRate_c are mmol C cell^–1, see discussion below.

The respiration rate follows a different scaling law from other traits: it scales in terms of cellular carbon content,

\[r^{\op{resp}}_j = \frac{\op{a\_respRate\_c(g)}}{Q^{\mathrm{c}}_j} \left( 12\cdot10^9 \cdot Q^{\mathrm{c}}_j \right)^{\op{b\_respRate\_c(g)}}\]

where

\[Q^{\mathrm{c}}_j = \op{a\_qcarbon(g)} \cdot V_j^{\op{b\_qcarbon(g)}} \;.\]

The units of a_respRate_c are mmol C cell^–1 s^–1. It now defaults to zero. In the quota model, the default was 3.21·10^–11/86400.