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

8.7.3.14. Respiration

Carbon is respired with a temperature-dependent rate. Respiration stops at \({c}_j^{\min}\):

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

For elements with fixed stochiometry, any excess is returned to the inorganic pool, e.g.,

\[R^{\mathrm{P}}_j = R^{\mathrm{P}:\mathrm{C}}_j R^{\mathrm{C}}_j \qquad\text{(without P quota)} \,.\]

For nitrogen, return fluxes to NH4 and NO2 are limited to not exceed uptake. If carbon respiration exceeds uptake, excess nitrogen goes to NO3,

\[ \begin{align}\begin{aligned}R^{\mathrm{N,NH4}}_j &= U^{\op{NH4}}_j \,,\\R^{\op{N,NO2}}_j &= U^{\op{NO2}}_j \,,\\R^{\op{N,NO3}}_j &= R^{{\mathrm{N}}:{\mathrm{C}}}_j R^{\mathrm{C}}_j - U^{\op{NH4}}_j - U^{\op{NO2}}_j\\\text{(if } R^{\mathrm{C}}_j &> U^{\op{DIC}}_j \text{ without N quota).}\end{aligned}\end{align} \]

For non-phototrophs, all nitrogen goes to NO3.

8.7.3.14.1. Parameters

Table 8.49 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

Xmin

a_Xmin

\(c^{\min}_j\)

0

mmol C m-3

minimum abundance for mortality, respiration and exudation
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.