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

8.7.3.18. Bacteria¶

To enable heterotrophic uptake for plankton type j, set bactType(j) to a non-zero value and set one of isAerobic(j) and isDenit(j) to 1. The allowed values and associated types are summarized in Table 8.55. Note that ammonia and nitrite oxidizers must be aerobic.

Table 8.55 Darwin bacteria types¶
bacttype	isAerobic	isDenit	Description
1	1	0	Aerobic particle-associated: POM \(\to\) inorganic, DOM
1	0	1	Denitrifying particle-associated: POM \(\to\) inorganic, DOM
2	1	0	Aerobic free-living: DOM \(\to\) inorganic
2	0	1	Denitrifying free-living: DOM \(\to\) inorganic

You may also set the corresponding group parameters, grp_bacttype, grp_aerobic and grp_denit.

To disable remineralization other than by bacteria, set the parameterized remineralization rates KDOC, … to zero, see Section 8.7.3.8. This is not done automatically.

Note that bacteria have fixed elemental ratios. For now, no elemental quotas may be turned on in DARWIN_OPTIONS.h. In the future, elemental quotas will be kept at fixed ratios if turned on.

8.7.3.18.1. Growth and energy sources¶

Bacterial growth is represented by a growth rate,

\[\partial_t{c}_j = \mu_j {c}_j \;,\]

which is computed from various limiting resources. Aerobic bacteria are limited by and take up oxygen,

\[\mu^{{\mathrm{O}}}_j = y^{\mathrm{O}_2}_j P^{\max}_{\mathrm{O}2} \mathrm{O}_2 \;,\]

\[U^{{\mathrm{O}}2}_j = \frac{1}{{y^{{\mathrm{O}}_2}_j}} \mu_j {c}_j \;,\]

denitrifiers nitrate,

\[\mu^{{\mathrm{O}}}_j = y^{\op{NO}_3}_j V^{\max}_{\op{DIN}} \dfrac{\op{NO}_3}{\op{NO}_3 + k^{\op{DIN}}} f^{\op{remin}}(T) \;,\]

\[U^{\op{NO3}}_j = \frac{1}{{y^{\op{NO}_3}_j}} \mu_j {c}_j \;.\]

The nitrogen is released as N₂ which is not represented in the model.

8.7.3.18.2. Generic particle-associated¶

BactType 1 consume POC, PON, POP, POFe and produce DIN, NH₄, PO₄ and FeT and, by hydrolysis, DOC, DON, DOP, DOFe. The growth rate is limited by the presence of particulate organic matter and oxygen or nitrate, see above,

\[\mu_j = \min(\mu^{\op{PON}}_j, \mu^{\op{POC}}_j, \mu^{\op{POP}}_j, \mu^{\op{POFe}}_j, \mu^{{\mathrm{O}}}_j)\]

\[\mu^{\op{PON}}_j = y_j {P^{\op{max}}_{{\mathrm{C}},j}} \frac{\op{PON}}{\op{PON}+ k^{\op{PON}}_j} f^{\op{remin}}(T)\]

\[\mu^{\op{POC}}_j = y_j {P^{\op{max}}_{{\mathrm{C}},j}} \frac{\op{POC}}{\op{POC}+ k^{\op{POC}}_j} f^{\op{remin}}(T)\]

\[\mu^{\op{POP}}_j = y_j {P^{\op{max}}_{{\mathrm{C}},j}} \frac{\op{POP}}{\op{POP}+ k^{\op{POP}}_j} f^{\op{remin}}(T)\]

\[\mu^{\op{POFe}}_j = y_j {P^{\op{max}}_{{\mathrm{C}},j}} \frac{\op{POFe}}{\op{POFe}+ {k^{\op{POFe}}}_j} f^{\op{remin}}(T)\]

The update rates for organic matter are

\[U^{\op{POC}}_j = \frac{{\alpha^{\op{hydrol}}}}{y_j} \mu_j {c}_j\]

\[U^{\op{POX}}_j = U^{\op{POC}}_j R^{X{\mathrm{C}}}_j \qquad X={\mathrm{N}},{\mathrm{P}},\op{Fe}\]

Part of POM is hydrolized to DOM:

\[H^{\op{POC}}_j = \frac{{\alpha^{\op{hydrol}}}- 1}{y_j} \mu_j {c}_j\]

\[H^{\op{POX}}_j = H^{\op{POC}}_j R^{X:\mathrm{C}}_j \qquad X=\mathrm{N},\mathrm{P},\op{Fe}\]

Part is respired back to inorganics:

\[R^{\op{DIC}}_j = \left( \frac{1}{y_j} - 1 \right) \mu_j {c}_j\]

\[ \begin{align}\begin{aligned}R^{\op{NH4}}_j &= R^{\op{DIC}}_j R^{\mathrm{N:C}}_j\\R^{\op{PO4}}_j &= R^{\op{DIC}}_j R^{\mathrm{P:C}}_j\\R^{\op{FeT}}_j &= R^{\op{DIC}}_j R^{\mathrm{Fe:C}}_j \;.\end{aligned}\end{align} \]

8.7.3.18.3. Generic free-living¶

BactType 2 consume DOC, DON, DOP, DOFe and produce DIN, NH₄, PO₄ and FeT. The growth rate is limited by the presence of dissolved organic matter and oxygen or nitrogen,

\[\mu_j = \min(\mu^{\op{DON}}_j, \mu^{\op{DOC}}_j, \mu^{\op{DOP}}_j, \mu^{\op{DOFe}}_j, \mu^{{\mathrm{O}}}_j)\]

\[\mu^{\op{DON}}_j = y_j {P^{\op{max}}_{{\mathrm{C}},j}} \frac{\op{DON}}{\op{DON}+ k^{\op{DON}}_j} f^{\op{remin}}(T)\]

\[\mu^{\op{DOC}}_j = y_j {P^{\op{max}}_{{\mathrm{C}},j}} \frac{\op{DOC}}{\op{DOC}+ k^{\op{DOC}}_j} f^{\op{remin}}(T)\]

\[\mu^{\op{DOP}}_j = y_j {P^{\op{max}}_{{\mathrm{C}},j}} \frac{\op{DOP}}{\op{DOP}+ k^{\op{DOP}}_j} f^{\op{remin}}(T)\]

\[\mu^{\op{DOFe}}_j = y_j {P^{\op{max}}_{{\mathrm{C}},j}} \frac{\op{DOFe}}{\op{DOFe}+ {k^{\op{DOFe}}}_j} f^{\op{remin}}(T)\]

The uptake rates for organic matter are

\[U^{\op{DOC}}_j = \frac{1}{y_j} \mu_j {c}_j\]

\[U^{\op{DOX}}_j = U^{\op{DOC}}_j R^{X{\mathrm{C}}}_j \qquad X={\mathrm{N}},{\mathrm{P}},\op{Fe}\]

Part of it is respired back to inorganics:

\[R^{\op{DIC}}_j = \left( \frac{1}{y_j} - 1 \right) \mu_j {c}_j\]

\[ \begin{align}\begin{aligned}R^{\op{NH4}}_j &= R^{\op{DIC}}_j R^{\mathrm{N:C}}_j\\R^{\op{PO4}}_j &= R^{\op{DIC}}_j R^{\mathrm{P:C}}_j\\R^{\op{FeT}}_j &= R^{\op{DIC}}_j R^{\mathrm{Fe:C}}_j \;.\end{aligned}\end{align} \]

8.7.3.18.4. Bacteria parameters¶

Table 8.56 Bacteria parameters¶
Trait	Param	Symbol	Default	Units	Description
bactType	grp_bacttype		0		1: particle associated, 2: free living bacteria, 0: not bacteria
isAerobic	grp_aerobic		0		1: is aerobic, 0: not
isDenit	grp_denit		0		1: is dentrifying, 0: not
	pcoefO2	\(P^{\max}_{\mathrm{O}2}\)	290.82 / 86400	s^–1	max O2-specific O2 uptake rate for aerobic bacteria
	pmaxDIN	\(V^{\max}_{\op{DIN}}\)	20/86400	mmol N mmol C^–1 s^–1	max C-specific DIN uptake rate for denitrifying bacteria
	ksatDIN	\(k^{\op{DIN}}\)	0.01	mmol N m^–3	half-saturation conc of dissolved inorganic nitrogen
	alpha_hydrol	\(\alpha^{\op{hydrol}}\)	2.0	1	increase in POM needed due to hydrolysis
PCmax	a,b_PCmax	\(P^{\op{max}}_{\op{C},j}\)	(1/day) · V^–0.15, see 1	s^–1	maximum carbon-specific growth rate
yield	yod (aerobic) ynd (denit)	\(y_j\)	0.2 (aerobic) 0.16 (denit)	1	bacterial growth yield for all organic matter
yieldO2	yoe	\(y^{{\mathrm{O}}_2}_j\)	0.2/4674/ (1-0.2)106	mmol C / mmol O₂	bacterial growth yield for oxygen
yieldNO3	yne	\(y^{\op{NO}_3}_j\)	0.16/4675/ (1-0.16)106	mmol C / mmol N	bacterial growth yield for nitrate
ksatPON	a_ksatPON	\(k^{\op{PON}}_j\)	1	mmol N m^–3	half-saturation of PON for bacterial growth
ksatPOC		\(k^{\op{POC}}_j\)	see below	mmol C m^–3	half-saturation of POC for bacterial growth
ksatPOP		\(k^{\op{POP}}_j\)	see below	mmol P m^–3	half-saturation of POP for bacterial growth
ksatPOFe		\(k^{\op{POFe}}_j\)	see below	mmol Fe m^–3	half-saturation of POFe for bacterial growth
ksatDON	a_ksatDON	\(k^{\op{DON}}_j\)	1	mmol N m^–3	half-saturation of DON for bacterial growth
ksatDOC		\(k^{\op{DOC}}_j\)	see below	mmol C m^–3	half-saturation of DOC for bacterial growth
ksatDOP		\(k^{\op{DOP}}_j\)	see below	mmol P m^–3	half-saturation of DOP for bacterial growth
ksatDOFe		\(k^{\op{DOFe}}_j\)	see below	mmol Fe m^–3	half-saturation of DOFe for bacterial growth

1: A more appropriate value for the maximum growth rate of bacteria is 5/day which was used in previous versions of the code.

The organic nitrogen half-saturation constant, ksatPON and ksatDON, are set from trait parameters. Others are computed from nitrogen ones using elemental ratios,

\[ \begin{align}\begin{aligned}k^{\op{POC}}_j &= \frac{1}{R^{\mathrm{N}:\mathrm{C}}_j} k^{\op{PON}}_j & k^{\op{DOC}}_j &= \frac{1}{R^{\mathrm{N}:\mathrm{C}}_j} k^{\op{DON}}_j\\k^{\op{POP}}_j &= \frac{R^{\mathrm{P}:\mathrm{C}}_j}{R^{\mathrm{N}:\mathrm{C}}_j} k^{\op{PON}}_j & k^{\op{DOP}}_j &= \frac{R^{\mathrm{P}:\mathrm{C}}_j}{R^{\mathrm{N}:\mathrm{C}}_j} k^{\op{DON}}_j\\k^{\op{POFe}}_j &= \frac{R^{\mathrm{Fe}:\mathrm{C}}_j}{R^{\mathrm{N}:\mathrm{C}}_j} k^{\op{PON}}_j & k^{\op{DOFe}}_j &= \frac{R^{\mathrm{Fe}:\mathrm{C}}_j}{R^{\mathrm{N}:\mathrm{C}}_j} k^{\op{DON}}_j\end{aligned}\end{align} \]