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

8.7.3.16. Exudation

If DARWIN_ALLOW_EXUDE is defined, an additional per-element loss term is introduced, e.g.,

\[\partial_tp_j = \dots - E^{\mathrm{P}}_j\]

with

\[E^{\mathrm{P}}_j = \kappa^{\op{exc}}_{{\mathrm{P}}\,j} ({c}_j - {c}_j^{\min}) Q^{\mathrm{P}}_j\]

and fed into organic matter pools, e.g.,

\[\partial_t\op{DOP}= \dots + \sum_j (1 - f^{\exp\op{exude}}_j) E^{\mathrm{P}}_j\]

and

\[\partial_t\op{POP}= \dots + \sum_j f^{\exp\op{exude}}_j E^{\mathrm{P}}_j\]

(Maybe should NOT use \({c}_j^{\min}\) in this case, or have a separate one for each quota?)

Table 8.51 Exudation parameters

Trait	Param	Symbol	Default	Units	Description
kexcc	a_kexcC	\(\kappa^{\op{exc}}_{\op{C} j}\)	0·V-0.33	s-1	exudation rate for carbon
kexcn	a_kexcN	\(\kappa^{\op{exc}}_{\op{N} j}\)	0·V-0.33	s-1	exudation rate for nitrogen
kexcp	a_kexcP	\(\kappa^{\op{exc}}_{\op{P} j}\)	0.024/day·V-0.33	s-1	exudation rate for phosphorus
kexcfe	a_kexcFe	\(\kappa^{\op{exc}}_{\op{Fe} j}\)	0.0/day	s-1	exudation rate for iron
kexcsi	a_kexcSi	\(\kappa^{\op{exc}}_{\op{Si} j}\)	0.0/day	s-1	exudation rate for silica
ExportFracExude	a_ExportFracExude	\(f^{\op{exp}\op{exude}}_j\)	UNINIT		fraction of exudation to POM