I.2 Respiration

The respiration rate is computed in a series of stages within the WQ Module, where the combination of these stages used for any given phytoplankton group depends on group configuration. These stages are described below. For clarity, supporting functions nested within respiration rate calculations (such as limitation functions) are initially presented in passing, but are cross referenced to detailed descriptions in subsequent sections.

The rate of respiration of a phytoplankton group is a /day rate. It is computed initially within the WQ Module as per Equation (I.6).

\[\begin{equation} R_{resp\langle computed\rangle}^{phy} = R_{resp}^{phy} \times \underbrace{\left[\theta_{resp}^{phy}\right]^{\left(T-20\right)}}_{\text{Influence of temperature}} \tag{I.6} \end{equation}\]

\(R_{resp}^{phy}\) is the user specified phytoplankton respiration rate at 20\(^o\)C, \(\theta_{resp}^{phy}\) is the temperature coefficient for respiration, and \(T\) is ambient water temperature. Figure I.1 presents the influence of \(\theta_{resp}^{phy}\) on \(R_{resp}^{phy}\), as a function of temperature.

Figure I.1: Move the slider to see the effect of changing temperature coefficient on the computed phytoplankton respiration rate

As for primary productivity, salinity limitation of respiration is not mandatory, and can be switched on and off by the user. If salinity limitation of respiration is implemented, then the \(R_{resp\langle computed\rangle}^{phy}\) computed above is further modified as per Equation (I.7).

\[\begin{equation} R_{resp\langle computed\rangle}^{phy} = R_{resp\langle computed\rangle}^{phy} \times L_{sal-r}^{phy} \tag{I.7} \end{equation}\]

\(L^{phy}_{sal-r}\) is the limitation function on respiration due to salinity, and is always greater than one. This limitation function can therefore be conceptualised as a respiration enhancer: it acts to reduce biomass via increasing respiration rather than reducing primary productivity. Salinity limitation is applied to only one of primary production (Section I.1) or respiration, depending on the salinity limitation model selected, and not both.

If a group’s ambient phytoplankton concentration is less than the user defined (or default) minimum concentration \(\left[PHY\right]_{min}\), then the respiration rate is set to zero.

Once the respiration rate has been computed, the corresponding flux of carbon (i.e. phytoplankton respiration) from a phytoplankton group due only to respiration (i.e. excluding mortality and excretive losses) is as per Equation (I.8).

\[\begin{equation} \href{AppDiags.html#WQDiagPhyResp}{F_{resp\langle computed\rangle}^{phy}} = R_{resp\langle computed\rangle}^{phy} \times f_{true-resp}^{phy} \times \left[PHY\right] \tag{I.8} \end{equation}\] \(f_{true-resp}^{phy}\) is the user specified (or default) fraction of respiration that corresponds to the generation of energy via consumption of stored chlorophyll a (i.e. the fraction that does not result in excretive or mortality losses) and \(\left[PHY\right]\) is the ambient phytoplankton group concentration. For a given phytoplankton group, net productivity is calculated as primary productivity, less the flux computed in Equation (I.8) (i.e. respiration due only to energy generation). These net productivity fluxes are summed over the number of simulated phytoplankton groups (i.e. n = 1 to num_phy) to compute the community net primary productivity as per Equation (I.9).

\[\begin{equation} \href{AppDiags.html#WQDiagCPhyNetProd}{F_{netprod\langle computed\rangle}^{comm}} = \sum_{n=1}^{\text{num_phy}} \left[ F_{prod\langle computed\rangle}^{phy_n} - F_{resp\langle computed\rangle}^{phy_n} \right] \tag{I.9} \end{equation}\]

The respiration fluxes of nitrogen and phosphorus corresponding to Equation (I.8) are as per Equations (I.10) and (I.11), respectively.

\[\begin{equation} \href{AppDiags.html#WQDiagPhyRespN}{F_{resp-N\langle computed\rangle}^{phy}} = R_{resp\langle computed\rangle}^{phy} \times f_{true-resp}^{phy} \times \left[IN\right] \tag{I.10} \end{equation}\]

\[\begin{equation} \href{AppDiags.html#WQDiagPhyRespP}{F_{resp-P\langle computed\rangle}^{phy}} = R_{resp\langle computed\rangle}^{phy} \times f_{true-resp}^{phy} \times \left[IP\right] \tag{I.11} \end{equation}\]

\(\left[IN\right]\) and \(\left[IP\right]\) are the internal phytoplankton nitrogen and phosphorus concentrations, respectively. These are either constant ratios of nitrogen and phosphorus to phytoplankton biomass (i.e. the basic phytoplankton model) or computed variables (i.e. the advanced phytoplankton model), and the WQ Module will use the appropriate value based on the phytoplankton model deployed, on a group by group basis.