# Appendix O Processes: pathogens

## O.1 Mortality

Natural mortality, or the ‘dark-death rate’ \(k_d^{pth}\) is an important process influencing protozoan, bacterial and viral dynamics in surface and coastal waters. Two of the predominant environmental factors known to modify this dark death rate are temperature and salinity, and as such the resultant mortality flux is computed via Equation (O.1). \[\begin{equation} \href{AppDiags.html#WQDiagPathMort}{F_{mor}^{pth}} = \left[k_d^{pth} + C_{SM}^{pth} \times S^{\alpha}\right] \times \left[\theta_{mor}^{pth}\right]^{T-20} \times \left(\left[PTH_a\right] + \left[PTH_t\right]\right) \tag{O.1} \end{equation}\] \(k_d^{pth}\) is the user specified dark death rate in freshwater at 20\(^o\)C, \(C_{SM}^{pth}\) is the salinity effect on mortality, \(S\) is ambient salinity, \(\alpha\) is a parameter controlling salinity dependence, \(\theta_{mor}^{pth}\) is the corresponding temperature coefficient, \(T\) is ambient water temperature, and \(\left[PTH_a\right]\) and \(\left[PTH_t\right]\) are the concentrations of free and attached pathogens, respectively. If attached pathogens are not simulated, then the latter concentration is set to zero for the purposes of the above flux calculation.

## O.2 Inactivation

Sunlight exposure is an important inactivation mechanism for all forms of pathogens and microbial indicators in both fresh and saline waters. In waters of high clarity, it has long been regarded as the most dominant inactivation mechanism. To compute this inactivation flux, the individual inactivation rates due to visible, UVA and UVB light are calculated and combined to compute an overall inactivation rate \(R_{invn}^{pth}\) via Equation (O.2). \[\begin{equation} \left.\begin{aligned} R_{invn}^{pth} = 10^{-6} \times \left(\underbrace{\left[\frac{\left[DO\right]}{K_{DO_{vis}}^{pth} + \left[DO\right]}\times \left[k_{vis}+c_{S_{vis}}S\right]\times PAR\right]}_{\text{Influence of visible light}} + \ldots \\ \underbrace{\left[\frac{\left[DO\right]}{K_{DO_{uva}}^{pth} + \left[DO\right]}\times \left[k_{uva}+c_{S_{uva}}S\right]\times UVA\right]}_{\text{Influence of UV-A light}} + \ldots \\ \underbrace{\left[\frac{\left[DO\right]}{K_{DO_{uvb}}^{pth} + \left[DO\right]}\times \left[k_{uvb}+c_{S_{uvb}}S\right]\times UVB\right]}_{\text{Influence of UV-B light}}\right) \end{aligned}\right\} \tag{O.2} \end{equation}\] \(K_{DO_{vis}}^{pth}\),\(K_{DO_{uva}}^{pth}\), and \(K_{DO_{uvb}}^{pth}\) are the user specified half saturation oxygen concentrations for visible, UV-A and UV-B light inactivation, respectively, \(k_{vis}^{pth}\),\(k_{uva}^{pth}\), and \(k_{uvb}^{pth}\) are the user specified freshwater inactivation rate coefficients for exposure to visible, UV-A and UV-B light, respectively, \(c_{S_{vis}}^{pth}\),\(c_{S_{uva}}^{pth}\), and \(c_{S_{uvb}}^{pth}\) are the user specified coefficients that enhance the inactivation effect of light under saline conditions for exposure to visible, UV-A and UV-B light, respectively, \(S\) is ambient salinity, and \(PAR\), \(UVA\) and \(UVB\) are the photosynthetically available, UV-A and UV-B radiation intensities at the centre of a model cell. The multiplier preceding the calculation is for units conversion purposes.

The inactivation rate \(R_{invn}^{pth}\) from Equation (O.2) is multiplied by free and attached pathogen concentrations to compute the inactivation flux at each model timestep in each model cell via Equation (O.3). \[\begin{equation} \href{AppDiags.html#WQDiagInvn}{F_{invn}^{pth}} = R_{invn}^{pth} \times \left( \left[ PTH_a \right] + \frac{\left[ PTH_t \right]}{2}\right) \tag{O.3} \end{equation}\] \(\left[PTH_a\right]\) and \(\left[PTH_t\right]\) are the concentrations of free and attached pathogens, respectively. If attached pathogens are not simulated then \(\left[PTH_t\right]\) is set to zero for the purposes of the above calculation. The reduced (50%) impact of \(R_{invn}^{pth}\) on attached pathogens reflects the shading of half of all attached pathogens by their associated sediment particles (i.e. those on the underside).

## O.3 Attachment

Enteric organisms may exist in isolation or be associated with either organic or inorganic suspended particles, depending on the surface properties of the organism and the nature of the suspended material within the system. The simulation of this attachment (and detachment) is therefore allowed for within the TUFLOW WQ Module as an attachment to total suspended sediment.

At each water quality timestep, the instantaneous attachment flux \(F_{att}^{pth}\) is estimated via Equation (O.4). \[\begin{equation} \href{AppDiags.html#WQDiagAttach}{F_{att}^{pth}} = \frac{1}{7}\times \left(f_{att}^{pth} \times \left(\left[PTH_a \right] + \left[PTH_t \right]\right) - \left[PTH_a \right]\right) \tag{O.4} \end{equation}\] \(f_{att}^{pth}\) is the user specified target attachment fraction, and \(\left[PTH_a\right]\) and \(\left[PTH_t\right]\) are the concentrations of free and attached pathogens, respectively. This assumes that left unperturbed, equilibrium would be reached in seven days. A positive (negative) flux represents attachment (detachment). The target attachment fraction is defined as follows, where the concentrations are relative targets, not actual simulated quantities (i.e. so cannot be algebraically cancelled if the expression for \(f_{att}^{pth}\) in Equation (O.5) is substituted into Equation (O.4)). \[\begin{equation} f_{att}^{pth} = \frac{\left[PTH_a \right]}{\left[PTH_a \right] + \left[PTH_t \right]} \tag{O.5} \end{equation}\]

## O.4 Settling

Unattached pathogens able to be settled within the WQ Module, at a user specified constant settling velocity, \(V_{settle}^{pth}\). This is applied equally to both unattached alive and unattached dead pathogens, and a negative velocity is downwards settling. The relevant fluxes are then calculated as follows.

\[\begin{equation} \left.\begin{aligned} \href{AppDiags.html#WQDiagAliveSedmtn}{F_{sedmtn\langle computed\rangle}^{pth_a}} =& \frac{V_{settle}^{pth}}{dz} \times \left[ PTH_a \right] \\ \\ \href{AppDiags.html#WQDiagDeadSedmtn}{F_{sedmtn\langle computed\rangle}^{pth_d}} =& \frac{V_{settle}^{pth}}{dz} \times \left[ PTH_d \right] \\ \\ \end{aligned}\right\} \tag{O.6} \end{equation}\] \(V_{settle}^{pth}\) is the user specified settling velocity and \(dz\) is the relevant cell thickness. The latter divides the flux to produce a per volume result for consistency with other corresponding diagnostics. \(\left[PTH_a\right]\) and \(\left[PTH_d\right]\) are the concentrations of unattached alive and dead pathogens, respectively. Settled pathogens are not permitted to resuspend.

If attached pathogens are simulated, then their settling velocity \(V_{settle}^{pth_t}\) is also specified as a constant (with a negative value again being downwards). This specification should be comparable to the settling velocity/ies specified in the TUFLOW FV Sediment Transport Module configuration. The relevant flux is then calculated as follows.

\[\begin{equation} \href{AppDiags.html#WQDiagAttachSedmtn}{F_{sedmtn\langle computed\rangle}^{pth_t}} =\frac{V_{settle}^{pth_t}}{dz} \times \left[ PTH_t \right] \tag{O.7} \end{equation}\]

The limitations of the above approaches to modelling pathogenic settling are recognised. Future releases of the WQ Module will offer direct linkages between the TUFLOW FV ST Module and WQ Module, and treat pathogens as sediment fractions that are transported using the advanced techniques and models offered by the ST Module, including resuspension.

## O.5 Other

### O.5.1 Total pathogens

Total pathogens is reported as a diagnostic variable computed as per Equation (O.8) \[\begin{equation} \href{AppDiags.html#WQDiagTotPath}{\left[ PTH \right]^{TOT}} = \left[ PTH_a \right] + \left[ PTH_d \right] + \left[ PTH_t \right] \tag{O.8} \end{equation}\] \(\left[PTH_a\right]\), \(\left[PTH_d\right]\) and \(\left[PTH_t\right]\) are the concentrations of free, dead and attached pathogens, respectively.