Table 4.

Water quality variables, model parameters and likelihood functions evaluated for the Sawgrass Lake model uncertainty analysis.

Variable	Inferred Model Parameter(s)a	Parameter Range (1/day)	Likelihood Function
OrgN	KOrgN	0.01–0.04	$L_{OrgN}\left({\mathrm{\theta }}_i\right)=\frac{{(2\pi )}^{-n/2}}{{\left({\sigma }_{{\epsilon }_{\mathit{\text{OrgNi}}}}\right)}^{n_{\mathit{\text{OrgN}}}}}\prod _{j=1}^{n_{\mathit{\text{OrgN}}}}exp\left\{-\frac{1}{2}{\left(\frac{{\epsilon }_{\mathit{\text{OrgNj}}}-{\mu }_{\mathit{\text{OrgNi}}}-{\varphi }_{\mathit{\text{OrgNi}}}\left({\epsilon }_{\mathit{\text{OrgNj}}-1}-{\mu }_{\mathit{\text{OrgN}}}\right)}{{\sigma }_{{\epsilon }_{\mathit{\text{OrgNi}}}}}\right)}^2\right\}$
NH4	KNit	0.025–0.1	$L_{NH4}\left({\mathrm{\theta }}_i\right)=\frac{{(2\pi )}^{-n/2}}{{\left({\sigma }_{{\epsilon }_{NH4i}}\right)}^{n_{NH4}}}\prod _{j=1}^{n_{NH4}}exp\left\{-\frac{1}{2}{\left(\frac{{\epsilon }_{NH4j}-{\mu }_{NH4i}-{\varphi }_{NH4i}\left({\epsilon }_{NH4j-1}-{\mu }_{NH4}\right)}{{\sigma }_{{\epsilon }_{NH4i}}}\right)}^2\right\}$
NO3	KDenit	0.05–0.3	$L_{NO3}\left({\mathit{\theta }}_i\right)=\frac{{(2\pi )}^{-n/2}}{{\left({\sigma }_{{\epsilon }_{NO3i}}\right)}^{n_{\mathit{NO}3}}}\prod _{j=1}^{n_{NO3}}exp\left\{-\frac{1}{2}{\left(\frac{{\epsilon }_{NO3j}-{\mu }_{NO3i}-{\varphi }_{NO3i}\left({\epsilon }_{NO3j-1}-{\mu }_{NO3}\right)}{{\sigma }_{{\epsilon }_{\mathit{NO}3i}}}\right)}^2\right\}$
TN	KOrgN, KNit, KDenit		$L_{TN}\left({\mathrm{\theta }}_i\right)=\frac{{(2\pi )}^{-n/2}}{{\left({\sigma }_{{\epsilon }_{TNi}}\right)}^{n_{\mathit{TN}}}}\prod _{j=1}^{n_{TN}}exp\left\{-\frac{1}{2}{\left(\frac{{\epsilon }_{TNj}-{\mu }_{TNi}-{\varphi }_{TNi}\left({\epsilon }_{TNj-1}-{\mu }_{TN}\right)}{{\sigma }_{e_{\mathit{TN}i}}}\right)}^2\right\}$
OrgP	KOrgP	0.1–0.5	$L_{OrgP}\left({\mathrm{\theta }}_i\right)=\frac{{(2\pi )}^{-n/2}}{{\left({\sigma }_{{\epsilon }_{\mathit{\text{Orgpi}}}}\right)}^{n_{\mathit{\text{OrgP}}}}}\prod _{j=1}^{n_{\mathit{\text{OrgP}}}}exp\left\{-\frac{1}{2}{\left(\frac{{\epsilon }_{OrgPj}-{\mu }_{OrgPi}-{\varphi }_{OrgPi}\left({\epsilon }_{OrgPj-1}-{\mu }_{OrgP}\right)}{{\sigma }_{{\epsilon }_{OrgPi}}}\right)}^2\right\}$
TP	KOrgP		$L_{TP}\left({\mathrm{\theta }}_i\right)=\frac{{(2\pi )}^{-n/2}}{{\left({\sigma }_{{\epsilon }_{TPi}}\right)}^{n_{TP}}}\prod _{j=1}^{n_{TP}}exp\left\{-\frac{1}{2}{\left(\frac{{\epsilon }_{TPj}-{\mu }_{TPi}-{\varphi }_{TPi}\left({\epsilon }_{TPj-1}-{\mu }_{TP}\right)}{{\sigma }_{{\epsilon }_{TNi}}}\right)}^2\right\}$
BOD	KBOD	0.1–0.5	$L_{BOD}\left({\mathrm{\theta }}_i\right)=\frac{{(2\pi )}^{-n/2}}{{\left({\sigma }_{{\epsilon }_{BODi}}\right)}^{n_{BOD}}}\prod _{j=1}^{n_{BOD}}exp\left\{-\frac{1}{2}{\left(\frac{{\epsilon }_{BODj}-{\mu }_{BODi}-{\varphi }_{BODi}\left({\epsilon }_{BODj-1}-{\mu }_{BOD}\right)}{{\sigma }_{{\epsilon }_{BODi}}}\right)}^2\right\}$
Chla	KGrowth KRespKDeath	1.75–2.75 0.08–0.15 0.05–0.15	$L_{Chla}\left({\mathrm{\theta }}_i\right)=\frac{{(2\pi )}^{-n/2}}{{\left({\sigma }_{{\epsilon }_{Chlai}}\right)}^{n_{Chla}}}\prod _{j=1}^{n_{Chla}}exp\left\{-\frac{1}{2}{\left(\frac{{\epsilon }_{\mathit{\text{Chlaj}}}-{\mu }_{\mathit{\text{Chlai}}}-{\varphi }_{\mathit{\text{Chlai}}}\left({\epsilon }_{\mathit{\text{Chlaj}}-1}-{\mu }_{\mathit{\text{Chla}}}\right)}{{\sigma }_{{\epsilon }_{\mathit{\text{Chlai}}}}}\right)}^2\right\}$

^aK_OrgN: OrgN mineralization rate to NH4, K_Nit: NH4 nitrification rate to NO3, K_Denit: NO3 denitrification rate to N2, K_OrgP: OrgP mineralization rate to PO4, K_BOD: BOD decay rate, K_Growth; K_Resp and K_Death: Phytoplankton growth, respiration and death rates respectively.