| D. Decay of PHY $ \left(D_{1}\right) $ with releases of NOR $ \left(D_{2}\right) $, POR $ \left(D_{5}\right) $, and SS $ \left(D_{7}\right). $ |
| $ D_{1} = k_{d 1} \times X_{P H Y}, D_{2} = k_{d 2} \times X_{P H Y}, D_{5} = k_{d 5} \times X_{P H Y}, D_{7} = k_{d 7} \times X_{P H Y}, $ |
| where |
| (ⅰ) $ k_{d 1} = -k_{d}, k_{d 2} = 0.1761 \times k_{d}, k_{d 5} = 0.1761 \times k_{d}, k_{d 7} = 0.379 \times k_{d}, $ |
| (ⅱ) $ k_{d} $ is a parameter whose value is given in Table 2. |
| G. Photosynthesis (Growth of PHY, $ G_1 $), with uptakes of NAM ($ G_3 $), NIT($ G_4 $), and PIN($ G_6 $). |
| $ G_1 = k_{g1}(t)\times X_{PHY} $, $ G_3 = k_{g3}(t)\times X_{PHY} $, $ G_4 = k_{g4}(t)\times X_{PHY} $, $ G_6 = k_{g6}(t)\times X_{PHY} $, |
| where |
| (ⅰ) $ k_{g 1}(t) = k_{g \max }(t) \times e f(L(t)) \times[ $ $ e f(N)+e f(P)] $ |
| is the growth rate of PHY; $ k_{g \max }(t) = k_{g \max 20} \times 1.047^{Tenp(t)-20} $ |
| is the effect of the temperature on the growth of PHY at temperature $ Temp(t){ }^{\circ} C $, where $ Temp(t) $ is the water temperature in at time $ t $ given by $ Temp(t) = Temp_{\min }+\frac{\left(Temp_{\max }-Temp_{\min }\right)}{2}\left(1-\cos \frac{360(t-76)}{365} \times \frac{\pi}{180}\right) $, |
| with $ Tem p_{\min } = 13.7 $ and $ Tem p_{\max } = 25.9 $; |
| $ e f $$ (L(t)) = \frac{L(t)}{L_{S}} \exp \left(1-\frac{L(t)}{L_{S}}\right) $ is the effect of light on the growth rate of PHY, where $ L(t) $ is the incident solar radiation (expressed in cal/$ \text{cm}^{2} $) given by |
| $ L(t) = L_{\min }+\frac{\left(L_{\max }-L_{\min }\right)}{2}\left(1-\cos \frac{(t-15) \times 360}{365} \times \frac{\pi}{180}\right) $
|
| with $ L_{\min } = 120 \mathrm{cal} / \mathrm{cm}^{2} $, and $ L_{\max } = 192 \mathrm{cal} / \mathrm{cm}^{2} $; |
| $ ef $$ (N) $ is the effect of nutrients due to the uptake of NAM and NIT, |
| $ ef $$ (P) $ is the effect of nutrients due to the uptake of PIN; their average values are given in Table $A2$; $ k_{g \max 20} $ and $ L_{S} $ are parameters, whose values are given in Table A2, |
| (ⅱ) $ k_{g 3}(t) = -0.1761 \times P_{N A M} \times k_{g 1}(t) $, |
| $ k_{g 4}(t) = -0.1761 \times\left(1-P_{N A M}\right) k_{g 1}(t) $, $ k_{g 6}(t) = -0.1761 \times k_{g 1}(t) $, |
| $ P_{N A M} $ is the preference term for NAM whose approximated value is also given in Table A2. |
| A. Adsorption of NAM $ \left(A_{3}\right) $ and PIN $ \left(A_{6}\right) $. |
| $ A_{3} = k_{A 3} \times X_{S S}, \ A_{6} = k_{A 6} \times X_{S S}, $
|
| where |
| (ⅰ) $ k_{A 3} = -\frac{S V_{S S}}{H} \times a_{NAM}, k_{A 6} = -\frac{S V_{S S}}{H} \times a_{P I N} $, |
| (ⅱ) $ S V_{S S}, a_{N A M}, H, a_{P I N} $ are parameters whose values are given in Table 2. |
| Set. Settling of PHY $ \left(S_{1}\right) $, NOR $ \left(S_{2}\right) $, POR $ \left(S_{5}\right) $, and SS $ \left(S_{7}\right) $ |
| $ \begin{align*} &Set_{1} = k_{S e t 1} \times X_{P H Y}, \ Set_{2} = k_{S e t 2} \times X_{N O R}, \ \quad Set_{5} = k_{S e t 5} \times X_{P O R}, \\ &Set_{7} = k_{Set7} \times X_{S S}, \end{align*}$
|
| where |
| (ⅰ) $ k_{Set1} = -\frac{S V_{P H Y}}{H}, \ k_{Set2} = -\frac{S V_{N O R}}{H}\left(1-C_{N O R}\right) $, $ k_{Set5} = -\frac{S V_{P O R}}{H}\left(1-C_{P O R}\right), \ k_{Set7} = -\frac{S V_{S S}}{H}, $ |
| (ii) $ S V_{P H Y}, \ S V_{S S}, \ S V_{N O R}, \ S V_{P O R}, \ C_{N O R}, \ C_{P O R} $ and $ H $ are parameters whose values are given in Table 2. |
| Am. Ammonification - Mineralization of NOR $ A m_{2} = k_{A m 2}(t) \times X_{N O R}, A m_{3} = k_{A m 3}(t) \times X_{N O R} $ where |
| (ⅰ) $ k_{A m 2}(t) = -k_{N min }(t) \times c_{N O R}, k_{A m 3}(t) = k_{N min }(t) \times c_{N O R} $, |
| (ⅱ) $ k_{N min }(t) = k_{N min } \times 1.047^{Temp(t)-20} $ |
| is the saturation constant for Nitrogen mineralization at $ Temp(t){ }^{o} C $, where the formula for $ Temp(t) $ is as given in the Photosynthesis process, |
| (ⅲ) $ c_{N O R} $ is a parameter whose value is given in Table 2. |
| N. Nitrification $ \left(N i t_{3}\right. $ and $ \left.N i t_{4}\right) $. |
| $N i t_{3} = k_{N i t 3}(t) \times X_{N A M}, N i t_{4} = k_{N i t 4}(t) \times X_{N A M}, $
|
| where |
| (ⅰ) $ k_{N i t 3}(t) = -k_{N i t}(t), k_{N i t 4}(t) = k_{N i t}(t), $ |
| (ⅱ) $ k_{N i t}(t) = k_{N i t 20} \times 1.047^{Temp(t)-20} $ is the nitrification rate at $ Temp(t)^{o} C $, where the formula for $ Temp(t) $ is as given in the Photosynthesis process. |
| (ⅲ) $ k_{N i t 20} $ is a parameter whose value is given in Table A2. |
| R. Endogenous respiration of PHY $ \left(R_{1}\right) $ with the release of NOR $ \left(R_{2}\right) $, NAM $ \left(R_{3}\right) $, POR $ \left(R_{5}\right) $ and $ \operatorname{PIN}\left(R_{6}\right) $. |
| $ \begin{align*} &R_{1} = k_{r 1}(t) \times X_{P H Y}, \ R_{2} = k_{r 2}(t) \times X_{P H Y}, \ R_{3} = k_{r 3}(t) \times X_{P H Y}, \\ &R_{5} = k_{r 5}(t) \times X_{P H Y}, \ R_{6} = k_{r 6}(t) \times X_{P H Y}, \end{align*} $
|
| where |
|
$ \text {(ⅰ) } k_{r 1}(t) = -k_{r}(t), \\ k_{r 2}(t) = 0.1761 \times f_{N O R} \times k_{r}(t), \\ k_{r 3}(t) = 0.1761 \times\left(1-f_{N O R}\right)\times k_{r}(t)\\ k_{r 5}(t) = 0.1761 \times f_{P O R} \times k_{r}(t), \\ k_{r 6}(t) = 0.1761 \times\left(1-f_{P O R}\right) \times k_{r}(t), $
|
| (ⅱ) $ k_{r}(t) = k_{r 20} \times 1.047^{Temp(t)-20} $ is the respiration rate at $ Temp(t)^{o} C, $
|
| where the formula for $ Temp(t) $ is as given in the Photosynthesis process, |
| (ⅲ) $k_{r 20}, f_{N O R} $ are parameters whose values are given in Table 2.
|
| P. Mineralization of POR $ \left(P_{5}\right. $ and $ \left.P_{6}\right) $. |
| $Min_{5} = k_{Min 5}(t) \times X_{P O R}, M i n_{6} = k_{Min6}(t) \times X_{P O R} $
|
| where |
| (ⅰ) $ k_{min 5}(t) = -k_{P min }(t) \times c_{P O R}, k_{Min 6}(t) = k_{P min }(t) \times c_{P O R} $, |
| (ⅱ) $ k_{P min } = k_{P min 20} \times 1.047^{Temp(t)-20} $ |
| is the mineralization rate of $ \mathrm{NOR} $ at $ Temp(t)^{o} C $, where the formula for $ Temp(t) $ is as given in the Photosynthesis process, |
| (ⅲ) $ c_{P O R} $ is a parameter whose value is given in Table A2. |
Download:
{{journal.titleEn}} 
Open Access Under a Creative Commons 
