a$)$ For each of the cases below, assuming al other parameters related to the dissolved oxygen $($DO$)$ sag curve remain unchanged, determine the effect of the following parameter variations on the critical point in a river. Provide a sketch of the dissolved oxygen sag curve for each scenario to assist in your explanation $($in comparison to a reference DO sag curve$).$ i$)$ Increased initial deficit and decreased reaeration rate i$)$ Decreased ultimate BOD and increased deoxygenation rate b$)$ Assess the trophic state of a lake which has a surface area of $1$x$10\backslash$deg m$?$ and receives a water and phosphorus inflow of $1$x$108$ m$\text{'}/$yr and $1$x$10?$ gP$/$yr respectively. A Vollenweider plot is given in Figure $\mathrm{.}1$ Based on your assessment, elaborate on the state of the lake in terms of at least $5$ important features. Figure $1$: A Vollenweider Plot