This problem is taken from the Dingman $(2015)$ Physical Hydrology, $3^{rd}$ Edition textbook. Source: Problem $6\mathrm{.}1,$ page $307.$ "Measurements of water$-$balance components have been made for a one$-$year period on a lake with an area of $4\mathrm{.}2k{m}^2,$ with the following results: $P=$ precipitation $=1083mm,Q_{in}=$ streamflow into the lake $=2\mathrm{.}33{10}^7{m}^3,G{W}_{in}=$ groundwater inflow to the lake $=2\mathrm{.}2{10}^5{m}^3,G{W}_{\text{o}\text{u}\text{t}}=$ groundwater outflow from the lake $=0\mathrm{.}6{10}^5{m}^3,Q_{\text{o}\text{u}\text{t}}=$ streamflow out of the lake $=2\mathrm{.}70{10}^7{m}^3.$ The lake$-$surface elevation, $h,$ at the end of the year was $108mm$ higher than at the beginning; this is used to estimate the change in lake storage $=S."$ Using the following equation, calculate the lake evaporation for that year in units of $\frac{m^3}{y}r$ :

$E=P+Q_{in}+G{W}_{in}-Q_{\text{o}\text{u}\text{t}}-G{W}_{\text{o}\text{u}\text{t}}-S$