Question $2[40$ marks$]$

Consider the following $($assumed$)$ data for the Kourris Reservoir Dam in Cyprus:

$.$ The dimensions of the lake are approximately $8$ km in length by $0\mathrm{.}5$ km in width.

The inflow to the dam, for the month of April, was measured at $15$ million cubic meters, while an outflow of $0\mathrm{.}05\frac{m^3}{s}$ can be assumed.

$.$ The total precipitation for the same month was measured to be $90$ mm $.$

$-$ The average air temperature during that time was $16C$ while the water temperature was on average at $18C.$ The wind speed averaged at $10k\frac{m}{h}$our and the relative humidity was at about $60\%.$

Assume that the area is characterized by Dothan loamy sand soils, which allow water to seep into the dam at a specific rate. Also assume that the total rain received in the area was witnessed during three separate main storm events, each of which lasted $6$ hours; therefore, you would expect some seepage into the dam during those storm events.

Finally, you can also assume a loss of water from the dam, due to seepage out of the dam $($i$.$e$.$ losses to the ground$),$ to have been at about $0\mathrm{.}5$ cm $,$ during the same time period.

Estimate the change in storage $($in million cubic meters$)$ in the dam during the month of April.