$(1)$ Consider the $5,953$ ha catchment below, with land use from $1951$ when the catchment was effectively in its natural state. The mean potential evaporation $(($:$E_{000}\}$ for that period was $1256m\frac{m}{?}$ year, and the mean stream flow was $42\mathrm{.}4M\frac{L}{d}.$

Below, the catchment is given with a reference grid and showing rainfall averages from four meteorological stations.

Figure $1$: Catchment plan, showing land use from $1951$ and the average annual rainfall $(1910-1953)$ at four meteorological stations.

$($a$)$ Using Thiessen polygons, determine the area$-$averaged rainfall for the catchment.

$($b$)$ What is the specific discharge and runoff$/$rainfall ratio for the catchment?

$($c$)$ Write a water balance equation for the catchment. Assign values to known parameters, and close the water balance on the basis of mean catchment fluxes. Describe your assumptions.

$($d$)$ Provide an initial approximation of the crop coefficient $(K_s)$ for the catchment in its undisturbed state.