Q$6.$ Dingman chapter $4,$ problem $7.$

$[7$ points$]$

Consider a drainage basin area of $1,611k{m}^2$ in which three precipitation gauges have been

operating for $20$ yr $.$ The average annual precipitation, hat$(P),$ at the three gauges is $1,198m\frac{m}{?}$

yr and the overall variance of annual precipitation, hat$(S{)}^2(p),$ is $47,698m\frac{m^2}{y}{r}^2.$ An analysis

of the spatial correlation structure of annual precipitation in the region gives a value of $c=$

$0\mathrm{.}0386k{m}^{-1}[$equation $(4$ B $3\mathrm{.}5$ c $)].$ Compute the variance reduction achieved by this mea$-$

surement program and compare the variance reduction that would have been achieved by

having four, rather than three, gauges in the region during the $20-$yr period.

${}_{\text{h}\text{a}\text{t}(P)}^2$