A while ago I was asked to review a paper about water infiltration into a variably saturated soil. In this paper, the authors propose propose a direct solution of the infamous infilltration

Equation of Green and Ampt $(1911).$ They approximate the cumulative vertical infilltration, $I0($centimeter$),$ into an unsaturated soil as follows

$I(t)=K_{0}t(0\mathrm{.}70635+0\mathrm{.}32415\sqrt[\phantom{2}]{1+9\mathrm{.}43456(\frac{S^2}{K_0^2})})$

where $K_0($cm$/$day$)$ is the hydraulic conductivity of the wetted $($transmission$)$ zone, $S($cm$/$day ${?}^{\frac{1}{2}})$ denotes the sorptivity of the soil and $t($day$)$ signifies time. The infillration rate, $i($cm$/$day$),$

may be calculated using

$i(t)=K_0(1+\frac{S^2}{2K_{0}I(t)})$

Write a function, GAapprox, which has three input arguments, K$0,$ S and $t,$ and two output arguments, I $(=$ cumulative infiltration$)$ and i $(=$ infiltration rate$).$ Call this function from this

Live Script using $K0=2c\frac{m}{?}$ day, $S=5c\frac{m}{?}$ day ${?}^{\frac{1}{2}}$ and $t=$ linspace $(0,3,300{)}^{\text{'}}.$ With these input arguments, the GAapprox function must create one figure window comprised of two

different graphs $($next to each other, thus in layout of $1$ row and $2$ colums$)$ of the $I(t)$ and $i(t)$ relationships. Add labels to the axes of the two graphs and a title.

The output arguments, I and i$,$ of the function GAapprox.m are vectors of size $300$ by $1.$ In your Live Script, print the value of element $150$ of $t,$I and i and save the vectors, $t,$I and

i in a text$-$readable $(-$ascii$)$ file, named GAoutput.txt$.$

Checklist: $(1)$ function GAapprox.m$,(2)$ graphs of $I(t)$ and $i(t),(3)$ labels and titles, $(4)$ element $150$ of $t,$I and $i,(5)$ text$-$readable $(-$ascii$)$ file GAoutput. txt $(=$ not the file but the

save statement itself$)$