Chapter$2$: Page $44,$ Example $2-$ repeat the steps given in Example to calculate the streamflow for the months of February, March, April $2015.$

EXAMPLE $2\mathrm{.}2$

The average monthly precipitation data recorded at the Whippany River Basin $($drainage area $29\mathrm{.}4m{i}^2)$ at Morristown, New Jersey, during $2015$ are given below. The monthly computed potential evapotranspiration values for the basin are also indicated. The model parameters are: $a=0\mathrm{.}98,b=25,c=0\mathrm{.}10,$ and $d=0\mathrm{.}35.$ Initial soil moisture storage and groundwater storage are ascertained to be $7\mathrm{.}8$ and $1\mathrm{.}5$ in$.,$ respectively. For each month, determine $($a$)$ moisture storage, $($b$)$ direct runoff, $($c$)$ groundwater recharge, $($d$)$ groundwater storage, $($e$)$ groundwater discharge, and $($f$)$ streamflow.

$\backslash$table$[[$Month:$,$J$,$F$,$M$,$A$,$M$,$J$,$J$,$A$,$S$,$O$,$N$,$D$],[$Precipitation $($in$.),1\mathrm{.}2,2\mathrm{.}2,0\mathrm{.}2,0\mathrm{.}75,0\mathrm{.}1,0\mathrm{.}6,7\mathrm{.}0,7\mathrm{.}8,5\mathrm{.}7,0\mathrm{.}88,0\mathrm{.}48,5\mathrm{.}5],[$Potential evapotranspiration,$1\mathrm{.}92,1\mathrm{.}96,2\mathrm{.}3,2\mathrm{.}4,3\mathrm{.}3,3\mathrm{.}4,3\mathrm{.}9,4\mathrm{.}0,3\mathrm{.}0,2\mathrm{.}1,1\mathrm{.}93,1\mathrm{.}95],[($in$.),,,,,,,,,,,,]]$

SOLUTION

The computations are made for successive periods; monthly for this problem.

For January $2015$:

From eq$.(2\mathrm{.}6),$

$W_1=P_1+S_0=1\mathrm{.}2+7\mathrm{.}8=9\mathrm{.}0in.$

From eq$.(2\mathrm{.}8),$

From eq$.(2\mathrm{.}9),$ soil moisture storage,

$S_1=8\mathrm{.}90e^{-\frac{1\mathrm{.}92}{25\mathrm{.}0}}=8\mathrm{.}24in.$

From eq$.(2\mathrm{.}10),$ groundwater recharge,

$(GR{)}_1=0\mathrm{.}10(9\mathrm{.}0-8\mathrm{.}9)=0\mathrm{.}01in.$

From eq$.(2\mathrm{.}11),$ direct runoff,

or

$(0\mathrm{.}09in.)29\mathrm{.}4m{i}^2\frac{1ft}{12in.},\frac{{5280}^{2}f{t}^2}{1m{i}^2},6\mathrm{.}15{10}^{6}f{t}^3$

or

$6\mathrm{.}15{10}^6\frac{f{t}^3}{\text{m}\text{o}\text{n}\text{t}\text{h}}\frac{1\text{m}\text{o}\text{n}\text{t}\text{h}}{31246060sec},2\mathrm{.}30cfs$

From eq$.(2\mathrm{.}12),$ groundwater storage,

or

$G_1$ depth drainage area

$1\mathrm{.}12in.29\mathrm{.}4m{i}^2\frac{1ft}{12in.}\frac{{5280}^{2}f{t}^2}{1m{i}^2}$

$76\mathrm{.}5{10}^{6}f{t}^3$

From eq$.(2\mathrm{.}13),$ groundwater discharge,

$()1$

Similar computations are performed for the month of February with starting values of $S$ and $G$ as $8\mathrm{.}24$ and $1\mathrm{.}12,$ respectively, and so on$.$