Chapter 24, Problem 3PEB

On an annual basis, the precipitation in a watershed is 1,778 mm, the actual evapotranspiration is 914 mm, and 61 percent of the surplus precipitation is runoff. what is the percentage contribution of each component of the watershed budget?

To determine

The percent contribution of actual evaporation, groundwater discharge andsurface runoffcomponent of the watershed budget.

Answer to Problem 3PEB

Solution:

$51.4\%$, $19\%$ and $30\%$

Explanation of Solution

Given data:

The precipitation in a water is $1778\text{ mm}$.

The actual evapotranspiration is $914\text{ mm}$.

$61\%$ of the surplus precipitation is runoff.

Formula used:

Write the watershed budget that can be expressed as precipitation equals actual evaporation plus groundwater discharge plus surface runoff:

$P=AE+Q_{\text{G}}+Q_{\text{s}}$

Here, $P$ is the precipitation, $AE$ is the actual evaporation, $Q_{\text{G}}$ is the groundwater discharge and $Q_{\text{S}}$ is the surface runoff.

Explanation:

Rearrange the watershed budget equation to derive an equation for each component in terms of the other components, and then write an equation that expression $Q_{\text{S}}$ in terms of the surplus.

$\begin{array}{l}P=AE+Q_{\text{G}}+Q_{\text{s}}\\ AE=P-\left(Q_{\text{s}}+Q_{\text{G}}\right)\end{array}$

Therefore, rearrange in terms of $Q_{\text{S}}$.

$Q_{\text{s}}=P-\left(AE+Q_{\text{G}}\right)$…… (1)

Now, rearrange in terms of $Q_{\text{G}}$.

$Q_{\text{G}}=P-\left(AE+Q_{\text{s}}\right)$…… (2)

And,

$Q_{\text{S}}=61\%\left(P-AE\right)$…… (3)

Substitute $61\%\left(P-AE\right)$ for $Q_{\text{S}}$ in equation (2).

$Q_{\text{G}}=P-\left[AE+61\%\left(P-AE\right)\right]$

Substitute $1778\text{ mm}$ for $P$ and $914\text{ mm}$ for $AE$.

$\begin{array}{c}{Q}_{\text{G}}=1778\text{ mm}-\left[914\text{ mm}+61\%\left(1778\text{ mm}-914\text{ mm}\right)\right]\\ =1778\text{ mm}-\left[914\text{ mm}+61\left(\frac{1}{100}\right)\left(864\text{ mm}\right)\right]\\ =336.96\text{ mm}\\ \approx \text{337 mm}\end{array}$

Substitute $1778\text{ mm}$ for $P$ and $914\text{ mm}$ for $AE$ in equation (3).

$\begin{array}{c}{Q}_{\text{S}}=61\%\left(1778\text{ mm}-914\text{ mm}\right)\\ =61\left(\frac{1}{100}\right)\left(864\text{ mm}\right)\\ =527\text{ mm}\end{array}$

The percentage is the ratio of each component to $P$ times 100 percent.

Calculate the percentage of each component of the watershed budget.

For actual evaporation,

$\%AE=\frac{AE}{P}\times 100\%$

Substitute $1778\text{ mm}$ for $P$ and $914\text{ mm}$ for $AE$.

$\begin{array}{c}\%AE=\frac{914\text{ mm}}{1778\text{ mm}}\times 100\%\\ =51.4\%\end{array}$

For surface runoff,

$\%Q_{\text{S}}=\frac{Q_{\text{S}}}{P}\times 100\%$

Substitute $1778\text{ mm}$ for $P$ and $527\text{ mm}$ for $Q_{\text{S}}$.

$\begin{array}{c}\%Q_{\text{S}}=\frac{527\text{ mm}}{1778\text{ mm}}\times 100\%\\ =29.64\%\approx 30\%\end{array}$

For groundwater discharge,

$\%Q_{\text{G}}=\frac{Q_{\text{G}}}{P}\times 100\%$

Substitute $1778\text{ mm}$ for $P$ and $\text{337 mm}$ for $Q_{\text{G}}$.

$\begin{array}{c}\%Q_{\text{G}}=\frac{\text{337 mm}}{1778\text{ mm}}\times 100\%\\ =18.95\%\approx 19\%\end{array}$

Conclusion:

The percent contribution of actual evaporation, groundwater discharge andsurface runoff component of the watershed budget are $51.4\%$, $19\%$ and $30\%$ respectively.