Water Balance and Budgets - Maple Help

Water Balance & Budgets

Main Concept

A water balance or water budget is the notion of accounting for the movements and transformations of water in a system (that is, watershed or drainage basin). The change in storage of water, or 'mass balance' is the main concept behind water balance. There are a number of components of this system:

 Input Storage Output precipitation groundwater inflow soil groundwater surface water evapotranspiration stream flow groundwater outflow

Water balance calculations can be useful for estimating evapotranspiration. There are some simple formulas involved in these calculations:

$\mathrm{ΔS}=\mathrm{Input}-\mathrm{Output}$

where, $\mathbit{ΔS}$ is the change in storage. To calculate the input, use the following formula:

$\mathrm{Input}=P+{G}_{\mathrm{input}}$

where, P is the precipitation and ${\mathbit{G}}_{\mathbit{input}}$ is the groundwater input. Similarly, you can calculate the output using the following equation:

$\mathrm{Output}=\mathrm{ET}+Q+{G}_{\mathrm{output}}$

where, ET is the evapotranspiration (combination of transpiration and evaporation), Q is the stream flow, and ${\mathbit{G}}_{\mathbit{output}}$ is the groundwater output. Combining all of these equations yields:

$\mathrm{ΔS}=P+{G}_{\mathrm{input}}-\left(\mathrm{ET}+Q+{G}_{\mathrm{output}}\right)$

However, in most cases, the difference between the groundwater input and output are negligible compared to the other terms; therefore, you can simplify the equation to the following:

$P-\left(\mathrm{ET}+Q\right)=\mathrm{ΔS}$

Similarly, in studies where long term water balance starts and ends at the same time of the year, the net change in storage is often small compared to the other terms in the equation. Therefore, making the assumption that $\mathrm{ΔS}\approx 0$, you can further simplify and rearrange the equation to solve for evapotranspiration:

$\mathrm{ET}=P-Q$

You will be able to further examine this relationship in the example below.

Example

Question

A 20 year study was conducted in a watershed area of 482 km${}^{2}.$ The precipitation was 101 cm/yr and the average stream flow was 5.32 m${}^{3}$/s. What is the annual evapotranspiration for this area over the 20 year study? (Assume net groundwater flows and the changes in storage are negligible. Also, assume the density of water is constant.)

Choose values for annual precipitation, average stream flow, and watershed areas. Click the button to see the evapotranspiration value. Click the check boxes to see each stage of the water cycle.

 Solution You can use the formula in the previous section to determine the evapotranspiration in the watershed area. However, you must do some unit conversions before that.     $P=4.87\cdot {10}^{8}$ m${}^{3}$/yr     $Q=1.68\cdot {10}^{8}$ m${}^{3}$/yr   You can now plug our known values into the equation in the previous section:   $\mathrm{ET}=P-Q$ $\mathrm{ET}=4.87\cdot {10}^{8}-1.68\cdot {10}^{8}$ $\mathrm{ET}=3.19\cdot {10}^{8}$ m${}^{3}$/yr   Therefore the average annual evapotranspiration in the watershed area over the 20 year study was $3.21\cdot {10}^{8}$ m${}^{3}$/yr.



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