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The Hydrologic Budget CE 421, Fall 2005
The hydrologic cycle is represented graphically below :
(source: http://pa.lwv.org/wren/pubs/primer.html)
Mathematically , we represent this picture for a watershed (the control volume) as:
I O
dt
dS
where S = total storage of water in the watershed, I = inflows, O = outflows
As you learned in fluid mechanics, this equation can be applied to any control volume (tank, lake, watershed, etc.). For a watershed, the boundaries are typically defined by the land surface (top), the bedrock surface (bottom), and topographic divides (sides).
Now, assuming (1) all groundwater in the watershed eventually discharges to the stream (might not be true for some geologic settings), and (2) there are no anthropogenic transfers of water across watershed boundaries, we can write the water budget equation for the watershed as:
P ET Q
dt
dS
= − − (a “ grave equation ”)
where P = precipitation, ET = evapotranspiration, Q = streamflow (baseflow + runoff) at the watershed outlet, and S = water storage (groundwater, soil moisture, lakes, snow, glaciers)
A note about units :
P and ET are typically given in L/t (in/day), but Q is in L^3 /t (cfs). P and ET are spatial measurements over the watershed, while Q is a point measurement at the outlet. The two are related by the watershed area: L/t x Area ( L^2 ) = L^3 /t
(in/day) * (acres) * (43,560 ft^2 /acre) * (1 ft/12 in) * (1day/86,400 sec) = ft^3 /s or cfs
Some important points regarding watershed water budgets:
1. Water budget calculations must always ha ve some associated time interval (usually monthly or
annual).
2. It is often assumed that I = O over a year’s time, that is the total annual precipitation ˜ total
annual streamflow + evapotranspiration. But, annual water budgets are not based on the calendar
year, they are based on the “hydrologic water year” (WY), which goes from Oct 1 to Sept 30 of
the following year (we don't use calendar years because water that falls in November and
December as snow may not melt until the next calendar year)
3. In temperate regions like Pennsylvania, annual Q is typically about 1/3 of P – this may vary
depending on geology, soil type, land use, and land development. It also varies from year to year
(from ~20 to 60%) due to weather, such as how intense the storms are that particular year, how
wet conditions are when it rains, periods of drought, etc.
Here’s another picture of the hydrologic cycle from a meteorologist’s point of view.
What’s missing that is critically important to a hydrologist?
