name
1) Last summer, your cornfield received 10 cm of rain in 5 hours. You decide to investigate
how the field might have fared under different conditions, using the method of Green &
Ampt. Assume that the field is flat and homogeneous, and the soil was at a uniform wetness.
You know that the soil
φ
= 0.47, and the water retention curve is approximately h = 5.1
θ
-2.8.
Before the rain, the soil was measured and found to have
θ
= 0.30. I have posted the
spreadsheet that you put together for these calculations.
(a) Given 5 hours of rainfall at 2 cm/hr, what Ks would result in 4 cm of runoff?
0.136 cm/hr.
(b) Given the Ks value from (a), what is the greatest antecedent volume wetness that would
give no runoff? 0.195
(c) For Ks = 0.2 cm/hr, plot the maximum 1-hour, 2-hour, and 5-hour rainfall rates that will
not produce runoff, as a function of antecedent volume wetness.
For this question, I set the antecedent wetness to each of several values, then
adjusted the rainfall rate so that, for the time period specified, the cumulative
precipitation was equal to the soil-limited infiltration rate. For example, for the 2-
hour rainfall, I must have B96 = E96. The left-hand graph shows that the
cumulative infiltration line passes through the point at which the infiltration rate
changes from rainfall-limited to soil-limited – this can help you visually identify the
right point. The right-hand graph shows the results. I did this both “by eye”, and
with the Solver.
0.1
1
10
100
1000
0.00 0.10 0.20 0.30 0.40 0.50
Antecedent volume wetness
Max. rainfall rate w/o runoff
1 hour
2 hour
5 hour
0
2
4
6
8
10
0123456
time, hrs.
infiltration rate, cm/hr
soil-limited
soil and rain-limited
Cumulative Precipitation
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