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Green and Ampt - Soil Physics - Solved Home Work, Exercises of Soil Physics

Soil physics is the study of soil physical properties and processes. It is applied to management and prediction under natural and managed ecosystems. (Wikipedia). Keywords in this solved assignment are: Green and Ampt, Flat, Uniform Wetness, Volume Wetness, Solver, Infiltration Rate, Kostiakov Model, Philips Model, Potential Difference, Hydraulic Conductivity

Typology: Exercises

2012/2013

Uploaded on 12/31/2013

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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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  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 K s would result in 4 cm of runoff? 0.136 cm/hr.

(b) Given the K s value from (a), what is the greatest antecedent volume wetness that would give no runoff? 0.

(c) For K s = 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.

1

10

100

1000

0.00 0.10 0.20 0.30 0.40 0. Antecedent volume wetness

Max. rainfall rate w/o runoff

1 hour 2 hour 5 hour

0

2

4

6

8

10

(^0 1 2) time, hrs. 3 4 5 6

infiltration rate, cm/hr

soil-limited soil and rain-limited Cumulative Precipitation

  1. Given the values saved in the spreadsheet (reproduced below), use the Solver to find the best fit values for the parameters of the (1st^ value is for all times, 2nd^ for starting at 2.25 hours)* a) Kostiakov model: B = 4.03, 3.26 n = 0.98, 0.

b) Green & Ampt model: b = 7.57 ic = 0.

c) Philips model: s = 35.4, 7.0 ic = -10.24, -0. or, with ic forced to 0.3: s = 20.17, 4.41 ic = 0.

d) Which model fits best? G&A. This isn’t a surprise, given that the “inputs” were generated by the G&A equation. G&A error was on the order of 10-11, while the others ranged from 10-2^ to 10^5.

e) Compare the i c values from the Green & Ampt, and Philip models. G&A gets the “correct” ic – the input Ks value – with good precision. Philip’s model converges with a negative ic, which is physically nonsensical. When I force the Philip model to have the correct ic value, the error term is greater.

Change only the red numbers antecedent volume wetness: 0. Suction at wetting front: 148 cm porosity 0. Ksat 0.3 cm/hr time step 0. precipitation rate 2 cm/hr available porosity 0.

  • Method: given these parameters, runoff starts at 2.25 hours. Before that, the infiltration rate is precipitation-limited. So I could use either (a) the soil-limited calculations starting from the first time step, or (b) the “actual” rate starting at the onset of runoff (rows 107:216) (I did both). The use of the Solver is similar to how we’ve used it before.