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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
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(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.
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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
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(^0 1 2) time, hrs. 3 4 5 6
infiltration rate, cm/hr
soil-limited soil and rain-limited Cumulative Precipitation
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.