Problem 57800. Compute infiltration and runoff under constant precipitation with the Green-Ampt method

Problem statement
Write a function that computes infiltration, depression storage, and runoff using the Green-Ampt method. It should take as input the rainfall intensity i, saturated hydraulic conductivity Ks, initial moisture content thetai, saturated moisture content thetas, average suction head Psi_av, maximum available depression storage Smax, and a vector of times t. If ponding occurs, the function should insert the ponding time into the time vector. It should then compute the cumulative infiltration F and depression storage S at each of the times, as well as the runoff Q during the periods between the times. The cumulative infiltration, depression storage, and runoff are expressed as depths.
Background
To compute runoff during a rainstorm, one must determine how much water infiltrates the soil. Then the excess rainfall will fill depressions, and any remaining water will run off. The infiltration rate f is the smaller of the rainfall intensity and the potential infiltration rate (or infiltration capacity) fp, and the cumulative infiltration F is the integral of the infiltration rate over time. When the infiltration rate is equal to the infiltration capacity, water will pond on the ground surface.
The infiltration capacity predicted by the Green-Ampt method is
fp = Ks(1+Psi_av(thetas-thetai)/F)
The cumulative infiltration at ponding and the time of ponding can be computed using this formula. After ponding starts, the cumulative infiltration is given implicitly as a function of time by
t = (1/Ks)[F-Psi_av(thetas-thetai) ln(1+F/Psi_av(thetas-thetai)]+tp-t'p
where
t'p = Fp/Ks-(thetas-thetai)(Psi_av/Ks) ln(1+Fp/(Psi_av(thetas-thetai)))
is the time to infiltrate Fp from the start of the storm under immediate ponding.

Solution Stats

60.0% Correct | 40.0% Incorrect
Last Solution submitted on Apr 24, 2023

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