1. Green and Ampt Infiltration
CEVE 412
January 30, 2018

2. Natural vs developed watershed
Developed watersheds typically have higher imperviousness
Affects infiltration and surface runoff

3. Factors affecting infiltration

4. Factors affecting infiltration
Soil types have a wide range of hydraulic conductivity (clay: lowest and sand: highest)
Level of compaction affects porosity

5. Various Soil types
Sand
Loam
Clay

6. Factors affecting infiltration
Rainfall intensity and magnitude can overwhelm infiltration rate and capacity

7. Horton vs Green and Ampt
𝑓= 𝑓 𝑐 + 𝑓 0 − 𝑓 𝑐 𝑒 −𝑘𝑡
𝑓= 𝐾 𝑠 (1 − 𝑀 𝑑 ψ 𝐹 )
Empirically derived to describe the exponential decay of infiltration rate over time
Decay coefficients difficult to determine
Assumes ponding regardless of actual rainfall intensity
Based on theoretical derivation of Darcy’s Law
Parameters can be determined from measurable soil parameters
Allows for calculation of ponding time

8. Principles (assumptions):
Soil is homogeneous and stable.
The supply of ponded water at the surface is not limited
Capillary suction is uniform and constant
A sharp wetting front exists and advances at the same rate as water infiltrates
The soil is uniformly saturated above the wetting front, the vol. water contents remain constant and below the advancing wetting front.

9. Green and Ampt Method (1911)
Used to predict cumulative infiltration as a function of time and readily available soil parameters.

10. Soil Properties - Terminology
F(t) = L (η - θi) = L Md
Moisture content (θ) = ratio of the volume of water to the total volume of a unit of porous media.
Md = the difference between the porosity and the initial moisture content
Porosity (η) = ratio of interconnected void volume to total sample volume.
Hydraulic conductivity (K) = volume of water that will flow through a unit soil column in a given time.
Capillary suction head (ψ) = measure of the combined adhesive forces that bind the water molecules to solid walls and the cohesive forces that attract water molecules to each other. Md η

11. Similarly, f = Ks 𝜕ℎ 𝜕𝑧 Darcy’s Law
q = -K(θ) ∂h/∂z
q = Darcy velocity
z = depth below surface
h = potential or head = z + ψ
K(θ) = unsaturated K
Similarly,
f = Ks 𝜕ℎ 𝜕𝑧
f = Ks ℎ1−ℎ2 𝑧1−𝑧2 = Ks ℎ0−(−𝐿−ψ) 𝐿 ≈ Ks 𝐿+ψ 𝐿
Substitute 𝐹 𝑀𝑑 for L, then:
f = Ks ψ𝑀𝑑+𝐹 𝐹 = Ks ψ𝑀𝑑 𝐹 +1 1 2

12. Equation for Green & Ampt Infiltration
f(t) = i for t ≤ tp
f(t) = Ks(1 + Mdψ/F) for t > tp
where:
f(t) = infiltration rate at t
Ks = vertically saturated K
Md = moisture deficit
Ψ = capillary suction F = cumulative depth of water infiltrated into the soil
i = rainfall rate or intensity
tp = the time it takes to have water begin to pond at the surface

13. Important Note When Ψ is given as positive, use Formula AB
When Ψ is given as positive, use Formula A
When Ψ is given as negative, use Formula B

14. three Infiltration Scenarios
Case 1: i < Ks (line A) f = i. Runoff will never occur and all rainfall will infiltrate regardless of the duration
Case 2: Ks < i < f (line B) f = i until it reaches ponding time, tp
Case 3: Ks < i and i > f (curve C) Runoff can occur.
f = Ks ψ𝑀𝑑 𝐹 +1
Ponding Time

15. Green and Ampt Parameters
Parameters Ks, ψ, and Md can be determined from physical measurements in the soil.
Data Sources:
U.S. Natural Resources Conservation Service (NRCS) Soil Data Mart. Note: There are two different data sets available: State Soil Geographic (STATSGO) and Soil Survey Geographic (SSURGO). SSURGO is more detailed.
See Rawls’ work to convert soil info to Green-Ampt parameters (Rawls, Brakensiek, & Saxton, 1982; Rawls, Brakensiek, & Miller, ).

16. Green and Ampt Parameters

17. Porosity & soil moisture contentMd η θe θi θr
1.0
θr = residual water content
Se = effective saturation

18. Porosity & soil moisture content
𝑆 𝑒 = θ 𝑖 − θ 𝑟 η− θ 𝑟 = θ 𝑖 − η− θ 𝑒 θ 𝑒
𝑆 𝑒 θ 𝑒 = θ 𝑖 −η + θ 𝑒
Since 𝑀 𝑑 = η− θ 𝑖 , then rearranging the above equation yields:
𝑀 𝑑 = θ 𝑒 1− 𝑆 𝑒

19. Double ring infiltrometer
Measures infiltration rate or hydraulic conductivity based on constant or falling head
Outer ring forms a buffer zone to ensure a 1-D vertical flow within the inner ring for accurate infiltration measurements

20. applications Agriculture: irrigation
Urban planning: green infrastructure
Hydrology: watershed/drainage studies, hydrologic models

21. Example 2-12 (Hydrology and Floodplain Analysis, 6th ed.)
Since i > Ks  Cases 2 and 3
f = i for 0 ≤F ≤Fp, and
f = Ks ψ𝑀𝑑 𝐹 +1 for F > Fp
where Fp = amount of water that infiltrates the soil before surface ponding occurs
Note: Md = θs - θi

22. Example 2-12 (Hydrology and Floodplain Analysis, 5th ed.)
Rearrange equation f = Ks ψ𝑀𝑑 𝐹 +1 to obtain Fp:
Fp = ψ𝑀𝑑 1−𝑖/𝐾𝑠 = −(9.37 𝑖𝑛)(0.518−0.318) 1−(7.858 𝑖𝑛 ℎ𝑟 )/(1.97 𝑖𝑛 ℎ𝑟 ) = in.
For 0 ≤F ≤Fp, f = i = 7.88 in/hr.
For F >Fp, f = Ks ψ𝑀𝑑 𝐹 +1
f = i
f = Ks ψ𝑀𝑑 𝐹 +1 Fp

23. Example 2-12 (modified)
How long does it take before the surface starts ponding?
tp = Fp / i = in / 7.88 in/hr = hr ≅ 4.8 mins
Also, how do we determine the infiltration depth, F after a certain time, t has elapsed?
Chow et al., 1988
Use goal seek in Excel to determine F.