Page 126 - Biosystems Engineering

Soil and W ater Conservation 107

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where S is the sorptivity [L/T ] and K [L/T] is the conductivity.
Taking the derivative of F with respective to t gives
S
f = + K (3.17)
2 t
The first term on the right-hand side represents the suction effect, and
the second term represents the gravity effect. For horizontal infiltration,
suction is the only force; therefore, the last term should be dropped.

Green–Ampt Model This is a more physically based approach than
the remaining models with an analytical solution (Green and Ampt
1911). Without going into details of derivation, the G–A model can be
written as
⎡ΨΔθ ⎤
ft() = K ⎢ + 1 ⎥ (3.18)
⎣ Ft() ⎦
where ψ is the wetting front suction head [L], Δθ = θ − θ , θ is the
s i s
saturated water content or porosity (= φ), and θ is the initial or ante-
i
cedent water content. In Eq. (3.18), f(t) depends on F(t). Therefore, to
solve for f(t) we first need F(t). F(t) can be obtained by using the rela-
tionship f(t) = dF(t)/dt and integrating both sides:
⎡ Ft() ⎤
Ft() = ΨΔθ ⋅ ln 1 + ⎥ + Kt (3.19)
⎢
⎣ ΨΔθ ⎦
Note that this is a nonlinear equation in F, which can only be solved
iteratively. A good starting point at the beginning of the iteration is to
assume that F = Kt. Rawls et al. (1982) provide summaries of various
soil parameter values for various soil types. Using Rawls et al. (1982) as
the source, Chow et al. (1988) reported values of parameters K, φ, and
ψ for various soil types in their widely used book Applied Hydrology
(Chow et al. 1988).
A very important detail is that derivations of the foregoing equa-
tions are based on the assumption that there are fully ponded condi-
tions of small water depth. Ponding occurs when the rainfall inten-
sity is higher than the soil infiltration capacity (i > f ). If ponding never
occurs, then the infiltration rate is simply equal to the rainfall inten-
sity. Solution for mixed conditions of ponding/nonponding is more
complicated and is not covered here. Interested readers on this topic
are referred to Chow et al. (1988).

3.5.2 Runoff
Runoff is the portion of precipitation flowing on overland planes
after interception infiltration and evaporation losses are met. Runoff
is especially important for the erosion process because sheet erosion
is driven by runoff water. Runoff water sometime can infiltrate back
into the soil when it flows over soil with very high hydraulic conduc-
tivity. This process is called runon.