Infiltration
The Green and Ampt model is a widely used analytic expression of cumulative infiltration:
1/ 2
⎛
h -h ⎞
I = (θ0 - θi ) ⎜ 2K0t 0 i ⎟
(1)
θ0 - θi ⎠
⎝
where I is cumulative infiltration (m); t, time (s); θ0, volumetric soil water content at saturated surface (m3m3); θi,
antecedent volumetric soil water content (m3m3); K0, hydraulic conductivity at the saturated surface (ms1); h0, hydraulic
head at the saturated surface (m); and hi, antecedent hydraulic head in the soil profile (m) (Jury et al. 1991). Temperature has
strong influence on two of the parameters in equation (1), the hydraulic conductivity (via the effect of temperature on water's
viscosity) and the antecedent hydraulic head (via an as-yet-unknown mechanism).
Figure 2. Viscosity of water between 0 and 50 C.
The viscosity of water decreases with increasing temperature (Fig. 2). The following relation describes the viscosity of
water (η, Pas) as a function of temperature:
⎛
B ⎞
ηl = η0 exp ⎜
(2)
⎟
⎝ T + T0 ⎠
where T is temperature (C) and η0, B, and T0 are fitted constants (Grant 2004). The hydraulic conductivity can be described
by
kρg
K0 =
(3)
η
ERDC/CRREL TN-04-6
3
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