SSC 107 Soil Physics
Dec. 1, 1999
Due Dec. 8, 1999 Problem Set #7
1. The CO2 vertical distribution in the crop root zone can be expressed as
o
m
2
m
gCz
D
L
z
D2
)z(C+
α
+
α
−=
Where Co is the CO2 concentration at the soil surface, Dm is the apparent diffusion
coefficient, z is the depth, L is the depth to an impermeable layer, and α is the CO2
production rate and assumed to be constant over time and depth. Assume that the
bulk-air diffusion coefficient a
g
D is 0.19 cm2/sec, the total porosity is 0.45 cm3/cm3,
the water content is 0.35 cm3/cm3 over the depth L of 600 mm. If the CO2
concentration at the surface is 400 ppm, show how the consumption rate affects the
CO2 distribution in the root zone. List any assumptions you make.
2. A soil has a volumetric water content of 0.3 cm3/cm3 and a bulk density of 1.4
g/cm3.
a. Calculate the volumetric heat capacity of the soil (heat required to raise the
temperature of 1 cm3 of wet soil by 1 oC.)
b. Calculate the heat capacity of the soil on a mass basis.
c. Calculate the thermal diffusivity if the thermal conductivity is 18 cal/cm hr oC.
d. If this soil exists in a field, calculate the heat required to increase the temperature
of a 15 cm deep soil, 2 hectare in area, by 5 oC.
3. The diagram below shows the temperature variation at the soil surface over a 24-
hour period.
a. Compute the angular frequency ω=2π/τ with τ denoting time in hours for one
complete temperature cycle.
b. Compute the damping depth of the soil if the thermal diffusivity of the soil
material is 10 cm2/hr.
c. Determine the amplitude of the wave (Ao) at the surface and calculate the
amplitude of the temperature wave at the 15-cm depth.
d. Compute the maximum temperature change at the 15-cm depth.
e. Compute the time (in hours) at which the maximum temperature occurs at the 15-
cm depth.
