BASICS OF A SOIL LAYER
MODEL
- Believe it or not, but measuring the soil temperature below the surface is
easier than measuring the skin temperature
- Soil temperature variations decrease exponentially with depth.
- only small fluctuations are observed at depths of about 1 meter.
- much smaller fluctuations are observed at depths of 10 meters!!
- Check out the graph to the right showing the soil temperature variation
over a period of three days at three different levels.
- Data was collected in dry, sandy loam soil.
- What two observations about this graph can you make? ANSWER
- Soil Temperatures depend on:
- latitude
- season
- net radiation at the surface
- soil texture
- moisture content
- ground cover
- surface weather conditions
- At greater depths (on order of 10 meters), temperature fluctuations having
a period of a year are observed.
- Again, check out the graph to the right ->
Thermal Properties of Soils
- So, in order to determine the skin temperature of the soil, it is
important to understand how heat is transferred upward and and downward
through the soil.
- The important heat transfer mechanism in this problem is conduction.
- Then, the ground heat flux at any depth in the soil can be given as:
(1)
where kg is the thermal diffusivity of the soil.
EXTRA CREDIT:
- Using the Second Law of Thermodynamics, show that a prognostic equation
for the soil temperature can be given by:
(2)
where Cg is the soil heat capacity (Cg =
soil density, r, times the soil specific heat,
c)
combining (2) with (1) yields:
(3)
where vg = kg/Cg = soil thermal
diffusivity.
- Given proper boundary conditions, (3) can be solved to find the soil
temperature at different levels as a function of time.
- With appropriate boundary conditions, solutions to (3) show that soil
temperature decreases exponentially with depth and that the phase of the
temperature changes with depth as well, consistent with the figures shown
above.
- Typical values of the mass density, specific heat, thermal conductivity
and thermal diffusivity for different materials are given in the table
below:
| MATERIAL |
CONDITION |
MASS DENSITY (r)
(kg m-3 x 103) |
SPECIFIC HEAT (c)
(J kg-1 K-1 x 103) |
THERMAL CONDUCTIVITY
(kg)
(W m-2 K-1) |
THERMAL DIFFUSIVITY
(vg)
(m2 s-1 x10-6) |
| Air |
20 Deg C, Still |
0.0012 |
1.01 |
0.025 |
20.5 |
| Water |
20 Deg C, Still |
1.00 |
4.19 |
0.57 |
0.14 |
| Ice |
0 Deg C, Pure |
0.92 |
2.10 |
2.24 |
1.16 |
| Snow |
Fresh |
0.10 |
2.09 |
0.08 |
0.38 |
| Snow |
Old |
0.48 |
2.09 |
0.42 |
0.05 |
| Sandy Soil |
Fresh |
1.60 |
0.80 |
0.30 |
0.24 |
| Clay Soil |
Dry |
1.60 |
0.89 |
0.25 |
0.18 |
| Peat Soil |
Dry |
0.30 |
1.92 |
0.06 |
0.10 |
| Rock |
Solid |
2.70 |
0.75 |
2.90 |
1.43 |
Table and figures from Arya, 2001
