Available Energy: Net Radiation and Soil Heat Flux - Transport in the Atmosphere-Vegetation-Soil Continuum - page 61

that the thermal properties of the soil are uniform. This assumption may be incorrect
owing to soil layering, vertical gradients in soil moisture content, and variation in the
presence of roots.
Question 2.22: Given a circular soil heat lux plate with the following characteristics:
λ m = 0.8 W m -2 K -1 , thickness 5 mm, diameter 10 cm. The lux plate is used in a satu-
rated loosely packed sandy soil.
a) The soil heat lux measured by the sensor is 55 W m -2 . What is the real soil heat lux
at that location?
b) Given the real soil heat lux calculated in (a), what would be the measured soil heat
lux if the lux plate were twice as thick?
Question 2.23: Assume that in Figure 2.18b the soil temperature measured at 5 cm
depth is representative of the temperature in the upper 5 cm of the soil (or at least the
time rate of change at 5 cm depth is comparable to that in the entire upper 5 cm). The
soil heat lux plate (of which the data are shown in Figure 2.26 ) is installed at a depth
of 5 cm.
a) Estimate from Figure 2.18b the instantaneous rate of increase of the soil temperature
at 5 cm depth, at 9 UTC.
b) Estimate the heat storage in the layer above the heat lux plate (assume a volumetric
heat capacity of the soil of 3.0 10 6 J K -1 m -3 ).
c) Estimate the real surface soil heat lux from the result of question (b), in combina-
tion with the observed soil heat lux at 5 cm depth ( Figure 2.26 ).
Question 2.24: Solve this question using the harmonic method. Because the solution
requires some iterations, use a spreadsheet program.
From a Fourier analysis of the soil temperature at 5 cm depth the amplitude and
phaseshift are determined for the irst and second harmonic of the diurnal cycle: A 1 =
6.9 °C, A 2 = 1.4 °C, φ 1 = -10.10 hour and φ 2 = -9.97 hour. The daily mean temperature
is 20 °C.
At a depth of 10 cm, the observed soil temperature is 18.4 at 10 hours and 22.7 at 16
hours. At 7 cm depth, the soil heat lux observed at 10 hours is 35 W m -2 .
a) Determine the damping depth for the diurnal cycle (irst harmonic) and the thermal
diffusivity.
b) Determine the soil thermal conductivity.
c) Determine the soil heat lux at the surface.
2.3.8 Snow and Ice
The presence of water in the solid phase, either on the soil (snow) or in the soil (ice)
has important repercussions for the surface energy balance. First, the thermal proper-
ties of snow and ice are different from those of the soil. Furthermore, the presence of
solid water implies that an extra phase change (from water to ice, or from snow/ice to
water) may occur, implying an extra release or consumption of latent heat.