Available Energy: Net Radiation and Soil Heat Flux - Transport in the Atmosphere-Vegetation-Soil Continuum - page 60

Figure 2.27 Measurement of soil heat lux: soil heat lux plate determines lux from
temperature difference (left); soil heat lux plate (black rectangle) is buried at some
depth ( z m ) so that the heat lux measured by the plate is less than the surface soil heat
lux (right).

There are roughly two ways to correct measurements at some depth for this change
in G with depth: the calorimetric method (e.g., Kimball and Jackson, 1975 ) and the
harmonic method (e.g., Horton et al., 1983 ; Verhoef et al., 1996 ).
The calorimetric method takes into account the heat storage between the sur-
face and the soil heat lux plate (located at a depth z m ). The change in tempera-
ture of that layer, T G , is measured. By integrating Eq. ( 2.30 ) with depth, we obtain
∂
∂ =

T
t

1

( )

G

GG −

, from which G 0 can be obtained (see Figure 2.27 ).

Cz

0 m

sm

In the harmonic method temperature observations from at least two depths ( z d1
and z d2 ) are needed, in combination with a soil heat lux observation at another depth.
The time series at one depth, z d1 , is decomposed into a Fourier series, so that not only
the sine of the diurnal cycle (with frequency ω ) is taken into account but also higher
harmonics (with frequencies 2 ω , 3 ω , etc.):

M

( )

∑

Tz t (,) =+ T   A ( z )sin nt ωφ + () z   (2.44)

d n d n d

n = 1

where A n ( z d ) and φ n z ( d are the amplitude and phase for harmonic n at depth z d .
The depth dependence of the amplitude and phase are Az

() = A () 0exp ( − nzD / )

n d n d

= −0 , respectively. The next step is to use the observed soil
temperature at the second level z d2 to estimate the optimal thermal diffusivity: κ s is
selected such that it produces (with Eq. ( 2.44 ) and the expressions for the amplitude
A n and phase φ n ) the best approximation for Tz t

and φ

() z φ () nzD /

n d n d

d2 , in a least-square sense. Then,
using the known κ s , the vertical derivative of Eq. ( 2.44 ) is evaluated at the depth of
the soil heat lux plate to infer the thermal conductivity λ s (with Eq. ( 2.29 )). Finally,
the vertical derivative of Eq. ( 2.44 ) is evaluated at the surface (with the known λ s ) to
determine the surface soil heat lux. This entire procedure relies on the assumption

(, )