182 J. Og´ee et al. Agricultural and Forest Meteorology 106 2001 173–186
Fig. 8. Daily sums of soil heat flux vs. daily sums of transmitted net radiation. The solid line is the linear regression line R
2
= 0.59,
slope = 0.27, intercept = −0.47.
5. Modelling soil heat flux
Models deriving soil heat flux from microclimatic measurements can be very useful, especially in the ab-
sence of soil measurements. Several empirical models have been suggested to calculate the daytime heat flux
in a bare soil from net radiation or sensible heat flux Camuffo and Bernardi, 1982; Cellier et al., 1996.
Some authors have studied how soil water content and mean wind speed may influence this type of relation
Idso et al., 1975. However, none of these models have been tested 1 under a forest canopy, 2 during
night-time and 3 for yearly variations of the meteo- rological data and soil properties. The purpose of this
section is then to find a simple parameterisation relat- ing the soil heat flux G = Q
h
0 to simple microcli- matic data such as transmitted net radiation, and that
would account for the seasonal variations in soil water content or soil cover fraction.
5.1. Soil heat flux and transmitted net radiation Modelling soil heat flux from net radiation is not
trivial because their relationship involves other fluxes through the energy budget equation. In the case of a
soil under a forest canopy, the radiation hitting the ground must go through the canopy and the under-
storey. Hence, it exhibits strong horizontal heterogene- ity, which can only be appreciated at the expense of a
heavy experimental set-up. As mentioned earlier net radiation above the understorey is estimated with a
modified version of the radiative transfer model of Berbigier and Bonnefond 1995. Because we did not
have a radiative transfer model for the understorey it- self, it was decided to use this flux in what follows.
We saw that the diurnal amplitude of G is correlated to R
n,t
and soil water content Sections 4.3 and 4.4. We also observed that the maxima of G and R
n,t
do not occur at the same time, G being systematically
delayed by an amount of about 30 to 60 min. Despite these qualitative observations, it seems difficult to find
a clear relation between the diurnal means and phases of these two fluxes as Cellier et al. 1996 did over a
bare soil.
However, as the litter is likely to absorb most of the incoming radiation, the radiative fluxes at the soil sur-
face must not be a dominant term in the energy budget equation. This encouraged us to seek a parameterisa-
tion scheme using the whole energy budget equation.
5.2. Energy budget equation at the soil surface Assuming that net radiation at the soil surface is
a fraction α of the net radiation transmitted at the understorey level, R
n,t
, the energy budget equation at the ground surface is given by
G = αR
n,t
− H
soil
− LE
soil
12 where H
soil
and LE
soil
are the sensible and latent heat fluxes at the soil surface, respectively, assuming that
the litter above is very porous. In order to account for the time shift observed between G and R
n,t
we introduce a time delay 1t in the first term on the RHS
of Eq. 12. We also use the following parameterisation for H
soil
: H
soil
= ρ
a
C
p
βT
l,s
− T
a,l
13 where T
l,s
is the litter temperature at the litter-soil interface, T
a,l
the air temperature at the air-litter inter- face, ρ
a
the air density and C
p
the air heat capacity. The coefficient β has the dimensions of a conductance
m s
− 1
and will be called ‘soil surface conductance’ in what follows. The lowest level of air temperature
available in the experiment is located 0.2 m above
J. Og´ee et al. Agricultural and Forest Meteorology 106 2001 173–186 183
Fig. 9. a Monthly sums of soil heat flux and b cumulative values of soil heat flux thick line and transmitted net radiation thin line throughout the year of study.
the soil surface. Using this temperature in Eq. 13 amounts to including part of the sensible heat flux
from above the litter. However, given the level of en- ergy input at this height, this flux can reasonably be
considered as conservative. Hence, in what follows, we use the air temperature T
a,0.2m
at 0.2 m above the soil surface. In Eq. 13 we use the litter temperature at
the soil-litter interface instead of the soil surface tem- perature extrapolated from the smoothed temperature
profile for T
l,s
, because it is preferable to have inde- pendent estimates of G and H
soil
. Tests showed that us- ing the soil surface temperature led in fact to the same
results. We saw earlier that soil evaporation is always small
compared to soil heat flux. If we neglect this term in Eq. 12 or include it in αR
n,t
, the soil energy budget finally reduces to
G = αR
n,t
t − 1t − βρ
a
C
p
T
l,s
− T
a,0.2m
14 In other words, G appears as a linear combination of
transmitted net radiation with unknown time shift and the temperature difference between the soil sur-
face and the air just above. 1t is taken constant for the whole data set and equal to 30 min because this is
the most common time delay observed throughout the year.
184 J. Og´ee et al. Agricultural and Forest Meteorology 106 2001 173–186
Fig. 10. For the period from September 1997 to August 1998: a monthly values of the best fit parameters α and β in Eq. 14;
b monthly values of the best fit parameter α with β set to 2.12. Dashed lines show the general trend of each parameter.
Fig. 11. Soil heat flux, G, modelled vs. measured values: a period with a fully developed understorey July–November: α = 0.02, β =
2.12 mm s
− 1
; R
2
= 0.89, slope = 0.89, intercept = 0.34 and b with little understorey December–June: α = 0.12, β = 2.12 mm s
− 1
; R
2
= 0.94, slope = 0.92, intercept = 1.25.
It is then possible to calculate the coefficients α and β
for each month of the year. Their month-to-month variation is represented in Fig. 10a. The coefficient
β is nearly constant throughout the year with mean
β ≈ 2.20 mm s
− 1
, e.g. β
− 1
≈ 455 s m
− 1
, except in July–August 1998 where β takes a smaller value than
during the preceding months. The reason for this is unclear. In what follows we will consider that β
is constant over the year and equal to 2.12 mm s
− 1
mean value including July and August. Such a large value of the resistance β
− 1
472 s m
− 1
is caused by the resistance to air diffusion through the litter and
the air layer at the soil surface, which is likely to be quite large in this environment with very low wind.
However, it is still much lower than a resistance to molecular diffusion through 5 cm of air, that can be
estimated about 2300 s m
− 1
, taking 21.5 mm
2
s
− 1
for the molecular diffusivity Campbell, 1977.
The values obtained for a can be grouped in two categories or periods: from September 1997 to Jan-
uary 1998, α ≈ 0.02 and from February to June 1998 α ≈
0.12. The first period during which α is nearly zero does not coincide well with the period when
the understorey is fully developed from late June to mid-November Loustau and Cochard, 1991. This is
in contradiction with the hypothesis that α essentially depends on the understorey leaf area index. However,
fixing β at 2.12 and then adjusting α alone leads to a yearly cycle of α in much better agreement with this
hypothesis Fig. 10b. Indeed, from December 1997
J. Og´ee et al. Agricultural and Forest Meteorology 106 2001 173–186 185
Fig. 12. Evolution of modelled and measured soil heat flux, G, for 20 days in September 1997 α = 0.02, β = 2.12 mm s
− 1
and 20 days in April 1998 α = 0.12, β = 2.12 mm s
− 1
.
to June 1998, α takes a mean value of 0.12 while it is nearly zero during the other months.
The coefficients α and β do not seem to change with soil water content, whereas we saw in a preced-
ing section that the daily amplitude of soil heat flux increases with soil water content. In fact, this is not
contradictory because soil water content is likely to influence also the amplitude of the difference between
air and litter temperatures.
Fig. 11a and b compare the modelled soil heat flux values for the two periods with experimental values.
The agreement is very good for the whole set of data. In particular, the model reproduces well the occa-
sional accidents in soil heat flux during periods of cooling or heating, as is visible in Fig. 12 that dis-
plays temporal variations of both fluxes in Septem- ber 1997 with understorey and April 1998 without
understorey.
A more deterministic model would consist in us- ing a simple two-layer model such as the force-restore
model Deardoff, 1978 along with Eq. 14, with the T
l,s
being the ‘surface’ temperature of the force-restore model. Then, we would need only the air temperature
at 20 cm to estimate, at the same time, the soil heat flux and the soil surface temperature. Such a model
could be integrated in a multi-layer model with a tur- bulent transfer sub-model that would compute, from
air temperature data above the canopy, air temperature profiles above and within the stand. This is the object
of current work.
6. Conclusion
