Integrated Applications - Transport in the Atmosphere-Vegetation-Soil Continuum - page 299

with a mean depth of 750 m, during 4 hours, and assuming no entrainment of heat 3 ,
the boundary layer would heat up by 1-2 K under normal conditions, with stronger
heating for the forest. For heat wave conditions the difference in heating over grass
and forest is much more pronounced: for grass the heating rate increases only slightly,
whereas over the forest it nearly doubles. One could argue that the higher sensible heat
lux over the forest will give rise to a deeper boundary layer owing to stronger convec-
tion. The deeper boundary layer would lead to a smaller temperature increase, but this
growth would also entail a larger entrainment of warm air.

8.4.4 Temporal Development of the Energy
and Water Balance
The previous analysis considered only the partitioning of available energy under con-
ditions that were assumed to be not limited by soil moisture: the differences in the
energy balance were solely due to the different atmospheric forcing. However, as time
progresses and soil moisture is not replenished by rainfall, the soil will dry out and the
transpiration may be reduced below its unstressed values.
To study the development of surface luxes during the dry down process a simple
soil water balance model is used, based on the Warrilow model introduced in Chap-
ter 4 . This model consists of the following components and parameter choices (which
are realistic but arbitrary):

• Unstressed daily evapotranspiration is based on the observations given in Table 8.6 . To

convert the average luxes during the 9-13 UTC period to a daily evapotranspiration the
fraction of the total lux that occurs between 9 and 13 UTC is assumed to be 0.3 (the data
in Teuling et al. ( 2010 ) show a range for this fraction of 0.3-0.4). Unstressed surface
luxes are supposed to be constant from day to day.
Available energy is assumed to be constant from day to day: a reduction in evapotranspi- •

ration will translate in an equal increase in sensible heat lux.
The rooting depth of grass and forest is set to 0.4 m and 0.6 m, respectively (the depth of •

the layer in which 80% of the roots are located; Zeng, 2001 ).
The volumetric soil moisture content at which reduction of evapotranspiration starts to •

occur is set to 0.2 and evapotranspiration stops at a water content of 0.1.
The initial soil moisture content is set at 0.3. •

With these ingredients, the development of the surface luxes (9-13 UTC averages) as
shown in Figure 8.8 can be simulated. As long as the soil moisture content is above the
critical value, evapotranspiration is controlled by the atmospheric forcing, and hence
constant in the present simple model. For the climatological conditions evapotrans-
piration of grass and forest are nearly identical, and hence the difference in timing of

3 If the entrainment of heat from the atmosphere above the boundary layer would be taken into account, the heating
would be approximately 20% higher.