(iv) By the energy balance of the surface, given that the flux to the soil is 10% of
the radiative balance, we have
0:9 S T À qS T þ e atm T
4
atm À e s T
4
s
À
Á
r
Â
à À H À LE ¼ 0
ð7:14Þ
where the T atm and T s referred to average air temperature and ground surface temperature, respectively. The variables e atm and e s refere to air and surface emissivity,
respectively. The emissivity of the atmosphere is obtained by Eq. (7.10) which
involves calculating the vapor pressure using Eq. (4.16) from the measured specific
humidity, as mentioned. Assuming e (ratio between the molecular mass of water
vapor and air) is 0.622 and the atmospheric pressure is 100 kPa at vapor pressure e,
using Eq. (4.16) gives 1734.73 Pa:
q ¼
e e
p
ð4:16Þ
Substituting this value into Eq. (7.10), we get
e atm ¼ 1:72
e
T
1=7
ð7:10Þ
We obtain an air emissivity value of 0.83.
Replacing several variables in Eq. (7.14), we obtain a surface albedo, q, of 0.27.
7.9 Example 8: Application of the Eddy Covariance
Method
A sonic anemometer and an analyzer were used to sample at a frequency of 0.1 Hz,
to measure temperature, velocity, and absolute humidity in a vegetated area.
Table 7.7 shows four sets of instantaneous measurements.
The aim is to calculate:
(i) Sensible and latent heat fluxes over vegetation
and,
(ii) Canopy aerodynamic resistance.
Consider that the air specific heat at constant pressure and the density are 1000
Jkg
−1 K
−1 and 1.2 kgm
−3 , respectively, and the value for the latent heat of water is
2500 Jg
−1 .
Solution:
(i) The sensible heat and latent fluxes are given by Eqs. (3.22) and (3.23) in
Chap. 3 as
7.8 Example 7: Application of the Aerodynamic Method
251
the radiative balance, we have
0:9 S T À qS T þ e atm T
4
atm À e s T
4
s
À
Á
r
Â
à À H À LE ¼ 0
ð7:14Þ
where the T atm and T s referred to average air temperature and ground surface temperature, respectively. The variables e atm and e s refere to air and surface emissivity,
respectively. The emissivity of the atmosphere is obtained by Eq. (7.10) which
involves calculating the vapor pressure using Eq. (4.16) from the measured specific
humidity, as mentioned. Assuming e (ratio between the molecular mass of water
vapor and air) is 0.622 and the atmospheric pressure is 100 kPa at vapor pressure e,
using Eq. (4.16) gives 1734.73 Pa:
q ¼
e e
p
ð4:16Þ
Substituting this value into Eq. (7.10), we get
e atm ¼ 1:72
e
T
1=7
ð7:10Þ
We obtain an air emissivity value of 0.83.
Replacing several variables in Eq. (7.14), we obtain a surface albedo, q, of 0.27.
7.9 Example 8: Application of the Eddy Covariance
Method
A sonic anemometer and an analyzer were used to sample at a frequency of 0.1 Hz,
to measure temperature, velocity, and absolute humidity in a vegetated area.
Table 7.7 shows four sets of instantaneous measurements.
The aim is to calculate:
(i) Sensible and latent heat fluxes over vegetation
and,
(ii) Canopy aerodynamic resistance.
Consider that the air specific heat at constant pressure and the density are 1000
Jkg
−1 K
−1 and 1.2 kgm
−3 , respectively, and the value for the latent heat of water is
2500 Jg
−1 .
Solution:
(i) The sensible heat and latent fluxes are given by Eqs. (3.22) and (3.23) in
Chap. 3 as
7.8 Example 7: Application of the Aerodynamic Method
251