Surface Fluxes of Momentum, Heat, and Water Vapor
71
Third order structure function
For velocity the third order structure function represents the averaged cubed velocity differences
over lag r, D"u,,(r) =< (u(x + r) - u(xW > (Monin and Yaglom, 1975, Ch.8). For temperature
the mixed third order structure function is Duoo =< (u(x + r) - u(x))(B(x + r) - B(X))2 >
These structure functions scale in the inertial sub range with r as
4
--c:r
5
(3.28)
(3.29)
Note that with this approach the dissipation rates for momentum and heat can be directly
computed without resort to empirical constants. This method is superior to the second order
methods in that no empirical constants are used and also the dissipation rate for temperature
variance is not dependent on prior numerical calculation of the dissipation rate for momentum.
This approach has been used by Albertson et ai. (1996) for momentum, and by Kiely et ai.
(1996) for heat. The application of dissipation rates derived by third order structure functions
to compute fluxes is shown below.
3.2 Experiments
Surface energy balance and atmospheric turbulence measurements were carried out in the summer of '94, at two sites in California (Albertson et aI., 1996; Kiely et aI., 1996). One was located
at the Campbell Tract research facility at the University of California at Davis in the Central
Valley of California and the second was at a dry lake bed at Owens Valley in southeastern
California. Eddy correlation equipment consisted of a one dimensional sonic anemometer with
a fine wire (dia. = 0.0127 mm) thermocouple and a Krypton hygrometer operating at 10 Hz,
with covariances taken over 20 minute averaging periods. This enabled the direct measurement
of the vertical fluxes of sensible and latent heat. A three-dimensional sonic anemometer was
used to record the three velocity components at 21 Hz for the Campbell Tract site and 56 Hz
for the Owens Lake site. Instantaneous air temperature was also measured from the speed
of sound recorded by the 3-D sonic. From the 3-D sonic we obtain direct measurements of
u. (and so the flux of momentum). The eddy correlation equipment ran continuously for the
experimental duration (six weeks at Davis and two weeks at Owens Lake) with data logged on
20 minute time increments. Typically, the 3-D sonic ran for up to 12 hours per day and the
data recorded to a new file every 20 minutes (i.e. 25200 data points at 21 Hz and 67200 points
at 56 Hz) to match the eddy correlation and energy balance time steps.
The Davis site is a flat bare soil field of 500 m by 500 m extent. In the northeast corner of
the field an irrigated portion extends 155 m in a north-south line and 115 m in an east-west
line. The surface roughness length is Zo = 2 mm. The fetch for uniform surface roughness
exceeded 400 m and for surface wetness the fetch exceeded 100 m. The experiments were
performed in June and July, with daytime highs of about 30°C and nighttime lows of about
15°C. The 3-D sonic anemometer was set at z=0.85 m for the initial 4 days and at z=1.5
m thereafter. Irrigations were performed at the beginning of the experiment and also three
weeks later. The three week period in between was dry, with no recorded rain. By saturating
the soil surface most of the available energy was forced to latent heat rather than to sensible
heat, thus extending the range of near neutral flows encountered. Throughout the experiment
71
Third order structure function
For velocity the third order structure function represents the averaged cubed velocity differences
over lag r, D"u,,(r) =< (u(x + r) - u(xW > (Monin and Yaglom, 1975, Ch.8). For temperature
the mixed third order structure function is Duoo =< (u(x + r) - u(x))(B(x + r) - B(X))2 >
These structure functions scale in the inertial sub range with r as
4
--c:r
5
(3.28)
(3.29)
Note that with this approach the dissipation rates for momentum and heat can be directly
computed without resort to empirical constants. This method is superior to the second order
methods in that no empirical constants are used and also the dissipation rate for temperature
variance is not dependent on prior numerical calculation of the dissipation rate for momentum.
This approach has been used by Albertson et ai. (1996) for momentum, and by Kiely et ai.
(1996) for heat. The application of dissipation rates derived by third order structure functions
to compute fluxes is shown below.
3.2 Experiments
Surface energy balance and atmospheric turbulence measurements were carried out in the summer of '94, at two sites in California (Albertson et aI., 1996; Kiely et aI., 1996). One was located
at the Campbell Tract research facility at the University of California at Davis in the Central
Valley of California and the second was at a dry lake bed at Owens Valley in southeastern
California. Eddy correlation equipment consisted of a one dimensional sonic anemometer with
a fine wire (dia. = 0.0127 mm) thermocouple and a Krypton hygrometer operating at 10 Hz,
with covariances taken over 20 minute averaging periods. This enabled the direct measurement
of the vertical fluxes of sensible and latent heat. A three-dimensional sonic anemometer was
used to record the three velocity components at 21 Hz for the Campbell Tract site and 56 Hz
for the Owens Lake site. Instantaneous air temperature was also measured from the speed
of sound recorded by the 3-D sonic. From the 3-D sonic we obtain direct measurements of
u. (and so the flux of momentum). The eddy correlation equipment ran continuously for the
experimental duration (six weeks at Davis and two weeks at Owens Lake) with data logged on
20 minute time increments. Typically, the 3-D sonic ran for up to 12 hours per day and the
data recorded to a new file every 20 minutes (i.e. 25200 data points at 21 Hz and 67200 points
at 56 Hz) to match the eddy correlation and energy balance time steps.
The Davis site is a flat bare soil field of 500 m by 500 m extent. In the northeast corner of
the field an irrigated portion extends 155 m in a north-south line and 115 m in an east-west
line. The surface roughness length is Zo = 2 mm. The fetch for uniform surface roughness
exceeded 400 m and for surface wetness the fetch exceeded 100 m. The experiments were
performed in June and July, with daytime highs of about 30°C and nighttime lows of about
15°C. The 3-D sonic anemometer was set at z=0.85 m for the initial 4 days and at z=1.5
m thereafter. Irrigations were performed at the beginning of the experiment and also three
weeks later. The three week period in between was dry, with no recorded rain. By saturating
the soil surface most of the available energy was forced to latent heat rather than to sensible
heat, thus extending the range of near neutral flows encountered. Throughout the experiment