98
Multiscale Hydrologic Remote Sensing: Perspectives and Applications
Next, linear trends were removed, and for these data, we did not apply a tapering window to any of the time series data. Although an excellent discussion on the
effects of applying a tapering window to time series data can be found in the work
of Kaimal and Finnigan (1994), we chose to adhere to the recommendation of Stull
(1988) to do as little conditioning of the original time series as possible. For our initial
analysis, we focused on surface conditions that maximized our instrument deployment configuration as well as what would be typical conditions during the growing
season at Bushland. This meant wind directions that were southerly, were steady, and
typically ranged between 4 and 8 m s –1 . The southerly winds took advantage of the
longest fetch condition to ensure that EC measurements represented the best possible
measurements of the turbulent fluxes representative of the cotton surface.
5.5.2 calculation of tuRBulent fluxeS
Once the data were despiked and detrended, hourly averages of H and LE were
computed using Equations 5.3 and 5.4. This represents the initial and most basic
turbulent flux calculation. Additional corrections are needed to extract the maximum
amount of information from the EC approach. The first correction involves a mathematical rotation of the individual wind and scalar covariances referred to simply as a
two-dimensional coordinate rotation. Tanner and Thurtell (1969) first defined a natural wind coordinate system to be a right-handed system where the x-axis is parallel
to the mean wind flow, with x increasing in the direction of the flow. This approach
assumes that, for a flat surface, there is no correlation between the lateral and vertical velocities ′ ′ =
(
)
v w 0 . The transformation to this coordinate is accomplished as a
two-step rotation procedure involving three rotation angles.
A complete description can be found in the original report of Tanner and Thurtell
(1969) and of McMillen (1988). Another approach preferred by some is the planar fit
coordinate rotation, and for a discussion of the application of this approach to more
complex terrain, the reader is directed to Wilczak et al. (2001) and Lee et al. (2004).
The next correction, which is now considered a standard and important procedure,
corrects for the influence of density fluctuations on trace gas concentrations; for this
topic, the water vapor flux is the WPL correction (correction according to Webb,
Pearman, and Leuning), which is fully developed by Webb et al. (1980) and further
discussed by Lee et al. (2004).
Additional corrections needed to recover turbulent flux losses are related to EC
instrumentation and the inability to completely sample all flux-containing eddies.
As a result, EC systems tend to underestimate the true boundary layer flux. This
underestimation or downward bias is a result of the physical limitations in instrument size and shape, separation distances between the sonic and IRGA, response
times of the sensors, electronic filters to reduce noise of the output signal, and processing algorithms used to separate fluctuations from a mean. Lee et al. (2004) discussed at length the various issues pertaining to flux attenuation. For this study, we
employed the corrections to the turbulent fluxes to account for spectral attenuation
losses from sensor separation and frequency response as described by Moore (1986)
and Massman (1991).
Multiscale Hydrologic Remote Sensing: Perspectives and Applications
Next, linear trends were removed, and for these data, we did not apply a tapering window to any of the time series data. Although an excellent discussion on the
effects of applying a tapering window to time series data can be found in the work
of Kaimal and Finnigan (1994), we chose to adhere to the recommendation of Stull
(1988) to do as little conditioning of the original time series as possible. For our initial
analysis, we focused on surface conditions that maximized our instrument deployment configuration as well as what would be typical conditions during the growing
season at Bushland. This meant wind directions that were southerly, were steady, and
typically ranged between 4 and 8 m s –1 . The southerly winds took advantage of the
longest fetch condition to ensure that EC measurements represented the best possible
measurements of the turbulent fluxes representative of the cotton surface.
5.5.2 calculation of tuRBulent fluxeS
Once the data were despiked and detrended, hourly averages of H and LE were
computed using Equations 5.3 and 5.4. This represents the initial and most basic
turbulent flux calculation. Additional corrections are needed to extract the maximum
amount of information from the EC approach. The first correction involves a mathematical rotation of the individual wind and scalar covariances referred to simply as a
two-dimensional coordinate rotation. Tanner and Thurtell (1969) first defined a natural wind coordinate system to be a right-handed system where the x-axis is parallel
to the mean wind flow, with x increasing in the direction of the flow. This approach
assumes that, for a flat surface, there is no correlation between the lateral and vertical velocities ′ ′ =
(
)
v w 0 . The transformation to this coordinate is accomplished as a
two-step rotation procedure involving three rotation angles.
A complete description can be found in the original report of Tanner and Thurtell
(1969) and of McMillen (1988). Another approach preferred by some is the planar fit
coordinate rotation, and for a discussion of the application of this approach to more
complex terrain, the reader is directed to Wilczak et al. (2001) and Lee et al. (2004).
The next correction, which is now considered a standard and important procedure,
corrects for the influence of density fluctuations on trace gas concentrations; for this
topic, the water vapor flux is the WPL correction (correction according to Webb,
Pearman, and Leuning), which is fully developed by Webb et al. (1980) and further
discussed by Lee et al. (2004).
Additional corrections needed to recover turbulent flux losses are related to EC
instrumentation and the inability to completely sample all flux-containing eddies.
As a result, EC systems tend to underestimate the true boundary layer flux. This
underestimation or downward bias is a result of the physical limitations in instrument size and shape, separation distances between the sonic and IRGA, response
times of the sensors, electronic filters to reduce noise of the output signal, and processing algorithms used to separate fluctuations from a mean. Lee et al. (2004) discussed at length the various issues pertaining to flux attenuation. For this study, we
employed the corrections to the turbulent fluxes to account for spectral attenuation
losses from sensor separation and frequency response as described by Moore (1986)
and Massman (1991).