I have been developing and testing the rotation of the sonic data
through prep.config using the sonic calibration files in $ASTER,
which contain sonic tilt and orientation angles. In parallel, I
I have also been rotating the data in the horizontal with the Splus
routine rotate.dir.
My naming convention for the resultant data files is
0 raw data, no rotation
1 apply tilt rotation
2 apply theodolite-measured azimuth angle
3 rotate each sonic to match its wind direction to the average of the
wind directions measured by all sgs sonics at the same height
(either s1-s5 or d1-d9).
Since I was creating duplicate (when successful) data files for these
various rotations, I have used e.g. 1 and 1b to distinguish them but
without any consistency as to which was done directly through
prep.config and which were additionally processed through rotate.dir.
However, I found that prep.config generates a single precision data
file while additional processing by rotate.dir outputs a double
precision file.
So far I have been working with a single 30-minute segment of data
starting on Sept 4 at 2:45 PDT, just looking at the 3m 9-sonic
data (in order to test my software for calculation of double-filtered
moments). Now I am writing code to calculate spatial derivatives,
so I also need the 5-sonic, single-filter data in order to calculate
vertical derivatives. Thus I will now distinguish the data as e.g.
2s or 2d.
SGS post-processing update, 11-28-00
After looking further at the sonic azimuth measurements and the wind
direction deviations, I have decided to not pursue additional
refinements of the sonic azimuths at this time. An uncertainty of one
degree in sonic orientation generates an uncertainty in the u and v
wind components (normal and parallel to the array) of
du = -S*sin(theta)*pi/180
dv = S*cos(theta)*pi/180
where theta = atan(v/u) and S = sqrt(u^2 + v^2).
Thus for 0 < theta < pi/4,
0 < du/S < 0.012
0.017 < dv/S < 0.012
In addition, I am not optimistic about determining an objective
correction to the sonic azimuths. The residual wind direction
differences (after application of the measured sonic azimuths) are not
constant for a given array, but are quite scattered with perhaps a weak
dependence on temperature and wind direction. Ed Swiatek has provided
some information on the variability of the CSAT3 head geometry. I will
look at that to determine its possible contribution to uncertainty in
the visual alignment of the sonics with the theodolite.
Thus for the moment, I have incorporated the measured sonic azimuths
and the measured sgs (CSAT3) array orientations in the sonic
calibration functions used by prep.config during data post-processing.
The sonic data will be rotated to a coordinate system with u normal to
the sgs array (nominally from the NW) and v parallel to the array
(nominally from the SW). Note that I have also placed the sonic data
from towers a and b in the same coordinate system. However, analysis
of data from those two towers may in some cases require resolving the
data into components parallel and normal to the line between the two
towers, which of course is not identical to a line normal to the sgs
arrays.
As I analyze data from various time periods and arrays, I will keep an
eye on the range of wind directions among the various sonics.
Hopefully they will remain on the order of 1-2 degrees or less. One
option during analysis will also be to reorient the data from the
individual sonics so that all sonics have a mean wind direction equal
to the mean for all sonics at the same height within the sgs array
(d1-d9 or s1-s5). I will examine how sensitive various statistics are
to this additional, somewhat ad-hoc processing.
Having specified the sonic orientations, the SGS data should soon be
ready for distribution. Gordon has proposed writing several sets of
CD's in NetCDF format for this purpose. Give Gordon a call if you are
unfamiliar with this format. I believe that he can provide utilities
to facilitate accessing the data. At this time the data will be
distributed only to a limited set of cooperative investigators who have
agreed to delay submitting papers until the first SGS paper by the PI's
is accepted for publication. Thus it is not permissible to
redistribute the data in any form to others. Further distribution
would also complicate correcting the data for any errors found during
the initial analysis.
Note that I found an error in the pre-project document that I wrote to
describe data analysis. On the bottom of page 2 where I discuss
matching the Tong crosswind filter with a streamwise Gaussian filter at
their half-power points, the sonic spacing S should be replaced with
S*cos(theta), where theta is the wind direction relative to the normal
to the array. S*cos(theta) is the effective sonic spacing for data
projected onto a line normal to the streamwise direction.
To: bstevens@atmos.ucla.edu, kleissl@jhu.edu, lenschow@ucar.edu,
mbparlange@jhu.edu, meneveau@jhu.edu, moeng@ucar.edu, mpahlow@jhu.edu,
oncley, pps@ucar.edu, weil@ash.mmm.ucar.edu
Cc: brac00@essc.psu.edu maclean, cole@ale.atd.ucar.edu, dcarlson,
eswiatek@campbellsci.com, wyngaard@ems.psu.edu
Subject: SGS update
Following is an update of recent progress on post-processing of the
SGS data. If you become bored with the update, you might at least skip
to the last two paragraphs where I introduce a question about one of
the details of data processing associated with off-normal wind
directions. Any feedback on that discussion will be appreciated.
Post-processing of the SGS data is proceeding more slowly than I had
optimisticaly anticipated in September (big surprise!). The principal
reason is that I took several days of vacation to "decompress" after 40
days and 40 nights of Kettleman City duty and to enjoy the beautiful
fall weather at home, but other responsibilities (such as reviewing
journal manuscripts) have also taken time away from SGS.
In October, I completed post-project wind tunnel tests of the 17 CSAT3
sonics, running three individual tests per sonic, and have now shipped
them back to their owners. The results, which I forwarded to you, show
very good consistency among the sonics. Two exceptions, SN 0251 from
UIA and SN 0423 from UMN, had offsets on the order of 6-8 cm/s, which
exceeds the factory spec of +/- 4 cm/s. These two sonics have been
sent to Campbell for recalibration. Ed Swiatek will provide the pre-
and post- calibration specs in case those can be useful for data
interpretation. Hopefully, the consequences of these small offsets
are negligible.
I have also calculated the sonic tilt coefficients and will incorporate
them in future data processing. Most sonics had tilt angles that were
less than 1 degree and all sonics had tilt angles that were less than 2
degrees. My recollection is that a tilt of 1 degree in the streamwise
direction can induce errors in u* and the sensible heat flux on the
order of 5%.
Most recently I worked on the corrections for sonic orientation.
Without any correction, the differences in the wind directions measured
by the sonics within each array varied over ranges of 1-5 degrees. In
general these differences were correlated with the sonic azimuths
measured with the theodolite, but after using those azimuths to correct
the wind directions, the range of wind direction differences were
reduced by only about 1 degree. The smallest range was for the last
array, number 4, with the smallest sonic spacing. This could be
because the true wind field was more uniform across the smaller
distance, because the actual array was more uniform due to the common
support structure, and/or because by then we were perhaps better at
measuring the sonic azimuths.
Based on a set of repeated theodolite measurements made by John
Militzer, it appears to me that the overall accuracy of the sonic
orientation measurements is on the order of 0.1-0.3 degrees. The
actual theodolite readings appear to be accurate to better than 0.1
degree, including a comparison of the direct solar technique using the
Nikon theodolite to the 'two triangle' technique using the digital
theodolite. The greater uncertainty is the visual alignment of the
theodolite placement with the u axis of the sonic. Thus the remaining
variance in measured wind direction is a little disappointing.
There are several factors for further consideration. First, the
internal alignment of the sonics is not exact. The actual alignment of
each sonic is precisely measured at CSI and used to convert the path-
averaged speeds to orthogonal wind components. Thus our visual
alignment of the theodolite with the array is not a precise alignment
with the true u axis. I have requested the actual rotation matrices
from CSI in order to investigate this further.
Second, the observed range of wind direction differences among the
sonics of each array is consistent with possible offsets in the
along-array wind component of +/- 4 cm/s, which is within the factory
spec. The possible contribution of these offsets is also consistent
with a temperature dependence of the wind direction differences for
some sonics.
Finally, I have no absolute standard for wind direction when making a
comparison among the sonics. The best that I can do is to use the
average wind direction for each array as a standard, which is not
completely satisfactory. A question at this time, then, is how much
effort to expend on the sonic alignment issue. The concomitant
question is how sensitive are the resolved and subgrid-scale statistics
to the remaining uncertainties in absolute wind direction for each
sonic.
One standard that I could use for evaluating the quality of the data,
including the sensitivity to absolute wind direction is the
repeatibilty of single-filtered (5-sonic) second moments. Originally,
I thought that a comparison of single-filtered and double-filtered
moments would be valuable for quality control, but this is simply an
identity and thus is perhaps most valuable as a test of the
computational software.
This brings me to looking once more at the details of the calculation
of spatially-resolved turbulence. One issue that has not been entirely
resolved is the consequence of off-normal winds. My feeling is that
the principle issue there is aliasing, as noted by John's student Mark
Kelly. Other issues can be addressed directly during processing of the
data. In order to minimize aliasing, I propose using a time-varying
wind speed and direction to project the data from the sonic array onto
a line normal to the current wind direction. Thus the horizontal box
used for spatial averaging of the flow variables would rotate in time
to follow the current wind direction. The 2-D box would also change in
size slightly because of the projection of the (fixed) sonic array onto
a line normal to the current wind direction.
This opens the question about what wind speed and direction to use for
projection of the data onto a line normal to the current wind
direction. Candidates vary from the instantaneous wind (measured at 20
Hz) to a mean wind calculated for a time period equal to that used to
achieve stationary turbulence statistics (e.g. 15-60 min). It is not
clear what standard or procedure can be used to establish the "correct"
wind speed and direction for this purpose. In the absence of a-priori
criteria for the appropriate "projection" wind speed and direction, I
propose that a natural candidate is the resolved-scale wind, that is
Projection wind speed = sqrt(ur^2 + vr^2)
projection wind direction = atan(vr/ur)
where (ur,vr) are the resolved-scale horizontal wind components. I
would like to hear any thoughts on this matter from the other PI's.
Tom