June 1965 Kenneth M. Barnett and Omer Clarkson, Jr. 377
RELATION OF THE TIME INTERVAL TO ACCURACY OF DOUBLETHEODOLITE
OBSERVATIONS
.. .- -. . KENNETH- M. .BARNETT ..
Meteorology Department, U.S. Army Electronics Research and Development Activity, Fort Huachuca, Ariz.
OMER CLARKSON, JR.
U.S. Weather Bureau Research Station, Fort Huachuca, Ariz.*
ABSTRACT
Low-level wind observations were made by manual theodolite readings of pilot balloon positions. Simultaneous
readings were made from three theodolites with time intervals ranging from 5 to 60 sec. and for altitudes up to 8,428
f t . above the surface. The theodolite readings were analyzed as three simultaneous double theodolite observations
of the wind vectors between the successively observed positions of the balloons. If the theodolite readings were
completely accurate, each of the three simultaneous wind vectors would be identical. The differences between the
magnitudes and directions of the horizontal components of the simultaneous wind vectors were used as a measure of
the observational accuracy of the balloon movements. Twenty-sec. intervals between theodolite readings were found
to give the greatest accuracy; the accuracy decreased rapidly as the time interval was shortened but the accuracy was
nearly the same as the time interval was increased.
I . INTRODUCTION
The simultaneous observation of a balloon from two
theodolites is one of the most accurate methods of measur-
ing low-levelwind conditions. When especially detailed
wind observations are wanted, the time interval between
successive readings of the balloon position is shortened.
As this interval becomes shorter there should be a mini-
mum time interval below which the accuracy of the wind
observations deteriorates rapidly. The purpose of this
investigation is to examine the accuracy of double theodo-
lite observations as the time interval is decreased.
9. APPROACH
The problem of using balloons to obtain accurate obser-
vations of wind conditions could be broken into at least
three parts. First, the successive positions of the balloons
must be observed accurately; second, it is assumed thac
a balloon accurately follows the flow of air particles; third,
it is assumed that the air flow shown by the balloon is the
same as the air flow a t slightly different times and loca-
tions. This report treats only the first part.
Five series of simulkaneous observations from three
theodolites were made at the U.S. Army Proving Ground,
Yuma, Ariz., in May 1964 by a combined group of experi-
enced U.S. Army and U.S. Weather Bureau meteorological
observers. The three theodolite sites (A, B, C) approxi-
mated an isosceles triangle with two sides 1,000 m. long
Mr. Clerkson’s present assignment is US. Weather Bureau, San Antonio, Tex.
and the other 1,414m. long. The altitudes of the sites
were329,394, and 426 ft. m.s.l., respectively. Observa-
tions were made using standard U.S. Army Signal Corps
Theodolites, Models MIA-247 and ”74 GM. Five
sequences of pilot balloon observations were made with
three theodolites on each of five different days. (25 bal-
loons were released.) On each day, one sequence was made
with a 5-sec. interval between readings, one with a 10-sec.
interval, one with a 20-sec. interval, one with a 30-sec.
interval, and one with a 60-sec. interval. Each theodolite
had two observers, and a seventh observer wasused to
coordinate the timing of observations. The azimuth and
elevation angles were read to Xoth of a degree. The
maximum heights of the balloons while observed ranged
from 1,870 f t . to 4,928 f t . above the surface.
The data were divided into three sets of double theodo-
lite readings: theodolites A and B, B and C, and A and C.
Simultaneous azimuth angle readings were used to calcu-
late (on a G-15 computer) the horizontal projection of the
balloon path betweentwo successive readings. This
resulted in three wind vectors to represent the wind
experienced by the balloon between each two successive
readings. If perfect observational accuracy had been
attained, the three wind vectors for each wind condition
would be identical in magnitude (m.p.h.) and in direction
(degrees azimuth).
For each of three wind vectors, the magnitude of the
smallest was divided by the magnitude of the largest to
obtain the “apparent horizontal windspeed ratio.” A
ratio of 100 percent could be attained only when all three
vectors were of exactly the same magnitude. As the
378 MONTHLY Vol. 93, No. 6
differences between vector magnitudes increased, the ratio
decreased.
Likewise, for each set of three wind vectors, the maxi-
mum difference in directions (degrees azimuth) between
any two vectors was called the “apparent horizontal wind
direction departure.” This was tabulated in degrees.
In this case, a smaller number indicates greater accuracy.
Several steps were taken to insure the validity of the
results. The five observations for the first day were not
used even though all observers were experienced. This
was to insure that each observer had some familiarity with
reading the instrument at the different time intervals.
Tlie order of the different reading time intervals was
different each day to minimize the influence of observer
fatigue or of diurnal wind changes. To eliminate the
mathematical uncertainty of finding the intersection point
of two nearly coincident lines, all sets of data for any one
reading were discarded if any azimuth angle was within 5”
of a base line to another theodolite. To exclude cases in
which a very slight difference between two wind vectors
would give an unreasonably adverse “wind speed ratio,”
data were discarded for wind speeds less than 3 m.p.h.
Finally, a larger number of short time interval readings
was made so all balloons traversed approximately the same
positions relative t o t h e theodolites; this minimized
geometric errors. See [l] for a comprehensive analysis of
geometric factors.
For each time interval, the means were found for the
“apparent horizontal wind speed ratio,” and for the
“apparent horizontal wind direction departure.’’ The
results are shown in figure 1. Note that a time interval
of20 sec. gives a ratio of 95.2 percent and a departure of
1.4 O; these were the best accuracies found. A total of
119 triple theodolite or 357. double theodolite readings
was used.
3. DISCUSSION
This analysis shows that the 2Osec. reading interval
was.the most accurate but was only slightly more accurate
than either the 30- or the 60sec. interval. This may
reflect an insufficient number of observations to attain
statistical significance, but the parallelism of the speed
and direction mean data tends to eliminate this conclusion.
The accuracy maximum at 20-sec. reading intervals
seemed so remarkable that a second series of triple theo-
dolite observations was made in the same area near Yuma
during August 1964 using 15-, 20-, 30-, and 45-sec. reading
time intervals. About half of the observers had participated
in the first series of observations. The data were analyzed
in the same manner with the results shown in figure 2.
Again an optimum time interval of 20 sec. was found with
a ratio of 93.7 percent and a departure of 4.16”. (The
over-all decrease in accuracy may have been a result of
the more intense heat during August.) The maximum
heights of the balloons while observed ranged from 3,917
ft. to 8,428 ft. above the surface. A total of64 triple
theodolite or 192 double theodolite readings was used.
NUMBER OF DOUBLETHEODOLITEREADINGS
81 81. 87 69 39
65
1 ;
5
IO
15
60
0 5 IO 20 30 60
TIMEINTERVALBETWEENREADINGS(SEC)
FIGURE 1.-Results of first test. Apparent horizontal wind speed
ratio (solid line) and apparent horizontal wind direction departure
(broken line) as functions of time interval between readings by
double theodolites.
n v) 0 15 .20 3b 45 (SEC)
TIME INTERVAL BETWEEN READINGS !2
n
FIGURE 2.-Results of second test. Apparent horizontal wind speed
ratio (solid line) and apparent horizontal wind direction departure
(broken line) as functions of time interval between readings by
double theodolites.
Since the experiment was “randomized,” it appears that
the possibility that the 20-sec. interval readings could have
been taken under consistently more favorable geometric,
wind, or atmospheric refraction conditions was greatly
minimized.
If the varying lengths of the runs were a significant
factor, there should be a more nearly linear variation
between the 5-sec. and the 60-sec. cases. As figures 1
and 2 indicate, this is not the case; the curves are peaked
at 20 sec. in both figures.
June 1965 Kenneth M. Barnett a n d O m e r Clarkson, Jr. 379
Since only azimuth readings were used in the analyses
there should be no contributing error due to differences in
the elevation of observing sites. A negligible error is due
to the earth’s curvature but this would not favor a 20-sec.
reading interval.
There is the possibility that the 20-sec. interval is the
minimum time required for the average observer to center
the balloon on the cross-hairs for each successive reading.
Less time may not be sufficient for this and more time may
permit the observer time enough to become distracted
thereby causing a late reading or a reading in which the
tracking instrument is not exactly on target.
4. SUMMARYANDCONCLUSIONS
Analyseswere made of 549 double theodolite readings
with reading intervals of 5, 10, 15, 20, 30, 45, and 60 sec.
to determine which reading interval gives the most
accurate observations of successive balloon positions.
The data indicate that for double theodolite runs of
short duration and using skilled observers, the time
interval of20 sec.between readings provided the most
accurate determination of horizontal winds of the lower
atmosphere. Accuracy decreased rapidly as time intervals
were made less than 20sec. For time intervals greater
than 20 sec., accuracy was slightly less.
ACKNOWLEDGMENTS
The authors wish to express their thanks to the U.S. Army and
U.S. Weather Bureau observers for collecting the triple theodolite
data and to Mr. Ernest Stenmark, Meteorology Department,
USAERDAA for developing and testing the computer programs
used in this study.
REFERENCE
1. R. W. Armstrong, “Accuracy of Two-Theodolite Pilot Balloon
Tracking Method of Measuring Low Level Winds,”
USASRDL Technical Report 2047, U.S. Army Signal Research
and Development Laboratory, Fort Monmouth, N.J., June
1959.
[Received November 17, 1964; rewised April 6 , 19651