Statistical quality control of wind profiler data

The quality of wind profiling radar data is evaluated by comparing the probability density function of the power density of sets of returned samples to an exponential function. The standard deviation of individual samples from the exponential function can be evaluated to identify possible sources of contamination of the wind profiler data.

FIELD OF THE INVENTION 
This invention relates to methods for evaluating wind profiler data, that 
is, to methods for evaluating the accuracy of measurements of wind 
velocity and direction in the atmosphere, and for evaluating the amount of 
contamination of such wind profile data due to birds or other reflectors. 
This invention also includes methods of discriminating between differing 
sources of contamination. 
BACKGROUND OF THE INVENTION 
There are many applications for accurate wind profile information. 
Knowledge of the immediate and prevailing wind patterns is important for 
studying movement of air pollution and the like, for optimizing fire 
fighting efforts, for planning aircraft flight patterns to reduce fuel 
consumption, and for prediction of wind shear and other possibly dangerous 
wind conditions for flying, as well as for better weather prediction. 
Radar systems for wind profiling have been in operation for more than a 
decade, at a number of locations. See Strauch et al, "The Colorado 
Wind-Profiling Network", J. Atmospheric and Oceanic Tech., Vol. 1, no. 1, 
March 1984. The Strauch et al reference discusses in detail the practice 
of wind profiling and also provides details and examples of a network of 
five wind profiling radars in the Colorado area. The present invention 
relates generally to improvement of the understanding of data gathered 
using this or similar wind profiling radar systems; where details of the 
method of the invention are not set forth in detail, they are generally as 
disclosed by Strauch et al. 
The basic process for monitoring the velocity of winds in the atmosphere 
using radar is as follows. Pulses of high-frequency power are directed 
into selected areas of the sky at regular intervals. Power back-scattered 
from all manner of reflectors, including birds, aircraft, wires, and 
foliage, as well as the ground, the sea, buildings, and the like is 
detected. Various processes are known for separating the components of the 
total power received according to the various reflectors. 
Radar pulses reflected from turbulence in the atmosphere can be detected 
and discriminated to provide indication of the wind velocity. More 
specifically, some of the radar power in the pulses is reflected back 
towards the transmitting antenna by turbulence, that is, temperature and 
humidity gradients in the atmosphere. Since the turbulence is distributed 
randomly throughout the region of the atmosphere illuminated by the 
transmitted pulses, the back-scattered return signal measured by the radar 
exhibits rapid fluctuations. By comparison, signals returned from point 
reflectors such as airplanes, or ground clutter, that is, reflection from 
the ground, buildings, power lines, or foliage, are normally sine waves 
with little randomness. Accordingly, it is relatively straightforward to 
discriminate the return signal from clear air or rain--that is, the 
"meteorological" return--from the return from airplanes or ground clutter. 
However, discriminating the return from meteorological reflectors from 
that caused by birds or insects is more problematic. 
More specifically, the wind velocity at any particular point in time and 
space is measured responsive to the Doppler shift of the received 
reflected electromagnetic radar pulses. The Doppler shift is determined by 
the difference in frequency between the transmitted and received signals. 
The difference in frequency is split into two channels, the in-phase or I 
and quadrature-phase or Q channels. Comparison of these two values allows 
determination of the wind direction. Typically, a series of I and Q values 
are sampled to produce a time series 64 samples long. The Fourier 
transform of this set of samples is then calculated to determine a Doppler 
spectrum of that set of samples. This process may be repeated 25-100 
times, the whole process consuming 15-60 seconds, and the spectra thus 
generated summed to produce an averaged Doppler signal indicating the 
average velocity of the wind in that particular region of the atmosphere 
at that particular time. This process is then repeated at a number of 
regions of the atmosphere and over a period of time, to generate a 
complete wind profile. See, e.g., FIG. 10 of the Strauch et al paper. 
Prior to the present invention, there has been no effective way to 
determine the likelihood that the reflected energy is in fact due to 
meteorological sources, e.g., wind or precipitation in the air, rather 
than birds, trees, or other forms of clutter. That is, while various 
methods of clutter removal are known, it is not always possible to rely on 
the efficiency of these methods to ensure that wind profiles are accurate. 
It would be preferable to measure the amount of "contamination" in the 
samples analyzed to measure the wind velocity. Further, given that there 
is in fact contamination, it would be desirable to be able to identify its 
source. 
OBJECTS OF THE INVENTION 
It is therefore an object of the invention to provide a wind profiling 
radar system capable of measuring the quality of wind profile data, that 
is, to determine the reliability of wind profile data, by discriminating 
between radar signals returned from turbulence or rain in the air and 
contaminating reflectors such as trees or birds. 
It is a further object of the invention to determine the source of 
contamination given that some minimum degree of contamination exists, that 
is, to discriminate between various possible sources of contamination. 
SUMMARY OF THE INVENTION 
According to the present invention, the reliability and accuracy of wind 
profiling data is determined by comparing a probability density function 
(PDF), preferably the cumulative distribution function (CDF), of the power 
density of a set of radar return data to an exponential function, 
corresponding to the PDF of the power density of returns from 
meteorological reflectors. The difference between the two PDFs is 
inversely indicative of the quality of the wind profiling data. 
Stated differently, it is known generally that the PDF of the power 
densities of radar returns from turbulence or rain, that is, from 
meteorological reflectors, obeys an exponential function. The PDF of the 
power densities of radar returns from birds, aircraft, trees, ground 
clutter, or the like, does not conform to an exponential probability 
density function. Accordingly, by comparing the PDF of the power densities 
of radar return data to a suitably scaled exponential PDF, the "quality" 
of the wind profiler data, that is, the likelihood that the return is due 
to turbulence or rain, can be determined. 
When the quality value indicates that a substantial portion of the return 
data being analyzed is due to non-meteorological contamination, the source 
of the contamination can be identified to a degree by measuring the 
standard deviation of the measured PDF from the known PDF. Again, stated 
somewhat differently, the typical variation in power density of returns 
from contaminating reflectors varies in character with the class of 
reflectors, such that the reflectors contributing to the contamination can 
be identified by monitoring the variation of the probability density 
function. Conveniently, this step is carried out by calculating the 
standard deviation of the quality control values.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
As indicated generally above, wind profiling radars have been used for more 
than a decade to monitor turbulence at spaced locations in the atmosphere 
over time to generate wind profiles. The process used in one successful 
wind profiling application is described in the Strauch et al paper 
referred to above. 
One of the persistent problems in wind profiling arises from the fact that 
the radar return from turbulence, which is indicative of wind, is very 
small as compared to the radar return from various sorts of contamination 
such as birds, aircraft, power transmission wires, trees, and the like. 
The prior art is replete with efforts to separate out various types of 
signals contributing to radar return, in particular to separate ground 
clutter, sea clutter, birds, aircraft, foliage and the like from one 
another and from meteorological returns, that is, from turbulence and 
rain, in order to generate wind profiles. 
The present invention provides a method which, instead of separating the 
radar return due to wind or the like from radar return due to birds or 
other clutter per se, as in the prior art, instead provides an objective 
indication of the reliability of the return ascribed to meteorological 
reflectors, i.e., indicates the "quality" of the radar return being 
analyzed to measure the wind velocity. According to the invention, a 
quality control value is determined which allows objective evaluation of 
the reliability of each datum of a large amount of wind velocity data used 
in wind profiling. According to a further aspect of the invention, the 
sources of the contamination may also be identified with a useful degree 
of reliability by a further evaluation step. 
FIG. 1 shows the principal steps in the method of the invention for 
calculation of the quality control values and the contamination source 
identification. 
The fundamental principle of the invention relies on the known fact that 
the power density of radar signals returned from meteorological 
reflectors, such as rain or turbulence, obey an exponential probability 
distribution function. When wind velocities are sought to be measured by 
radar, a pulsed radar signal is transmitted into an area of the sky at 
intervals, and the intensity of energy reflected is measured. The values 
for the intensity of the reflected energy, that is, the power density 
values corresponding to each pulse, obey an exponential probability 
density function (PDF) if the reflections are solely from meteorological 
reflectors, i.e., turbulence or rain. That is, the vast majority of radar 
returns from meteorological reflectors will be of relatively low power 
density values, and fewer of the power density values will exhibit higher 
returned energies. Stated differently, the probability of a return signal 
of a particular power density being detected is described by an 
exponential function. Essentially this is simply because it is unlikely 
that a substantial amount of energy will be reflected from turbulence in 
the air, or from rain. It is known that the decreasing likelihood of 
measurement of increased power densities of the radar returns from such 
meteorological reflectors can be described mathematically by an 
exponential function. 
By comparison, the power densities of radar signals reflected from other 
classes of reflectors, such as birds, wires, trees, aircraft and the like, 
obey different PDFs. According to an important aspect of the invention, 
the statistical characteristics of the radar return are compared to an 
exponential function in order to determine whether in fact the radar 
return signals are reflected from meteorological sources, that is, wind or 
rain, as opposed to some other source. 
FIG. 1 shows broadly the steps in this process. At step 10, a set of 
samples of the reflected energy are collected. These are simply a series 
of values for the intensity of the reflected energy. Typically both 
in-phase (I) and quadrature-phase (Q) components of the reflected energy 
are detected, as these values are necessary in order to calculate the wind 
velocity (i.e., speed and direction) according to the usual technique used 
in the Strauch paper referred to above. However, this is not literally 
necessary to the practice of the invention. In step 12, the power density 
of the reflected energy is calculated. Where the samples each consist of 
an I and Q component, the power density is simply I.sup.2 +Q.sup.2 ; 
again, the exact means by which the power density is calculated is not 
itself critical to the present invention. 
The calculated values of the power density are then sorted at step 14 and 
normalized at step 16; that is, the power density samples are all ordered 
and multiplied by a scale factor such that their values range from zero to 
one. This set of ordered and normalized values represents the cumulative 
distribution function (CDF) of the power densities of the set of samples. 
Calculation of the CDF by ordering and normalizing the values simplifies 
their comparison with a stored set of values also ranging from zero to 
one, but known to conform to an exponential function, that is, to a stored 
CDF of an exponential function. The comparison step is carried out in step 
18; effectively, the area between a curve representing the sorted and 
normalized samples and a curve representing a corresponding set of stored 
samples fitting an exponential function is calculated. Conveniently, the 
area is calculated simply by summing the differences between each of the 
sorted and normalized set of samples and the corresponding members of the 
stored set of samples. 
This process is repeated as indicated by a return loop 20 until a desired 
number of areas have been thus calculated in repeated performance of steps 
10-18. At the chosen time, determined in decision step 22, the average 
area is calculated at step 24. The average area is equivalent to the 
quality control number for that group of sets of samples. That is, each 
set of samples, typically 64 each of I and Q samples, is processed through 
steps 10-18 to calculate a single area value. This process is repeated 
typically between 25 and 100 times, over a period of 15-60 seconds, so 
that 25 to 100 individual area values are calculated. These are then 
averaged at step 24; the average value of the areas indicates the average 
deviation of the power densities measured from the exponential function. 
Accordingly, the average area value thus calculated indicates the 
"quality" of all the sets of wind samples gathered during that 15-60 
second period, i.e., indicates the degree to which the determined values 
of the wind velocity calculated for the corresponding period are 
contaminated by non-meteorological reflectors such as birds or the like. 
In step 24, the standard deviation of the individual values for the areas 
calculated in step 18 is also calculated. As will be understood by those 
of skill in the art, calculation of a standard deviation in effect 
provides statistical determination of the amount by which individual 
values of a set depart from the average value; that is, the standard 
deviation of a set of values indicates the degree of randomness or 
variability of the individual values. It has been found by the present 
inventor that the standard deviation of the area provides an indication of 
the source of contamination, while as indicated the degree of 
contamination can be evaluated by the average departure of the CDF of the 
power density of the radar return from an exponential function. Birds, for 
example, provide relatively high radar returns, but in a relatively random 
fashion, such that the presence of returns from birds in a particular set 
of samples leads to relatively great departure of that set from the 
average area values. By comparison, trees blowing in the wind contaminate 
the measured wind values in a more uniform fashion. Thus, a high value for 
the standard deviation indicates contamination by birds, as opposed to a 
lower value, suggesting that the wind velocity values are contaminated by 
radar return from trees or other relatively consistent sources. 
Therefore, in step 26, in accordance with a further significant aspect of 
the invention, the average area is used to produce a quality assurance 
(QA) value and the standard deviation of the individual area values is 
used to produce an standard deviation (SD) value. These values can then be 
used (in a manner discussed in detail below) to evaluate the relative 
reliability of wind velocity values having been determined by processing 
the same samples using known techniques. 
As indicated at step 28, in a typical processing sequence, steps 10-26 are 
then repeated for other areas of the sky as indicated by a return loop 
path 30; when all areas of the sky of interest have been similarly 
processed, the process is begun again, as indicated at step 32 and by a 
second return loop 34. Thus, each area of the sky is examined in sequence, 
after which the entire process is begun again. Therefore, a series of 
values for the QA and SD values over time are provided for each region of 
the sky. These values may be charted as contamination maps, as indicated 
at 36. Examples of contamination maps showing QA values and the SD values 
as a function of the region of sky and the time at which the samples were 
taken are shown in FIGS. 10 and 11, as discussed further below. The 
contamination maps can then be compared to wind profiling maps, e.g., as 
shown at FIGS. 10 and 12 of the Strauch paper, to allow an observer to 
evaluate the reliability of the wind profile information shown therein. 
FIGS. 2-6 compare probability density functions (PDFs) of radar return data 
to an exponential PDF, to illustrate the reliability of the process by 
which the invention identifies the presence of non-meteorological 
reflectors, i.e., contamination, in wind profile data. The specific PDFs 
shown in FIGS. 2-7 are cumulative distribution functions (CDFs). The 
choice of the CDF is discussed below. 
In FIG. 2, for example, the solid curve shows a PDF of radar return signals 
from clear air turbulence, that is, wind. The dashed curve in FIG. 2 
represents a similarly scaled exponential function, that is, a series of 
calculated values representative of the theoretical power density of radar 
returns from clear air. The atmospheric return illustrated by the solid 
curve correlates very closely with the exponential PDF shown by the dashed 
curve; that is to say, the area between the two curves, which is a 
convenient way of evaluating the conformity of the two, is very small. 
Thus, the area calculated in step 18 (FIG. 1) with respect to such clear 
air sample data would be very low. 
FIG. 3 shows a comparable figure, wherein the solid line shows the PDF of 
radar return data from rain, which is nearly exponential, but wherein the 
area of the difference between the rain PDF and the exponential PDF is 
larger than for the clear air PDF of FIG. 2. 
By comparison, FIG. 4 compares a PDF for ground clutter, that is, the PDF 
of power density values determined with respect to radar return from the 
ground, to the exponential PDF. Here obviously the area between the curves 
is very large, such that radar return data conforming to the solid curve 
of FIG. 4 would be evaluated to be very highly contaminated by the method 
of the invention. 
Similarly the PDF of radar return data from birds is compared in FIG. 5 to 
the exponential PDF, and again the area between the curves is quite large. 
Similarly in FIG. 6, sea clutter, that is, the PDF of radar return data 
from the ocean, also departs very significantly from the exponential PDF 
shown by the dotted line. 
FIG. 7 shows a somewhat different graph, illustrating the relationship 
between the area between a curve of a measured PDF contaminated by birds 
and the exponential PDF versus the percentage of bird contamination. Where 
the percentage of bird contamination is low, that is, on the left side of 
FIG. 7, the area between the curves of the exponential PDF and the PDF of 
the radar signal returned therefrom is similarly small; as the percentage 
of bird contamination increases, the area between the curves increases, 
such that the area between the curves might be used to evaluate the source 
of contamination. 
However, those of skill in the art will recognize that other sources of 
contamination may contribute to the area between the curves, such that the 
area alone cannot be used as an objective identifier of the source of the 
contamination in all circumstances. Other information may be useful, 
however, in evaluating the source of contamination; for example, ground 
clutter and sea clutter obviously do not contribute at high elevations, 
where the problem is reduced to separating bird contamination from 
aircraft. Aircraft typically make a more uniform contribution to the 
contamination than do birds; therefore, according to an important aspect 
of the invention, the standard deviation (SD) of the individual area 
measurements is calculated, so as to distinguish between sources of 
contamination. The SD of returns from aircraft would tend to be lower than 
the SD of signals returned from birds. According to this aspect of the 
invention, the source of contamination can be identified in certain cases 
by consideration of the area between the curves of the radar return signal 
and the stored exponential PDF, by consideration of the area of the sky 
from which the radar return data is taken, and by calculation of the 
standard deviation of the areas. 
FIG. 8 shows a more detailed flow diagram of processes according to the 
invention, providing additional detail with respect to the flow diagram of 
FIG. 1, and also illustrating the manner in which the invention is added 
to conventional wind profiling processes as described by Strauch et al. 
The process begins at step 40 by transmission of a set of radar pulses 
into a particular area of the sky. Typically 64 pulses may be transmitted 
in each set, although the invention is not so limited. The number of 
pulses in each set is normally a power of two, to simplify calculation of 
the wind velocity using the usual Fast Fourier Transform (FFT) algorithm, 
but this also is not critical to the invention claimed per se. For similar 
reasons, the in-phase (I) and quadrature-phase (Q) components of the 
return power are measured at step 42; again, the return power measured in 
some other way might be used to practice the invention. 
The power density of the return signals is then calculated at step 44; 
again, where the I and Q values of the return power are monitored for use 
in Doppler velocity calculations, the power density is simply I.sup.2 
+Q.sup.2. The power density values, 64 in the example, are sorted in order 
of their intensity and normalized at step 46. The result is a set of 
ordered values ranging from zero to one. From these, the cumulative 
distribution function (CDF) is calculated at step 48. 
As will be understood by those of skill in the art, a probability density 
function (PDF), of which a CDF is a particular type, essentially 
represents the number of samples of an overall set of values falling 
within each of a number of "bins" within an overall range of values. The 
CDF of a normalized set of samples ranges from zero to one, such that the 
shape of a curve showing a CDF represents the probability, between zero 
and one, of various possible values. In implementation of the invention, 
processing the power density samples to determine their CDF enables 
convenient computation of the difference between the CDF of the set of 
samples, and a stored CDF similarly ranging between zero and one, and 
known to correspond to an ideal exponential function. It would be 
mathematically equivalent to calculate the PDF of the measured set of 
power density values, and compare this PDF to an exponential PDF; however, 
it is computationally more efficient to carry out the process with respect 
to the corresponding CDFs instead. 
Therefore, in the preferred implementation of the invention, the CDF of the 
power densities of each set of samples is calculated at step 48, and is 
compared to a stored CDF at step 50, such that the area between the curves 
represented by the two CDFs is evaluated; the value of the area is then 
stored. 
Further, in connection with this invention, a CDF is to be considered a 
particular type of PDF. Accordingly, it is to be understood that 
calculation of the difference between a PDF of a set of samples and a PDF 
of a set of samples corresponding to an exponential function by any known 
means is considered to be within the scope of the invention. 
The stored CDF represents an exponential function, as noted. In one 
preferred implementation of the invention, the stored CDF includes a set 
of values generated by applying an exponential function to the output of a 
random number generator at step 52 and stored at step 54. This set of 
values represents the CDF of the power density of samples from known 
meteorological reflectors, that is, wind and rain, for comparison to the 
calculated CDFs at step 50. 
When all the sets of 64 samples in a given group, the group typically 
including 25-100 sets of samples collected over a period of 15-60 seconds, 
have been processed, as determined at step 60, the average area is 
calculated in step 62; this value is the average of the 25-100 areas 
determined in step 50 between the curves representing the stored CDF and 
the calculated CDFs. The average area becomes a single datum representing 
the average contamination of the return values for that particular group 
of sets of samples, and may be later used in step 64 to produce a QA 
contamination map. 
Equivalently, the calculated CDFs could be averaged, and this "average CDF" 
compared to the stored CDF to determine an average area. However, in the 
preferred embodiment, the individual areas are calculated and stored so 
that their standard deviation (SD) can be determined, as shown at step 66. 
As discussed above, this calculation of the "randomness" of the individual 
areas used in calculating the average area is of use in identifying the 
possible source of the contamination. 
The QA values are ultimately used to produce a contamination map in step 
64, as indicated, and the SD of the areas can be used to produce an SD 
contamination map in step 67. The same steps, that is, calculating the 
average area and the SD of the areas, are repeated for groups of samples 
measured with respect to other areas of the sky, as indicated at step 68; 
when all areas of the sky have been thus evaluated, each region yielding a 
single point, in effect, on the QA and SD contamination maps, the same 
process is performed repeatedly over time, typically for 12 to 24 hours. 
Ultimately the result is a pair of contamination maps, as discussed below 
in connection with FIGS. 10 and 11. 
FIG. 9 shows schematically the processing of return signals according to 
the invention as a function of time. As indicated by the legend at 80, 
25-100 sets of radar return samples, typically 64 samples per set, are 
collected from a particular region of the sky, typically over a period of 
15-60 seconds. Each set of samples includes 64 values for the in-phase 
component (I) of the reflected energy, as indicated at 82, and 64 values 
for the quadrature-phase component (Q) thereof, as shown at 84. The power 
density of each pair of samples is calculated at step 86 as I.sup.2 
+Q.sup.2. These values are then sorted and normalized at 88, and processed 
to form their CDF. Where the radar return is in fact from meteorological 
sources, i.e., wind and rain, the CDF will conform to a generally 
exponential function. At 90, the areas between each CDF curve 92 and a 
curve 94 representing a set of values for the CDF of an exponential 
function are calculated. When each of the 25-100 sets of samples have been 
thus processed, the average area, that is, the average of all the areas 
between the curves 92 and the stored curve 94, is determined at step 96; 
the resulting value is the quality control number for the group of 25-100 
sets of samples from a given region. The standard deviation of each area 
from the average area value is calculated at 98 and indicates the source 
of contamination of the return data from non-meteorological sources as 
indicated at 98. 
FIGS. 8 and 9 also illustrate the manner in which the process of the 
invention conforms to known processes for profiling wind velocity, as 
disclosed in the Strauch et al paper. For example, at step 100 (FIG. 8) 
the I and Q values are used as indicated by Strauch et al to calculate the 
Doppler spectrum of the set of samples measured in response to each 
particular transmitted pulse of energy, and this spectrum is stored. The 
Fourier spectrum of a typical set of 64 samples is shown at 102 in FIG. 9; 
as indicated, each set of 64 I and Q values is used to generate a Fourier 
spectrum. These spectra are then averaged as indicated at step 104 of 
FIGS. 8 and 9 to yield an average spectrum as illustrated at 106 in FIG. 
9. The average wind speed is determined by the principal peak appearing in 
the averaged Fourier spectra. This value, which represents the average 
wind velocity in that particular region of the atmosphere during the 15-60 
second sampling time, makes up a single contribution to a wind profile, 
e.g., as shown in FIG. 10 of the Strauch et al paper. 
According to the invention, contamination maps may be generated for 
evaluating the reliability of such wind profiles. FIG. 10 shows a quality 
assurance (QA) contamination map while FIG. 11 shows the standard 
deviation (SD) of the FIG. 10 map for the same time period. In FIG. 10, 
the axis labeled from zero through 250 represents sampling times, 
extending rightwardly from late afternoon through the following morning; 
approximately twelve hours' data is shown. The vertical axis represents 
altitude above the ground; in this figure, the atmosphere is divided into 
38 vertical layers with a maximum height of approximately 4 kilometers. 
The legend showing a density scale varying between zero and approximately 
27 (in arbitrary units) represents the quality control value; in this 
Figure, a low value represents high quality radar data, that is, indicates 
that the wind profiler data is relatively less contaminated, as determined 
according to the invention. That is, in these examples of the present 
invention, when the quality control number is low, the data is relatively 
reliable; when the quality control number is high, then the analysis 
carried out according to the invention indicates that a substantial 
fraction of the radar return used in calculating the wind speeds may 
include radar return from other sources, i.e., birds, trees, power lines, 
or the like. Thus, it will be immediately apparent that the data from near 
the ground is more highly contaminated than the data from higher in the 
atmosphere, which is hardly surprising. The bands 110, 112, 114, and 116 
appearing at approximately 1, 3, 8, and 13 units of altitude of FIG. 10, 
can be determined according to the invention to be due to ground clutter, 
and are eliminated in the SD plot of FIG. 11. 
The SD plot of FIG. 10 represents the contamination map of FIG. 10 having 
been reprocessed to show those data where the SD is relatively low as 
light in color and those where the standard deviation is high as darker in 
color. As indicated above, radar return from the relatively stationary 
sources such as trees, the ground and the like is relatively consistent, 
and its SD is low, that is, the area of the difference between the 
calculated CDFs and the stored CDF is consistent from sample to sample. 
Therefore, contamination due to the ground or the like is relatively 
deemphasized in the SD plot of FIG. 11. By comparison, where the standard 
deviation is high, e.g., due to birds or the like, which would normally 
contribute only to individual samples used in calculating the areas, the 
standard deviation is relatively high. Therefore, ground clutter is 
largely removed from the FIG. 11 plot as compared to FIG. 10, and the 
remaining contamination plotted can be presumed to be due largely to 
birds. 
It will be appreciated by those of skill in the art that while an improved 
method of evaluating the quality of wind profiling data has been provided 
and discussed in detail, there are additional modifications and 
improvements thereon that could be made without departure from the 
invention as disclosed and claimed. Therefore, the above disclosure of the 
invention should be considered as exemplary only and the scope of the 
invention should be measured only by the following claims.