Small-comet "atmospheric holes" are instrument
noise
F.S. Mozer,
J.P. McFadden, I. Sircar, and J. Vernetti
Space Sciences Laboratory,
University of California, Berkeley
Abstract
Frank and Sigwarth claim that dark pixel clusters
observed by the VIS Earth Camera are atmospheric holes created by small
comets. We have examined their catalog, which contains about 700,000 of
these "atmospheric holes", for consistency with this small-comet hypothesis
and with instrument noise. A geometrical requirement of the small-comet
hypothesis is that the number of pixels in a typical cluster must vary
by a factor >100 with spacecraft altitude because of the inverse-square
law of the apparent cluster area versus distance. We find no systematic
variation of cluster size with spacecraft altitude. The Iowa catalog data
are consistent with instrument noise because neither the size distribution
nor the event rate of dark pixel clusters depend on altitude. At altitudes
outside of the radiation belts during the one day of available raw data,
more than 75% of the dark pixel clusters result from the process that Frank
and Sigwarth employ to remove bright pixels caused by energetic particles.
This data processing also causes additional meaningless dark pixel clusters
to occur in the dark sky or over the dark Earth.
Introduction
Frank and Sigwarth (hereafter
designated as F&S) have hypothesized the existence of small comets
to explain dark pixels observed by UV imagers on the DE-1 (Frank et al.,
1986) and Polar (Frank and Sigwarth, 1997a, 1997b, 1997c, 1997d) satellites.
This hypothesis has been criticized on several grounds (see Dessler, 1991,
and references therein; Parks et al., 1997, 1998). F&S have produced
a catalog of about 700,000 dark pixel clusters observed by the VIS imager
on Polar during a 120-day interval in 1997. This Iowa catalog is examined
for internal consistency under two hypotheses, (a) that the events are
produced by an external source at low altitude, such as atmospheric holes
generated by small comets, and (b) that they are the tail of an instrumentally
generated distribution of dark pixel clusters. This study differs from
all others that have objected to the small-comet hypothesis in that it
considers events produced by the major proponents of this hypothesis from
data provided by their own Polar instrument. It presents simple, direct,
evidence that the dark pixel clusters in the Iowa catalog are the tail
of an instrumental noise distribution --they are not produced by atmospheric
holes. This same result was demonstrated by Cragin et al. (1987) for the
original DE-1 small-comet data, who showed that there was no change in
the angular size of the purported atmospheric holes with altitude. Thus,
12 years ago, as today, it is shown that the "atmospheric holes" are instrument
noise.
The definition of a cluster in
the Iowa catalog is that five or more contiguous dark pixels are observed
in the Earth's dayglow. A dark pixel is typically defined as one whose
intensity is two or more local standard deviations below the local mean,
where both the local mean and local standard deviation are determined for
the pixel of interest from the 32 outer pixels in a nine by nine array
of pixels centered on the pixel of interest. Examination of the number
of clustering events as a function of size (Fig. 3 of McFadden et al.,
1998) or number of standard deviations (Fig. 4 of Frank and Sigwarth, 1997a)
shows that there are no inflections or other features of the distributions
that suggest the selected values. In fact, the selected values are in the
tails of smoothly falling distributions that look like noise. F&S appear
to pick an arbitrary point in each of two smoothly falling distributions
and to ask readers to believe that everything to the left of these points
is noise and everything to the right is due to small comets! Thus, the
first suggestion that the catalog data results from instrument noise is
that F&S do not explain why thresholds of five pixels and two standard
deviations were selected.
Frank (private communication,
1998) has modified his definition of atmospheric holes to include the requirement
that an acceptable dark pixel cluster must have a standard deviation greater
than 7.5. It is noted that this criterion excludes every dark pixel clustering
event described in Frank and Sigwarth (1997a, 1997b). It also removes 36%
of the catalog events in the outer radiation belt and 15% of the events
at higher L values. This removal does not alter any of the conclusions
of this paper, which has ignored this new criterion because the catalog
data did not include it.
The catalog data was obtained
on January 31, 1998, from the world-wide-web. As stated by F&S at their
web site, "the purpose of the atmospheric hole catalog is to allow coordination
with ground-based facilities in the study of atmospheric holes." Because
the catalog was prepared by F&S from data produced by their instrument
for the scientific purpose described above, it is taken at face value in
this paper. The only catalog data in this paper is that appearing in
Table
1. It is noted that none of this data was accumulated in the outer
radiation belt. The remainder of the atmospheric hole data in this paper
was obtained from a single day of raw data, kindly provided by F&S.
This one day of data exhibits the same statistical properties as does the
catalog data in
Table 1, albeit with less statistical
precision. Parks et al. (1998) also arrive at the same conclusion as that
reached by analysis of the catalog data in Table 1.
Expected altitude dependence of dark pixel cluster
sizes for external objects at low altitude or internal sources
A geometric requirement that
distinguishes low altitude external sources of dark pixel clustering from
internal noise is that the image area of an external object varies as the
inverse-square of the distance between the object and the optical system,
i.e., essentially as the inverse-square of the Polar satellite altitude.
By contrast, the image area associated with an internal source, such as
instrument noise, does not vary with altitude. Everyone has practical experience
with the inverse square law as applied to the optical system of the human
eye, because any object (such as a building) appears to grow bigger as
one walks towards it.
This inverse-square law is further
illuminated by consideration of two objects and their images. The first
object is a 100 km diameter atmospheric hole that is created at a 500 km
altitude by a small comet whose motion perpendicular to the line of sight
during the 36 second exposure is small compared to the hole diameter. The
diameter of its image, in units of the diameter of a VIS pixel, is obtained
from the 0.08
o angular field of view of
a VIS pixel as
d = 71,600/h
(1)
where h is the distance between
the atmospheric hole and the VIS imager. The area of the image is therefore
3.14* (71,600/2h)2 pixels, i.e., it is
inversely proportional to h2. The second
object moves 500 km during the exposure. Its image has an area that is
about 6d2 or 6(71,600/2h)2. Thus, for either a moving
or non-moving object, the area of the image, in pixels, is proportional
to the inverse square of the distance from the object to the imager. For
F&S's typical 100 km diameter atmospheric hole, the image sizes from
these equations are 40-80 pixels at a spacecraft altitude of 10,000 km
and 1.5-3.0 pixels at 50,000 km.
This inverse square law dependence
has been questioned (Frank, private communication, 1998) on grounds that
the image and pixel areas are comparable near apogee, and that this combines
with the point spread function for the instrument and the motion of the
water cloud to mask the inverse-square altitude dependence. (The point
spread function causes the image of a point source to spread over an area
greater than a point. Its effects are discussed by McFadden et al. (1998).)
These three effects are simulated in a computer analysis that gives the
average image size of a 100 km atmospheric hole as a function of altitude
in Fig. 1. The data of this figure are
for an atmospheric hole moving at 20 km/sec at an angle of 60o
with respect to the line of sight, and it shows that the inverse square
law dependence is followed to altitudes that are at least twice the apogee
of Polar. Thus, arguments that there is no altitude dependence of the image
area because the small comets move, or because the image size is too small,
or because of the point spread function, are specious.
For an internal source of the dark
pixel clustering, there can be no altitude dependence of the dark pixel
cluster sizes or occurrence frequencies because instrument noise does not
care at what altitude it is recorded.
Comparison of the Iowa catalog data with the hypothesis
of low altitude objects
To compare the Iowa catalog data
with the altitude dependence required of the small-comet hypothesis or
any other low altitude external source,
Table 1 summarizes
the Iowa catalog entries at two altitudes. It is emphasized that each of
these altitudes are outside that of the outer radiation belt (15,000-25,000
km), so none of the results in the present analysis are affected by the
known creation of dark pixel clusters by outer belt penetrating particles.
There are 14,828 dark pixels
clusters at altitudes of 9,000 +/- 1,500 km in the Iowa catalog, and they
range in area from the assumed threshold of five pixels to 15 pixels. A
15 pixel cluster viewed at an altitude of 10,500 km is smaller than the
five pixel threshold when viewed from any altitude above 18,200 km, according
to the inverse-square law requirement for an external source at low altitude.
Similarly, this 15 pixel cluster has an area of 0.73 pixels at 47,500 km.
Thus, consistency with the small-comet hypothesis requires that no clusters
containing more than five dark pixels be observed above 18,200 km altitude
and that there should certainly be no five-pixel or larger clusters above
47,500 km. However, there are 134,180 dark pixel clusters above an altitude
of 47,500 km in the Iowa catalog, and they range in area from five to 17
pixels. This result alone renders the small-comet hypothesis untenable
and requires that any altitude, annual, or local time correlations found
by F&S be due to an effect (such as temperature variations, light leaks,
penetrating radiation, etc.) other than small comets. It also rules out
the possibility that any other external source at low altitude produces
the data in the Iowa catalog.
Comparison of the Iowa catalog data with the internal
source hypothesis
For the Iowa catalog data to
be consistent with an internal noise source, neither the size distribution
nor the event rate should vary with altitude. The cluster areas of 5-14
pixels at high altitude and 5-15 pixels at low altitude are essentially
identical (see also McFadden et al., 1998), so the requirement of similar
size distributions at the two altitudes is met.
The event rate at high altitude,
of 134,180/47,468 = 2.8 events/minute, is essentially the same as that
at low altitude, namely 14,828/6,448 = 2.3 events/minute. To compare these
event rates further, they must be corrected for the relative amount of
dayglow in the images at the two altitudes because dark pixel clusters
enter the Iowa catalog only when they are observed in the dayglow. This
information is not available in the catalog. However, data for June 1,
1997, has been provided by F&S. For this day, the average number of
dayglow pixels per image is given as a function of altitude in
Fig.
2, where dayglow pixels are defined as pixels having digital numbers
greater than 50 counts. The peak in this figure is due to penetrating particles
from the outer radiation belt. For this day, the ratio of dayglow pixels
per image at the high and low altitudes is about 1.4. If the ratio of events/minute
at the two altitudes (2.8/2.3) is corrected for this dayglow factor, the
ratio of high to low altitude events is 0.87. This value is fully consistent
with a noise source producing the dark pixel clusters in the Iowa catalog.
To complete the proof that the
dark pixel clusters are consistent with instrument noise, it is necessary
to explain the size distribution of the dark pixel clusters. This is done
by McFadden et al. (1998).
Expected and observed low altitude dark pixel clusters
If the high altitude data of
Table
1 is extrapolated to 9,000 +/- 1,500 km by the inverse-square law,
the cluster area increases by a factor of 21-48. Thus, the 5-14 pixel events
at >47,500 km should be 100-670 pixel events at 9,000 +/- 1,500 km. The
expected occurrence frequency of these large clusters is decreased from
the high altitude rate by two factors. The first factor results because
the instrument field-of-view can include a full hemisphere of the Earth
at altitudes above 45,000 km, at most 11% of a hemisphere at an altitude
of 10,500 km and 5.6% of a hemisphere at 7,500 km. The second factor is,
again, the ratio of the total amount of dayglow observed in all of the
images at each of the two altitude ranges. Approximating this factor as
the amount of time spent within the two altitude ranges gives an additional
factor of 7.4 decrease of the expected rate. Thus, the inverse-square law
of the small-comet hypothesis predicts that the catalog should contain
134,180x(.056 to .11)/7.4 = 1,015-2,000 clusters of 100-670 pixels each
in the 1,424 images in the Iowa catalog for altitudes of 9,000 +/- 1,500
km. In addition, clusters that are not registered at >47,500 km because
they are smaller than five pixels, can be as large as 670 pixels at altitudes
of 9,000 +/- 1,500 km. To summarize, an average of more than one cluster
per image with a cluster area greater than 100 pixels is expected at 9,000
+/- 1,500 km according to the inverse-square law.
Iowa's automated method of finding
dark pixel clusters is insufficient for clusters as large as those expected
by this extrapolation of the high altitude data. However, if such large
clusters existed in the VIS data, they would be identified visually, as
Fig.
3 shows. This figure contains about 10% of the area of a single VIS
image obtained at 2239:29 UT on June 1, 1997 at a magnetic local time of
0915 and an altitude of 11,000 km. It displays the raw image as linear
digital numbers plotted on a logarithmic color scale. The sunlit Earth
fills the field-of-view in this image and the dayglow causes the general
green-blue background. The pixel counts are not smoothed or interpolated
so the individual pixel responses may be seen. The bright pixels are caused
by penetrating radiation and their density is typical of the Iowa images
when the spacecraft is not in the outer radiation belt.
An oval array of about 250 darkened
pixels appears in
Fig. 3. This array
was produced by computer subtraction of 2.0 standard deviations from each
pixel within the array. The standard deviation was computed separately
for each pixel by the Iowa prescription, described earlier. Dark clusters
of the size of this oval in
Fig. 3 cannot
be missed in a visual inspection of either the raw or corrected VIS data.
The 1,335 images in the raw data provided by F&S for this day were
examined for such large dark pixel arrays and none were found.
The white square in
Fig. 3 is the border of a seven by seven pixel array, within which
a dark pixel clustering event was found by the Iowa algorithm for a two
sigma darkening threshold. This dark pixel cluster may be contrasted with
the computer generated oval to appreciate how deficient the events in the
Iowa catalog are compared to expectations from extrapolation of the high
altitude data. Two additional dark pixel clusters are also in Fig.
3. It is left as an exercise for the reader to find the locations of
these clusters.
Iowa method for removing penetrating radiation
The number of dark pixel clusters
found by the Iowa method in the full image, from which
Fig.
3 was obtained, is seven before removal of the penetrating radiation,
and 25, after this removal. This provides additional evidence that they
are not geophysical. The dark pixel cluster within the white square of
Fig.
3 was one of those produced by this removal of penetrating radiation.
That the dark pixel clustering
rate increases when penetrating radiation is removed is due to the decrease
of the calculated standard deviation associated with this removal, as is
explained by reference to
Table 2. This table displays
two nine by nine arrays of pixel counts, each centered on the dark pixel
clustering event identified in
Fig 3.
The upper array gives the pixel counts before removal of the penetrating
radiation and the bottom array gives the pixel counts after removal. To
remove the penetrating radiation from an image, a new "median" image is
first created in which the value associated with each pixel is the median
of the counts in a seven by seven array of pixels centered at the pixel
of interest, in the original array. Any pixel whose count is more than
30 digital numbers greater than that of the corresponding pixel in the
median image is a "high-count" pixel. All high-count pixels, and the eight
pixels surrounding each such high-count pixel, have their counts replaced
by the values in the median image. This process produces the lower array
of
Table 2. The central pixel in each of the arrays
of
Table 2 has 63 counts and is 1.35 sigma below
the mean before removal of the penetrating radiation and 2.23 sigma below
the mean afterwards. This decrease below the two sigma threshold occurs
because sigma, as computed from the standard deviation of the counts around
the border of the array, was reduced by replacement of five different counts
in the bottom row with the single value of 103. Similarly, the counts in
four additional contiguous pixels moved below the mean by more than two
sigma after removal of penetrating radiation. These decreases of sigma
changed the result from no dark pixels within the white square before removal
of penetrating radiation to five dark pixels afterwards, and this produced
the "atmospheric hole." For a two sigma threshold on June 1, 1997, more
than 75% of the dark pixel clusters occurring in the dayglow and outside
the outer radiation belts result from processing the data to remove the
penetrating radiation.
The Iowa methods also produce
"atmospheric holes" against backgrounds of the dark sky or the dark Earth,
as illustrated in
Fig. 4. In this image,
the Earth is observed from above the north polar region. Dayglow and the
auroral oval are seen, and 10 dark pixel clusters are found by the Iowa
methods. Three or four of these dark pixel clusters are above the dayglow,
two are viewed against the dark sky, and four or five are viewed against
the dark Earth. Two of the clusters over the dayglow and three of the clusters
over the dark Earth were produced by removing the penetrating radiation.
Events over the dark Earth or against the dark sky have been excluded from
the Iowa catalog by definition because they are both meaningless and devastating
in the context of the small-comet hypothesis.
Acknowledgments
The authors thank L.A. Frank and J.B. Sigwarth
for providing a day of raw data from the VIS Earth Camera, for software
to view the data, and for assistance in understanding the software and
the data. The summary data of Table 1 was obtained from the Iowa small-comet
catalog on the world wide web on January 31, 1998.They also thank Alex
Dessler and another friend for helpful discussions. This work was performed
under NASA grant NAG5-3182.
References
Cragin, B. L., W. B. Hanson,
R. R. Hodges, and D. Zuccaro, Comment on the papers "On the influx of small
comets into the Earth's upper atmosphere I. Observations and II. Interpretation,"
Geophys.
Res. Lett., 14, 573-576, 1987.
Dessler, A. J., B. R. Sandel, and V. M. Vasyliunas,
Terrestrial cometary tail and lunar corona induced by small comets: Predictions
for Galileo,
Geophys. Res. Lett., 17, 2257-2260, 1990.
Dessler, A. J., The small
comet hypothesis,
Rev. Geophys., 29, 355-382, 1991.
Frank, L. A., J. B. Sigwarth,
and J. D. Craven, On the influx of small comets into the Earth's upper
atmosphere, I, Observations,
Geophys. Res. Lett., 13, 303-306, 1986.
Frank, L. A., and J. B. Sigwarth,
Atmospheric holes and small comets, Rev. Geophys., 31, 1-28, 1993.
Frank, L. A., and J. B. Sigwarth,
Transient decreases of Earth's far-ultraviolet dayglow, Geophys. Res.
Lett., 24, 2423-2426, 1997a.
Frank, L. A., and J. B. Sigwarth,
Simultaneous observations of transient decreases of Earth's far-ultraviolet
dayglow with two cameras, Geophys. Res. Lett., 24, 2427-2430, 1997b.
Frank, L. A., and J. B. Sigwarth,
Detection of atomic oxygen trails of small comets in the vicinity of Earth,
Geophys.
Res. Lett., 24, 2431-2434, 1997c.
Frank, L. A., and J. B. Sigwarth,
Trails of OH emissions from small comets near Earth, Geophys. Res. Lett.,
24, 2435-2438, 1997d.
McFadden, J. P., F. S. Mozer,
J. Vernetti, and I. Sircar. An instrument source for the dark pixel clusters
in the Polar VIS and UVI instruments, Geophys. Res. Lett., in press,
1998.
Parks, G., M. Brittnacher,
L. J. Chen, R. Elsen, M. McCarthy, G. Germany, and J. Spann, Does the UVI
on Polar detect cosmic snowballs?, Geophys. Res. Lett., 24, 3109-3113,
1997.
Parks, G., M. Brittnacher,
M. McCarthy, J. Omeara, G. Germany, and J. Spann, Comparison of dark pixels
observed by VIS and UVI in dayglow images,. Geophys. Res. Lett.,
25, 3063-3066, 1998.
Figure captions
Figure
1. The average image size as a function of distance from a 100 km diameter
external source moving at 20 km/sec at an angle of 60 with respect to the
line of sight. These results show that the inverse-square law of image
size versus object distance is obeyed by the VIS camera to altitudes at
least twice that of the Polar apogee.
Figure 2.
The average number of dayglow pixels per image as a function of altitude
on June 1, 1997.
Figure
3. Ten percent of a raw image of the Earth taken by the VIS Earth Camera
at an altitude below the outer radiation belt. The bright pixels are produced
by penetrating particles. An oval array of about 250 darkened pixels is
created by computer subtraction of 2.0 sigma from each pixel in this array.
It illustrates the typical dark pixel cluster size expected by extrapolation
of the high altitude data. The white square encloses a typical dark pixel
cluster found by the Iowa algorithm.
Figure
4. VIS image collected over the north pole, illustrating the dayglow,
the auroral oval and 10 dark pixel clusters, of which two are viewed against
the dark sky and five are viewed over the dark Earth. The appearance of
"atmospheric holes" where there should be none, demonstrates again that
the so-called atmospheric holes are, instead, noise.
(received April 13, 1998;
revised July 15, 1998; accepted July 20, 1998.)
Table 1. Dark pixel clustering
events in the Iowa catalog
in two altitude ranges.
Table 2. Counts in a nine by nine
array of pixels before and
after removing penetrating
radiation.