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 0.08o 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.


 
Altitude in KM
Number of Holes
Holes Sizes
Events / Min
7,500-10,500
14,828
5-15
2.3
47,500-50,500
134,180
5-14
2.8

 
 

Table 2. Counts in a nine by nine array of pixels before and
after removing penetrating radiation.


 
130
91
91
85
103
88
67
91
112
97
88
74
109
130
109
112
112
127
114
114
81
172
224
127
117
112
106
91
117
130
103
81
100
106
103
85
85
97
109
63
63
59
88
97
97
59
67
81
100
81
63
74
103
109
78
85
103
97
70
71
100
97
109
109
74
91
196
145
106
97
103
114
120
120
149
236
122
88
91
103
81
After Removal
130
91
91
85
103
88
67
91
112
97
88
97
97
97
97
112
112
127
114
114
91
97
97
97
117
112
106
91
116
91
91
97
100
106
103
85
85
97
109
63
63
59
88
97
97
59
67
81
100
81
63
74
103
109
78
85
97
97
100
100
100
97
109
109
97
97
97
100
100
97
103
114
120
103
103
103
103
103
91
103
81