CAMSFlorida observes the November 2019 alpha Monocertid (AMO#246) outburst
The MeteorNews article dated 6 Nov 2019 by Esko Lyytinen and Peter Jenniskens alerted meteor observers to the possibility of a “shortlived outburst” of the alpha Monocertid (AMO#246) meteor shower on the night of November 2122. The prediction was for the outburst to last from 1540 minutes, centered on 22 Nov 04:50 UT with a zenithal hourly rate (ZHR) ranging from “about a hundred to even storm level (with a ZHR of more than 1,000).” The last outburst of this meteor shower occurred in 1995, and the prospect of another one generated much interest in the meteor community. [https://www.emeteornews.net/2019/11/06/likelyalphamonocerotidsamo246outburstonthemorningofnovember222019/.]
The CAMSFlorida Network
The CAMSFlorida network monitors an annulus about $latex 77,000\text{ }k{{m}^{2}}$ in area at 90 kilometers altitude, centered at 29.3N, 82.3W (Figure 1). Stations of the CAMSFlorida network are listed in Table 1.
CAMSFlorida consists of twentynine video cameras at five locations. The network employs an array of cameras based on the 1/2 inch chip (Watec 902H2 Ultimate) and 1/3 inch chip (Sony ICX 672 and ICX 810). Using 12mm f/1.2 lenses, the Watec cameras have a limiting meteor magnitude of +4, while the other cameras use 8mm f/1.0 lenses to achieve a meteor limiting magnitude of +3.5. Fields of view are $latex {{22}^{o}}x{{30}^{o}}$ for the Watec cameras, and $latex {{26}^{o}}x{{34}^{o}}$ for all others. For timekeeping, each CAMSFlorida station uses either a GPS time server or Network Time Protocol (NTP).
Location  Longitude  Latitude  No. of Cameras  Operator 
Gainesville  82.3752  29.66915  10  A. Howell 
New Smyrna Beach  81.1259  28.91578  2  B. Harris 
Melbourne  80.62403  28.06245  1  C. Palotai 
Ocala  82.1739  29.16576  8  E. Kisvarsanyi 
Ocklawaha  81.86585  29.09941  8  J. Cheney 
Figure 1: CAMSFlorida Area Coverage
Observing the AMO outburst
As the sky darkened above Florida on the evening of Nov 2122, skies were mostly clear. Ten minutes before local midnight (21 Nov 23:50 EST = 22 Nov 04:50 UT), when the outburst was predicted to reach its peak, the radiant would be between 21 and 23 degrees above the eastern horizon. CAMSFlorida cameras operated without interruption during the night. UFOOrbit software [http://sonotaco.com/soft/e_index.html#ufoo] was used the next morning to calculate radiants and orbital parameters. The results showed that CAMSFlorida had detected fortyfour alpha Monocerotid meteors.
Table 2 lists the times, in order of appearance, of the fortyfour coincident meteors. The outburst’s first coincident meteor was spotted at 4:38:27.746 UT, and the nexttolast was detected at 5:36:57.258 UT. A lone straggler came into view 2 1/2 hours later at 7:55:40.143 UT, yielding the night’s final total of 44 confirmed meteors from the AMO outburst. Each meteor was seen by a minimum of two geographically separated sites.
(01) 04:38:27.746  (12) 04:53:31.329  (23) 05:02:26.832  (34) 05:10:57.548 
(02) 04:39:06.173  (13) 04:56:35.504  (24) 05:04:21.051  (35) 05:11:48.137 
(03) 04:45:38.553  (14) 04:57:32.778  (25) 05:05:26.889  (36) 05:13:15.219 
(04) 04:45:51.050  (15) 04:57:43.983  (26) 05:07:15.487  (37) 05:13:54.659 
(05) 04:46:06.777  (16) 04:58:18.763  (27) 05:07:17.999  (38) 05:18:03.757 
(06) 04:46:19.289  (17) 04:59:30.117  (28) 05:07:22.125  (39) 05:20:22.182 
(07) 04:49:07.775  (18) 04:59:39.201  (29) 05:08:07.771  (40) 05:23:24.288 
(08) 04:49:44.127  (19) 04:59:58.872  (30) 05:08:27.972  (41) 05:26:25.138 
(09) 04:51:14.843  (20) 05:01:33.036  (31) 05:08:33.820  (42) 05:30:52.123 
(10) 04:51:21.510  (21) 05:01:45.301  (32) 05:08:36.208  (43) 05:36:57.258 
(11) 04:51:36.248  (22) 05:02:22.511  (33) 05:10:02.467  (44) 07:55:40.143 
Interarrival time and the arrival rate of meteors
Meteor interarrival times provide a way to estimate a meteor shower’s rate, event by event, as meteors come into view. Interarrival times is defined $latex {{T}_{i}}=U{{T}_{i}}U{{T}_{i1}}$ for $latex i=1,2,…,n$, where $latex U{{T}_{i}}$ is the UT time of the ith meteor, and $latex n$ is the number of meteors seen.
Meteor arrival rate and interarrival time are inversely related. When interarrival time is short, the arrival rate of meteor arrivals is high. When interarrival time is long, the arrival rate of meteors is low. Low lightlevel video meteor cameras and GPS timing are ideally suited to measure interarrival time $latex T$ with a precision of 3040 milliseconds. The utility of interarrival times is that they give a nearly instantaneous reading of the level of meteor activity.
An intuitive method to estimate the meteor arrival rate, $latex \lambda $, is to take the reciprocal of interarrival time, $latex \hat{\lambda }=1/T$. For example, if $latex T=10$ seconds, then $latex \hat{\lambda }=0.1$ second, equivalent to a rate of 360 meteors per hour.
[Note: $latex {\hat{\lambda }}$ is the statistical estimator of the parameter, $latex \lambda $, which is the “true” (but unknown) arrival rate of meteors. It can be shown that $latex \hat{\lambda }=1/T$ is the maximum likelihood estimator of the arrival rate. (Ross, p. 267)]
The calculated value of meteor arrival rate, $latex {\hat{\lambda }}$, is a point estimate. By itself, it gives no information about the precision of the estimate. For this reason, it is desirable to calculate upper and lower bounds that constrain, with a specified level of confidence, the likely range of $latex \lambda $.
Confidence interval of the arrival rate of meteors
The number of meteors seen during a specified time interval is often modeled as a Poisson process. The Poisson model has just one parameter, $latex \lambda $, the rate parameter. Three conditions are necessary for the Poisson model to apply: (1) Events are indpendent of one each other; (2) The average rate (events per time period) is constant; (3) Two events cannot happen at the same time. [https://towardsdatascience.com/thepoissondistributionandpoissonprocessexplained4e2cb17d459.]
The Poisson model has a close connection with interarrival times. If the occurrence of meteors conforms to a Poisson process with parameter $latex \lambda $, then the distribution of interarrival times follows an exponential distribution with mean $latex 1/\lambda $. [Ross, page 182]
The exponential distribution has the important property that it is “memoryless.” That is, prior history does not affect the time until the next event (i.e., meteor arrival). The probability of seeing a meteor during the next period of time is the same regardless of how long one has already been waiting.
Suppose one has n observations of meteor interarrival time, whose sample mean is is $latex \bar{T}=\sum\limits_{i=1}^{n}{{{T}_{i}}/n}$. The reciprocal of this statistic yields the maximum likelihood estimator of the meteor arrival rate, $latex \hat{\lambda }=1/\bar{T}$. From this, one constructs a $latex 100\left( 1\alpha \right)\%$ confidence interval of $latex \lambda $, where $latex \alpha $ is the “miss rate” of the confidence interval:
$latex \left( \hat{\lambda }\frac{\chi _{1\alpha /2,2n}^{2}}{2n},\hat{\lambda }\frac{\chi _{\alpha /2,2n}^{2}}{2n} \right)$
When analyzing a meteor shower’s outburst, it’s desirable to get the highest possible time resolution. For this purpose, set n=1, which yields the confidence interval of meteor arrival rate from a single observation of meteor interarrival time:
$latex \left( \hat{\lambda }\frac{\chi _{1\alpha /2,2}^{2}}{2},\hat{\lambda }\frac{\chi _{\alpha /2,2}^{2}}{2} \right)$
As before, $latex \hat{\lambda }=1/\bar{T}$, which simplifies to $latex \hat{\lambda }=1/T$, where T is the measured interarrival time. The chosen value of miss rate, $latex \alpha $, determines the width of the confidence interval. A smaller $latex \alpha $ generates a wider confidence interval. Using the convention that the confidence interval encompasses ±1 standard error (S.E.), set $latex \alpha =0.317$, which produces a $latex 100(10.317)\%=68.3\%$ confidence interval. ±1 standard error captures the central $latex 68.3\%$ of a normal distribution.
$latex \left( \hat{\lambda }*0.1728,\hat{\lambda }*1.8410 \right)$
Simulations of interarrival time in an Excel spreadsheet show that the confidence interval calculated this way works as expected. The simulations tested meteor arrival rates $latex \lambda $ = 1, 10, 100, and 1000 per hour. In each of these trials, the calculated confidence intervals correctly captured the population parameter, $latex \lambda $, very nearly equal to the theoretical expectation of $latex 100\left( 1\alpha \right)\%$. When the confidence interval did not include $latex \lambda $, the parameter landed with nearly equal frequency on both sides of the confidence interval.
Results
Instantaneous hourly rate of the AMO meteors
Table 3 presents the list of fortyfour alpha Monocerotid meteors observed by CAMSFlorida. A minimum of two cameras at two different sites observed each meteor. The start time of each meteor’s track varied slightly between cameras. For onehalf (50%) of the observed meteors, the start times agreed within 38 milliseconds, and the average time difference was 78 milliseconds. The largest recorded time difference in start time was 324 milliseconds, which is explained by the time delay to enter a camera’s field of view, whenever a meteor first appeared outside the field of view. The arrival time of each meteor was set equal to the time of earliest detection by the ensemble of cameras.
UT  T  1/T  HR  −1 S.E.  +1 S.E. 
04:38:27.746  —  —  —  —  — 
04:39:06.173  38.427  0.026023  93.68  16.18  172.47 
04:45:38.553  392.380  0.002549  9.17  1.58  16.89 
04:45:51.050  12.497  0.080019  288.07  49.77  530.34 
04:46:06.777  15.727  0.063585  228.91  39.54  421.42 
04:46:19.289  12.512  0.079923  287.72  49.71  529.71 
04:49:07.775  168.486  0.005935  21.37  3.69  39.34 
04:49:44.127  36.352  0.027509  99.03  17.11  182.32 
04:51:14.843  90.716  0.011023  39.68  6.86  73.06 
04:51:21.510  6.667  0.149993  539.97  93.28  994.10 
04:51:36.248  14.738  0.067852  244.27  42.20  449.70 
04:53:31.329  115.081  0.008690  31.28  5.40  57.59 
04:56:35.504  184.175  0.005430  19.55  3.38  35.99 
04:57:32.778  57.274  0.017460  62.86  10.86  115.72 
04:57:43.983  11.205  0.089246  321.29  55.50  591.49 
04:58:18.763  34.780  0.028752  103.51  17.88  190.56 
04:59:30.117  71.354  0.014015  50.45  8.72  92.88 
04:59:39.201  9.084  0.110084  396.30  68.46  729.60 
04:59:58.872  19.671  0.050836  183.01  31.62  336.93 
05:01:33.036  94.164  0.010620  38.23  6.60  70.38 
05:01:45.301  12.265  0.081533  293.52  50.71  540.37 
05:02:22.511  37.210  0.026874  96.75  16.71  178.12 
05:02:26.832  4.321  0.231428  833.14  143.93  1533.83 
05:04:21.051  114.219  0.008755  31.52  5.44  58.03 
05:05:26.889  65.838  0.015189  54.68  9.45  100.67 
05:07:15.487  108.598  0.009208  33.15  5.73  61.03 
05:07:17.999  2.512  0.398089  1433.12  247.58  2638.41 
05:07:22.125  4.126  0.242365  872.52  150.73  1606.32 
05:08:07.771  45.646  0.021908  78.87  13.62  145.20 
05:08:27.972  20.201  0.049502  178.21  30.79  328.09 
05:08:33.820  5.848  0.170999  615.60  106.35  1133.32 
05:08:36.208  2.388  0.418760  1507.54  260.43  2775.41 
05:10:02.467  86.259  0.011593  41.73  7.21  76.83 
05:10:57.548  55.081  0.018155  65.36  11.29  120.33 
05:11:48.137  50.589  0.019767  71.16  12.29  131.01 
05:13:15.219  87.082  0.011483  41.34  7.14  76.11 
05:13:54.659  39.440  0.025355  91.28  15.77  168.04 
05:18:03.757  249.098  0.004014  14.45  2.50  26.61 
05:20:22.182  138.425  0.007224  26.01  4.49  47.88 
05:23:24.288  182.106  0.005491  19.77  3.42  36.39 
05:26:25.138  180.850  0.005529  19.91  3.44  36.65 
05:30:52.123  266.985  0.003746  13.48  2.33  24.82 
05:36:57.258  365.135  0.002739  9.86  1.70  18.15 
07:55:40.143  8322.885  0.000120  0.43  0.07  0.80 
Terminology
UT = time of meteor detection by the first camera to detect
T = interarrival time in seconds
1/T = rate per second
HR = 3600/T = rate per hour
−1 S.E. = one standard error lower confidence limit of HR
+1 S.E. = one standard error upper confidence limit of HR
alpha Monocerotid (AMO#246) Hourly Rate versus Time
Hourly Rate is a log scale
Timeline of the alpha Monocerotid outburst
Time (UT)  Remarks 
04:38  The AMO outburst begins with detection of the first coincident meteor, when the rate is about 10/hour. 
04:3805:08  Rate increases steadily to a peak of 100200/hour. Within the upward trend, there are indications of momentary surges to even higher rates. 
05:08  Outburst peaks at 100200/hour.

05:13  Rate is 40/hour.

05:35  Rate is 10/hour, signaling that the end of the outburst is near. 
07:55  The last coincident AMO meteor is detected. Rate is below 1/hour. 
Discussion
This report gives a statistical method to estimate meteor arrival rate using interarrival times. Each new arrival of a meteor gives another measurement of the rate of a meteor shower. Measurements are inherently more powerful than the counting data that meteor observers have historically used.
The analysis of interarrival times of the AMO outburst shows that CAMSFlorida observed a peak hourly rate of 100200 per hour, with possible shortlived spikes up to 1000 per hour. The duration of peak rate was short, lasting no more than 1015 minutes.
The results reported by CAMSFlorida are apparent rates, not zenithal hourly rates (ZHR). Further work is needed to convert the observed rates to ZHR, accounting for such factors as (1) radiant elevation; (2) population index; (3) camera limiting magnitude; and (4) areal coverage of CAMSFlorida. Put another way, calibration of the measurement system is necessary before definitive conclusions can be made regarding zenithal hourly rate.
References
Downey, Allen B. “Think Stats.” (2011): http://greenteapress.com/thinkstats/thinkstats.pdf.
Koehrsen, Will. “The Poisson Distribution and Poisson Process Explained.” Towards Data Science Accessed 20 Jan 2020, https://towardsdatascience.com/thepoissondistributionandpoissonprocessexplained4e2cb17d459.
Lyytinen, Esko, and Jenniskens, Peter. “Likely Alpha Monocerotids (Amo#246) Outburst on the Morning of November 22, 2019.” MeteorNews (2019): https://www.emeteornews.net/2019/11/06/likelyalphamonocerotidsamo246outburstonthemorningofnovember222019/.
Ross, Sheldon M. Introduction to Probability and Statistics for Engineers and Scientists. 4th Edition. Academic Press, 2009.
SonotaCo. “UFOOrbit.” Accessed January 21, 2020. http://sonotaco.com/soft/e_index.html#ufoo