INTERNATIONAL JOURNAL OF CLIMATOLOGY, VOL. 16, 113-1 17 (1996)

SHORTER CONTRIBUTION

FULL MOON AND EMPTY SKIES? T. J. LAUROESCH

Webster; New York, USA

J. R. EDINGER, JR. 295 Burky Road, Rochester. New York 14612. USA

AND

J. T. LAUROESCH Chicago, Illinois

Received 27 October 1994 Accepted 3 May 1995

ABSTRACT The hypothesis that weather is influenced by the occurrence of the full moon has been explored with respect to cloud coverage. Statistical analysis of 44 years of data has shown no apparent correlation between a clear sky and the occurrence of the full moon.

KEY WORDS: New York; statistical approach; moon; cloud cover

1. INTRODUCTION

It is often heard stated that ‘the sky is always clear on the night of the full moon’. As a matter of fact, some correlation between the phase of the moon and weather seems to have been accepted as common knowledge by early English explorers of the Arctic. Captain Sir George Back (1836) (noted):

As it was now about full moon, we looked for a favourable change of the weather, not without some anxiety; for I was apprehensive that, with the constant drenchings and fatigue together, two or three of the weaker hands might be laid up.

Tagan (1981), a more modem observer, noted:

As an amateur astronomer, I became interested in accurate weather forecasting, to schedule better my limited viewing hours. I noticed an apparent relation between the occurrence of the clearer nights and, unfortunately, the first-quarter to full phases of the moon.

We have made a statistical analysis on this hypothesis covering a 44 year period for the Rochester, New York area. This has been done by combining ephemeris data and official weather observations to compare the cloud cover on the date of the full moon with the cloud cover for a control date. Our analysis shows that there is no apparent correlation between the occasion of the full moon and clearer skies. Although there may be extended periods when ‘the sky is clearer on the night of the full moon’ and the cloud cover on the date of the full moon averaged slightly less than on the control date, the difference between the mean cloud cover for the date of the full moon and for the control date has not been shown to be significant statistically.

EXPERIMENTAL

To begin the analysis, data were first obtained on the dates and times of full moon occurrences for the 44-year period January 1950 to December 1993, inclusive. We obtained this information from The American Ephemeris

CCCO899-84 1 8/96/0 10 1 13-05 0 1996 by the Royal Meteorological Society

114 T. J. LAUROESCH, J. R. EDINGER AND J. T. LAUROESCH

Table I. A comparison of average cloud coverage on the date of the full moon (FM) to the first of the month

Cloud Coverage (tenths)

Year Full Control FM minus moon date control

1950 1951 1952 1953 1954 1955 I956 1957 1958 1959 I960 1961 1962 I963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 Mean: SD:

7.44 7.17 6.09 5.67 6.8 1 6.73 6.17 6.74 6.06 6.70 6.22 6.59 5.88 7.68 5.49 7.1 1 6.19 8.28 7.36 6.47 7.74 5.78 6.03 7.48 6.63 6.88 7.14 7.04 6.25 7.73 7.2 1 6.06 6.75 5.08 7.84 6.86 7.23 1.54 6.89 6.21 8.33 6.8 1 7.20 7.18 6.79 0.73

6.27 6.71 6.07 6.25 7.58 6.13 6.86 5.55 6.02 8.10 5.22 7.13 5.52 5.25 6.09 6.98 6.45 6.35 7.2 1 8.34 7.15 6.83 8.33 8.12 8.09 6.95 7.71 7.13 6.60 8.61 8.63 8.00 6.97 6.76 7.59 7.65 7.67 7.93 6.5 1 6.83 5.97 7.29 6.89 7.73 7.00 0.90

1.17 0.46 0.02

-0.58 -0.77

0.60 -0.69

1.19 0.04

-1.40 1 .oo

-0.54 0.36 2.43

-0.60 0.13

-0.26 I .93 0.15

-1.87 0.59

- 1.05 -2.30 -0.64 - 1.46 -0.07 -0.57 -0.09 -0.35 -0.88 -1.42 - 1.94 -0.22 - 1.68

0.25 -0.79 -0.44 -0.39

0.38 -0.62

2.36 -0.48

0.3 1 -0.55 -0.21

1.04

and Nautical Almanac. The 24-h Universal Time (UT) was converted to Eastern Standard Time (EST) (for Rochester, NY) by subtracting 5 h. On some occasions the subtraction caused a date change, making an apparent disagreement with the dates shown on most calendars.

Some simple ground rules were made for designating the night of occurrence of the full moon. The date used was that on which the moon was full after 12-noon that date and before 12-noon the following day. For example,

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the moon was full on 4 February 1977 at 03:56 UT or 22:56 EST on 3 February. The moon was full on 5 January 1977 at 12: 10 UT or 07:lO EST on 5 January. By the ground rules these full moons occurred on 3 February and 4 January, respectively. Weather data were obtained from the public library using the Local Climatological Data for the Rochester, New York station.

The procedure was to use the average of the consecutive observations starting at hour 13 on the date of the full moon established by the ground rules. Thus, in the case of the full moon on 4 February 1977 at 03:56 UT or 22:56 EST 3 February, the sky cover observations used were from hour 13 on 3 February (the date of the full moon) through hour 10 on 4 February. In this case the average sky cover (in tenths) was 8.5 from the eight observations.

As a control sample for statistical comparison, the first day of each month was chosen. The sky cover observations were averaged starting with hour 13 on the first of the month to hour 10 on the second of the month. Choosing a particular date for the control was deemed appropriate because over a long period it would occur at different times in the lunar month. Because a comparison was being made, dates were eliminated from both sets when the full moon occurred on the control date, i.e. first of the month.

Statistical anabses

Having accumulated nearly 8500 pieces of data, rigorous analysis using classical statistical methods was possible. The data are broken down and summarized in Table I. Represented are average cloud cover (in tenths) for each of the 44 years covered by this study. Averages for both the dates of the full moon and the control dates (first of the month) are listed in columns two and three, respectively. Two statistical tests (Rickmers and Todd, 1967) were applied to the data: the sign test, and the t-test for paired data.

The sign rest. One of the simplest statistical tests is based on the hypothesis that if there were no real difference between two sets of data, subtracting one set from the other would yield a series of values, half of which would be positive and half negative. Naturally, one should not expect the signs to be distributed exactly half and half, but the distribution should not depart too far from that ideal. As a rule of thumb for 40 sets of data, if two populations are truly the same the probability is less than 5 per cent for one sign to occur as few as 13 times. For our 44 years, the lesser occurring sign (positive when subtracting the control date cloud cover from the full moon cloud cover) occurs seventeen times-a not unlikely probability of occurrence if the two populations are the same.

A more definitive sign test based on the x2 distribution can be applied:

where E is the expected number of plus (and of minus) signs and 0 is the observed number of signs. For our data:

(27 - 22)2 + (1 7 - 22)2 22

= 2.273

The value calculated by the above formula must be greater than 3.841 to say, with 95 per cent confidence, that the two sets of data are not the same. Because our calculated value is less than 3.841, we should accept the null hypothesis: we have not shown the two sets of data to be different statistically.

t-tesrforpaired data. This second test is based on the assumption that if two sets of paired data are the same then the average of the differences between the pairs should be zero. Our data consist of 44 pairs: one pair for each year studied. As with the sign test described above, for each year the average cloud cover for the control date was subtracted from the average cloud cover for the date of the full moon. An average and standard deviation were then calculated for these differences. The results are listed in the table at the bottom of the fourth column.

116 T. J. LAUROESCH, J. R. EDINGER AND J. T. LAUROESCH

Avoraga Y d y Difference In Cloud Cover Between the Dates of the Full Moon and the Control

Note: Negalive value indicates skies averaged dearer on the dates of the Full Moon than the Contml dates.

50 55 60 65 70 75 80 85 90

Figure 1. Average yearly difference in Claud cover between the dates of the full moon and the control

If the hypothesis is true that cloud cover on the date of the full moon is significantly less than that on the control date, the average of the differences between the two sets of data must be significantly less than zero. The greater the departure from zero, the greater the probability that the cloud cover on the date of the full moon is the lesser. The following formula is used:

t = d/(s/&) where d is the mean difference between the two sets of data, s is the standard deviation on the differences, and n is the number of data pairs.

t = -0.21/(1-04/@)

t 1-1.342

If the calculated value is less than - 1.697 we may, with 95 per cent confidence, reject the null hypothesis. As our calculated value, however, is not less than - 1.697, we should accept the null hypothesis: the difference between the pairs has not been shown to be significantly different from zero.

CONCLUSION

The results of the two statistical tests are the same. With a confidence of 95 per cent, the null hypothesis should be accepted: for the Rochester, New York region, the cloud cover on the date of the full moon and the cloud cover on the control date have not been shown to be significantly different.

Figure 1 graph shows the data analysed on a year-by-year basis. Interestingly, from 1971 to 1983, the nights of the full moon did average less cloud cover than the control date. This curious tendency for clear full-moon skies during an extended period may warrant further study. Yet, it is most likely a statistical anomaly. Data runs like this, although remarkable, are not unheard of and merely reinforce the need for adequate sampling.

In conclusion, it seems that weather (at least with respect to cloud coverage) is probably not influenced by the phase of the moon. The comment, ‘the sky is always clear on the night of the full moon’, may arise from persons

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simply noticing a full moon on clear nights and not noticing a full moon on nights when the sky is overcast- simply because the sky is overcast.

REFERENCES Back, Captain G. 1836. Narrative of the Arctic Land Expedition to the Mouth of the Great Fish River, and Along the Shores of the Arctic

Ocean, in the Years 1833, 1834, and 1835. John Murray, London, p. 283. Tagan, F. X. 1981. ‘Letters to the Editor’, Sky and Telescope, January 1981, 29. Rickmers, A. D. and Todd, H. N. 1967. Statistics: An Introduction, McGraw-Hill, New York, pp. 87-88, 392-395.