Jeff Beish, Former A.L.P.O Senior Mars Recorder

In a four part series of A.L.P.O.
Mars Section reports I presented results of a computerized
statistical analysis of the meteorology of Mars (**Beish et al**, 1986 and 1987). Using computer programs
developed for analysis of the Martian environmental and climatic
surveys, an extensive statistical evaluation of fourteen
apparitions was presented. A statistical analysis for past
meteorological activities for clouds, bright surface frosts, and
dust clouds are shown by general table of percentage of
occurrence sub-divided in seasonal intervals and averaged over
fourteen apparitions.

The statistical method discussed
in this article was used in a paper Don Parker and I published in
the Journal of Geophysical Research some years ago (**Beish et al**, 1990). Complex cyclical data can be used to
forecast this trend analysis, or to plot a time series. The trend
can be thought of as the average departure from the
"mean."

From an interesting concept taken
from an old college outline (**Longley-Cook,**
1970) I selected methods detailed in a chapter on "Time
Series" to show the trends in observed cloud activity on
Mars during a period from 1969 through 1985.

To calculate the Seasonal Index we first determine the tabular values from:

Column (**I**) is the 30 degree period or
sub-season.

Columns (**II**) total clouds counted during the 8 apparitions
for each period.

Column (**III**) is the Period Mean or average period found by
(**II**) / 8.

Column (**IV**) is the Unadjusted Seasonal Index or
(**III**) /
S (**III**).

Column (**V**) is the Adjusted Trend or [1 + **monthly trend** ( period – 1)].

Column (**VI**) is the Adjusted Seasonal Index Adjusted for
Trend.

Column (**VII**) is the Seasonal Index in Column (**VII**)
from (**VI**) * 12 /
S (**VI**)

**NOTE:** The **monthly trend** is found by dividing the **annual trend** by 12. The annual trend is determined by
the average number of clouds from the first half (1969-1975) and
second half (1978-1984) of the complete 8-years
series.

From the external tables we determined the
period mean for number of clouds for the first half of the series
(1969-1975) was **8.2** and **27.0** for second half of the
series (1978-1984). So, the **annual trend** is (27.0 – 8.2) /
2 = 9.4. The **monthly trend** is: 9.4 / 12 = 0.783. We
find that the Adjust Trend (At) = [1 + 0.783 (period – 1)], where
"period" starts at integer 1 and increasing until end
of series (1, 2, 3……). This causes the mean "seasonal
index" for all 12 periods to equal 1. We find
S (**III**) / 12 = 211.7 / 12 = 17.6 and Column
(**IV**) from Column (**III**) /
S (**III**) / 12, then find Column (**V**) = [1 +
0.783 (period – 1)]. From (**IV**) / (**V**) we find the
Adjusted Seasonal Index in Column (**VI**).

Table 1. A typical set of twelve 30-degree Ls periods of recording the number of Martian discrete clouds observed from 1969 through 1984 by ALPO/IMP. The Martian year of four seasonal and 12 sub-seasonal periods start with its vernal equinox at 0° planetocentric longitude (Ls) and moves eastward in its orbit through the seasons or 360 degrees.

We can then produce a plot of the times
series trend line for discrete clouds observed on Mars during
eight apparitions and forecast an approximate number of clouds an
observer is likely to see in future apparitions for a particular
season. This study has been extended to include the 1965
apparition and the 1988, 1990, 1993, and 1995 apparitions. Using
the first study to test the second time series model it was
determined that a very close correlation exists between the two
studies (* Beish,* 1999).

Plot 1. Two-part plot of Martian discrete clouds of the average number and trend-adjusted seasonal indices from 1969 through 1985. Top plot represents the average number of clouds observed per degree Ls. Bottom plot gives the seasonal indices for the number of clouds observed. A probability index (dashed line) was derived from additional information and tables based on the number of clouds seen per degree Ls by more than one observer.

**References**

Longley-Cook, L.H., **Statistical
Problems and How to Solve Them**, Barnes and Nobles, New York,
1970.

Beish, J.D., Parker, D.C., and Capen, C.F.,
"Meteorology of Mars - Part I," **Journal
of the Association of Lunar and Planetary Observers
(J.A.L.P.O.),** Vol.31, Nos. 11-12, November 1986.

Beish, J.D., Parker, D.C., and Capen, C.F.,
"Meteorology of Mars - Part II,"
** J.A.L.P.O.**, Vol.32, Nos. 1-2, March 1987.

Beish, J.D. and Parker, D.C., "Meteorology of
Mars - Part III," **J.A.L.P.O.**, Vol 32, Nos.
5-6, October 1987.

Beish, J.D., and D.C. Parker, "Meteorological
Survey of Mars, 1968-1985," **Journal of
Geophysical Research (JGR)**, Vol. 95, B9, 14657-14675, August
20, 1990.

Beish, J.D., "Meteorological Survey of Mars
For Opposition Years 1965 – 1995," **The ALPO
Internet Web Page: The Digital Lens,** November 1999.
http://www.m2c3.com/alpocs/tdl1999/meterological110199/MOM.html