A Trend Analysis for Predicting Dust Storms on Mars
Jeff Beish, Former A.L.P.O Senior Mars Recorder

INTRODUCTION

Numerous studies of the meteorology on Mars by the A.L.P.O. Mars Section indicates seasonal periods when we might expect to see a dust storm on Mars  [Beish and Parker, 1986], [Beish and Parker, 1987], [Beish and Parker, 1990 and Beish, 1999]. Our hypnosis is confirmed by the results of continued studies throughout the 1980’s and 1990’s and we have found several periods of dust event activity follows very closely to our earlier statistical analysis summarized in "Meteorology of Mars - Part III.  As expected, major storms are often observed when Mars is closer to the Sun during Perihelic apparitions.

Our statistical analysis indicates that the number of dust clouds is more often observed from mid-southern summer, between 241° and 270° Ls, with a peak period at 255° Ls. In the past, many of the major dust events occurred during the same seasonal period and led some researchers to refer to these major dust storms as "precursor storms prior to planet-encircling events." When a major dust event does occur during this period then we find that the highest probability of predicting planet-encircling dust storms occurs during mid-southern summer at or near 315° Ls.

Figure 1. A Graphic Ephemeris for the 2003 Perihelic Apparition of Mars with darken sectors indicating the seasonal periods for the probability of sighting a dust cloud or storm on Mars. The first period is from 241° Ls trough 270° Ls with a peak period occurring on 255° Ls. The second period is around 315° Ls. Original graph prepared by C.F. Capen and modified by J.D. Beish.


A recent survey by professional researchers shows that dust events can occur during virtually any season [Martin and Zurek, 1993]. Their paper reinforces our study for a main peak period for dust events is 285° Ls (just after southern summer solstice) and a secondary peak has been observed in early northern summer, around 105° Ls. Their paper articulates our hypnosis that dust storms occurring during southern summer are larger and more dramatic: they can even grow rapidly to enshroud the whole planet.

An exception to this was the 2001 planet-encircling storm that occurred at around 185 degrees Ls or 65 degrees before perihelion. This was the earliest major storm on record, and it surprised us because is started nearly two Martian "months" before the observed dusty "season" and four "months" before the high probability period of 315° Ls.

Figure 2. Two CCD images made during the 2001 apparition of Mars that demonstrates how fast the Red Planet is shrouded in dust when a planet-encircling dust storm occurs. Left image: DC Parker image on 11 June 2001. This shows a fairly clear Mars with a cloud streak or wave in the southwestern Hellas that may have indicate winds in that area. Right image: Kent De Groff on 7 July 2001. Image shows Mars completely enshrouded in dust.


We now know what the early observers of Mars -- who never had the experience of witnessing a planet-encircling or global storm -- never imagined. Dust appears to be a major player in both short- and long-term climate changes on Mars (for that matter, it is probably more significant than it has hitherto been regarded on Earth; satellite images have recently shown plumes -- virtual rivers -- of dust transported by stratospheric winds from the Gobi desert across the Pacific over a matter of a few days). This was dramatically illustrated during the now classic Great Dust Storm of 2001 [Sheehan, 2003].

STATISTICAL METHOD

The statistical method is discussed here can be found in a paper that the ALPO Mars Section published in the Journal of Geophysical Research some years ago (Beishand Parker, 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) the methods discussed in this article was found in a chapter of the book on "Time Series." We applied this method to show the trends in observed cloud activity on Mars during a period from 1968 through 1985 [Beish, 2002]. This method is discussed in more detail in an article located at URL:  Trend Analysis

We then produced a plot of the time series trend line for dust 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].

Figure 3. Two-part plot of Martian dust 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.


Table 1. A typical set of twelve 30-degree Ls periods of recording the number of Martian dust 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.

Period mean for the number of dust clouds for 1969 - 1975 = 7.1. For the probability of occurrence for 1969 – 1975 = 2.0, the number of dust clouds for 1978 – 1984 = 2.6, and for the probability of occurrence 1978 – 1984 = 0.6. The trend adjustment is a linear trend based on the apparent short term trend between apparitions. The seasonal index is found by dividing the 8-years total by the trend adjustment and then multiplying the results by a constant: for the number of dust clouds this is 0.016955; for the probability it is 0.056302. This causes the mean "seasonal index" for all 12 periods top equal one (1).


Figure 4. Two-part plot of Martian dust 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.
 
 
Table 2. A typical set of twelve 30-degree Ls periods of recording the number of Martian dust clouds observed from 1873 through 2003. 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.

Period mean for the number of dust clouds for 1969 - 1975 = 7.1. For the probability of occurrence for 1969 – 1975 = 2.0, the number of dust clouds for 1978 – 1984 = 2.6, and for the probability of occurrence 1978 – 1984 = 0.6. The trend adjustment is a linear trend based on the apparent short term trend between apparitions. The seasonal index is found by dividing the 8-years total by the trend adjustment and then multiplying the results by a constant: for the number of dust clouds this is 0.016955; for the probability it is 0.056302. This causes the mean "seasonal index" for all 12 periods top equal one (1).


Discussion

The Martian dusty period will begin on July 01, 2005 (241° Ls) and end August 16, 2005 (270° Ls).  The observer will have the highest probability of seeing a dust cloud or storm by on July 24, 2005 (255° Ls), if Mars behaves "normally."  This can be deceiving because in nature we find that accurate predictions are nearly impossible to make because of the complexities and unknown variables.  So, cheating statisticians is an almost daily occurrence.

It should be remembered, however, that these global dust storms are quite rare - only ten have been reported since 1873, and all but two have occurred since 1956. Much more common is the "localized" dust event, often starting in desert regions near Serpentis-Noachis, Solis Lacus, Chryse, or Hellas. During the 1997 apparition, CCD and HST observations revealed localized dust clouds over the north polar cap early in northern spring.

Dr. Richard McKim, Director of the Mars Section of the British Astronomical Association (BAA), performed an exhaustive historical study of Martian dust storms and has concluded that there have been only ten planet-encircling events reported since 1873. These took place in 1909, 1924, 1956, 1971, 1973, 1975, 1977 (2 storms), 1982, and 2001. Of these, only the 1971 storm was considered truly "global." Most of the major dust events have occurred during the last three decades and a cursory look at the record reveals that the frequency of massive dust events is on the increase.

In addition, the great dust storm of 2001 was most unusual in that it commenced just after the southern spring equinox. This planet-encircling dust storm occurred during a season when very few dust events of any type had been reported. In view of this increasing frequency and severity of major dust storms, many astronomers predict that there is an excellent chance that Mars will be obscured by dust around opposition time in August.

As local dust traps sunlight, it heats the atmosphere further. The warmer air flows to cooler regions where it generates local winds and raises more dust. Regional clouds spread continuously. However, a major dust storm often progresses through the quickening of activity at a number of additional cores, as in 2001. This appears to represent a classic example of a non-linear response -- true catastrophic phenomena, where only a small change in circumstances, such as an increase in the solar radiation from the Sun, can produce a huge shift [Sheehan, 2003].

Observers should be happy if during the next apparition of Mars no major dust storms occurred to block our view of the clouds and surface of the Red Planet (see Figure 3).  However, we should be alerted to the probability of seeing dust storms by at least by closest approach on October 30, 2005 (315° Ls) if Mars’ windy season follows a more normal course of behavior. Note that the 2005 opposition occurs when Mars is at perihelion, 250° Ls: a time when Mars may be very dusty indeed! What does this mean for the amateur observer?

References

Beish, J.D., Parker, D.C., and Capen, C.F. (1986), "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.

Beish, J.D., Parker, D.C., and Capen, C.F. (1987), "Meteorology of Mars - Part II," Journal of the Association of Lunar and Planetary Observers (J.A.L.P.O.),, Vol.32, Nos. 1-2, March.

Beish, J.D. and Parker, D.C. (1987) , "Meteorology of Mars - Part III," Journal of the Association of Lunar and Planetary Observers (J.A.L.P.O.), Vol 32, Nos. 5-6, October.

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

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

Beish, J.D. (2002), "A Trend Analysis for Predicting Cloudy Periods on Mars," ALPO Internet Web Page: The Mars Section, June 2002. http://groups.yahoo.com/group/Mars-ALPO/files/MetTrend.htm

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

Martin, L. J. and R. W. Zurek (1993). "An Analysis of the History of Dust Activity on Mars." Journal of Geophysical Research, Vol. 98, no. E2, pp. 3221-3246.

Sheehan, William, excerpts from article with collaborating ALPO Mars Section authors, to be published at a future date.