THE PREDICTION OF TROPICAL CYCLONES OR NO TROPICAL CYCLONES BY MEANS OF THE SOLAR CYCLONE STRIKE INDEX

BY: Jill F. Hasling and John C. Freeman, Ph.D
Weather Research Center - Houston, Texas
December 1993

ABSTRACT: The development of the Solar Cyclone Strike Index (SCSI) is based on the premise that the phenomenon that causes the sunspot cycle on the Sun has a similar effect on the large scale circulation patterns of the Earth which in turn could be reflected in the tracks of North Atlantic tropical cyclones. To investigate this premise, the sunspot cycle is used as a tool to develop an index. The Atlantic and Gulf of Mexico coastlines have been arbitrarily divided into zones and the crossing of the coast of tropical storms and hurricanes in each year has been designated a "strike". The year of the minimum in the solar cycle is designated as the first Phase of the SCSI. The first year after the sunspot minimum is Phase 2, up until the next sunspot minimum. Ten and half cycles were studied to determine the probability of a strike in each coastal zone. These probabilities were grouped by the phases and make up the SCSI.

The probabilities of a strike or no strike that were greater than 60% and more than one standard deviation from the mean were taken as phases and locations where a tropical cyclone would be forecasted to strike or not to strike. The probabilities of the index were tested with pure chance indices to test the stability of the SCSI. These pure chance indices never verified as close as the model.

1.0 INTRODUCTION

The study of sunspots and weather is at least a hundred years old as indicated in a paper by Bigelow (1903, 1904). Research on relationships between the sunspot cycle and hurricanes was first carried out by Willett (1951). Willet's writing prior to 1955, predicted, correctly, that the 30 year period 1959 to 1990 would have a relatively small number of hurricanes in the North Atlantic ocean. Nielson (1993) in a recent article on Hurd Willett stated

First, Willett forecast that by 1965 tropical storms would cease to trouble the East Coast, unlike the spate of deadly and destructive hurricanes that had begu with the famous New England Hurricane of 1938 and had continued through 1955 when three tropical storms caused 150 deaths in the northeast. The storms would return to tracks along the Carribbean and open Atlantic to dissipate on all but "rare occassions".

This is an example of a successful long range forecast of tropical cyclone activity based on sunspot cycles. Willet (1973) also found that the 11-year sunspot cycle is more related to the climate in the tropics than the 22 year Hale Cycle. Cohen and Sweetster (1977) showed that there is a statistical relation between the power spectrum of the sunspot cycle and the number of tropical cyclones and the length of the Atlantic season.

The most convincing evidence that the general circulation of the atmosphere could be related to the sunspot cycle was found by Labitzke and Van Loon (1987). They showed that the solar cycle correlated highly with the general circulation depending on the phase of the quasi-biennial- oscillation (QBO). When the QBO was in the phase of west winds at the equator, the high altitude temperature at the north pole was in phase with the solar cycle with a correlation coefficient of 0.76. When the QBO was in the east phase, the temperature in the north polar region was negatively correlated with the solar cycle with a coefficient of -0.45. The overall correlation coefficient between the temperature and the sunspot cycle was 0.15. These two papers give a scientific basis to the premise that the sunspots are coincident with changes in the general circulation of the Earth's atmosphere.

The fact that changes in the general circulation have an effect on hurricane statistics has been pointed out by Gray(1989), namely the biennial oscillation's effect on hurricane and the effect of the existence of El Nino Southern Oscillation (ENSO) on hurricanes. Gray started seasonal hurricane forecasting in 1984, inspired by his example and convinced that there was a long term trend in tropical cyclones on the North Atlantic coast, the authors began research on this problem, in late 1985.

2.0 SOLAR CYCLONE STRIKE INDEX (SCSI)

The Solar Cyclone Strike Index (SCSI) is based on the premise that the phenomenon that causes the sunspot cycle on the Sun has a similar effect on the large scale circulation patterns of the Earth which in turn could be reflected in the tracks of North Atlantic tropical cyclones. To investigate this premise, the sunspot cycle (Waldimeir, 1961) was used as a tool to develop an index. This general idea concerning the general circulation has a long history as illustrated by the following quote from Bigelow (1903) [a translation from a German meteorology text by Dr. A. Sprung written prior to 1903):

Therefore, a connection between the sun-spot frequency and the changes in our atmosphere can not well be denied. It is probable that the periodic changes in the atmosphere are not caused directly through sun spots, but both phenomena are brought about through one common or by several interacting causes, whereby a displacement of the periods relative to one another becomes possible.

Fairbridge (1984) also emphasized that the effect of the Sun's orbit on the Sun, which includes sunspots, would have an effect on the Earth. The maximum of sunspot activity is caused by the added tidal action of the major planets (Jupiter and Saturn) to the Sun's own rotation causing turbulence. This theory was put forth by Clyde Stacy (Fairbridge, ed. 1967).

When the Sun goes through its orbit around the center of rotation of the solar system, the Earth undergoes some of the same motion (See Figure 1. Since the Sun, as a result of these forces changes its general circulation, it is assumed for this research that the Earth's general circulation could respond to these changes. The Sun has a "year" that varies from 10 to 12 Earth years referred to in this paper as the "sol-year". The sol-year begins when the sunspots are at a minimum (the lowest or no observed sunspots)

The assumption is made that the general circulation of the Earth's atmosphere undergoes changes during the sol-year and that the changes in general circulation result in tropical cyclones having similar paths in corresponding phases (Earth years) of the sol-year. For this research, each sol-year was considered a solar cycle and each Earth year falls into a phase of the solar cycle making up the SCSI, see Table 1. All of the Earth years in which the Sun- spot minimum occurred are in Phase 1 (or are the first Earth year of the sol-year), each Earth year one year past the sunspot minimum are in Phase 2, etc. The "*" on Table 1 indicates the years when the sunspot maximum occurred and the moderate to very strong El Nino years are indicated with "M" or "S". The El Nino years are marked since Gray showed that there are less storm activity during these years. At this time a correlation between the solar cycle and El Nino events has not been found. Table 1 shows the years that are in certain phases of the sunspot cycle and the best information that is available on the beginning and end of the sol-year. The minima were taken from Waldimier(1961) and subsequent publications of the Swiss Federal Observatory. The sol-year was eleven Earth years in the cycles that begin in 1878 and 1933 and twelve Earth years for the cycles that began in 1889, 1901 and 1964 and all other cycles were 10 Earth years.

The tracks of North Atlantic tropical cyclones (Neumann, Cry, Caso, and Javienen, 1978) where then grouped into the phases and cycles of the index. The geographic boundaries studied were Mexico, Texas, Louisiana to Alabama, West Florida, East Florida, Georgia - North Carolina, Virginia - Maine. The number of years that experienced storms along a particular section of the North American coast line were tabulated and the results are given in percent in Table 2. For example, phase 1 is made of up of the following ten years; 1878, 1889, 1901, 1913, 1923, 1933, 1944, 1954, 1964 and 1976. During these ten years, there were 4 years out of 10 that a tropical storm or hurricane made landfall along the Mexican coast. This resulted in a strike probability of 40% for the coast of Mexico during Phase 1. This computation was made for the first 10 phase of the sol-year for each section of the North American coastline in order to develop the probabilities in Table 2. The result was 70 different probabilities of cyclone strikes.

3.0 SOLAR CYCLONE STRIKE INDEX FORECASTS

Forecast for particular sections of the North American coast are made by determining the highest probability by cycle and phase in the index as compared to the average probability. These values were then averaged and the times when the probability of a storm strike that were at least one standard deviation greater than the average probability were considered to be a time when a forecast could be made. Similarly when the probability was below one standard deviation from the mean, and below 20% a forecast of no storm was made.

The SCSI appears in Table 2 and gives the probability of a storm, in each of the first ten phases, striking the portion of the coast that appears along the top of the table. The table also includes the average probability and standard deviation for all the cycles of the index. The times and places for which a strike was predicted are the bold numbers with dashes. There are twelve forecasts of a storm strike and there is an expectation of a storm striking during these twelve periods with a total average probability of 71%. There are eight forecasts of no storm strikes and the expectation of no storm striking during these eight periods has a total average probability of 78%. Therefore a total of twenty forecasts could be made and are indicated by the bold numbers in Table 2.

4.0 FORECAST VERIFICATION

Figure 2 indicates that 12 forecasts of storm strikes could justifiably be made with an expected accuracy rate of 71%. The places that tropical storms or hurricanes struck the North American coast for each phase during the period 1986 to 1990 for Phases 1 to 5 and 1872 to 1876 for phases 6 through 10 are listed in Table 3. This data was used to verify the SCSI. A summary of the verification is shown in of Figure 2 and 3. There were twelve forecasts made of a storm strike. Storms struck in eight of the phases and places for 67% hits. The expectation was for 71% hits. There were eight forecasts made of no storm strike and five of these verified for a 63% score for hits. The expectation was for 78% hits. Figure 2 shows the raw verification of these forecasts. Figure 3 shows the verification comparing expectation of the cyclone strikes was 71% and there were 67% hits.

In practice a forecast was made that a storm will hit when the expectation is greater or equal to 60% and is is as high as the second highest expectation. For instance, in Phase 3, a forecast of a storm hit for Mexico, West Florida and East Florida would be made. In Phase 7, a forecast of a storm hit Texas, Louisiana, and West Florida would be made. These verify with about the same results as the ones reported here. Figure 4 shows the part of the coast with the highest two probabilities from 1986 to 1992. An estimate of no storm will hit an area was not made since the practical forecast is to determine which part of the coast is at highest risk.

Error Analysis with Pure Chance Indices

In order to determine if this forecast method gets results that could be obtained by pure chance, ten pure chance (random) indices were made with the results shown in Figure 5. These indices were made by picking 100 years randomly and placing them in a 10 by 10 index. The storms paths were then grouped and the Atlantic storms along the North American coast counted. Applying the same methods that were applied to the SCSI, eight to fifteen forecast were made in various indices. The results appear in Figure 5. Using the same ten years to verify these forecasts, the percent of verified forecast ranged from 10 to 50% with the expected accuracy rate of 59 to 80%. These forecasts were much less accurate than the ones made with the SCSI.

Another test of the SCSI was devised, each of the cycles from 1878 to 1976 were used as data to verify the 12 forecasts. The results were compared with the forecast made by the best pure chance cycle. The results of these forecast are given in Figure 6. These tests indicate that the SCSI seems to be a good tool to forecast the probability of storm strikes along the North Atlantic coasts. Figures 5 and 6 indicate that the pure chance was not as good as the SCSI for forecasting hurricanes.

Figure 7 gives the forecast made on ten pure chance indices of no-storm. This shows that the forecast of no storm is not as good as the SCSI compared to pure chance for predicting when no-storm will occur. The same exercise that developed the probabilities of a storm strike for randomly made up cycles was used to predict the probability of no storms. In two cases, the pure chance cycles made a good prediction for no storm while in eight cases it did not.

Table 4 gives the combined percentage, which is climatology, by strike zones. The error in the forecast of each coastline ranged from 0% to 36%. The combined percent error was 12% compared to a 4% combined error for the SCSI. This seems to indicate that the SCSI is as effective as climatology in predicting storms but provides more detailed information. Climatology is usually accepted as an indication of storm strikes along a coast line especially if a large enough sample is taken. In this case, climatology was a good indication (3% error) of what would happen on the coasts of Mexico, Texas, Georgia and from Virginia to Maine. However, it was a poor indicator (21% error) for the Gulf Coast from Louisiana to the tip of Florida and for the east coast of Florida. On the other hand the SCSI was accurate to within 4% for this period.

5.0 COMPARISON OF THE SCSI WITH SOME OTHER CYCLES

Other cycles such as the sunspot maximum, decades, and other combinations of solar cycles were thought to be a good bases for forecasts. Indices using these cycles were developed in the same manner as the SCSI. When an index using the sun spot maximum was developed using the maximum as Phase 1, twelve forecast could be made and only three verified. The expectation was 70% and 25% were hits.

An index was developed using four year plus the maximum as Phase 1. Once again twelve forecast could be made with 5 of them verifying. The expectation was 67% and the hit percentage was 45%. An index based on decades was developed. Using decades, it was possible to make 14 forecast and only 4 verified. The expectation was 71% and hits had a percentage of 29%. These results of these other indices appear in Table 5. This table gives the number of forecasts that could be made as well as the expectation percentages.

6.0 CONCLUSIONS AND FURTHER RESEARCH

The SCSI seems to be a better indication of a cyclone strike than pure chance or climatology. This research shows the SCSI can be used scientifically for forecasting some storm paths for the 10 years after a minimum in the sunspot cycle. However further research is also indicated, such as investigating if other divisions of the coast line would improve the strike probabilities. The methods used in this paper were state boundaries which might not be the best dissection of the US coast line. Investigation if other solar cycles such as starting with the sunspot maximum as phase 1 of the index or using the 22 year solar cycle, would possibly improve strike probabilities.

The researchers have also found very interesting matches within phases of the SCSI that point out a need for further research, such as significant category 5 hurricanes occurring during the same phase of the sol-year. Other parameters, such as month of occurrence, number of storms, and origin should also be investigated. The same in-depth analysis discussed in this paper should be carried out for other tropical basins of the world in spite of the fact pointed out by Gray and Willet that the variability is higher in the Atlantic basin.

Figure 8 shows the phases of the sunspot cycle and the occurrence of storms in southern Florida. The greatest number seems to occur in Phase 7 of the index. 1992 was in phase 6 of the index and Hurricane Andrew devastated Homestead, Florida.

REFERENCES - HURRICANE OUTLOOKS

Bigelow, Frank H, M.A., L.H.D, Studies of the Circulation of the Atmosphere of the Sun and the Earth, Reprints from Monthly Weather Review, October and November, 1903, 1904.

Cohen, T.J. and E.I. Sweetster, 1974: "The 'Spectra' of the Solar Cycle and of Spectra for Atlantic Tropical Cyclones", Nature, Vol., 256, p. 295-296.

Dunn, Gordon M. and Banner I. Miller, 1960: Atlantic Hurricanes, Louisiana State University Press

Fairbridge, Rhodes, ed.,1967: The Encyclopedia of Atmospheric Sciences and Astrogeology, Reinhold Publishing Corporation

Gray, William M, 1989: Forecast of Atlantic Seasonal Hurricane Activity for 1989, Department of Atmospheric Science, Colorado State University, Fort Collins, Co.

Herman, John R. and Richard A. Goldberg, 1978: Sun Weather and Climate, NASA, Washington, D.C.

King, J. W., 1975: Sun Weather Relationships, Astronaut, 13, 10-19

Labitzke, Karin and Harry Van Loon, 1987: Associations Between the 11-year Solar Cycle, the QBO, and the Atmosphere, Part I. The tropsphere and stratosphere in the Northern Hemisphere in Winter, J. Atmos Terr. Physics

Ludlum, David M., 1963: Early American Hurricanes 1492-1870, AMS

Nielson, Clifford H, 1993: Hurd Willett Forecaster Extraordinaire, Weatherwise, August/September 1993.

Neumann, Charles J., George W. Cry, Eduardo C. Caso and Brian R. Jarvinen, 1978: Tropical Cyclones of the North Atlantic Ocean 1871-1977, NCDC, Asheville, NC

Pittock, A.S., 1978: A Critical Look at Long Term Sun- Weather Relationships, Reviews of Geophysics, 16:400-420

Pittock, A., 1983: Solar Variability Weather and Climate" An Update, Quaterly Journal Royal Meteorological Society, 109: 23-55.

Simpson, Robert H. and Herbert Riehl, 1981: The Hurricane and Its Impact, Louisiana State University Press

Tannehill, Ivan Ray, 1943: Hurricanes, Princeton University Press

Waldmeer, Prof M., 1961: The Sunspot-Activity in the Years 1610-1960, Zurich Schultess & Co.AG

Willet, H.C., 1955: A Study of the Tropical Hurricane Along the Atlantic & Gulf Coasts of the United States, Interregional Insurance Conference, New York City

Willet, H. C., 1973: Recent Statistical Evidence in Support of the Predictive Significance of Solar-Climate Cycles, Monthly Weather Review, Vol., 102, No. 10, p. 679-686 Weather Research Center
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