One Of The Most Massive Scientific Projects Which Few Know About

This would be the monumental Solar -Terrestrial Predictions Workshop and its relevant volume (over 630 pages - see cover) completed in the 1980s. The project saw the input from over two  hundred solar and space physicists covering every aspect of the problem of solar-terrestrial interactions, including: long, medium and short term solar  forecasting, geomagnetic activity and auroral (substorm) forecasts, as well as ionospheric predictions.

I was at the University of the West Indies at the time, and recruited by Dr. Donald F. Neidig of the Air Force Geophysics Laboratory to make a contribution to the specialized area of statistical limitations on flare forecasts, and specifically how Poisson statistics play a role in such forecasting. My paper ‘Limitations of Empirical-Statistical Methods of Solar Flare Prognostication’ appears on pp. 276-284 of the Proceedings and received much attention from the other contributors - since of course it impacted in multiple ways on their work as well.

Sadly, this massive work - the end product of millions of man-hours of intense scientific  collaboration and research-   is now mostly relegated to the mists of time forgotten. Even googling the header 'Solar Terrestrial Predictions Proceedings- Meudon' brings up nothing of relevance or substance.  Like so many things, because it was never digitized,  it was as if it never occurred or the work never published (The final book, though dated '1984' - did not actually appear in print format until 1987.)

The concept of a Poisson-based “delay time” for build up of magnetic free energy, was first postulated by me in 1984,  for application to “SID” (sudden ionospheric disturbance-generating) flares, with the release attendant on a change in initial free magnetic energy (E _m = B²/2m ) given by[i]:

¶ / ¶  t  { ò_v  B²/2m  dV} = 1/m  ò_v div[(v  X B) X B] dV 

 -   ò_v  {h_an | J_ms |² }dV       

where the first term on the right side embodies footpoint motion, and the second, joule dissipation, but with J_ms the current density at marginal stability – since the marginal stability hypothesis is required for a driven process, and h_an  is the anomalous resistivity. In the same paper, it was shown how the flare distribution corresponds to a Poisson process of the form P(t) =   exp (- l)   l^t  / t!, where theoretically the Poisson mean rate of occurrence is: l_m =   l Dt, with Dt  = t,  assuming the time interval Dt = 1d. In reality, measuring constraints (say achieving uniformly equal time intervals between successive Mt. Wilson magnetograms), will usually ensure  Dt ¹ 1d, so Dt  ¹  t thereby introducing a selection effect variability, complicating computation of P(t).  It was also suggested, but not proven, that variability in l arises from  variability in vertical magnetic gradients (B_z) and critical changes in the associated current density at marginal stability (Jz_ms) such that: d(Ñ(+ B_z) ) Þd Jz_ms Þ dJ_z  ( dt)/ dt, where J_z  is the vertical current density associated with putative footpoints magnetic induction (+ B_z ) and rate of change in |B_z| modulated by significant evolutionary changes (dt) in the lifetime of the magnetic field, especially critical if  dt < Dt

Since magnetic gradients and associated scale lengths (ℓ_B) also will change in time, there would be scope for accepting a Poisson process of form P(t) = f(dt,dℓ) which would embody an energy modulation with some inbuilt variance, with the latter having to be known to determine how much energy might be released and when. In other words, the differing scale factors inevitably introduced variabilities that were difficult to account for. The Poisson statistics therefore had to be able to take these differing modalities into account.

More recently, Wheatland and Craig (2003)[2] have argued that the waiting time distribution (WTD) in individual active regions is consistent with a Poisson process in time, which would conform to: P(t) =   l(t) exp (-lt)  where l(t) is the mean rate of flaring or “tick rate”.  It must be noted here that a priori l(t) ¹ l_m Dt since the latter variability also takes into account variation in data indices, selection effects arising therefrom (already noted in a paper I had co-authored with Constance Sawyer, in Solar Physics, 1985,  98, 193.) In effect, we had forecast the later work of Wheatland and Craig by at least 18 years.

Being appointed to assist in this huge project - never mind it's no longer on most peoples' radars - remains one of the high points of my scientific career!

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[i] Stahl, P.A. and  Achong, A.: 1984a, Proceedings of the Second Caribbean Physics Conference, Ed. L.L. Moseley, pp. 1-11.

[2] Wheatland, M.S. and Craig, I.J.D.: 2003, Astrophys. J., Vol. 595, p. 458