Cosmic Rays and Space Weather Lev I. Dorman


Discussion on the supposed method



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4.7. Discussion on the supposed method


Obtained results show that the considered method of automatically searching for the onset of great, dangerous FEP on the basis of one-minute NM data practically does not give false alarms (the probability of false preliminary alarm is one in about 1300 years, and for false final alarm one in years). None dangerous solar neutron events also can be separated automatically. We estimated also the probability of missed triggers; it was shown that for events with amplitude of increase more than 10% the probability of a missed trigger for successive two minutes NM data is smaller than (this probability decreases sufficiently with increased amplitude A of the FEP increase, as shown in Table 1). Historical ground FEP events show very fast increase of amplitude in the start of event (Dorman, 1957; Carmichael, 1962; Dorman and Miroshnichenko, 1968; Duggal, 1979; Dorman and Venkatesan, 1993; Stoker, 1995). For example, in great FEP event of February 23, 1956 amplitudes of increase in the Chicago NM were at 3.51 UT - 1%, at 3.52 UT – 35%, at 3.53 UT – 180%, at 3.54 UT – 280 %. In this case the missed trigger can be only for the first minute at 3.51 UT. The described method can be used in many Cosmic Ray Observatories where one-minute data are detected. Since the frequency of ground FEP events increases with decreasing cutoff rigidity, it will be important to introduce described method in high latitude Observatories. For low latitude Cosmic Ray Observatories the FEP increase starts earlier and the increase is much faster; this is very important for forecasting of dangerous situation caused by great FEP events.
5. On-line determination of flare energetic particle spectrum by the method of coupling functions.
5.1. Principles of FEP radiation hazard forecasting

The problem is that the time-profiles of solar cosmic ray increases are very different for different great FEP events. It depends on the situation in the interplanetary space. If the mean free path of high-energy particles is large enough, the initial increase will be sharp, very short, only a few minutes, and in this case one or two-minute data will be useful. Conversely when the mean free path of high energy particles is much smaller, the increase will be gradual, possibly prolonged for 30-60 minutes, and in this case 2-, 3- or 5-minute data will be useful. Moreover, for some very anisotropic events (as February 23, 1956) the character of increase on different stations can be very different (sharp or gradual depending on the station location and anisotropy). Dorman et al. (2001) described the operation of programs "FEP Search-K min" (where K=l, 2, 3, and 5). If any of the "FEP Search-K min" programs gives a positive result for any Cosmic Ray Observatory the on-line program “FEP Collect” is started and collects all available data on the FEP event from Cosmic Ray Observatories and satellites. The many "FEP Research" programs then analyze these data. The real-time research method consists of:



  1. Determination of the energy spectrum above the atmosphere from the start of the FEP-event (programs "FEP Research-Spectrum");

  2. Determination of the anisotropy and its energy dependence (program "FEP Research-Anisotropy");

  3. Determination of the propagation parameters, time of FEP injection into the solar wind and total source flux of FEP as a function of energy (programs "FEP Research-Propagation", "FEP Research-Time Ejection", "FEP Research-Source");

  4. Forecasting the expected fluxes and the spectrum in space, in the magnetosphere and in the atmosphere (based on the results obtained from steps 1-3 above) using programs "FEP Research-Forecast in Space", "FEP Research-Forecast in Magnetosphere", and "FEP Research-Forecast in Atmosphere";

  5. Issuing of preliminary alerts if the forecast fluxes are at dangerous levels (space radiation storms S5, S4 or S3 according to the classification of NOAA. These preliminary alerts are from the programs "FEP Research-Alert 1 for Space", "FEP Research-Alert 1 for Magnetosphere", and "FEP Research-Alert 1 for Atmosphere".

Then, based on further on-line data collection, more accurate Alert 2, Alert 3 and so on are sent. Here we will consider three modes of the research method:

  1. a single station with continuous measurements and at least two or three cosmic ray components with different coupling functions for magnetically quiet and disturbed periods;

  2. two stations with continuous measurements at each station and at least two cosmic ray components with different coupling functions; and

  3. an International Cosmic Ray Service (ICRS), as described in Dorman et al. (1993), that could be organized in the near future based on the already existing world-wide network of cosmic ray observatories (especially important for anisotropic FEP events).

These programs can be used with real-time data from a single observatory (very roughly), with real-time data from two observatories (roughly), with real-time data from several observatories (more exactly), and with an International Cosmic Ray Service (much more exactly). Here we consider how to determine the spectrum of FEP and with a simple model of FEP propagation in the interplanetary space, and how to determine the time of injection, diffusion coefficient, and flux in the source. Using this simple model we can calculate expected fluxes in space at 1/2, 1, 3/2, 2 and more hours after injection. The accuracy of the programs can be checked and developed through comparison with data from the historical large ground FEP events described in detail in numerous publications (see for example: Elliot (1952), Dorman (1957), Carmichael (1962), Dorman and Miroshnichenko (1968), Duggal (1979), Dorman and Venkatesan (1993), Stoker (1995)).

5.2. Main properties of on-line CR data used for determining FEP spectrum in space; available data for determining the FEP energy spectrum

Let us suppose that we have on-line one-minute data from a single observatory with least 3 cosmic ray components with different coupling functions (if the period is magnetically disturbed) or at least 2 components (in a magnetically quiet period). For example, our Emilio Segre' Observatory (ESO) at 2020 m altitude, with cut-off rigidity 10.8 GV currently has the following different components (Dorman et al., 2001): total and multiplicities m=1, 2, 3, 4, 5, 6, 7, and ?8. A few months ago we started to construct a new multidirectional muon telescope that includes 1441 single telescopes in vertical and many inclined directions with different zenith and azimuth angles. From this multidirectional muon telescope we will have more than a hundred components with different coupling functions. Now many cosmic ray stations have data of several components with different coupling functions, where the method described below for determining on-line energy spectrum can be used. Also available are real-time satellite data, what are very useful for determining the FEP energy spectrum (especially at energies lower than detected by surface cosmic ray detectors).


5.3. Analytical approximation of coupling functions

Based on the latitude survey data of Aleksanyan et al. (1985), Moraal et al., 1989; and Dorman et al. (2000) the polar normalized coupling functions for total counting rate and different multiplicities m can he approximated by the function (Dorman, 1969):



, (5.1)

where m = tot, 1, 2, 3, 4, 5, 6, 7, ?8. Polar coupling functions for muon telescopes with different zenith angles can be approximated by the same type of functions (1) determined only by two parameters and . Let us note that functions (1) are normalized: at any values of and . The normalized coupling functions for point with cut-off rigidity , will be



, if , and , if (5.2)
5.4. The First Approximations of the FEP Energy Spectrum

In the first approximation the spectrum of primary variation of FEP event can be described by the function



, (5.3)

where , is the differential spectrum of galactic cosmic rays before the FEP event and is the spectrum at a later time t. In Eq. 3 parameters b and depend on t. Approximation (3) can be used for describing a limited interval of energies in the sensitivity range detected by the various components. Historical FEP data show that, in the broad energy interval, the FEP spectrum has a maximum, and the parameter in Eq. 5.3) depends on particle rigidity R (usually increases with increasing R) that can be described by the second approximation.



5.5. The Second Approximations of the FEP Energy Spectrum

The second approximation of the FEP spectrum can be determined if it will be possible to use on-line 4 or 5 components with different coupling functions. In this case the form of the spectrum will be



, (5.4)

with 4 unknown parameters . The position of the maximum in the FEP spectrum will be at



, (5.5)

which varies significantly from one event to another and changes very much with time: in the beginning of the FEP event it is great (many GV), but, with time during the development of the event, decreases very much.


5.6. On-line determining of the FEP spectrum from data of single observatory
The Case of Magnetically Quiet Periods (); Energy Spectrum in the First Approximation

In this case the observed variation in some component m can be described in the first approximation by function :



(5.6)

where m = tot, 1, 2, 3, 4, 5, 6, 7, ?8 for neutron monitor data (but can denote also the data obtained by muon telescopes at different zenith angles and data from satellites), and



(5.7)

is a known function. Let us compare data for two components m and n. According to Eq. 6 we obtain



, where (5.8)

as calculated using Eq. 5.7. Comparison of experimental results with function according to Eq. 5.8 gives the value of , and then from Eq. 5.6 the value of the parameter b. The observed FEP increase for different components allows the determination of parameters b and for the FEP event beyond the Earth's magnetosphere.


The Case of Magnetically Quiet Periods (); Energy Spectrum in the Second Approximation

Let us suppose that on-line are available for, at least, 4 components i=k, l, m, n with different coupling functions. Then for the second approximation taking into account Eq. 5.4, we obtain



(5.9)

where i=k, l, m, n and



. (5.10)

By comparison data of different components we obtain



, , , (5.11)

where (i, j=k, l, m, n)



(5.12)

is calculated using Eq. 5.10. The solving of the system of Eq. 5.11 gives the values of , and then parameter b can be determined by Eq. 5.9: for any i=k, l, m, n.


The Case of Magnetically Disturbed Periods (); Energy Spectrum in the First Approximation

For magnetically disturbed periods the observed cosmic ray variation instead of Eq. 5.6 will be described by



, (5.13)

where is the change of cut-off rigidity due to change of the Earth's magnetic field, and is determined by Eq. 5.2 at . Now for the first approximation of the FEP energy spectrum we have unknown variables , b, , and for their determination we need data from at least 3 different components k=l, m, n in Eq. 5.16. In accordance with the spectrographic method (Dorman, 1975) let us introduce the function



, (5.14)

where


. (5.15)

Then from



, (5.16)

the value of can be determined. Using this value of , for each time t, we determine



, , (5.17)

In magnetically disturbed periods, the observed FEP increase for different components again allows the determination of parameters and b, for the FEP event beyond the Earth's magnetosphere, and , giving information on the magnetospheric ring currents.



The Case of Magnetically Disturbed Periods (); Energy Spectrum in the Second Approximation

In this case for magnetically disturbed periods we need at least 5 different components, and the observed cosmic ray variation, instead of Eq. 5.13, will be described by



, (5.18)

where i=j, k, l, m, n. Here are determined by Eq. 5.2 at and are determined by Eq. 5.10. By excluding from the system of Eq. 5.18 linear unknown variables and b we obtain three equations for determining three unknown parameters of FEP energy spectrum of the type



=, (5.19)

where


. (5.20)

In Eq. 5.19 the left side is known from experimental data for each moment of time t, and the right side are known functions from , what is calculated by taking into account Eq. 5.10 and Eq. 5.2 (at ). From the system of three equations of the type of Eq. 5.19 we determine on-line , and then parameters b and :



, (5.21)

. (5.22)

5.7. Using real-time cosmic ray data from two observatories

For determining the on-line FEP energy spectrum in the first and in the second approximations (Eq. 5.3 and 5.4, correspondingly) it is necessary to use data from pairs of observatories in the same impact zone (to exclude the influence of the anisotropy distribution of the FEP ground increase), but with different cut-off rigidities and .
Magnetically Quiet Periods (); the FEP Energy Spectrum in the Interval ÷

If it is the same component m for both observatories (e.g., total neutron component on about the same level of average air pressure ), the energy spectrum in the interval ÷ can be determined directly for any moment of time t (here is determined by Eq. 5.1):

, (5.23)
Magnetically Quiet Periods (); the FEP Energy Spectrum in the First Approximation

In this case for determining b and ? in Eq. 5.3 we need on line data at least of one component on each Observatory. If it is the same component m on both Observatories, parameter ? will be found from equation



, where , (5.24)

and then can be determined



. (5.25)

If there are different components m and n, the solution will be determined by equations:



, where , (5.26)

. (5.27)
Magnetically Quiet Periods (); the FEP Energy Spectrum in the Second Approximation

In this case we need at least 4 components: it can be 1 and 3 or 2 and 2 different components in both observatories with cut-off rigidities and . If there are 1 and 3 components, parameters will be determined by the solution of the system of equations



, (5.28)

and then we determine



(5.29)

If there are two and two components in both observatories with cut-off rigidities and , the system of equations for determining parameters will be



, (5.30)

and then we determine



(5.31)

Magnetically Disturbed Periods (); the FEP Energy Spectrum in the First Approximation

In this case we have 4 unknown variables: . If there are 1 and 3 components in both observatories with cut-off rigidities and , the system of equations for determining is



, (5.32)

, (5.33)

, (5.34)

. (5.35)

In this case we determine, from Eq. 5.33-5.35, , b, and as it was described above by Eq. 5.14-5.17. From Eq. 5.32 we then determine



. (5.36)

If there are 2 and 2 components in both observatories, we will have the same system as Eq. 5.32-5.35; however, Eq. 5.33 is replaced by



. (5.37)

From the system of Eq. 5.32, 5.37, 5.34 and 5.35 we exclude linear unknown variables b, and finally obtain a non-linear equation for determining :



, (5.38)

where


(5.39)

can be calculated for any pair of stations using known functions (calculated from Eq. 5.7), and known values , , and (calculated from Eq. 5.2). After determining we can determine the other 3 unknown variables:



, (5.40)

, (5.41)

. (5.42)
Magnetically Disturbed Periods (); Energy Spectrum in the Second Approximation

In this case we have 6 unknown variables , thus from both observatories we need a total of at least 6 components in any combination. This problem also can be solved by the method described above, only instead of functions F and the functions and will be used. Here we have not enough space to describe these results; it will be done in other paper.


5.8. Using real-time cosmic ray data from many observatories (ICRS)

Using the International Cosmic Ray Service (ICRS) proposed by Dorman et al. (1993) and the above technique, much more accurate information on the distribution of the increased cosmic ray flux near the Earth can be found. We hope that for large FEP events it will be possible to use the global-spectrographic method (reviewed by Dorman, 1974) to determine, in real-time, the temporal changes in the anisotropy and its dependence on particle rigidity. It will allow a better determination of FEP propagation parameters in interplanetary space, and of the total flux and energy spectrum of particles accelerated in the solar flare, in turn improving detailed forecasts of dangerous large FEP events.



5.9. Determining of coupling functions by latitude survey data

The coefficients and for the coupling functions in Eq. 5.1 and 5.2 were determined from a latitude survey by Aleksanyan et al. (1985) and they are in good agreement with theoretical calculations of Dorman and Yanke (1981), and Dorman et al. (1981). Improved coefficients were determined on the basis of the recent Italian expedition to Antarctica (Dorman et al., 2000). The dependence of and on the average station pressure h (in bar) and solar activity level is characterized by the logarithm of CR intensity (we used here monthly averaged intensities from the Climax, USA neutron monitor as ; however, the monthly averages of the Rome NM or monthly averages of the ESO NM (with some recalculation coefficients) can be approximated by the functions:



, (5.43)
, (5.44)
(5.45)
(5.46)
Instead of Climax, other stations can be used in Eq. 5.43-5.46 with the appropriate coefficients.
5.10. Calculation of integrals and

The integrals of Eq. 5.7 are calculated for values of from -1 to +7, for different average station air pressure, h, cut-off rigidities, , and different levels of solar activity characterized by the value according to



. (5.47)

Results of calculations of Eq. 5.47 at different values of from -1 to +7 show that integrals can be approximated, with correlation coefficients between 0.993 and 0.996, by the function



. (5.48)

Results of calculations of functions (for the second approximation of the FEP energy spectrum) will be present in another paper.


5.11. Calculation of functions , and

Functions determined by Eq. 5.8 now by using Eq. 5.48 becomes



, (5.49)

Eq. 5.14 becomes



, (5.50)

and Eq. 5.39 becomes



. (5.51)
5.12. Examples of determination of the FEP energy spectrum

For example let us compare Eq. 5.49 and Eq. 5.8: the spectral index is



(5.52)

Then from Eq. 5.6 we determine



. (5.53)

So for magnetically quite times the inverse problem can be solved on-line for each one-minute data interval during the rising phase. For magnetically disturbed times the inverse problem can also be solved automatically in real-time, using the special function described in Eq. 5.50 (for observations by at least three components at one observatory), or by using the function described in Eq. 5.51 (for observations by two observatories). Note that for the first approximation we have assumed a two-parameter form of the energy spectrum. In reality the FEP energy spectrum could be more complicated; may also change with energy. If the spectrum can only be described by three or four-parameters (considered in the second approximation given previously) then observations from a range of neutron monitors (including those with low cut-off rigidities) and from satellites will be needed. We conclude that in these cases solutions can also be obtained for the energy spectrum, its change with time and the change of cut-off rigidities. The details of these solutions will be reported in another paper.


5.13. Special program for on-line determining of energy spectrum for each minute after FEP starting (for the case of single observatory).

Let us consider data from neutron monitor with independent registration of total flux and 7 multiplicities as input flux of data as vector , where i –is number of time registration index, m- number of channel (–total flux, different multiplicities). For estimation of the statistical properties of input flux we calculate mean and standard deviation for each channel and on the 1-hour interval, preceded to i-time moment on 1-hour. During next step we calculate vector of relative deviations :



(5.54)

and correspondent standard deviation . On the basis of deviation’s vector we calculate matrix



(5.55)

of ratios deviations for different energetic channels m, n at the time moment i and its standard deviation . On the basis of Eq. 5.52 and Eq. 5.53 by using Eq. 5.54 we calculate matrix of the spectral slope , matrix of amplitude and estimations of correspondent standard deviations and .

For conversation of matrix output of estimated slope to the scalar’s form we use estimation of the average values taking into account the correspondent weights W of the individual values determined by the correspondent standard deviations

, (5.56)

that


. (5.57)

The same we made for parameter :



. (5.58)

where


(5.59)

By found values of and can be determined FEP energy spectrum by using Eq. 5.3 for each moment of time:



(5.60)

We checked this procedure on the basis of neutron monitor data on the Mt. Gran-Sasso in Italy for the event September 29, 1989. We used one minute data of total intensity and multiplicities from 1 to 7. The number of minutes is start from 10.00 UT at September 29, 1989. Results are shown in Fig. 5.1.

Upper limit of indexes m, n we choose about 3÷4, since for higher multiplicities accuracy level decreases fast and we may decrease confidence of the estimation. From the right side of fig. 5.1 in the 3 graphical windows it may be seen observed total intensity variation (the top window), values of calculated according to Eq. 5.57 on the basis of matrix data (the middle window), and estimated amplitude calculated according to Eq. 58 on the basis of matrix data (the bottom window). Horizon axes is time started from 10.00 UT at September 29, each point is 1 minute data, time axes is divided in three 1-hour blocks.

In the left side of fig. 5.1, in four windows are situated for output of table data in ASCII form. There is output relative amplitude in the top window; output ratio of relative amplitude for total and first multiplicity channels; flux at the choose moment for analysis (in this output – moment of the maximum) and estimation of the gamma matrix (spectral slope in this moment of time) for different combination m,n; matrix of estimations for output amplitude of FEP. In Table 5.1 are shown final results of determining , , and .



Fig. 5.1. Simulation of real-time monitoring and analysis of FEP on example of event 29 September 1989. Data of 3NM-64 on Mt. Gran-Sasso. Details in text.

6. On-line determination of diffusion coefficient in the interplanetary space, time of ejection and energy spectrum of FEP in source.
6.1. On-line determination of FEP spectrum in source when diffusion coefficient in the interplanetary space and time of ejection are known

According to observation data of many events for about 60 years the time change of FEP flux and energy spectrum can be described in the first approximation by the solution of isotropic diffusion from the pointing instantaneous source described by function



. (6.1)

Let us suppose that the time of ejection and diffusion coefficient are known. In this case the expected FEP rigidity spectrum on the distance r from the Sun in the time t after ejection will be

, (6.2)

where is the rigidity spectrum of total number of FEP in the source, t is the time relative to the time of ejection and is the known diffusion coefficient in the interplanetary space in the period of FEP event. At AU and at some moment the spectrum determined in Section 4, will be described by the function



(6.3)

where and are parameters determined the observed rigidity spectrum in the moment , and is the spectrum of galactic cosmic rays before event (see Section 4). From other side, the FEP spectrum will be determined at according to Eq. 6.1. That we obtain equation



=. (6.4)

If the diffusion coefficient and time of ejection (i.e., time relative to the time of ejection) are known, that from Eq. 6.4 we obtain



. (6.5)
6.2. On-line determination of diffusion coefficient in the interplanetary space when FEP spectrum in source and time of ejection are known

Let us consider the case when FEP spectrum in source and time of ejection may be known (e.g. from direct gamma-ray measurements what gave information on the time of acceleration and spectrum of accelerated particles). In this case from Eq. 6.4 we obtain the following iteration solution



. (6.6)

As the first approximation in the right hand of Eq. 6 can be used for galactic cosmic rays obtained from investigation of hysteresis phenomenon (Dorman, 2001, Dorman et al., 2001a,b). The iteration process in Eq. 6.6 is very fast and only few approximations is necessary.


6.3. On-line determination of the time of ejection when diffusion coefficient in the interplanetary space and FEP spectrum in source are known

In this case we obtain from Eq. 6.4



. (6.7)

As the first approximation in the right hand of Eq. 6. 7 can be used obtained from measurements of the start of increase in very high energy region where the time of propagation from the Sun is about the same as for light. The iteration process in Eq. 6. 7 is very fast and only few approximations is necessary.


6.4. On-line determination simultaneously of FEP diffusion coefficient and FEP spectrum in source, if the time of ejection is known

Let us suppose that and are unknown functions, but the time of ejection is known. In this case we need to use data at least for two moments of time and relative to the time of ejection (what is supposed as known value). In this case we will have system from two equations:



, (6.8)

, (6.9)

By dividing Eq. (6.8) on Eq. (6.9), we obtain



, (6.10)

from what follows



. (6.11)

The found result for will be controlled and made more exactly on the basis of Eq. 6.11 by using the next data in moments and , as well as for moments and , then by data in moments , and , and so on. By introducing result of determining of diffusion coefficient on the basis of Eq. 6.11 in Eq. 6.5 we determine immediately the expected flux and spectrum FEP in the source:



, (6.12)

where is determined by Eq. 6.11.


6.5. On-line determination simultaneously time of ejection and FEP spectrum in source if the diffusion coefficient is known

Let us suppose that diffusion coefficient is known, but the time of ejection is unknown. In this case we need measurements of FEP energy spectrum at least in two moments of time. Let us suppose that in two moments and were made measurements of energetic spectrum as it was described in Section 4. Here times , and are in UT scale. Let us suppose that



, (6.13)

where and are times relative to the moment of FEP ejection into solar wind, and and are known UT and is unknown value what can be determined from the following system of equations:



, (6.14)

. (6.15)

By dividing of Eq. (6.14) on Eq. (6.15), we obtain



, (6.16)

From Eq. 6.16 unknown value x can be found by iteration:



, (6.17)

where


. (6.18)

As the first approximation we can use what is a minimum time of relativistic particles propagation from the Sun to the Earth’s orbit. Then by Eq. (6.18) we determine and by Eq. 6.17 determine the second approximation . To put in Eq. 6.18 we compute , and then by Eq. 6.17 determine the third approximation , and so on. After determining and UT time of ejection we can determine the FEP spectrum in the source:



. (6.19)

6.6. On-line determination simultaneously time of ejection, diffusion coefficient and FEP spectrum in the source.

Let us suppose that the time of ejection , diffusion coefficient and FEP spectrum in the source are unknown. In this case for determining on-line simultaneously time of ejection , diffusion coefficient and FEP spectrum in the source we need information on FEP spectrum at least in three moments of time , and (all times T are in UT scale). In this case instead of Eq. 6.13 we will have for times after FEP ejection into solar wind:



, (6.20)

where - and - are known values, and x is unknown value what we need to determine by solution of the system of equations



, (6.21)

From this system of equations by dividing one equation on other (to exclude ) we obtain



, (6.22)

(6.23)

By dividing Eq. 6.22 on Eq. 6.23 (to exclude ) we obtain



, (6.24)

where is function very weekly depended from x:



. (6.25)

Eq. 6.24 can be solved by iteration method: as the first approximation we can use, as in Section 6.5, what is a minimum time of relativistic particles propagation from the Sun to the Earth’s orbit. Then by Eq. 6.25 we determine and by Eq. 6.24 determine the second approximation . To put in Eq. 6.25 we compute , and then by Eq. 6.24 determine the third approximation , and so on:



, (6.26)

After solving Eq. 6.24 and determining the time of ejection , we can compute diffusion coefficient from Eq. 6.22 or Eq. 6.23:



. (6.27)

After determining time of ejection and diffusion coefficient we can determine the total flux and energy spectrum in source from Eq. 6.21:



, (6.28)

where was determined by Eq. 6.24, and by Eq. 6.27.


6.7. Controlling on-line of the used model of FEP generation and propagation

The on-line controlling of using model can be made by data obtained in the next minutes , and others. For example, we can determine the time of ejection , diffusion coefficient and FEP spectrum in the source on the basis of data obtained in moments , then in moments , then in moments , or for any other combinations of time moments, for example, at , and so on. Obtained values of , and in the frame of errors must be the same what obtained on the basis of data in time moments . If this condition will be satisfied for any combinations of , it will be meant that the used model of FEP generation and propagation in the interplanetary space is correct and it can be used also for prediction of expected FEP fluxes in space, in the magnetosphere, and in the Earth’s atmosphere. If this condition will be not satisfied, it will be meant that the real model of FEP generation and propagation in the interplanetary space is more complicated. In this case the using of data from only one observatory is not enough, it is necessary to use data from many cosmic ray observatories to determine anisotropy of FEP fluxes on the Earth and parameters of more complicated model. On the basis of consideration of many FEP events we expect that after some short time FEP distribution became isotropic and considered above simple model of FEP generation and propagation in the interplanetary space became correct. This moment can be determined automatically by the described above method of estimation of , and for different combinations .


7. On-line forecasting of expected FEP flux and radiation hazard for space-probes in space, satellites in the magnetosphere, jets and various objects in the atmosphere, and on the ground in dependence of cut-off rigidity.
7.1. Prediction of expected FEP energy spectrum, FEP flux and FEP fluency (proportional to the radiation doze) in the space on different distances from the Sun

If the controlling described in the Section 5.7 will give positive result, we can predict the expected FEP rigidity spectrum in the space at any moment T and at any distance r from the Sun:



(7.1)

The expected flux inside any space-probe at distance r from the Sun with the threshold energy will be



(7.2)

and the fluency what will receive a space-probe during all time of event (determined the radiation doze) will be



(7.3)
7.2. Prediction of expected FEP energy spectrum, FEP flux and FEP fluency (radiation doze) for satellites at different cut-off rigidities inside the Earth’s magnetosphere

Inside the Earth’s magnetosphere the expected FEP energy spectrum will be determined by Eq. 7.1 at . For satellites at different cut-off rigidities inside the Earth’s magnetosphere the expected FEP flux will be



(7.4)

where is determined by the orbit of satellite. The expected fluency what will receive a satellite with orbit during all time of event (proportional to the radiation doze) will be



(7.5)
7.3. Prediction of expected intensity of secondary components generated by FEP in the Earth’s atmosphere and expected radiation doze for planes and ground objects on different altitudes at different cut-off rigidities.

The expected intensity of secondary component of type i (electron-photon, nucleon, muon and others) generated in the Earth’s atmosphere by FEP at moment of time T will be in the some point characterized by pressure level and cut-off rigidity as following



, (7.6)

where is the coupling function. The expected total fluency (proportional to the radiation doze) for planes and ground objects on different altitudes at different cut-off rigidities will be determined by integration of Eq. 7.6 over all time of event and summarizing over all secondary components:



, (7.7)
7.4. Alerts in cases if the radiation dozes are expected to be dangerous

If the described in Sections 7.1-7.3 forecasted radiation dozes are expected to be dangerous, will be send in the first few minutes of event preliminary "FEP-Alert_1/Space", "FEP-Alert_1/ Magnetosphere", "FEP-Alert_1/ Atmosphere”, "FEP-Alert_1 /Ground”, and then by obtaining on-line more exact results on the basis of for coming new data will be automatically send more exact Alert_2, Alert_3 and so on. These Alerts will give information on the expected time and level of dangerous; experts must operative decide what to do: for example, for space-probes in space and satellites in the magnetosphere to switch-off the electric power for 1-2 hours to save the memory of computers and high level electronics, for jets to decrease their altitudes from 10-20 km to 4-5 km to protect crew and passengers from great radiation hazard, and so on.


7.5. Conclusion to the consideration of the problem on the on-line forecasting of FEP radiation hazard by using on-line data of CR ground observations.

Obtained solutions described in Sections 7.1-7.3 gave possibility on the basis of determining on-line by one-minute NM data FEP energy spectrum (Section 4) during several minutes after start of great event (the start is also determined automatically, see Section 3) - to determine on-line the time of FEP ejection into solar wind, the diffusion coefficient for FEP propagation in the interplanetary space, and total FEP flux and energy spectrum in the source (as it was described in Section 5). It is important that the used simple model can be controlled on-line by using data for the next few minutes (see Section 5.7). The obtained on-line information can be considered as basis for the next working on-line programs for determining expected FEP fluxes and radiation dozes what will be obtained space-probes in space at different distances from the Sun, satellites in the magnetosphere on different orbits, jets in the atmosphere on different air-lines and different objects on the ground at different altitudes and cut-off rigidities (Sections 7.1-7.3). If the forecasted radiation dozes are expected to be dangerous, will be send automatically on-line correspondingly Alerts to protect computer memory and electronics on space-probes and satellites, cosmonauts in space-ships, crew and passengers in jets and so on from great radiation hazard.



As we mentioned above, obtained here solutions for , , and are valid if the propagation of FEP in the interplanetary space can be described by the simple model of isotropic diffusion. The consideration of more complicated model of FEP generation and propagation on the basis of on-line one-minute data from many cosmic ray observatories is now in processing and will be present in near future.
8. Cosmic ray using for forecasting of major geomagnetic storms accompanied by Forbush-effects.
8.1. On the influence of geomagnetic storms accompanied with CR Forbush-decreases on people health and technology.

There are numerous indications that natural, solar variability-driven time variations of the Earth's magnetic field can be hazardous in relation to health and safety. There are two lines of their possible influence: effects on physical systems and on human beings as biological systems. High frequency radio communications are disrupted, electric power distribution grids are blacked out when geomagnetically induced currents cause safety devices to trip, and atmospheric warming causes increased drag on satellites. An example of a major disruption on high technology operations by magnetic variations of large extent occurred in March 1989, when an intense geomagnetic storm upset communication systems, orbiting satellites, and electric power systems around the world. Several large power transformers also failed in Canada and United States, and there were hundreds of misoperations of relays and protective systems (Kappenman and Albertson, 1990; Hruska and Shea, 1993). Some evidence has been also reported on the association between geomagnetic disturbances and increases in work and traffic accidents (Ptitsyna et al. 1998 and refs. therein). These studies were based on the hypothesis that a significant part of traffic accidents could be caused by the incorrect or retarded reaction of drivers to the traffic circumstances, the capability to react correctly being influenced by the environmental magnetic and electric fields. The analysis of accidents caused by human factors in the biggest atomic station of former USSR, "Kurskaya", during 1985-1989, showed that ~70% of these accidents happened in the days of geomagnetic storms. In Reiter (1954, 1955) it was found that work and traffic accidents in Germany were associated with disturbances in atmospheric electricity and in geomagnetic field (defined by sudden perturbations in radio wave propagation). On the basis of 25 reaction tests, it was found also that the human reaction time, during these disturbed periods, was considerably retarded. Retarded reaction in connection with naturally occurred magnetic field disturbances was observed also by Koenig and Ankermueller (1982). Moreover, a number of investigations showed significant correlation between the incidence of clinically important pathologies and strong geomagnetic field variations. The most significant results have been those on cardiovascular and nervous system diseases, showing some association with geomagnetic activity; a number of laboratory results on correlation between human blood system and solar and geomagnetic activity supported these findings (Ptitsyna et al. 1998 and refs. therein). Recently, the monitoring of cardiovascular function among cosmonauts of “MIR” space station revealed a reduction of heart rate variability during geomagnetic storms (Baevsky et al. 1996); the reduction in heart rate variability has been associated with 550% increase in the risk of coronary artery diseases (Baevsky et al. 1997 and refs. therein). On the basis of great statistical data on several millions medical events in Moscow and in St. Petersburg were found an sufficient influence of geomagnetic storms accompanied with CR Forbush-decreases on the frequency of myocardial infarcts, brain strokes and car accident road traumas (Villoresi et al., 1994, 1995). Earlier we found that among all characteristics of geomagnetic activity, Forbush decreases are better related to hazardous effects of solar variability-driven disturbances of the geomagnetic field (Ptitsyna et al. 1998). Fig. 8.1 shows the correlation between cardiovascular diseases, car accidents and different characteristics of geomagnetic activity (planetary index AA, major geomagnetic storms MGS, sudden commencement of geomagnetic storm SSC, occurrence of downward vertical component of the interplanetary magnetic field Bz and also decreasing phase of Forbush decreases (FD)). The most remarkable and statistically significant effects have been observed during days of geomagnetic perturbations defined by the days of the declining phase of Forbush decreases in CR intensity. During these days the average numbers of traffic accidents, infarctions, and brain strokes increase by (17.4±3.1)%, (10.5±1.2)% and (7.0±1.7)% respectively. In Fig. 8.2 we show the effect on pathology rates during the time development of FD. All FD have been divided into two groups, according to the time duration T of the FD decreasing phase. Then, the average incidence of infarctions and traffic accidents was computed beginning from one day before the FD-onset till 5 days after. For the first group (T<1 day) the average daily incidence of infarctions and traffic incidence increases only in the first day of FD; no effect is observed during the recovery phase (that usually lasts for several days). Also for the second group (1 day


Fig. 8.1: Myocardial infarction (a), brain stroke (b) and road accident (c) incidence rates per day during geomagnetic quiet and perturbed days according to different indexes of activity.


Fig 8.2: Infarction (full squares) and road accidents (full triangles) incidence during the time development of FD. (a): CR decrease phase T<1 day; (b): CR decrease phase 1 day
Table 8.1. The extended NOAA scale of geomagnetic storms influence on people health, power systems, on spacecraft operations, and on other systems (greatest three types, mostly accompanied with Forbush-decreases). In the original NOAA scale are included biological effects according to results discussed above.

    1. Geomagnetic Storms

  1. Kp values


Number per solar cycle




G5

Extreme

Biological effects: increasing on more than 10-15% of the daily rate of infarct myocardial, brain strokes and car road accidents traumas for people population on the ground

Power systems: widespread voltage control problems and protective system problems can occur, some grid systems may experience complete collapse or blackouts. Transformers may experience damage.

Spacecraft operations: may experience extensive surface charging, problems with orientation, uplink/downlink and tracking satellites.

Other systems: pipeline currents can reach hundreds of amps, HF (high frequency) radio propagation may be impossible in many areas for one to two days, satellite navigation may be degraded for days, low-frequency radio navigation can be out for hours.

Kp = 9

4 per cycle
(4 days per cycle)


G4

Severe

Biological effects: increasing on several percents (up to 10-15%) of the daily rate of infarct myocardial, brain strokes and car road accidents traumas for people population on the ground

Power systems: possible widespread voltage control problems and some protective systems will mistakenly trip out key assets from the grid.

Spacecraft operations: may experience surface charging and tracking problems, corrections may be needed for orientation problems.

Other systems: induced pipeline currents affect preventive measures, HF radio propagation sporadic, satellite navigation degraded for hours, low-frequency radio navigation disrupted.

Kp = 8, including a 9-

100 per cycle
(60 days per cycle)


G3

Strong

Biological effects: increasing on few percents of the daily rate of infarct myocardial, brain strokes and car road accidents traumas for people population on the ground

Power systems: voltage corrections may be required, false alarms triggered on some protection devices.

Spacecraft operations: surface charging may occur on satellite components, drag may increase on low-Earth-orbit satellites, and corrections may be needed for orientation problems.

Other systems: intermittent satellite navigation and low-frequency radio navigation problems may occur, HF radio may be intermittent.

Kp = 7

200 per cycle
(130 days per cycle)




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