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INTERNATIONAL STANDARD

ISO TS 15391
Technical specification Version 2004 October



______________________________________________________________ Space Environment (Natural and Artificial) Probabilistic model for fluences and peak fluxes of solar energetic particles Part I Protons

Memorandum

Reference No. ISO 15391

SPACE ENVIRONMENT (NATURAL AND ARTIFICIAL) Probabilistic model for fluences and peak fluxes of solar energetic particles: Part I - protons
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Memorandum-2004 (October)
(Memorandum is compiled by recommendations of ESA)
CONTENT

1. Purposes and scope 1.1 Purposes of the Standard 1.2 Users of the Standard 1.3 The users' requirements 1.4 The model used in the represented Standard Draft 2. The main criteria of the validity of SEP models 2.1 The initial (input) experimental data 2.2 Methodology of data analysis and synthesis 2.2.1 The definition of a Solar Energetic Particle (SEP) «event". 2.2.2 SEP particle fluxes during "quiet" Sun years. 2.2.3 On the hypothesis of SEP flux independence on solar activity during the 7-year "active" Sun period 2.2.4 Solar activity and SEP event frequency 2.2.5 The SEP distribution function 2.2.6 The energy spectra of events in the SEP models 2.3 Development of the model description of the fluxes (output data requirements) 11 11 13 17 21 4 4 4 5 6 6 8 8 9

3. Short review of the present-day models 3.1. The J.King model 3.2 The JPL-91 model 3.3. The supplemented JPL-91 model (SPENVIS ­ ESA) 3.4. The CREME-96 SEP flux worst-case model 3.5. The ESP fluences and peak fluxes model(s) (Xapsos et al.) 4. The review of MSU SEP fluence and peak flux model (version 2004) 4.1. Experimental data bases, used for developing the model 4.2 The mean SEP event occurrence frequency 4.3. The SEP event distribution function 4.4. Energy spectra of Solar Energetic Particles 4.4.1 Energy spectra at 30 MeV 4.4.2 The energy spectra at E<30 MeV

23 23 23 24 24 24 26 26 29 29 34 34 36
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4.4.3. Summary about the energy spectra 4.5 The model development 5. Uncertainty analysis of the MSU model outputs 5.1. Estimation of the MSU model outputs errors 5.1.1 Estimation of the statistical errors of the SEP proton fluence model outputs 5.1.2 Estimation of the statistical errors of the SEP proton peak flux model outputs 5.2. The issue of methodical errors, associated with approximations of model calculated particle fluxes by uniform energy spectra. 5.3 The statistical and systematical errors of the SEP fluxes models 5.4 Conclusions 6. SEP flux models and their agreement with experimental data 6.1 The main output of the MSU model 6.1.1 The annual missions fluences and peak fluxes 6.1.2 The solar cycle mission fluences and peak fluxes 6.2 The model outputs and experimental data 6.2.1 SE proton fluences and peak fluxes during the "quiet" Sun period 6.2.2 Annual fluences and peak fluxes 6.2.2.1 Annual (cumulative) fluences 6.2.2.2 Annual peak fluxes 6.2.3 Fluences and peak fluxes for the solar cycle duration missions 6.3 Conclusion 7. Summary 8. References

38 38 42 42 42 49 53 55 56 57 57 57 63 65 65 67 67 72 74 77 78 82

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1. Purpose and scope
1.1 Purpose of the Standard The present Standard is intended for calculating the fluences and peak fluxes of solar energetic protons, which are expected to occur during a given time interval at any known or predicted solar activity level and to exceed their calculated sizes with a given probability. In combination with the ISO 15390 Standard ­ Model of Galactic Cosmic rays, this Standard provides a description of the radiation environment, induced by high-energy particle fluxes in the Earth's orbit and interplanetary space and serves as the basis for describing the radiation environment in interplanetary space during interplanetary missions, and for calculating particle fluxes, penetrating into near-Earth spacecraft and space station orbits. The Standard establishes a probabilistic model for the SEP event proton fluences and peak fluxes in the near-Earth space beyond the Earth magnetosphere under varying solar activity. The Standard is oriented to calculating the solar proton radiation impact on the spacecraft equipment and structure materials and on the biological objects (including human organism) when in space. The Standard can be of assistance in analyzing the scientific results of various experiments, permitting to reveal methodological errors in the measurements. Besides, the Standard is a certain generalization of copious experimental data to be used in testing theoretical models. Notes. 1.1.1 When determining the proton fluxes in the spacecraft orbits, the Standard should be supplemented with the model for charged particle penetration into the Earth's magnetosphere. 1.1.2. When calculating proton fluxes for interplanetary missions, the fluxes, predicted by the Standard should be corrected for flux attenuation with increasing distances from the Sun, and flux strengthening for decreasing distances to the Sun. 1.2. Users of the Standard The Standard is developed for scientists and engineers? Working in the field of space radiation environment and radiation impact on the spacecraft equipment and structure materials and biological objects (including human organism) when in the space, as well as the consequences of the impact. 1.3. The users' requirements The users require such a Standard that would permit them to determine the space radiation environment induced by solar energetic particles (SEP). Since the SEP occurrences are of probabilistic nature, the models that underlie the Standard must also be probabilistic. The required features of the Standard are as follows. 1.3.1. As the SEP occurrence probability is a function of solar activity, the Standard must predict the SEP fluxes as dependent on any solar activity level. 1.3.2. As the SEP impact is a function of the particle energy (the energy transfer to matter and the cross-sections for inelastic interactions are all energy-dependent), the particle fluxes must be known for any energy, i.e., the differential SEP energy spectrum must be determined. The spectrum must be known at least from 5 MeV to 1 GeV. The outputs of the Standard are to be expressed in analytical form (beside the plots and tables) in order to facilitate its applications. 1.3.2.1. The proton fluence energy spectrum must be known in order to determine the total energy transfer and the secondary particle fluxes in matter. 1.3.2.2 The peak flux energy spectrum must be known in order to determine the maximum (peak) load on equipment, materials, and biological objects. 1.3.3. The model predictions should be reliable. Since usually experimental data sets reveal large systematic errors and there are significant discrepancies between different data sets, a preliminary agreement which data should be considered most reliable should exist.

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To conform to the above requirements, the Standard must determine the differential energy spectra of the proton fluences and peak fluxes beyond the Earth's magnetosphere, which are exceeded with a given probability for any given time interval at any known or predicted solar activity level. 1.4 The model used in the Standard Draft The Statistical model of the SEP fluences and peak fluxes is the Version 2004 of the model, developed at the Institute of Nuclear Physics, Moscow State University ( the MSU model). One of the versions of "The probabilistic model for fluences and peak fluxes of solar energetic particles: Part I. Protons" in 2001 has been adopted to be a Russian State Standard (GOST R 25645.165-2001). Before becoming a State Standards of the Russian Federation, the Draft Standard was extensively discussed and referred in over 10 scientific and science-industrial enterprises involved in space research and technology.

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2. The main criteria of the validity of SEP models
According to 'the users requirements' any particle flux model, aiming to be an international standard should describe particle fluxes for any period of time and any solar activity level, and in combination with the GCR model should provide a complete description of the radiation environment in the Earth orbit. This major requirement concerns solely the output data of the models. Since modern theoretical models of generation, acceleration and transport of solar energetic particles cannot provide a reliable quantitative description of these particle fluxes, modelling typically involves empirical and semi-empirical models, based on the results of experimental data analysis and synthesis (generalization). The development of such models can be separated into three stages: 1. Choice of the basic experimental data (input data) 2. Methodology of analysis and synthesis 3. Development of the model description of particle fluxes (output data) The reliability of the model depends on the reliability of all these stages of model development. 2.1 The initial (input) experimental data Comparative analysis of experimental data, corresponding to the same SEP events, but measured by different instruments on differed satellites shows that such data can differ significantly, sometimes by factors of several tens. The discrepancies in the data are usually systematic. Thus, the peak proton fluxes for the same SEP events, measured on IMP-8 and GOES-7 at energies > 100 MeV differ by a factor reaching 10 (Fig. 2.1) (see Mottl and Nymmik, 2003). It is clear that models based on experimental data measured by different instruments will also differ, and the degree of reliability of models which are based on data sets which were not analyzed for reliability remains uncertain. In particular, one of the examples of such discrepancies was noted in the paper by T.F.Gleghorn and G.D.Badhwar (1999). The authors showed, that the version of the MSU model, based on IMP data successfully describes heavy particle fluxes, measured by this satellite, but poorly describes the proton flux data, measured by GOES. If there are discrepancies in the SEP flux data, measured by different instruments, then the only way to establish the reliability of the data is to compare the measurements of the fluxes in the same events made by different instruments and different techniques. An example of such comparison is given in Fig. 2.2. In the analysis we used data on 13 large SEP events (the events occurred on 25 July 1989, 16 August 1989, 29 September 1989, 19, 22, and 24 October 1989, 15 November 1989, 21, 24, 26, and 28 May 1990, 11 and 15 June 1991), for which the peak fluxes were measured on IMP-8, GOES-7 and Meteor satellites and also neutron monitor data. The energy spectra of all the n=13 events, measured by the same instrument were logarithmically averaged :

< F (E ) >= 10

1 n


i =1

n

lg Fi ( E

)

(2.1)

and the integral fluxes, measured by Meteor and the neutron monitors (all data according to Sladkova et al., 1998) were recalculated to differential spectra. The differential energy spectra of peak fluxes according to data of IMP-8 ( IMP-8 web-site http://hurlbut.jhuapl.edu/IMP/cpme) and GOES7 (GOES web-site: http://spidr.ngdc.noaa.gov)were were calculated using proton flux data measurements in each energy channel.
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Fig 2.1 Energy dependence of the ratio of peak fluxes measured on IMP-8 and GOES. The squares are the ratios of the integral peak fluxes on IMP-8 and GOES-6 (corrected) taken from the respective Internet sites. The solid curve is the ratio of the energy spectra of SEP events averaged over cycle 22 using Eq.(2.1). The curve with black circles is the ratio of the same events also calculated using Eq.(2.1) from the IMP-8 and GOES-7 (uncorrected) data.

Fig. 2.2 Logarithmically averaged energy spectrum of the peak fluxes for 13 SEP events. The data sources are indicated in the figure and described in the text.

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The results show that the measurements of GOES (initial, uncorrected data), Meteor and neutron monitors coincide. The data of IMP-8 and GOES-7 (corrected by the authors of the experiment) for energies around 400 MeV disagree with the other data. Without going into details of the reasons of such discrepancy, we come to the conclusion that IMP- 8 data in the high energy range is not very reliable, and the correction introduced into GOES data in the same energy range is erroneous, furthermore, it contradicts the description of this correction given by one of the authors of this experiment (Zwickl). Actually, on the one hand, according to the GOES web-site explanation for high-energy channels (Zwickl), the corrected fluxes are claimed to be smaller than the measured ones, because of the additional fluxes from outside of the geometric factor and from the products of particle interactions in the detectors. However, if we compare the corrected and uncorrected data from INTERNET GOES experimental data sate, we should conclude that the situation is opposite and the corrected fluxes are higher than the uncorrected ones. Therefore, if the real corrections are opposite to the explanation, we recommend to avoid using corrected GOES data moreover, as the results, demonstrated on the Fig. 2.2. Below, when comparing model predictions with experimental data we will show, that some discrepancies in the model descriptions of SEP particle fluxes, which are revealed between the JPL91 (Feynman et al., 1993) and the MSU model (present work) are, in particular, due to the use of data from different satellites. Thus, one of the basic conditions of the model validity is the reliability of all the experimental data used when developing the model. 2.2 Methodology of data analysis and synthesis Even the use of the most reliable experimental data does not ensure the final validity of the model. The most important factor here is the methodology of modeling: analysis techniques and generalization (synthesis) of experimental data. Utilization of analysis techniques which are inadequate for the task, inevitably lead to erroneous modeling results. Below we will consider a number of issues of the methodology for analyzing SEP flux experimental data . 2.2.1 The definition of a Solar Energetic Particle (SEP) «event". The SEP event is treated by most researchers in terms of the formal definition of an event to be "the total fluence occurring over series of days during which the proton fluence (or local peak flux) exceeded the selected threshold" (Feynman et al., 1993). This definition underlies also most of the relevant databases and SEP models. It should be noted, that the above definition is of the engineering (technical, customer ­ definitions from different papers) nature and is far from defining the SEP event in terms of its physical meaning. This is readily understandable, considering that the true events trail each other, so the fluxes of the events get overlapped during high solar activity, in particular. The following three examples are relevant here. 1. The large SEP events of 19,22, and 24 October 1989 are taken by physicists to be three events. In terms of the engineering, they are treated to be a single event (see Table 2.1). 2.The same comments are valid for the large SEP events 21, 24, 26 and 29 May 1990 (see Table 2.1). 3. The example is the "engineering" event that commenced on 24 April 1981 and lasted for 30 days (Feynman et al., 1990), which is taken by Bazilevskaya et al. (1990) to be nine successive events.

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Table 2.1 The proton fluences and peak fluxes of the physical and engineering SE protons Data 19 22 24 Engineering October 1989 Fluence 1.84109 7.4108 4.0108 2.62109 Peak flux 6.4103 1.2103 5.7102 6.410
3

Data 21 24 26 28

May 1990 Fluence 3.0107 3.2107 2.4107 2.0107 1.06108

Peak Flux 90.5 55.1 39.0 14.7 90.5

The substance of the engineering event concept is obviously variable with varying solar activity. Namely, single physical events are treated during low solar activity, and the sequences of physical events during high solar activity. The engineering approach to the SEP event concept can readily be shown to change (distort) the event distribution function and the dependence of the event occurrence frequency on solar activity so, that for "engineering" events it is rather difficult to reveal such a simple regularity, as the proportionality of the SEP events frequency to solar activity. Therefore, the engineering event concept of a chain of particle flux increases observed in the Earth orbit cannot serve as the basis for the development of SEP flux models because this concept makes it impossible to find the relevant fundamental regular features, inherent to the physical events. 2.2.2. SEP particle fluxes during `Quiet Sun' years. Most of the present-day SEP analyses have concluded that the 11-year solar cycle ``is divided into two clearly defined phases" (Feynman et al., 1990) called "active" and "quiet" Sun periods. The "active" Sun years are proposed to occur when "the hazardous period for enhanced proton fluences is seven yeas long and extends from two years before sunspot maximum to four years after maximum when the sunspot maximum epoch is defined to 0.1 years'' (Feynman et al., 1990, 1993). The rest years are defined to be the 4-year "quiet" Sun period, when the SEP may be neglected. The consequences of the above definition were developed in the SEP models (JPL-91 by Feynman et al., 1993; ESA by Xapsos et al. 1996,1998a,b,1999a,b,2000 model) that disregarded the SEPs for the "quiet" Sun periods and proposed the SEP event occurrence frequency and fluences to be constant during the "active" Sun (solar maximum) periods. Following Feynman et al. (1990,1993), the "quiet" Sun periods are defined to be 4-year periods of the 11-year cycle. Considering that the solar cycle duration is variable (around 11 years), we take the "quiet" Sun period to be 4/11 of the total period of the lowest solar activity of the last three or four solar cycles, when the SEP event protons were actually measured. The 4/11 (0.364) Wolf number integral distribution level corresponds to sunspot numbers 40.1 and 39.4 for the last three and four solar cycles, respectively (the mean value is 39.8). Actually, nobody argues that during these years SEP events are infrequent and small in size. But we should ask ourselves the question: relatively to what are they small and on what grounds they can be neglected? Earlier it was stated, that the task of SEP flux modeling is to describe the radiation environment in space including GCR particle fluxes. Therefore, SEP particle fluxes can be neglected only if they are much smaller than GCR particle fluxes during the considered period of solar activity. Very unfortunately, the researchers who put forward the idea of neglecting SEP fluxes during years of the quiet Sun (King, 1974, Feynman et al., 1990) never made such an analysis. We have several times pointed out (Kuznetsov et al. ,1999, 2002), that since 1965, 22 events with 30 MeV proton fluences in excess of 106 protons/cm have been recorded in quiet sun periods The total fluence in these events at energies <100 MeV significantly exceeds the total fluence of GCR particles over the corresponding time period. We will once again illustrate this using the example of the last SA minimum, covering the 4year period from December 1993 to November 1997, for which very precise measurements of
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particle fluxes are available. 4 SEP events were recorded with proton fluences E30 MeV F106 /cm2 (1994 Febr. 20, 1995 Oct. 20, 1997 Nov. 06 and 08). Fig.2.3 shows the total proton fluence in these SEP events in /m2MeVyear units, in the way they were recorded by DOME and TELESCOPE instruments on GOES-7. The same figure shows the energy spectrum, approximating these experimental data, and the energy spectrum of mean GCP proton fluences for the same period, calculated monthly using the Model of Galactic Cosmic Rays (ISO 15390, . also Nymmik et al. 1996). These data show, that during the last SA minimum at E<130 MeV the fluence of SEP protons exceeded the fluence of GCR protons, and this excess at E10 MeV reached a factor of 105 ! Therefore, it is unacceptable to neglect SEP particle fluxes during SA minima. Hence, valid models should give the possibility to make SEP particle flux calculations not only for the "active" Sun but for the «quiet» Sun period too.

Fig. 2.3 The proton fluence for SEP events (circles) and GCR (asterisks) uring the last SA minimum, covering the 4-year period from December 1993 to November 1997. The spectra are differential. References: Kuznetsov N.V., Kuznetsov N.V., Kuznetsov N.V., Kuznetsov N.V.,

Nymmik R.A., Popov V.D., Khamidullina N.M., 1999. Nymmik R.A., and Panasyuk M.I., 2001a. Nymmik R.A., and Panasyuk M.I., 2001b and Nymmik R.A., 2002.

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2.2.3. On the hypothesis of SEP flux independence on solar activity during the 7-year Active Sun period Another hypothesis, which underlies the SEP particle flux models (Feynman, 1991, Xapsos, 1998,1999) is the assumption that the particle flux values during the 7-year Active Sun period do not depend on SA. We will show that this assumption is wrong. In order to do this we will use the smoothed sunspot number for the day of SEP event occurrence as the SA as a characteristic of solar activity, and as the time interval describing SA we will use the mean monthly averaged sunspot number. Such characteristics substantially differ from such crude characteristics of solar activity as the annual period (or mean annual sunspot number), counted from minimum (Smart&Shea, 1989, 1999) or maximum (Feynman et al., 1990a,b) SA, which essentially are not quantitative, but rather visually-qualitative characteristics of SA. The use of such characteristics for describing solar activity is similar to an attempt to resolve lines spaced by 1A° using an instrument with poor resolution (>>10A°) in spectral analysis. In order to illustrate the analysis technique used by us, in Fig.2.4 we show the curve of smoothed sunspot number , the days of SEP occurrence are also noted. The values of the peak fluxes can be estimated using the vertical scale on the right. The dashed lines denote logarithmically equal SA intervals used in the analysis. It is easy to establish to which SA level each event corresponds and how many months of measurements lie within the given solar activity interval. We analyzed the whole set of SEP events, starting from the time when measurements on IMP-8 began (1974 October) and ending in December 2003. We calculated the total fluence value for E30 MeV protons in all the events, which occurred in each selected SA interval. This value was divided by the duration of the measurement in the corresponding SA interval. The results of the calculation are shown in Fig.2.5. The calculated values of the mean annual SEP fluences increase with increasing SA. However, the scatter of the calculated fluence values lie totally within statistical fluctuations, due to the random nature of event occurrence in scope of the distribution function. (see below). This is confirmed by the probabilities of occurrences of total SEP fluences, calculated for the measurement duration period (1974-2003) in each interval of solar activity using the model of the current standard. From the data shown in Fig. 2.5 it can be seen, that for 4 SA intervals, the fluences were recorded with probabilities, close to the expected mean value (0.5), for one interval below the mean value, and for the interval 100< <128 such actually observed fluxes were expected with the probability of 0.05. It can also be noted, that the expected equally-probable fluence value (0.5) from 40 to 150 increases by more than an order of magnitude. It is improbable that such an effect can be regarded as independence of two quantities. Finally, we can conclude that the hypothesis of the independence of SEP particle fluxes on solar activity for 7 years of active Sun is not valid. 2.2.4. Solar activity and SEP event frequency Inconsistency between the analysis technique and the event character is the reason of another erroneous statement - the absence of a direct connection between the SEP event occurrence frequency and SA level. In this work we compared the mean annual sunspot numbers and the number of events during the corresponding calendar year. It is asserted, that the obtained correlation coefficient value (0.6) for the time period of the last three SA cycles does not permit to speak about any kind of close connection between the number of SEP events and SA.

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Fig.2.4. To the issue of determining the solar activity level The beginning of the 23rd SA cycle: the smoothed sunspot hand scale) and the SEP event occurrence dates and the scale). . The dashed lines denote logarithmically equal SA

for the moment of SEP event occurrence. number versus time (solid curve and leftpeak 30 MeV flux sizes (the right-hand intervals used in the analysis.

Fig.2.5 The calculated total fluence value for E30 MeV protons in all in each selected SA interval during the time period from October (asterisks). The other markers and their approximation lines denote the of fluxes occurrence, calculated for some of solar activity levels and selected SA interval.

the events, which occurred 1974 to December 2003 different probability levels total time periods in each

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However, using the analysis technique, described in the previous section (Fig.2.4), we obtain, for the data set covering the same three last solar activity cycles the result, which we have repeatedly published (Nymmik,1999a,b,2001, Mottl&Nymmik, 2001), that the SEP event occurrence frequency within the statistical errors is proportional (or very close to proportionality) to the smoothed sunspot number ­ Fig. 2.6. The reduced example once again illustrates how important it is, that analysis techniques used in the modeling, should correspond to the character of the events. We would also like to draw attention to the paper Nymmik, 2001, which shows on the basis of data measured during cycles 19-22, that there is full agreement between the total sunspot number in the SA cycle and the number of SEP events, recorded over this time period. 2.2.5. The SEP distribution function One of the most important characteristics of the models value, expected during future space missions. Since the limited, and includes at most 300 events, the maximum value depends on the reliability of distribution function fluxes, which have not been recorded experimentally.

is the maximum predicted particle flux data base used for developing the models is predicted (with a certain probability) flux approximation to the region of such high

Fig.2.7 shows the distribution of SEP events according to the fluence size of E30 MeV protons ­ for the largest available set of events (all together 354 events, and 304 of them with fluence F30 106 protons/cm2). This data set includes: 1956-1975 ­ data on the SEP events given in Feynman et al. 1990a, 1976-1985 ­ SEP data , which were selected and calculated by us according to the measurements made by instruments on IMP-8 (http://hurlbut.jhuapl.edu/IMP/cpme), 1986-2003 - SEP data, which were selected and calculated by us according to the data measured by instruments installed on GOES-7,8,11 (http://spidr.ngdc.noaa.gov). Fig.2.7 shows the model approximations of the distribution function in the same way as they are given for F30 fluences in the papers of Feynman et al. 1993 ­ as a log-normal distribution: [log( )] = 1 2 exp - [log( ) - log( )

{

]

2

/ 2

2

}

(2.2)

with parameters =7 and =1.1 and Xapsos et al. 1999 ­ distribution according to the maximum entropy principle: -b - -b ( ) = -min b -b min - max with parameters b=0.36 and
max

(2.3)

=1.321010.

In Fig.2.7 the experimental data are approximated by a probability function used in the model of the present model:

( ) =

- exp 30 o

(2.4)

with parameters =0.32 and o=8.9109.

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Fig. 2.6 The dependence of the SEP event occurrence frequency on the solar activity level (smoothed sunspot number on the day of the event generation).

Fig. 2.7 Distribution functions of the SEP events for E30 proton fluences: circles ­ experimental data, solid line ­ their approximation using Eq. (2.4); dashed line ­ JPl-91 model (Feynman et al. 1991) lognormal distribution function Eq.(2.2); dotted line ­ ESA model maximum entropy principle function (Xapsos et al. 1999), Eq. (2.3).
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The JPL-91 and ESA model distribution functions shown in Fig.2.7 differ from the experimental data distribution calculated by us, the main (but not the only) reason for this discrepancy is the technique which we used when selecting the SEP events over the 1976-2003 time period. The main factor which should be noted here is the different size of the fluences for events, predicted by model SEP event distributions outside the measurement range, for extremely large fluences. For the same probability of 10-4 the JPL-91model predicts the occurrence of events with a fluence of F21011, the Xapsos et. al (1999) model predicts fluences which are a factor of 15 smaller 1.321010 protons/cm2, and the proposed standard gives the value of 3.21010. Keeping in mind, that knowledge of the distribution function at the level of 10-4 ensures a 20% accuracy in the prediction of the expected fluence for a 7-year mission at the probability level of 0.1, a factor of 15 discrepancy between the distribution functions in the JPL-91 and ESA models will also lead to a factor of 15 discrepancy in the predicted flux values. Naturally, this puts forward the very vital issue of the reliability of the technique used for SEP proton flux modeling at the level of the approximation function used for the distribution of the single events (worst case distribution of single SEP events). We will make just a number of comments, regarding the main forms of the distributions. Use of the log-normal distribution in model JP-91, as we have shown in the paper Kurt and Nymmik, (1997), appears to us to be erroneous, since its parameters are significantly and primarily determined by the left branch of this distribution. The form of this branch is the consequence of selection of small-size SEP events against the background of GCR fluxes and further subjective selection of SEP events according to the peak flux value (selection threshold). If we arbitrarily changing these selection criteria we automatically change the parameters of the log-normal distribution in general, describing in particular the right-hand branch of the distribution, which is responsible for probabilistic forecast of extremely large events. Therefore, the use of the log-normal distribution for predicting the probability of the occurrence of events with extremely large fluences can hardly be considered reliable. As for the maximum entropy principle, used to determine the form of the distribution function in Xapsos et al., (1999) we can say the following. On the one hand, the limiting fluence value in this paper is defined stringently, without any analysis of the statistical or (possible) methodical errors in the initial experimental data. Secondly, it is quite obvious, that if we split the available set of SEP data into several parts, e.g., according to individual solar cycles, we obtain absolutely different values of the limiting fluences. Such a task was performed by us for 4 periods: 1954-1973, 1974-1985, 1986-1996 1997-2003 and we obtained the following limiting fluence values: 1.71010, 7.7108, 2.7109 and 8.5109. The scatter of the limiting fluence values, calculated for the individual periods can reach a factor of 22. Hence, the predicted maximum fluence value depends on the completeness of the data set statistics. For the following 50-year period (e.g., 2004-2059) it may turn out to be absolutely different, than the one calculated according to 1954-2003 data. We have applied the maximum entropy principle to the experimental distribution, calculated by us (Fig.2.08) and obtained the limiting fluence value in a single SEP event equal to SEP 1.1·1010 protons/cm2 instead of 1.32·1010 in the original work of Xapsos et al. 1999. The 20% discrepancy between the values is of methodical nature and due to the different approaches which were used by us to define and select SEP events for data, measured after 1974. If we assume the point of view, that the SEP event is of random nature, and the distribution function has the form of a power-law function with an exponential turn-off (Eq.2.4), then we can estimate, what are the possible random distributions of 300 random SEP events and calculate the maximum event fluences, corresponding to the maximum entropy principle for each of the cases. In Fig. 2.09 we show the maximum fluence distributions, which we calculated 4000 random distributions, each containing 300 SEP events.
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Fig. 2.08 SEP event distribution functions: 1- used in the JPL-91, 3 ­ the experimental data approximated according to the ESA model (maximum entropy principle); the solid line is the mean curve, dotted lines are statistical deviations of this calculated curve.

Fig. 2.09 The maximum fluence (ESA models parameter) distributions, which we calculated for 4000 random distributions, each containing 300 SEP events. The maximum value of the ESA model is shown (see also text).
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Naturally, in half of the cases the ESA model "maximum possible fluences" are larger, than it was established, according to observations accumulated over 50 years. It appears, that the fluence values, established using the maximum entropy principle is a formal characteristic of a random set of events from the last 50 years of observations and any new extremely large event occurrence can change this estimate towards larger values. It is also necessary to mention here, that the maximum possible fluence value is always somewhat larger than the largest event observed over this time period. Finally, we will mention, that whilst the assumption of the log-normal character of the distribution function is easily rejected as methodically erroneous, the existence of a stringent limiting value, calculated according to the maximum entropy principle or the exponent turn-off character of the distribution function currently is very difficult to reject or confirm. It is only clear, that any new solar cycle can provide experimental data, after which the parameters of both distribution functions will have to corrected again and again. However, in any case the distribution used in the proposed standard allows for the occurrence of events with values exceeding limiting values max in the Xapsos et al. model. 2.2.6 The energy spectra of events in the SEP models Sometimes, when modeling SEP particle fluxes, generalizations of the particle fluxes in the form of energy spectra are used. Historically, the energy spectra of particles in the form of exponents or containing exponents of energy or particle rigidity, are widely used. Such a generalization can be appropriate in those cases when the considered particles have non-relativistic (or intermediate) energies. In order to describe fluxes of particles at energies E30 MeV, at all energies including relativistic ones, however, the energy spectra of SEP particles are purely power-law (not exponential or containing an exponent) functions of particle momentum (rigidity for protons). Since in the MSU model the energy spectra play a key role, the issue of the energy spectrum form requires special attention. Having analyzed the particle (protons and heavy ions) peak fluxes and fluences in hundreds of SEP events, measured by different instruments, we have repeatedly demonstrated (Nymmik, 1993,1999, Mottl and Nymmik 2001) that the power-law particle rigidity (R [MV]) function
d C = dE R R o
-

(2.5)

most successfully describes all the SEP particle energy spectra at energies 30 MeV. Here R = E ( E + 2mc 2 ) is momentum per nucleon, = R / R 2 + m 2 is the relative velocity; R0 = 239 MV corresponds to E=30 MeV and is the same for all kinds of solar particles (heavy ions included). Function (2.5) was shown to be also valid in the <30 MeV range R <239 MV) under the assumption that in this energy range the spectral index depends on the energy (the droop effect):
= o
E , 30


(2.6)

where is the spectral droop index and o is the spectral index at E30 MeV. In Fig. 2.10 and 2.11 we demonstrated once again the large set of experimental data of protons and different heavy ions of SEP and their approximation by the Eqs. (2.5 and 2.6). As to the works (Ellisson&Ramaty,1985; Mazur et al, 1992, 1993, Tylka et al. 2001) and others, which claim to observe the previously mentioned rollover as an exponent at <100 MeV/nucl, not only qualitative, but even simple visual analysis shows that there occurs a depression of the power-law spectrum as the particle energy falls below 30 MeV/nucleon, rather than the rollover as the particle energy increases (see Fig. 2.12) with the data from Ellisson&Ramaty,(1985).

17


Fig. 2.10 The integral proton peak fluxes of the 21 May 1990 SEP event. The markers denote METEOR data (circles), GOES data (squares), IMP8 (black circles), balloon data (triangles), and neutron monitor data (black squares). The energy spectra are shown as power-law functions of momentum (rigidity) (curve 1) and energy (curve 2), rigidity exponent (curve 3).

Fig. 2.11 SEP fluxes of the event of 18th August, 1979 according to Mazur J.E., et al. 1992 (broken lines) and their approximations by expressions (2.5) (2.6). As shown above, with increasing energy, the relativistic-energy solar proton fluence and peak flux energy spectra measured in the Earth orbit do not exhibit any marked softening of the powerlaw spectrum of proton momentum predicted in paper Ellison and Ramaty (1985). Here we shall
18


demonstrate that the spectrum does not soften with increasing energy at low energies either. Fig. 2.12 shows the measured proton fluxes of the 7 and 21 June 1980 events, which were presented in Ellison and Ramaty (1985) to confirm the exponential turnoff of the spectra at >10 MeV. We approximated the fluxes by the functions (4) and (5) and by the power-law momentum functions (4) divided by the exponent, which is believed (Ellison and Ramaty, 1985) to describe the spectral turnoff at as low energies as >10 MeV. Using Monte-Carlo simulation, varying the spectral parameters and applying the least-square technique to determine their combination, we have found the spectra presented in Figure 2.12 for both approximations. In case Eqs.(2.5) and (2.6) are used, the standard deviations are smaller (0.037 and 0.020) compared with the their values inferred from the formulas of Ellison and Ramaty (1985) (0.046 and 0.027). In the 7 and 21 June 1980 events, therefore, we see the typical SEP event power-law proton momentum spectra that get harder at <30 MeV, as takes place for all other SEP spectra. Therefore, the power-law spectra with turnoff as energy increases in the range of tens of MeV seem to be a groundless assumption that has never be realized for SEP spectra. It should also be emphasized that the indices of the power-law momentum spectra of the 7 and 21 June 1980 events (p=6.99 and p=4.72) are quite common in the power-law spectra of particle momentum. Another example. In the paper Xapsos et al. 2000 there is another suggestion to describe the energy spectra of SEP protons by a formula, containing an exponent. Figs. 2.13 2.14 show the results of comparison of the differential and integral spectra and their approximations of the peak SEP flux data for the event of May, 5th, 1990, (measured by GOES-7) obtained using Eq. 2.5-2.6 and the Xapsos et al. 2000 paper:

dF = Fo k E dE
where Fo, k and - are parameters of the spectrum.

-1

exp - kE

(



)

,

(2.7)

Fig.2.13 also shows the differential spectrum, recalculated from the integral one, plotted according to the data of neutron monitors (Fig.2.14). It can be seen, that due to the exponent of energy in Eq. (2.7), the approximation according to Eq.(2.7) is in poorer agreement with the neutron monitor data, than Eq.(2.5). This discrepancy is visible even clearer in the integral spectra (Fig.2.14), calculated from the differential ones with parameters Eq. (2.7) - Fig.2.15. In both cases approximation of GOES data by the spectrum of Eqs. (2.5 and 2.6) ­ a power-law function of momentum perfectly agrees with neutron monitor data, but the integral spectrum, corresponding to Eq. 2.7, which is an exponent :

F (> E ) = Fo exp - kE

(



)

(2.8)

clearly cannot be used for describing the experimental data outside the range of fluxes, measured by the GOES satellite. Thus, experimental data on SEP particle peak flux and fluence at energies E30 MeV and up to relativistic energies (including them) are essentially power-law functions of particle momentum (or rigidity for protons), and any attempt to approximate these data by functions containing an exponent has no perspective.
Comment. The spectra Eq. 2.5 and 2.6 cannot be used when dealing with individual spectra, corresponding to a certain moment of time.

19


Fig 2.12 The measured peak proton fluxes in the June 21st (the upper dots) and June 7th (the lower dots) events of 1980 according to Ellison and Ramaty (1985). Approximations of the measurements by Eqs. 2.5 and 2.6 (the solid lines) and by the power-law momentum functions (the dashed lines) with the exponential spectral droop as energy increases, according to Ellison and Ramaty (1985). The A'-A and B'-B straight lines are the power-law momentum spectra without spectral softening droop at <30 MeV.

Fig. 2.13 The 21 May 1990 SEP event differential peak fluxes, measured by GOES-7 instruments (horizontal lines) and their approximation by Eqs. (2.5) and (2.6) (solid line with square markers) and Eq. (2.7) (solid line with open circle markers). The differential spectrum, calculated from integral neutron monitor peak flux data (see Fig. 2.14) is also shown (solid line with asterisks).
20


Fig. 2.14 The 21 May 1990 SEP event integral peak flux energy spectra according the GOES-7 measurements (see Fig. 2.16) according to the MSU model Eqs. (2.5 and 2.6) (solid line with square markers) and Xapsos et al. - Eq. (27)(solid line with circle markers) . The experimental data of the neutron monitor measured integral peak fluxes (black circles) and their approximation (solid line with asterisks) are also shown.

2. 3 Development of the model description of the fluxes (output data requirements)

It is appropriate, that the output data should satisfy the following basic requirement ­ they should adequately describe the experimental data on the SEP particle fluxes (and not contradict them), corresponding to a space mission with any duration at any level of solar activity. The reliability of the experimental data used to develop the model and methodology details contribute only to the achievement of the final result and are not object of discussion about the validity of SEP models. We can also add, that the currently developed models are either empirical or semi-empirical and in no case aspire to be physical models. Nevertheless, high reliability of the model can be achieved only in the case if it utilizes to the maximum extent the regularities, inherent to the phenomena, responsible for the appearance of the modeled effect. Additional requirements for the model output are: 1. The maximum possible range of energies, for which the fluxes can be defined. 2. The output data should be provided in a format, which is convenient for modern calculation techniques. They should also be presented in analytical form as differential energy spectra, permitting further computer-made calculations of particle penetration, ionization losses, nuclear interaction effects, etc. 3. Complete models should provide the description of: the total (cumulative) particle fluence for space missions and the value of the maximum (peak) flux for the same period. 4. The model technique should provide its extension from proton fluxes to fluxes of all other highenergy SEP ions (from z=2 to z=28). 5. The particle fluxes should be described for any solar activity levels and any space mission durations, from one month long missions during solar activity maximum, to missions lasting up to two solar cycles (up to 20 years long).
21


6. In order to have the possibility solar activity level, it is desirable Since the input parameters of the numbers, the input parameters of other parameters, unambiguously

to compare effects, caused by GCR and SEP particles at the same to have the same input parameters of the SEP and GCR models. international GCR standard (ISO 15390) are the smoothed sunspot the SEP model should also be smoothed sunspot numbers W or connected with W.

Agreement between the output data of different models and the experimental data, which is the main criterion of model validity, will be discussed below in Section 6 of the current Memorandum.

22


3. Short review of the present-day models
This review includes only the prevalent models, which have been described, to an extent, in the scientific and technical publications, i.e., (in the order of their appearance dates): a. The King model (proton fluences only) b. The JPL model (proton fluences only) c. The supplemented JPL-91 model (SPENVIS­ESA, proton fluences only) d. The CREME-96 SEP limitation model (proton and heavy ion fluences) e. The probability model (ESP) for the worst-case and cumulative SEP fluences and peak fluxes (Xapsos et al.,1999, protons only). Some of the models are not official State Standards; their usage is only recommended by individuals or national institutions. One of the previous versions of the presented ISO Draft Standard "Probabilistic Model for Fluences and Peak Fluxes of Solar Energetic Particles. Part I" in 2001 became the official Standard of Russian Federation (GOST R 25645 165-2001).
3.1 The King model

J.King (1974) was the first who developd a complete empirical statistical model for solar energetic proton fluences, basing on a number of regular features relevant to the SEP fluxes. J.King divided the total set of the SEP events into two classes: ordinary (regular) and anomalously large events and determined the occurrence frequencies of the specified classes of events during active Sun separately. The J.King model accounts for following principal regular features: - the occurrence probability of different numbers of SEP events is presented by Burrell's (1972) extension of the Poisson statistics. - the SEP event fluences in this model are distributed log-normally (Eq.2.1). The energy spectra of the proton fluences are expressed as either different exponential functions of energy, with the e-folding energy Eo being 3Â30 MeV: E (3.1) (E ) = J o exp - E o or a sum of two different exponents. The present-day experimental data analysis has demonstrated that most aspects of the J.King model are erroneous, namely, - there are no 7-year active Sun period during which SEP's occur and 4-year "quiet" Sun periods when SEP events can be neglected (see 2.2.2, 2.2.3). - there are no separate classes of `ordinary' and `anomalously' large SEP events; instead, a uniform fluence distribution of the events sizes persists (Gabriel&Feynman ,1996; Kurt&Nymmik 1997; Nymmik 1999) - the SEP events are really not distributed according to lognormal function (1); actually, they are distributed according to the power-law function (Gabriel&Feynman, 1996) with the rollover for large-size events (Nymmik, 1999) (Eq. 2.4), or (Xapsos et al. 1999) (Eq. 2.3). - the proton fluence energy spectra are not exponents; actually, they are independent of the event size and are described best by power-law functions of proton rigidity (or momentum) with a spectral droop at low energies (E<30 MeV) (Lockwood et al., 1974,1990, Nymmik, 1993, 1995, Mottl et al. 2001a; From the above it follows that the J.King model predictions of proton fluences disagree with experimental data in both the fluence sizes and the form of energy dependence.
23


3.2 The JPL-91 model The latest JPL model version (Feynman et al. 1993) assumes that: - the SEP event occurrence frequency is the same throughout the 7-year active Sun period, which begins 2.5 years before, and ends 4.5 years after, solar maximum; - SEP fluences are neglected to occur during the 4-year quiet Sun period of 11-year solar cycle; - it is only the mean 1,2,4 and 7 year flux records above five energy thresholds of 1, 4, 10, 30, and 60 MeV that count - the model was developed, using the technique of cumulative occurrence probability of the measured mean daily proton fluences, whose distribution is supposed to be lognormal (Eq. 2.1). According to our experimental data analysis, the JPL-91 model seems to be erroneous in the following respects: - the 7-year active Sun period when SEP's occur and 4-year "quiet" Sun period, when SEP events can be neglected is very crude description of reality, and does not actually exist; - the model assumes that the SEP event occurrence frequency is the same starting from SA period with mean monthly sunspot number 40. As the mean SEP event occurrence frequency is proportional to sunspot number (Nymmik, 1999b) (see Fig. 3.1), this assumption leads to systematic errors of a factor of up to 5 in the 1-year proton fluences determined at sunspot numbers W = 40 and 200; - the model neglects the SEP fluences at low solar activity levels (W<40) ­ the application of such a model will lead to an underestimation of particle fluxes in interplanetary space at energies E<100 MeV by many orders of magnitude. - the SEP events are not distributed according to lognormal function (1) ­ such an assumption leads to an erroneous overestimation of the predicted SEP proton fluxes (see 2.2.4 and Fig.2.7) . - instead of providing differential energy spectra, the model determines the proton fluences for only five values of the integral proton fluences and is only valid at 60 MeV and below. 3.3. The supplemented JPL-91 model (SPENVIS ­ ESA) To extend the JPL-91 model to the energy range above 60 MeV, the authors of SPENVIS developed two supplemented versions. They assumed that the proton fluences above 60 MeV (the boundary of the JPL-91 integral energy spectra) are exponents of either energy or rigidity. Such an extrapolation of the JPL-91 spectra were made with two fundamental methodological mistakes. First, as the 60 MeV fluence in the JPL-91 has been too overestimated (see Figs6.16-6.18, 6.28), the end of the JPL-91 model energy spectra is too hard and is supplemented with an exponent (Fig. 6.29). Second, neither at E>60 MeV nor at least 5 GeV is any exponent inherent to the SEP energy spectra. (see Fig. 2.10-2.14) From Fig.6.29 it follows that the supplement is invalid because the proton fluences measured at high energies during solar cycles 21 and 22 are by no means exponential. 3.4 The CREME-96 worst case SEP flux model In its essence, the CREME-96 SEP model is not a model, compared with the other discussed models. Its authors establish the fluxes of the 19 October 1989 SEP event to be the "worst case " for the 5-minute (the peak fluxes), one-day, and week-long (7.5 days) periods. Bearing in mind the arbitrary choice of the 6-year measurement period (1980.5-1983.5 and 1989.0-1992.0), the CREME-96 authors estimated the confidence level of that kind of "worst cases" to be 99%. Obviously, the models of such a type can only be used to make very rough estimates of the probability for large particle fluxes to occur. 3.5 The ESP fluences and peak fluxes models (Xapsos et al.) 1998, 1999, 2000 Xapsos et al. has published several not very detailed reports, dedicated to different versions of the Emission of Solar Protons (ESP) model. These are:
24


1. Probability model for peak fluxes of solar proton events (for E10 MeV only) ­ Xapsos et al. (1988). 2. Probability model for worst case solar proton events (for E1, E3...... E100 MeV) ­ Xapsos et al. (1989a). 3. Probability model for cumulative solar proton events (declared E1, E3...... E300 MeV) ­ Xapsos et al. (1989b).. The basic principles of the model are as follows: - like JPL-91, the model uses the concept of, and is so valid only for, the 7-year active Sun periods and assumes, that for all years and all cycles the proton fluxes are the same; - the events are identified on the basis of the principle that the beginning and end of an event are defined by the threshold proton flux, so that a prolonged event may consist of several successive rises and falls in the flux (engineering events); - the data used (the total set of the cycles 20-22 SEP events) are for cycles 20-21 the same as in the JPL-91 model (IMP data), but for the 22nd cycle data of GOES were used; - nineteen fluence energy thresholds have been analyzed for worst case solar proton events but the output results have not been published for model validity analysis; - the energy range for cumulative fluence model 1-300 MeV is declared (compared with 1-60 MeV in JPL-91), but the data of the paper reflect experimental proton cumulative fluence distribution for 3 energies only. No data has been published in major referenced (and easily accessible) journals or as conference publications, therefore, there is no possibility to compare the model output with the experimental data. The main distinctive features of the model are as follows. - the distribution function for worst case fluence is not lognormal but is taken to be a power law with the distribution restricted according to the maximum entropy principle. In spite of certain advances of the new model, which removed some shortcomings of the JPL-91 and the improved JPL-91, it still includes some of the earlier erroneous propositions: - it is valid only for the 7-year "active" Sun period and neglects s any probability for SEPs to occur during the 4-year "quiet" Sun period; - it assumes that the SEP event occurrence frequency and annual fluences are the same during the 7-year "active" Sun period for all solar activity cycles; - it neglects the SEP fluences during low solar activity (W<40); A separate issue for discussion is the use of the maximum entropy principle, which underlies all its versions. Keeping in mind, that the currently available set of experimental data is random, and any future time period may bring data, which could significantly change the values of extreme possible values of the predicted fluences and peak fluxes.

Remark In this paper the "probability" is marked sometimes as "p", and sometimes as "". Excuse!

25


4. Review of MSU SEP fluence and peak flux model (version 2004)
All the above empirical models attempted to find approximations for the distributions of the measured SEP fluences and peak fluxes only. The methodological approach of this kind is, first of all, limited by possibility for SEP's to be measured above the galactic cosmic ray threshold. Therefore, it is inapplicable for high-energy protons and heavy ions. Moreover, the seeming simplicity of the method fails to study the detailed regularities in the SEP event characteristics, such as the occurrence frequency and its dependence on solar activity level, the form and properties of the SEP distribution function, energy spectra and etc. Therefore all the above models may be considered empirical. The probability model of the SEP fluences and peak fluxes developed at Moscow University is based on a number of regularities inherent to the SEP events and flux characteristics that are hidden beyond the probabilistic nature of the SEP. The pre-requisites which permit to reveal such regularities are as follows: 1. When analyzing the experimental data we use objects and their characteristics (SEP events, solar activity, etc.) as physical events and processes, which are described by concrete quantitative characteristics, reflecting their physical nature. Thus: - instead of the engineering (technical, commercial) definition of an SEP event, we used the physical definition, associated with a single vent of high energy particle generation in the chromosphere of the Sun with a possible subsequent acceleration of the ejected particles in the heliosphere. - instead of such qualitative and crude (from the point of view of describing SA) notions, as mean annual solar activity, calculated according to SA maximum or minimum, we used running (concrete) values of smoothed Wolf numbers, corresponding to concrete days of months of SEP occurrence (irrelevantly to the solar cycle phases ­ growth, maximum, decline or minimum) 2. Analysis techniques, corresponding to the character of events and their statistical nature were used. Threshold effects, associated with SEP particle measurement were accounted for. The statistical errors of the experimental data were also taken into account. 3. The model output data at all stages of the model development were compared with independent experimental data. Here we mean, that a simple generalization of experimental data itself does not ensure the validity of the model, since hidden flaws of the initial data base and development methodology can be revealed during the process of model development. 4. We used only the most reliable experimental data. The existence of large systematic errors in the results of individual experiments, leads to the necessity of analyzing such errors, in order to reveal and disregard the least reliable data. Use of all available data without analyzing their reliability leads to uncertainties in the model output. Hence, the main features of the selected experimental data and the main regularities of the SEP phenomenon, which in the model development, are as follows:
4.1. Experimental data bases, used for developing the model As it was shown above, (Fig.2.1) of present memorandum), the results of SEP proton flux measurements made by different instruments, show discrepancies, giving evidence of significant systematic errors inherent to different instruments (Mottl, Nymmik, 2003). Also, it was shown, that the most reliable data on proton fluxes at high energies (E>30 MeV) are the data, measured by the TELESCOPE and DOME instruments on satellites of the GOES series, furthermore, those results, which were not corrected at high energies by the authors (Fig. 2.2). Unfortunately, the series of GOES monitoring data are limited in time and cover only the period through 1986-2003, i.e. less than two solar cycles. This restricts the statistical accuracy of the models, if they are to be based only on GOES data, since full period of monitoring flux observations from 1956 to 2003 is almost 3 times longer than the GOES measurements.

26


The basis of all SEP models is the particle distribution function. We will consider the issue, to what extent differ the distribution functions, determined according to the same experimental data, measured by different instruments (on different satellites) In order to do this we calculated the distribution function of SEP in flux values for the same set of experimental data, measured during 1986-2002 on IMP-8 and GOES- 7&8. The SEP events were determined according to uniform criteria of physical (using indicators of single physical, not technical or commercial ) events (see Section 2.1). Here we used the count rates in the differential channels of the IMP-8 and GOES instruments (primary data, uncorrected by the authors) and according to Eqs. (2.5 and 2.6) calculated the differential energy spectra. These spectra served each time for determining the integral proton fluxes. Using the integral proton fluxes at E10, 30, 60, 100 and 300 MeV we calculated the distribution functions, shown in Fig. 4.1 and 4.2. From the data in Fig. 4.1 it follows, that whilst the distribution of peak proton fluxes, calculated according to data of IMP-8 and GOES, for E10 MeV at moderate flux values almost coincide, they show sharp discrepancies at high flux values. Without going into the reasons of such discrepancies, we can note, that it is the issue of events, having extremely large fluxes, which is of key importance for any SEP model. Discrepancies in this issue, leave open both the issue of the reliability of the experimental data used in the model, and the reliability of the model, based on these data. The distribution functions for proton fluxes with energies E60 MeV are of certain interest. The measured data, for fluxes with such energy, in agreement with data in Fig.2.1 and 2.2 indicate, that the fluxes, measured by IMP-8 at this energy are overestimated by a factor of 3. The distribution functions for protons of these energies are shifted relatively to each other likewise (Fig. 4.1). Therefore, there is the same or larger overestimation of the output values in the JPL-91 model, and all other models, which use IMP-8 data. The distribution functions for proton fluxes with energies E30 MeV, though they don't exactly coincide, differ by a factor of not more than 2. Comparison of the distribution function for proton fluxes at energies E300 MeV vividly illustrates the modern state of the reliability of experimental data, concerning SEP particle flux measurements at high energies. The available experimental data could have been compared during a 15 year time period, however, the discrepancy with a factor of 25 was for some reason neglected by the authors of the experiments, or any other scientists. Taking into account the above stated results, it was decided, that in the current model, in order to increase its statistical accuracy, we would use early proton measurements at energies E30 MeV, made on satellites of the IMP series. The data, corresponding to the time period before 1974, were taken from the paper Feynman et al. 1990, and for the period of 1974-1986 the SEP events and E30 MeV proton fluxes in the events were determined by us and calculated on the basis of the data, measured by CPME instrument on IMP-8 ((Internet, IMP-8). For modeling the fluxes of particles with other energies (E>5 MeV), however, we used the parameters of the SEP event spectra, determined using uncorrected data of the measurements made on the GOES satellite (TELESCOPE and DOME instruments).

27


Fig. 4.1 The distribution functions for the SEP events which occurred during 1986-2002 according to IMP-8 and GOES-7&8 spacecraft measurements for E10 and E60 MeV proton fluences and their approximations using Eqs. (2.5 and 2.6).

Fig. 4.2 The distribution functions for the SEP events which occurred during 1986-2002 according to IMP-8 and GOES-7&10 spacecraft measurements of E30 and E300 MeV proton fluences and their approximations by Eqs. (2.5 and 2.6). 4.2 The mean SEP event occurrence frequency
28


When undistorted by the detection and selection threshold effects, and when used the physical (not engineering, commercial!) definition of SEP event, the mean SEP event occurrence frequency <> is approximately proportional to a solar activity level expressed as the 12-month smoothed Wolf numbers (see Nymmik, 1999a, 2001, and Fig.2.6 in the present memorandum): = k (F30 ) W (4.1) where k (F30 ) is a factor defined by the SEP event frequency with the fluence of E30 MeV proton and F30106. T N Therefore = 2003 tot = 0.00 675 (4.2) k (F30 ) = W T Wm
1974

T- total observation time (1974-2003), during which Ntot=183 "physical" SEP events with F30106 cm-2 were recorded and during which the sum of the mean monthly sunspot numbers was Wm=27110. The threshold effects of SEP event detection and selection include: · the number of SEP events detectable against galactic background, which increases with decreasing of SEP event size; · the number of SEP events excluded by selection criteria basing on peak flux size, which increases with decreasing SEP event size. Note: The result of the two effects is that, as the SEP event size 30 decreases, the "gradual" events get missed, so the "impulsive" events alone are recorded. · the small events ( 30 10 5 Â 10 6 protons/cm2), which are unobservable against the background of large SEP events whose sizes are a few orders as high, are missed during high solar activity. Taking the above mentioned into account, we think that when developing particle flux models it is necessary to take into account the small events, which are not always recorded due to threshold effects. This is important for determining the radiation environment in the case of low solar activity and missions with small duration, when the probability of large SEP event occurrence is small. In the next section it will be shown, that the distribution function undistorted by threshold effects in the range of events with F30<107 -2 essentially is a power-law function with the index of ­ 1.32. This means, that the occurrence frequency for events with F30105 -2 is 100,32=2 times greater, that for events with F30106 -2. Therefore, for the mean SEP occurrence frequency for SEP events with F30105 -2 in the present model it is accepted, that = 0.0135 W (4.3)
4.3 The SEP event distribution function The distribution function of SEP event sizes is a power law (Gabriel&Feynman, 1996) with a possible rollover in the range of large events (Lingenfelter and Hudson, 1980, Goswami et al., 1988; Xapsos et al. 1999, Nymmik, 1999b) (Fig. 2.7 of present memorandum). This means that the SEP event distribution function is similar to the distribution function of solar flares (Lu et al., 1993). We will consider the distribution functions, calculated separately for the SEP events in the last three solar cycles (Fig.4.3) (the events of the 21st cycle according to IMP-8 data, events of the 22nd cycle according to GOES-7 data, and the 23-rd cycle according to GOES-8&11, event selection and calculations of the proton fluxes were performed by the authors of the model, the GOES used data were uncorrected). We also show the total distribution of all the events, recorded over the whole

29


1976-2003 time period. Here, the number of events in each cycle were divided by the sum of mean monthly Wolf numbers in the cycle, and for the distribution over the whole time period ­ by the sum of the mean monthly Wolf numbers over the whole three cycle period, respectively. Given the statistical accuracy of the experimental data accumulated by now, the integral distribution function of the F30106 protons/cm2 SEP event is best calculated from differential function

dN =C dF30 Wm
m

30

F30 F exp 30 F c



(4.4)

where C30=0.134, =-1.32 and Fo=7.9109 protons/cm2. The tilt values for the distribution and exponent determine the prediction reliability for large size events, which is one of the main issues in SEP flux modeling. Besides, the reliability of the model output data is determined by the statistical accuracy of the experimental data set, which was used to determine the shape of the distribution function.

Fig. 4.3 The normalised (by total Wolf number in the cycle) distribution functions for individual solar activity cycles and for the complete data set (with the approximation function ­ solid line).

The value of the exponent index Fc. is especially sensitive to the experimental data, primarily to the largest events. In the whole experimental data set, the largest event is the one of November 12th, 1960. Though the SEP data sets for the 19th and 20th solar cycles have a number uncertainties, such as unclearly formulated criterea of event definition and the threshold values for event selection and recording, large errors in the determining the event size, etc. we decided to combine these events with the data set, which could be used to determine the distribution parameters. In Fig. 4.4 we show the event distributions in the 19th and 20th SA cycles, and the distribution, plotted using the whole experimental data set (1956-2003). Though the data in Fig.4.4 show obvious systematic errors of the experimental data in cycles 19 and 20, it turns out, that the parameters of the resulting distribution function, calculated for the whole data set : (4.5) C30=0.17, = - 0.32 and Fo=8.9109 protons/cm2,
30


differ insignificantly from those, which were calculated using a limited set of data over cycles 21-23, excluding the value Fo, which due to the account for the event of November 12, 1960 increased by a factor of 1.23.

Fig.4.4 The normalised (by the total Wolf number in the cycle) distribution functions for individual solar activity cycles 19 and 20 (data measured by IMP) and for the complete data set (with the approximation function ­ solid line, used in MSU model development).

The minimum difference in the distribution functions is most vividly demonstrated by the data, brought together in one figure (Fig.4.5). According to the distribution function, calculated for the complete data set, we accepted for the current version of the SEP model the parameter values of =1,32 and Fc=8,9109 protons/cm2 . We will consider a similar distribution for the peak fluxes (Fig. 4.6). It is plotted using the data base of 1974-2003. The peak flux value of f30=1.2 protons/cm2ssr is shown in the figure. For this peak flux value the total number of recorded events is the same as for events with the fluence of F30. The parameters of the peak flux distribution according to Eq.4.4 are =-1,32 and Fc=8.7103. A distinctive feature of the distribution function is its independence (invariance respectively to) on solar activity level (Nymmik, 1999). We will once again demonstrate this on the basis of experimental data for the 1974-2003 time interval, which we processed using our criteria. Fig. 4.7 shows the distribution functions for all the events and separately for the events, recorded during days, when the smoothed Wolf numbers were smaller and greater that 80. In our opinion, the number of events at W<80 is the minimum, required for statistical analysis. From the data in Fig. 4.7 it can be seen, that all the distributions have the same shape. To be even more convincing, we will divide the distributions by the sum of the mean monthly Wolf numbers, observed when recording the corresponding groups of events (Fig.4.8). It can be seen, that within the statistical errors, both distributions coincide, proving that the SEP event distribution function is invariant relatively to solar activity. Therefore, at any solar activity it is possible to use the same distribution function, only the mean expected number of SEP events will differ.

31


Fig. 4.5 The normalized (by the total Wolf number in the cycle) distribution functions. The black dots are the 1976-2003 IMP-9 and GOES spacecraft measured data, the solid line is the function, calculated from these data; the asterisks denote the complete experimental data set used and the solid line is the final distribution function used in model.

Fig. 4.6 The normalized (by the total Wolf number) distribution function for peak fluxes. The data is the sum of IMP-8 (1956-1985) and GOES (1986-2003) data.

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Fig. 4.7 The distribution functions for the full numbers of SEP events, measured for the complete measurement period and separately for the high solar activity period (W80) and the period of low and moderate solar activity (W<80).

Fig. 4.8

The same distributions, as in

Fig. 4.7, but divided by the sum of Wolf numbers.

33


4.4 Energy spectra of Solar Energetic Particles The SEP particles energy spectra of peak fluxes or fluences are power-law functions of particle momentum (rigidity for protons) without any marked rollover up to at least 5 GeV/nuc (Lockwood et al, 1974, 1990, Lovell et al. 1998), irrespective of SEP event size 30 (see section 2.2.6). In Fig. 2.12-2.17 we showed a large set of experimental data of protons and different heavy ions of SEP and their approximation by the Eqs. (2.5 and 2.6). We showed, that any approximations of the spectra, containing exponents, though sometimes satisfactorily describe particle fluxes in some energy ranges, inevitably contradict the experimental data outside this range. The energy spectra in Eqs. (2.5-2.6) are described by three parameters: the spectral coefficient D, the spectral index o and the droop index . The first two define the spectra at 30 MeV/(nucl). 4.4.1 Energy spectra at 30 MeV The spectral indices of fluence n and peak flux x energy spectra for the same SEP events are not equal but their mean values are close (Fig. 4.9). The Fig-s below correspond to the mean spectral indexes =(n+x)/2. The spectral indices of the proton fluence or peak flux energy spectra are distributed not normally, but rather log-normally (Fig. 4.10) 1 2 2 [log( )] = exp - [log( o ) - log( o ) ] / 2 (4.6) 2

{

}

The mean spectral index is independent from SEP event size (Fig.4.11): =5.9 or =0.77 The standard deviation of the log distribution is: = 0.15 if F30<1.0·109 for fluences or f30<1.2·103 for peak fluxes or = 0.075 if F301.0·109 for fluences or f301.2·103 for peak fluxes.

(4.7) (4.8a) (4.8b)

Fig. 4.9 The plots of spectral index values for peak flux and fluence energy spectra for the same SEP events.

34


Fig. 4.10 Distribution of the SEP events in spectral indexes (mean of peak flux and fluence energy spectra).

Fig. 4.11 The mean spectral indexes of the SEP event energy spectra versus of the event size/106 (event size is definite as the E30 MeV proton fluence value). Solid line is the mean of the spectral index, dashed lines noted the standard deviations of their lognormal distribution. (see Fig. 4.12)
35


Fig. 4.12 Dependence the standard deviation of the lognormal spectral index distribution on the SEP event size (dashed line). Dots are the experimental data. 4.4.2. The energy spectra at E<30 MeV Compared with a higher-energy range, the E<30 MeV/(nucl) SEP event energy spectra observed in the Earth orbit are often drooped to an extent (Price et al. 1973; Lockwood et al, 1974, 1990; Nymmik, 1993, 1995, 1997; Mottl et al. 2001 a,b (see Figs. 2.12 ­ 2.16). As shown in Rames&Kahler (1997), this effect is due primarily to the process of accelerated particle propagation from the shock region (in the chromosphere, or from an off-Sun CME) to the observation point. Qualitatively, the effect is caused by the differences in the obstacles for the lowenergy particles to traverse the Interplanetary Magnetic Field. If the energy range smaller than 30 MeV/nuc. energy spectra is also described by Eq. 2.5 it is necessary to assume that the spectral index decreases gradually in this energy range (Eq. 2.6). The droop indexes of the fluence and peak flux spectra for the same events are close to each other (Fig. 4.13). Therefore in Figs. 4.14-4.15 below we used also values of mean spectral droop indexes =(n+x)/2. The mean spectral droop index (for analysis we use A= +1) depends on event size (F30 or f30) and spectral index o (Fig. 4.14 and 4.15):

< lg A >= lg(1.16

0.059

were in case of proton fluence =F30/106 and for the peak flux =f30/1.2. The value of the parameter A is distributed lognormal with the parameters of Eq. (4.10). After the random value of A is determined, the value of droop index is determined as: =10 log(A)-1 (4.10) If the random generated spectral droop index was < (0.4o0.4-1) (4.11) then, these random values of were neglected.

o 5.84

0.143

) and logA=0.0777

(4.9)

36


Fig. 4.13 The plots of spectral droop index values for peak fluxes and fluence energy spectra for the same SEP events.

Fig. 4.14 The dependence of the mean droop spectral indexes on the event size/106.

37


Fig. 4.15 The dependence of the spectral droop indexes on the spectral indexes.

4.4.3. Summary about the energy spectra Eqs.(2.5 and 2.6) are good expressions for describing the SEP energy spectra because each of its parameters partially carries different information on the physical processes that lead to SEP flux appearance in the Earth orbit The spectral coefficient D describes the SEP event size. If the fluence F3 0 and peak fluxes f30 are known the spectral coefficient D of differential SEP event proton fluence or peak flux spectrum (Eq.2.4) is determined as:
D= 30 ( o - 1) 239
(4.12)

The spectral index o is defined by the degree of shock wave compression in the acceleration region (chromosphere or shock wave), which seems to be the principal mechanism of particle acceleration up to high energies. The droop index reflects (at least, basically), the distortions of spectra introduced by the interplanetary magnetic field to the low-energy side of the spectrum because of the different positions of the shock relative to the particle detection point (the Earth, for instance).

4.5 The model development
The dependence of the mean SEP event occurrence frequency on solar activity, the proton fluence size distribution of the SEP events, and the characteristic features of the SEP event proton energy spectrum being all known, the SEP fluxes can be calculated as probabilistic over time intervals with predictable solar activity levels.
4.5.1

The techniques for calculating the proton fluences and peak fluxes, which are expected within a prescribed probability to be exceeded at a certain solar activity level over time
38


interval T, imply calculations of the mean number, , of SEP events expected on the average within time interval T:
n = k (
30

) W (t )dt
0

T

= k (

30

)
m1

m2

W

m

(4.13)

Here, m1 and m2 are, respectively, the beginning and end of a selected time interval measured in months; is the mean monthly sunspot number; k(30)=0.0135 for 30105 prot/cm2 is the value accepted in the Draft Standard as model parameter.
4.5.2 Knowing the value, we must calculate the number of random versions of fluences or peak fluxes N, which are large enough to determine the probability function from the total fluence or peak flux distribution (the author use N=100 000 ordinary). For that propose, we must consecutively determine for each scenario: 4.5.2.1. The random number of the SEP events in . The rule for this procedure is the Poisson (if <8) or normal (if 8) distribution. 4.5.2.2. The size of the each SEP event 30 should be determined as a random from the distribution function (Eq.4.4) and parameters Eq. (4.5). 4.5.2.3. The energy spectrum Eqs. (2.5 and 2.6) for each random SEP event, which necessitates determination of the random value of the spectral and droop indices. The random spectral index of each SEP event as a random from the lognormal distribution with the mean and standard deviations according to Eqs. (4.6, and 4.7). After that, the spectral coefficient of the fluence or peak flux energy spectrum D should be determined by Eq. (4.12); 4.5.2.4 The random droop index of each SEP event as a random from the lognormal distribution with the mean and standard deviations according to Eqs. 4.09-4.11. 4.5.3 After the energy spectra are determined for each random SEP event, it is possible to calculate the fluences or peak fluxes for each selected energy or for even energy scale. This scale is recommend to calculate as a regular sequence of energies Ej on logarithmic scale, for instance,

(4.14) E k = 3.981 10 where j=1,2,3... ; the scale factor L=5 or 10 or 20 or... .: - The total fluence for each of the random versions of fluences N (item 4.5.2) should be calculated to be a sum of fluences of each of the selected particle energies. - The peak flux for each of the random versions of peak fluxes N should be calculated to be the largest among the peak fluxes of each selected particle energy.
4.5.4. The set of N calculated random fluences or peak fluxes form the probability function for each selected energy. (see on the Fig. 4. 16 for fluences and Fig. 4.17 for peak fluxes). 4.5.5. Given the fluence or peak flux values for different energies and for the same probability, we must unite them in terms of a unified energy spectrum. At energies above 5 MeV, these spectra can be expressed to be power-law functions similar to Eqs. (2.5,2.6) with the parameters D, and , which allow us to calculate the energy spectra for any time interval with a known or predicted solar activity, which are expected to exceed the spectrum within a given probability (see on the Fig. 4.18 for fluences and Fig. 4.19 for peak fluxes).

E j = 10

[10+ (

j -1 L

)]

j -1 L

39


Fig. 4.16 The selected energies probability functions for proton fluences in case of the model parameter =32 .

4.17. The selected energies probability functions for proton peak fluxes in case of the model parameter =32.

40


Fig. 4.18 The model output energy spectra for proton fluence in case of model =32 for different probabilities for exceed the given values.

Fig. 4.19 The model output energy spectra for proton peak fluxes in case of model parameter =32 for different probabilities for exceed the given values.
41


5. Uncertainty analysis of the SEP models output
In this section we discuss the issue of errors in the outputs of the SEP flux model. This issue is quite complicated and has never been discussed previously by the authors of other models. It is obvious that the errors in the outputs of any model contain statistical and systematic errors of the data bases, which served as the basis of these models. Besides, the errors in the model outputs are always larger, than those of the data bases, since the latter are usually aggravated by errors inherent to the modeling methodology. Below we give a detailed analysis of the MSU model output errors, due to statistical errors of the data bases used. According to the above stated, these errors are the lower limits of the model output errors. We also give an estimate of the methodical uncertainty of the MSU model, which arises due to approximation of the proton calculation results by a single energy spectrum (see 4.21 of Draft Standard and 4.5.5 of Memorandum). At the end of this section we will compare the values of the derived errors with some results of our studies of the systematic errors of the data bases.
5.1. Estimates of the MSU model outputs errors In terms of the methods that underlie the MSU model, the high energy proton peak flux and fluence sizes are determined using two independent distributions, namely, (1) the distribution function of SEP event sizes (taken to be 30 MeV solar events proton peak fluxes or fluences), Eq.(4.4); (2) the lognormal distribution function of SEP event spectral indices (Eq. 4.6). Both these dependencies have been determined using a limited experimental data set, which is a sub-set of the total one. However, such sub-sets are known to display statistical errors. 5.1.1 Estimation of the statistical errors of the SEP proton fluence model outputs The errors of determining the peak flux or fluence sizes that arise from the distribution function errors can be found by calculating the statistical deviation of the distribution function both upper and lower limits (see Figs. 5.1 curves 2 and 3). The parameters of these curves are: =1.32 for both and F02=1.421010 and F03=4.95109. The relative errors of determining the peak fluxes and fluences, which are due to the statistical errors in the distribution functions, were determined from the expression: 1 (+ ) (5.1) ( E ) = (- ) - 1 , 2

where ( + ) ( E ) and ( - ) ( E ) are the energy spectra (Fig. 5.2), calculated via the parameters of the distribution functions shown as the upper and lower dashed curves in Fig. 5.1. The energy dependence of the errors in the proton fluences (Eq. 5.1) due to the distribution function statistical errors were calculated for the tabulated values of and probabilities . Examples of such errors are shown in Fig. 5.3 , the calculation was made for model parameter =32. From Fig.5.3 it can be seen that: - the statistical errors of the model, caused by statiatical errors of the distribution functions reach maximum values at energies of 30 MeV (at which the distribution function was determined) and, - these errors abruptly increase with decreasing probability to observe the proton fluxes larger, than model predicted. For the probabilities =0.9 and =0.5 the errors at E=30 MeV do not exceed 30 %, but for =0.01 they increase to 90% (in case of =32).

42


Fig. 5.1 Normalized experimental data for SEP event distributions according to fluence values (points with statistical errors) and approximations : 1 ­ mean used in the model; 2- maximum; 3minimum standard deviation of the distribution function.

Fig. 5.2 Integral energy spectra of the model outputs (proton fluences) for =32 and different probabilities (numbers next to the curves). The solid lines are spectra, calculated according to the distribution function 2; the dashed lines are spectra, calculated using distribution function 33 (see Fig. 5.1).

43


Fig. 5.3 The relative errors of determining the SEP fluences, caused by the statistical errors in the distribution functions in case of model parameters (numbers next to the curves).

- the errors decrease with increasing energy. At high energies the errors are caused by statistical errors of the spectral index distribution function (independently from event size) and will be analyzed below. It is necessary to note, that the error value at E=30 MeV describes the statistical error, inherent to the JPL-91 and ESP models, where the statistical errors of the output proton fluences are actually determined from the distribution function and contain statistical errors of the data base (see section 5.5). The statistical errors in determining the fluences sizes arise from the statistical errors in the distribution of spectral indices. Fig. 5.4 shows the distribution of the spectral indices as lognormal. The approximating functions have been calculated with account for statistical weight of experimental points. According to Fig.5.4 the parameters of the lognormal function (see Eqs. 4.6 and 4.7), used as the model inputs were = 0.773(mean) and log o = 0.138 (standard deviation) and these

data were determined from the experimental data with the standard error of ±0.011. According to that the 4 versions of statistic deviations of these parameters: (1) max min = 0.153 ; (4) log o = 0.127 were used to max=0.783; (2) min=0.757; (3) log o calculate model outputs separately for the lognormal functions' mean and standard deviation errors. The corresponding lognormal functions are shown in Fig. 5.4.

44


Fig. 5.4 The lognormal distribution of the spectral indices. ­ . Vertical dashed lines ­ denoted the standard declinations of the distribution functions mean, dashed and dotted lines at the histogram are the versus of declinations of the standard deviations of the distribution function.

Fig. 5.05 The integral energy spectra of model output proton fluences for parameter =32 and different probabilities (numbers next to the curves). The other curves: A ­ the calculation result for a combination of parameters (1) and (3) ­see text; B ­ (1) and (4); C ­ (2) and (3); d ­ (2) and (4).

45


The energy spectra, determined by statistical deviations of the mean value of and standard deviation were calculated in pairs ­ see examples in Fig.5.5. After that, according to Eq. 5.1we ( ) ( ) calculated the values of the relative error ( E ) and ( E ) . The sum of the errors, caused by errors in mean and standard deviations of spectral index determination were calculated for model parameters ( and ) as:
( (E ) = ) ( E ) 2 + ( E ) 2 (5.2) Examples of the model outputs spectra dependence on the statistical errors of the spectral index distribution function, in case of the model parameter =32 and probability =0.1 is shown in Fig. 5.6. In the energy range of 10Â100 MeV the errors, caused by statistical errors in spectral index distribution are small, however, they increase with increasing energy.
( )

Fig.5.6 The errors of the fluence model output , caused by statistical errors in mean ( line with

black circles) and standard deviations (line with open circles )in the spectral index distribution and for sum of this error, calculated using Eq. (5.2) of spectral index determination in case of model parameters =32 and =0.1.
Note that these error values are close to zero when the errors determined by the distribution functions are the largest. The total systematic error of the model output consists of two independent errors (calculated above) and is calculated according to the expression:
( ( = ) ( E ) 2 + ) ( E ) 2 (5.3) Figs 5.7 ­ 5.09 show the results of calculating the relative mean square errors in the fluence model outputs for three combinations of the and values, namely, 1. =4 - corresponds to a one-year mission under solar activity conditions W=25 (Fig. 5.07); 2. =32 - corresponds to 2-year mission under solar activity conditions W=97 (Fig.5.08); 3. =256 ­ corresponds to a mission throughout the 2 solar cycles with the sum of the annual Wolf numbers W=800 each (Fig. 5.09).





(E )

46


Fig. 5.07 The results of calculating the relative mean square errors in the fluence model outputs for model parameters (numbers next to the curves).

Fig. 5.08 The results of calculating the mean square errors in the fluence model outputs for model parameters (numbers next to the curves).

47


Fig. 5.09 The results of calculating the mean square errors in the fluences model outputs for model parameters (numbers next to the curves).

It should be mentioned, that we do not estimate the model output errors for the E << 30 MeV fluences. The systematical errors of the E<10 MeV solar proton fluxes measured by different instruments have not been analyzed by us, but seem to be no less than a factor of 2 or 3. As a result, because of the uncertainties in the databases, we do not attempt to extend our model range to energies smaller than 5 MeV and do not estimate the errors sizes in the E parameter of the model (with increasing solar activity and mission time) and also with decreasing probability of the proton fluence to exceed fluxes, defined as model outputs. For the probability of =0.01 the errors do not exceed 90%, and for =0.1 ­ 70%. When estimating the fluence values, expected with the probability of =0.5, the largest statistical errors do not exceed 50%. Since the maximum statistical errors were determined by statistical errors of the SEP event distribution function, which was calculated in this paper, using practically all the available data on all the events, recorded over the whole period of monitoring observations, the above mentioned estimates of the statistical errors are the minimum possible for any current SEP fluence models. However, it should be noted, that in reality the errors of the model outputs could be significantly higher, if they use data bases containing measurement data with systematic errors.

48


5.1.2 Estimates of the statistical errors of the SEP proton peak flux model outputs When calculating the statistical errors of the proton peak flux model outputs it is necessary to pay attention, that the distribution function in this case is calculated on the basis of a smaller set of SEP events (1974-2003), than in the case of proton fluences (1956-2003). This inevitably leads to large statistical errors in the model outputs. Indeed, the exponent values, describing the `upper' and `lower' limits of distribution functions (see Fig. 5.10 curves 2 and 3) f02=1.66104 and f03=4.41103 differ more than the exponents, describing the distribution functions of events in fluence.

Fig. 5.10 Normalized experimental data for SEP event distributions (points with statistical errors) in peak fluxes and their approximations: 1- the mean, accepted in the model; 2- the maximum; 3the minimum standard deviations of the distribution function.

Following the chain of calculations used above in the case of fluences we can immediately see, that the statistical errors, determined by the statistical errors of the distribution function in the case of =0.01 this time are larger by a factor of 1.7 (Figs. 5.11 and 5.12). The data in Fig.2.13 and 2.14 confirm the obvious fact that for the same distribution functions the errors (which they are responsible for) are also the same. The final Figs. 2.15-2.17 confirm the expected result, that due to larger statistical errors of peak flux distribution functions , the statistical errors of the model output are significantly higher and reach 140%. It only remains to conclude, that if the author of the model possessed reliable monitoring data on the peak SEP proton fluxes during 1956-1974, then the accuracy of the peak flux model could be extended to that of the fluence model.

49


Fig. 5.11 The integral energy spectra of peak flux model outputs for different values of the parameter and different probabilities (see Fig.). The sold lines are spectra calculated according to distribution function 2; the dashed lines are spectra, calculated using distribution function 3 (see Fig.5.10)

Fig. 5.12 The relative errors of determining the SEP peak fluxes, caused by the statistical errors in the distribution functions in case of model parameters (numbers next to the curves).

50


Fig. 5.13 The integral energy spectra of peak flux model outputs for model parameters (numbers next to the curves). Curve A is the calculation result for a combination of parameters (1) and (3) ­ see text; B ­ (1) and (4); C ­ (2) and (3); d ­ (2) and (4).

Fig. 5.14 The errors of the peak flux model output, caused by statistical errors in mean (line with black circles) and standard deviations (line with open circles )in the spectral index distribution and for sum of this error, calculated according to Eq. (5.2) of spectral index determination in case of model parameters (numbers next to the curves). .
51


Fig. 5.15 The results of calculating the relative mean square errors in the peak flux outputs for model parameters (numbers next to the curves).

Fig. 5.16 The results of calculating the relative mean square errors in the fluences model outputs for model parameters (numbers next to the curves).

52


Fig. 5.17 The results of calculating the relative mean square errors in the fluences model outputs for model parameters =256 and =0.9 (9), =0.5 (5), =0.1 (1) and =0.01(01).

5.2. The issue of methodical errors, associated with approximations of model calculated particle fluxes by uniform energy spectra

The current model contains a certain approximation, associated with the approximations of the proton fluxes (fluences and peak fluxes) calculated at different energies ( see 4.2.6 of Model and 4.5.5 of Memorandum). Fig.5.18 shows the values of the fluences, calculated for certain energies and some model parameters. It can be seen, that the energy spectra only to a certain extent describe the calculated flux values Fig. 5.19 shows the differences between logarithms of the fluxes, directly determined by model and the spectra, which are an approximation of these data (Fig. 5.18). The same Fig.5.19 shows as dashed lines the statistical error values for the flux calculation at the same model parameters (see Fig. 5.07-5.08). As it can be seen from this data, the approximation used in the model introduces errors of not more than 20% into the model outputs, which can be neglected if compared with the statistical errors of the model.

53


Fig. 5.18 Fluence values, calculated for given proton energies (different markers) and the energy spectra, used for their approximation which are model outputs.

Fig. 5.19 Dependence the flux logarithm differences of model-calculated data and their approximations (see Fig. 5.18 on energy. Dashed lines are the model calculated statistical errors (see Fig. 5.07-5.09)

54


5.3 The statistical and systematical errors of the SEP fluxes models

None of the authors of the SEP flux models have published any error estimates of their model outputs, therefore we cannot compare our results with other data. However, our calculations permit to estimate some major features of errors of various SEP models. We can very roughly estimate the systematical errors, what are caused by the use of IMP spacecraft data for developing the model development in the range of high-energy proton fluxes. Therefore, we estimated the systematical errors occurring in our model outputs, in the case if we replace the mean spectral index <>=5.9 (as measured by GOES) by <>=3.3 (as measured by IMP8) and neglect the droop index (=0). In Fig. 5.20 we show the calculation results in case of using IMP measured flux data spectral indexes and in the case of our model parameter =32 . It can be seen, the IMP-8 energy spectra are harder and similar to the JPL-91 model outputs for 2 year missions (probabilities of 0.5 and 0.1). Certainly, the energy spectra in Fig. 5.20 are similar to data shown in Figs. 6.6, 6.16, 6.17, 6.18. Therefore, the discrepancies between the JPL-91and MSU models are caused, primarily, by the use of different databases. Fig. 5.21 shows the output error calculation results of the model, using the IMP-8 measured spectral indexes. The errors of the MSU model for the same parameters are demonstrated too. It can be seen from the data, the IMP-8 based (close to JPL-91 model results but using a different distribution function) errors for every probability are much larger than those calculated according to the MSU model. From the data in Fig.5.21 it can be seen what effect systematic errors of the data bases can have on SEP model development. And what large systematic errors could have been introduced, if the authors had used IMP-8 experimental data at high energies >>30 MeV.

Fig. 5.20 The calculation results in case of IMP measured fluxes (solid lines) and our model (dashed lines) parameters (based on the GOES spacecraft measured data). JPL-91 model calculation output results are demonstrated (asterisks) also.

55


Fig. 5.21 The output errors of the model, employing IMP-8 measured spectral indexes (solid lines). The statistical errors for the MSU model outputs for the same model parameters are demonstrated too (dashed lines). 5.4 Conclusions

The results of the analysis described in this section are essentially of an approximate nature and can only be regarded as estimates. Nevertheless, they show, that whilst the model ouputs are restricted by the experimental data set and do not use extrapolations of these data outside the measured data set (this is true for estimating particle fluxes during relatively short missions and non-extreme probabilities), the relative statistical errors of model ouputs for proton fluences insignificantly exceed 50%. For peak fluxes the statistical errors of the current model are somewhat higher, which is due to limited statistics of the used data bases (only data of the 21-22 SA cycles). However, the issue of systematic errors, which the authors of the experiments appear to try to conceal (for, example, refusing to answer direct questions) and the authors of the models refuse to discuss still remains very important. At present, we believe, that systematic errors in the flux measurements have been determined with an accuracy of not worse than a factor of 2, and, therefore, the issue of systematic errors of the model makes sense only in the case when estimates of extremely large fluxes, employing extrapolations of the distribution function well outside the set of available experimental data, are made.

56


6. SEP flux models and their agreement with experimental data
6.1 The main output of the MSU model First of all we will describe the MSU Solar energetic proton fluence and peak flux (fluxes, for short) model outputs and compare them with the results of other existing models. We show the annual and solar cycle calculation results first. The intermediate time periods will be partially analyzed in the next section (6.2. ). 6.1.1 The annual missions fluences and peak fluxes

The MSU model permits to calculate the solar protons fluxes for any arbitrary solar activity period, which should be characterized by the sum of the monthly mean smoothed Wolf numbers (Eq. 4.3). Of course, for different probabilities, the fluxes exceeding a certain specified value will be different.
The annual conditions calculated for the mission were as follows: 1. Annual mean =25 (the sum of the monthly smoothed sunspot number


1

12

< W >= 300 ,

mean number of E30 MeV events with fluences F30105 cm-2 =4.05 - see Eq. 4.3). 2. Annual mean =50 (
12 1 12


1

12

< W >= 600 ,=8.1).

3. Annual mean =100 ( 4. Annual mean =150 ( 5. Annual mean =200 (


1 1 12

< W >= 1200 , =16.3) < W >= 1800 , =24.4) < W >= 2400 , =32.6)

These periods, for short, may be identified as: =25 - typical "quiet", =50 - low activity, =100 - moderate activity, =150 - high activity and =200 - extremely high activity. First of all, Fig. 6.1 demonstrates the energy spectra of proton fluences for probability of 0.5. These spectra do not contain any model assumptions and are solely a reflection of the databases used; their reliability, inherent statistical errors and generalization methodology. For the periods, identified by the authors of JPL-91 and Xapsos et al. models as "active" Sun period with the same fluences, our model fluence outputs for low and extremely high SA periods are not equal (as it is proposed in JPL-91 and ESP models), but differ by a factor of 14. Fig.6.1 also shows the fluences from the paper of ESP for the "active" Sun period. These data are consistent with our spectra for =80. Such solar activity, in fact, is not the mean for "active" Sun years, but is noticeably smaller. This disagreement is caused by the fact, that our model database includes fluences of the 23rd SA cycle, what were much larger, than the fluences from SA cycles 22, used in Xapsos et al. 1999. In Fig. 6.2 we compare our model output with the JPL-91 output data. The JPL-91 disagree stronger with the form of our model energy spectra, than the ESP model data. This disagreement will be discussed later in this paper. Figure 6.3 shows the integral energy spectra of peak fluxes output according to our model. The peak flux spectra are similar to the fluence spectra. The only point, which is available for the other models is from ESP (Xapsos et al., 1998) for active Sun years. Because of different databases, the Xapsos et al. data correspond to the =80 solar activity level of our model.

57


Fig. 6.1 The model calculated SEP proton fluence energy spectra for probability of 0.5 at different solar activity levels according to the MSU model and 1 `active Sun' year according to the ESP model.

Fig. 6.2 The model calculated SEP proton fluence energy spectra for probability of 0.5 at different solar activity levels according to the MSU model and for 1 `active Sun' year according to the JPL91 model.

58


Fig. 6.3 The model calculated SEP proton peak flux energy spectra for the probability of 0.5 according to different solar activity levels in the MSU model and for 1 active Sun year according to the ESP model

Fig. 6.4 demonstrates the situation for fluences, exceeding the given energy spectra with 0.1 probability. The energy spectra for different solar activity come nearer to each other because in the range of high fluences the distribution function turns-off sharply (see Fig.4.5). Compared with the ESA model there is a small difference, because different distribution functions were used (see Figs. 2.7 and Eqs. 2.3 and 2.4).

59


Fig. 6.4 The model calculated SEP proton fluence energy spectra for probability of 0.1 at different solar activity levels according to the MSU model and for 1 `active Sun' year according to the ESP model.

Fig. 6.5 shows the energy spectra for 0.01 probability. Curves for all solar activity are much closer to each other, because the energy spectra reflect the rare extreme fluences, which can randomly appear in one out of each hundred or thousand of missions. There is no data for this probability published by Xapsos et al., but it is possible to compare this result with JPL-91 data. The energy spectra, retrieved from the data in the paper by Feynman et al. 1993, is in poor agreement with our data. There are a lot of reasons for this circumstance. The first one of them is, that the JPL-91 model is based on the IMP-8 spacecraft data, the SEP energy spectra recorded onboard this satellite are systematically harder, than spectra measured on the GOES spacecraft's. Secondly, as it was demonstrated in Fig.2.7, the lognormal function used in the JPL-91 model, in our opinion, is not best to describe the SEP distribution's experimental data (see discussion above (2.2.5), and Kurt and Nymmik, 1997).

Fig. 6.5 The model calculated SEP proton fluence energy spectra for probability 0.01 at different solar activity levels according to the MSU model and for 1 `active Sun' year according to the JPL91 model Fig. 6.6 shows the energy spectra plotted for an annual mission period of =150 (high solar activity condition) for different probabilities of fluences to exceed the spectra. First of all, it is necessary to mention, that the discrepancies in the integral fluences for fixed energies for annual missions depending on probabilities can be large enough.. Thus, for E31.6 MeV protons the rate of fluences at =0.9 and =0.1 is equal to 50. This means, that in 20% of annual missions the fluences may differ by a factor of more than 50 times. Secondly, it can be noted, that the curves for the JPL-91 and our model are quiet different. The spectra of JPL-91 are too hard and the E10 MeV proton fluences with the probability =0.5 in the JPL-91 model correspond to probabilities of =0.9 in the MSU model, similarly, fluences for the probability of 0.1 in the JPL-91model correspond to fluences with probability of 0.5 in the MSU model. As it was mentioned above, it is because the JPL-91 model is based on the 10-21 SA period data only, when the statistics of large solar events was small, whereas the MSU model incorporates all
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the large SEP events of the 22nd and 23rd SA cycles. The hardness of JPL-91 spectra is primarily caused by the hardness of the energy spectra measured on the IMP satellites.

Fig. 6.6 The model calculated SEP proton fluence energy spectra for solar activity level of W=150 for probabilities 0.9,0.5, 0.1 and 0.001 according to the MSU model and for 1 `active Sun' year according to the JPL-91 model for probabilities 0.5, 0.1, 0.01 and 0.001.

Fig. 6.7 shows the ESP model data. Their spectral indices are close to those calculated according to our model for W=150 , but ESP =0.5 data are close to our =0.9 data and ESP =0.1 data are close to our =0.5 data. This discrepancy is large enough and caused by the large events of the 23rd SA cycle, which were taken into account in our model.

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Fig. 6.7 The model calculated SEP proton fluence energy spectra for the solar activity level of W=150 for probabilities of 0.9,0.5, 0.1 and 0.001 according to the MSU model and for 1 `active Sun' year according to the ESP model for probabilities of 0.5 and 0.1.

Fig. 6.8 shows the ESP model (=50). The spectral indices to each other. But it should be lower, than the mean value for a

data again, but our model data are calculated for moderate SA and the spectra for the same probabilities for these models are close noted, that SA =50, used for our model calculation is much 7-year solar active period.

Fig. 6.8 Model calculated SEP proton fluence energy spectra for the case of moderate solar activity =50 for probabilities of 0.9, 0.5, 0.1, 0.01 according to the MSU model and the ESP model for 1 active year for probabilities 0.5 and 0.1. Fig.6.9 shows the model calculated peak flux integral energy spectra for different probability to exceed given values for the mean year solar activity =150. There are only Xapsos et al. 1998 paper model calculated data for E10 MeV available to compare with our model data. These data are close to those predicted by our model.

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Fig. 6.9 The model calculated SEP proton peak flux energy spectra in case of W=150 solar
activity level for probabilities 0.9,0.5, 0.1 and 0.001 according to for MSU model and for 1 active Sun year for ESP model for probabilities 0.5, 0.1 and 0.01.
6.1.2 The solar cycle mission fluences and peak fluxes

Because of the relatively small difference between the sum of Wolf numbers for different solar cycles (the maximum sum of smoothed mean month Wolf number is for cycle 19 and equals to W19=11500 (=156) and the minimum is for 20 cycle W20=8400 =114) the model calculated SA fluences and peak fluxes are close too. In Fig. 6.10 we demonstrate the model calculated SA cycle energy spectra in the case of a 0.5 probability (fifty-fifty case) for cycles 19-23 (the last cycle is not finished yet). The model calculated fluences differ for E31.6 MeV by a factor of 1.4. In the Figure we show that for the JPL-91 7 solar active years (this equals to the SA cycle in our model) the calculated fluences spectrum is smaller and harder, than the spectrum calculated according to the MSU model. In Fig. 6.11 this circumstance is analyzed in more detailed using the data of the 22nd SA cycle data. In this Figure we show the spectra for probabilities of =0.9 and =0.5 calculated according to the MSU model, also for the probability of =0.5 we show the spectrum calculated with account for the statistical error defined by the statistical accuracy of the data base used (see Fig.5.2). For E<20 MeV the spectrum for probability of =0.5, calculated according to the JPL-91 model is smaller, than according to our model at the probability of =0.9 . Since the =0.5 data reflect only the database used in the model development and do not contain any approximation assumptions, this large difference seems to be the effect of quite different databases, used in different models.

Fig. 6.10 The model calculated SEP proton fluence energy spectra in case of different solar activity cycles for probability 0.5 according to the MSU model and for the JPL-91 7-active year period.
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Fig. 6.11 The model calculated SEP proton fluence energy spectra for different solar activity cycles and probability of 0.5 according to for MSU model and for the JPL-91 7-active year period.

In the case of a =0.01 probability (Figs.6.12 and 6.13) the situation changes. At the E<10 MeV range the different model calculated fluences are close to each other, but for E>20 MeV fluences the IPL-91 data are overestimated. For E60 data the JPL-91 data are overestimated by 5.5 times. In this case the large overestimation is caused by both: the IMP-8 detectors particle flux overestimation at E>30 MeV and irrelevant lognormal distribution function, used in JPL-91 model as the distribution function approximation (see section 2.2.5).

Fig. 6.12 The model calculated SEP proton fluence energy spectra for different solar activity cycles and probability of 0.01 according to the MSU model and for the JPL-91 7-active year period.

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Fig. 6.13 The model calculated SEP proton fluence energy spectra for the 22nd solar activity cycle for probability of 0.01 according to the MSU model (solid line) and model statistical error (dashed line) and according the JPL-91 7-active year period. 6.2 The model outputs and experimental data

The reliability of the model is determined by the accuracy with which the can describe experimental data. It is surprising that none of the authors, except us, have ever compared the outputs of their model calculations with experimental data. Furthermore, all our presentations at the COSPAR Assembly, in which such comparisons were made have (for unknown reasons) remained unpublished. Here we make a comparison of the model calculated energy spectra with reliable SE proton experimental data. First of all, these experimental data are the GOES satellite (DOME and TELESCOPE instruments) differential channels measured (uncorrected) fluxes. These data are available since 1985. For peak flux analysis sometimes we also use neutron monitor data and data of the Meteor satellite. Data measured on the IMP satellite are sometimes used to analyze E<40 MeV proton flux data.
6.2.1 SE proton fluences and peak fluxes during the "quiet" Sun period We calculated the differential energy spectra (cumulative) fluences exceeding the given values with probability of the 0.9, 0.5 and 0.1 for conditions of quiet Sun period from 1993 to 1997. As it can be seen from Figure 6.14, the experimental data for this period are described by spectrum of a 0.5 probability.

In Fig. 6.15 we show the experimental results and model calculated peak flux energy spectra for the same "quiet" Sun period. The largest peak fluxes during this period occurred in the 1994, 20 February and 1997 4, November SEP events. The peak fluxes for this period are demonstrated to be between model calculated energy spectra for peak flux exceeding this spectra with probabilities of 0.09 and 0.4.

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Fig. 6.14 The differential energy spectra (cumulative) fluences exceeding given values with probability of 0.9, 0.5 and 0.1 according to the MSU model for quiet Sun conditions during the 1993-1997 time period, fluences, measured by GOES (horisontal lines) and corresponding energy spectra (solid line with triangles). The GCR cumulative fluence for this period is also shown.

Fig. 6.15 The maximum peak fluxes appeared in period 1994-1997 and channel by channel measured by GOES-7, in the 1994, 20 February and 1997 4, November SEP events and the MSU model calculated peak flux energy spectra for the same "quiet" Sun period in case of probabilities -0.9, 0.5, 0.1 and 0.001.

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Note that besides our model, there are no other models describing the SEP fluxes for this low SA or "quiet" Sun period.
From the above calculations it follows that the SEP event proton fluences are significant during all solar activity periods, including the "quiet" Sun period. Therefore, the SEP models, which neglect the SEP events in the periods of low solar activity, cannot be used in practice for complete high energy particle flux condition analysis since such models lead to an inaccuracy of up to a few orders of magnitude in determining the particle fluxes in interplanetary space. 6.2.2 Annual fluences and peak fluxes 6.2.2.1 Annual cumulative fluences In order to estimate the output reliability of the different models we conventionally divided the annual fluences measured on the GOES spacecraft into 3 groups: 1. With mean annual sunspot numbers W100 (years 1989, 1990, 1991, 200, 2001, 2002); 2. 40W<100 (years 1988, 1992, 1993, 1998, 1999, 2003); and 3. W<40. Here we analyze the experimental data for first two groups only, because there is no model output data (besides MSU model) for solar activity of W<40 and since the data for such periods were analyzed above (6.2.1). In Fig. 6.16 we show the JPL-91 model outputs for active years according to Feynman et al. (1993). We approximated the fluence data calculated in this paper for E4, 10, 30 and 60 MeV by smooth lines in order to obtain the energy spectra of model annual fluence output . In the same Fig. 6.16 we also show the energy spectra for years of first group. It can be seen from this data, that the energy range of JPL-91 model outputs is divided into 2 parts ­ beyond and above E=30 MeV.

Fig. 6.16 The JPL-91 model outputs for active years fluences according to Feynman et al. (1993) for probabilities 0.5, 0.1 and 0.001. Also the annual fluence energy spectra for years of 1. group activity levels (W>100 , see text) are demonstrated.

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First of all, it is necessary to note, that proton fluences for 3 of the total 12 total "active" Sun years (which is 0.25 of the total) have fluences large or equal to energy spectra for 0.02 probability. This contradiction is explained, because the JPL-91 database do not include the large SEP events of 23 SA cycle. Secondly, and this is more important, the slopes of model calculated energy spectra above 30 MeV contradict the experimental data. The same can be said about the energy spectra of the remaining 6 "active" Sun years ­ Fig. 6.17. If we summarize the data of both the last Figures, we can conclude, that the fluences of protons with energies below E=30 only in 3 cases out of 12 are smaller, than model predicted 0.5 (fiftyfifty) probability. For a better illustration of the situation we calculated the mean logarithmic spectra (see Eq. 2.1) for both of annual spectra groups, 1 and 2. The results are shown in the Fig. 6.18. Firstly, these data obviously demonstrate, that the JPL-91 and Xapsos et al. model's basic concept, concerning the same solar energetic particle fluxes for all 7 years of active Sun, is erroneous. The annual SEP fluences for 2 groups shown in Fig. 6.18 differ by a factor of 20.
Secondly, the solar energetic particle fluxes with energies E>20 MeV are the most important for radiation safety consideration onboard spacecraft and space stations, the energy spectra of JPL-91 model are too short and have erroneous slope to describe the SEP particle radiation influence.

Fig. 6.17 The JPL-91 model outputs for active years fluences according to Feynman et al. (1993) for probabilities o.5, 0.1 and o.001. Also the annual fluence energy spectra for years 40W<100 (2. group activity levels see text) are demonstrated

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Fig. 6.18 The JPL-91 model outputs for active year fluences, according to Feynman et al. (1993) for probabilities o.5, 0.1 and o.001. The calculated mean logarithmic spectra ( Eq. 2.1) for both of annual spectra groups, 1 and 2 are demonstrated.

Fig. 6.19 The same as on the Fig. 6.15 6 annual fluence energetic spectra from W>100 solar active periods and model output of the MSU model for the annual Wolf number W=130 (mean SA condition for the demonstrated 6 years) (=0.9; =0=.5; =0.1 and =0.01).
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In Fig. 6.19 we demonstrated the same 6 annual fluence energetic spectra from W>100 solar active periods and model output of the MSU model for the annual Wolf number W=130 (mean SA condition for the demonstrated 6 years). All experimental data for these annual fluences in the full range of energy from 4 to thousands of MeV are located between the model calculated probabilities for 0.9 to 0.1, which is quite normal. The SEP model energy spectra slopes coincide with the experimental data. In Fig. 6.20 we show the model output spectra together with logarithmically averaged spectrum for the same 6 events. The averaged experimental data are close to the 0.5 (fifty-fifty) probability model calculated energy spectrum.

Fig. 6.20 The logarithmically averaged ( Eq. 2.1) 6 annual fluence energetic spectra from W>100 solar active periods and model output of the MSU model for the annual Wolf number W=130 (mean SA condition for the demonstrated 6 years) (=0.9; =0=.5; =0.1 and =0.01).

For periods with <100 the annual fluences lie within the W=40-100 SA range. This range is too broad to compare with a single MSU model calculation output. Therefore in Fig. 6.21 we compare MSU model outputs with 3 smaller annual fluences (for "active" Sun period) ­ 1993 (=56), 1998 (=62) and 2003 (=70). 2 years out of the total 3 have fluences between predicted output probabilities 0.1<<0.9. One of them is characterised by a probability smaller, than the value corresponding to =0.9. According to statistics this is normal too. In Fig. 6.22 we showed 6 logarithmically averaged annual fluences for the range Wy<100 (=78). The experimental data (unlike the JPL-91 model output (Fig.6.18)) in form and size correspond to the model output curve for p=0.5 (fifty-fifty).

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Fig.6.21 The MSU model outputs for model parameters W=43 (p=0.9; p=0.5; p=0.1) and W=50 (p=0.9); , and 3 smaller annual fluences spectra for "active" Sun period ­ 1993 (=56), 1998 (=62) and 2003 (=70).

Fig.6.22 The logarithmically averaged 6 annual fluences for the range Wy<100 (=78) (black squares). The curves are the MSU model outputs for probabilities p=0.9; p=0.5 p=0.1 and p=0.01.

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Fig. 6.23. The ESP SEP model cumulative fluence output (Xapsos et al. 1999b) for active years. The calculated mean logarithmic spectra ( Eq. 2.1) for both 2 annual spectra groups, 1 and 2 are demonstrated. Short summary for annual fluence output. The model outputs for annual fluences calculated for probabilities smaller than 0.1 are based on the measured distribution function of SEP events and do not contain any assumptions regarding extrapolation of the functions to the superhigh fluence range. Since the distribution function is based on data measured on different satellites (IMP and GOES), the measured particles fluxes at energies >30 MeV are different, and the models outputs are different too. In our opinion, the SEP proton fluxes at energies E>30 MeV, measured by the IMP satellite are overestimated, therefore, the JPL-91 model outputs for all probabilities at the same energies are overestimated too. When develping the MSU model we did not use SEP flux data for E>30 MeV protons measured on the IMP satellite. For the development of the ESP model the authors used not only GOES data but also data of IMP-3,4,5,7,8 . The GOES data of 22 SA cycle contains a large number of large SEP events, with large fluxes measured to the highest energies. For this reason the ESP model, is in better agreement with the experimental data at high energies. Tha last suggestion is rather preliminary, since there are no detailed descriptions of the model development methodology and no outputs for ESP model. 6.2.2.2 Annual peak fluxes Here we analyze whether the outputs of our model agree with experimental data. The ESP model outputs are published only for the E10 MeV annual SEP proton fluences. These data primarily reflect the quality of the used experimental data, ruling out the possibility for detailed analysis. For model output analysis we use the annual peak flux for all years with solar activity of 40 measured by GOES. Because the enery spectra of the annual peak fluxes include, as a rule, the peak fluxes from several SEP events, we have divided the experimental data into 4 groups: with =145, 110, 93, and 63 (see Figs. 6.24-6.27). All the annual peak fluxes for different solar activity ranges measured by GOES ­ 7 (22 SA cycle) and GOES-8,11 (23 cycle) are in good agreement with the corresponding model outputs.
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It is important, that the MSU model outputs are valid for proton fluxes with energies upto ten thousands of MeV. Calculations of peak fluxes (and fluences) for such high energies are not possible in the modelling methodology, used in JPL-91 and ESA model development.

Fig. 6.24 The MSU model output peak flux annual energy spectra for (W)=63 and maximum peak flux spectra, measured on the GOES spacecrafts during the years 1998,1998 and 2003.

Fig.6.25 The MSU model output peak flux annual energy spectra for (W)=93 and maximum peak flux spectra, measured on the GOES spacecrafts during the years 1988, 1990, and 1992.

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Fig. 6.26 The MSU model output peak flux annual energy spectra for (W)=110 and maximum peak flux spectra, measured on the GOES spacecrafts during the years 2000,2001 and 2003.

Fig. 6.27 The MSU model output peak flux annual energy spectra for (W)=145 and maximum peak flux spectra, measured on the GOES spacecrafts during the years 1989,1990, and 1991. 6.2.3 Fluences and peak fluxes for the solar cycle duration missions The model calculated solar cycle fluence and peak flux energy spectra are especially sensitive to the SEP event distribution function approximations to the range of extremely large fluxes. Indeed, we have data about the SEP event fluxes during the five SA cycles, but the model outputs predict the 7-active year fluxes up to probabilities even =0.001 (as it is predicted in JPL-91 model). We have measured characteristics for N=60 SEP events in each cycle (300 events measured SEP events in total). Therefore, the prediction of the solar cycle fluxes with the =0.001 with relative error 100% needs the measurement of N*1000=6104 events, with relative errors 10%
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- 6106 events (we have measured 300). Therefore, the exact prediction of the SA cycle cumulative fluxes for =0.001 should be based on the justified extrapolations in range 6106/300=20000 times large, than measured SEP event distribution function. That kind of extrapolations are rare fantastic, than scientific. In Fig. 6.28 we show the JPL-91 model outputs together with the 22 and 23 cycle cumulative fluences integral energy spectra, measured on board of GOES spacecraft and approximated by Eq. 2.4. As it can be seen from the Figure, the slopes of experimental data energy spectra from 10 MeV to 60 MeV differ significantly from those predicted by the JPL-91 model.

Fig. 6.28 The JPL-91 model outputs together with the 22 and 23 cycle cumulative fluences integral energy spectra, measured onboard the GOES spacecraft.
An attempt to reduce this discrepancy was done by authors of the SPENVIS model. They extended the JPL-91 outputs (Fig. 6.28) by means of energy or rigidity exponents (Fig. 6.29). As it is seen from the experimental data, demonstrated also on the Figure 6.29, this attempt is also unsuccessful. The expression in King's model is also in poor agreement with experimental data (Fig. 6.29). If the difference of the solar activity for different cycles is same, as in cycles 19-23, the MSU model outputs for different cycles differ insignificantly (Figs. 6.9-6.11). Therefore, in Fig. 6.30 we show for the 22nd solar cycle the calculated MSU model output together with the experimental data of SEP proton cumulative fluences of 22 and 23 SA cycles, measured on GOES. The 22nd SA cycle experimental data for the complete energy range (from 5 to 600 MeV) corresponds to the p=0.5 model prediction, the 23 cycle data ­ to the interval of 0.5-0.1 probability. This is a normal coincidence of the model outputs with the experimental data. Unfortunately the authors of the ESP have not published their model outputs for the solar cycle duration periods. The same can be said about the ESA model outputs for peak fluxes for the solar cycles.

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Fig. 6.29 The JPL-91 model, improved by SPENVIS (added are the exponents of rigidity or energy) and experimental data for 22 and 23 SA cycles. The `King's model output is shown too.

Fig. 6.30 The MSU model output for the 22nd solar cycle conditions together with the experimental data of SEP proton cumulative fluences of 22 and 23 SA cycles (measured by GOES spacecrafts).

In Fig. 6.31 we show the MSU model peak flux outputs for the 22 and 23 solar cycle periods. There is satisfactory agreement of the model predictions and the experimental data up to energies of 10 GeV.

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Fig. 6.31 The MSU solar cycle outputs for probabilities 0.9, 0.5, 0.1 and 0.01 for peak fluxes and the largest peak fluxes from the 22 and 23 solar cycle SEP events.

6.3 Conclusion
As it is seen from above, the MSU SEP fluxes model (proton fluences and peak flux) reliably describes the experimental data of any solar activity conditions and any space mission duration for proton energies 4 MeV (high energies are not limited). Such efficiency of the semi-empirical model is achieved primarily due to the account for fundamental regularities inherent to solar energetic particle events and fluxes and cannot be achieved by the empirical methodology (used in the development of JPL-91 and ESP models).

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7. Summary
As it was shown above, attempts to develop SEP flux models using only a mathematical generalization of the final effect ­ the SEP event distribution, lead to serious errors in the model descriptions of the phenomena. The main common errors of these models (JPL-91 and ESP), called `empirical' are: 1. SEP fluxes during the so-called 4-year periods of "quiet" Sun are disregarded; 2. the dependence the SEP event frequency and particle fluxes on certain solar activity level is disregarded. These errors lead to the erroneous estimation of the radiation environment in the near-Earth space, and the relative roles of two main components of high energy radiation ­ the Galactic Cosmic Rays and Solar Energetic Particles. The additional sources of the errors in empirical model developments are: 1. use of unverified experimental data, which contain systematic measurement errors (IMP data used in the JPL-91 model), and lead to an incorrect energy dependence of the modeled particle fluxes. 2. neglecting the threshold effects of SEP event registration and selection, which leads to an erroneous distribution function and also its approximation (the lognormal function in JPL-91 model). The situation with the SEP flux models is similar to the history of the early GCR model development, when the primary empiric CREME-81 model and Soviet State Standard ­ GOST (which were based on the sinusoidal dependence of the GCR fluxes during the 11-year SA cycles) were replaced by a semi-empirical model, developed at Moscow State University. The latter model takes into account the dependence of the particle flux on the concrete solar activity level, regularities in the particle flux changes against solar activity, dependence of the particle fluxes on the 22-year cycle of the general magnetic field of the heliosphere. Later, when the MSU model was made available as the CREME-96 GCR model, it became an International Standard (on January 1st, 2003). All the above listed shortcomings of the JPL-91 SEP flux model lead us to the development of the more detailed semi-empirical model of SEP fluxes. In the process of solving various problems, associated with SEP model development, we established the regularities inherent to the events and fluxes of solar energetic particle were published in a number of papers starting from 1993. The first versions of the model were reported at COSPAR Scientific Assemblies as invited reports in Birmingham, (1996) and Nagoya (1998), at the ESA workshop ("Environment modeling for space based applications", ESTEC, Noordwijk, September 1996), and at the NASA workshop ("Impact of Solar Energetic Particle Events for design of human Missions", Houston, September ,1997), workshop "Space Radiation Environment Modeling: New Phenomena and Approaches" (October 1997, Moscow), NATO Advanced Research Workshop, "Effects of Space Weather on Technology Infrastructure", (Rhodes, Greece, 2003, March), the International Space Environment Conference 2003, (Sept. 2-5, Toulouse, France). These papers are published in the proceedings and abstracts of all these conferences (excluding the Nagoya COSPAR Assembly proceedings, where the papers were not published for unknown reasons). Since the discussions concerning the draft of this model at the ISO Working group 4 meeting, 4 additional versions of the model were developed and officially distributed (as Draft Standard versions and attached memorandums) . Additional paper with SEP model descriptions were published in: N.V.Kuznetsov and R.A.Nymmik, Radiation single event upsets in spacecraft microelectronics caused by solar cosmic rays, Cosmic Research 35(5), 434-446, 1997. Nymmik R.A., 1998, Radiation environment induced by cosmic ray particle fluxes in the international space station orbit according to recent Galactic and Solar cosmic ray models, Adv. Space Res. 21(12), 1689-1698. Nymmik R.A., (1999c) Probabilistic Model for Fluences and Peak Fluxes of Solar Particles, in Radiation Measurements 30, 287-296.
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Nymmik R.A., The problems of cosmic ray particle simulation for the near-orbital and interplanetary flight conditions, Radiation Measurements, 30, 669-677,1999. N.V.Kuznetsov and R.A.Nymmik, The dependence of solar energetic particle fluxes in the EarthMars-Earth route on solar activity period, Adv. Space Res. 30(4), 981-984, 2002. Kuznetsov N. V., R. A. Nymmik, M. I. Panasyuk, Models of solar energetic particle fluxes: the main requirements and development prospects . ­ Invited report on the 34th COSPAR Scientific Assembly, Houston, 2002, Unpublished invited report on the 34th COSPAR Scientific Assembly, Houston, Oct. 2002. Paper is available on the website http://srd.sinp.msu.ru/nymmik/, 2002. It needs to be mentioned, that all these model versions contain not only proton but also heavy ion peak fluxes and fluences. The present version, developed in 2003-2004, differs from previous versions because it takes into account the results of the reliability analysis of a large set of the SEP particle events and flux databases. As a result of the model was revised, and elaborated and some functional regularities and numeral parameters of the model were changed.
Once again we will note, that the MSU semi-empirical solar energetic particle model is based on the following regularities, inherent to solar energetic particles events and fluxes: 1. The SEP event frequency is proportional (in the early papers it is a power law function with spectral index 0.75) to the smoothed Wolf number. R.A.Nymmik, On the dependence of the rate of events of solar cosmic rays on solar activity, Cosmic Research, 35(2), 198-200, 1997. D.A.Mottl and R.A.Nymmik, Solar activity and the events of the Solar Cosmic Rays, Izvestiya Akademi Nauk, ser. Phys., 65(3), 317-320. Nymmik R.A., Relationships among Solar Activity, SEP Occurrence Frequency, and Solar Energetic Particle Event Distribution Function, Proceedings of the 25th ICRC V.6, pp. 280283, 1999a. Nymmik R.A., 2001, The main characteristics of the solar energetic particle events relevant to solar activity, in Proc. of ICRC2001, 3197. 2. The undistorted distribution function of SEP events is a power law function with an exponential turn-off in the range of large fluxes (fluences and peak fluxes) V.G.Kurt, and R.A.Nymmik, The >30 MeV proton fluence size distribution of SEP events, Space Research, v.35, No.10, 1997, pp.598-609. Nymmik R.A., 1999b., SEP event distribution function as inferred from Spaceborne measurements and Lunar rock isotopic data, Proceedings of the 26th ICRC, Salt Lake City, Nymmik R.A., Relationships among Solar Activity, SEP Occurrence Frequency, and Solar Energetic Particle Event Distribution Function, Proceedings of the 25th ICRC V.6, pp. 280-283, 1999a. 3. The distribution function does not depend (is invariant) on solar activity Nymmik R.A., Relationships among Solar Activity, SEP Occurrence Frequency, and Solar Energetic Particle Event Distribution Function, Proceedings of the 25th ICRC V.6, pp. 280-283, 1999a. 4. The SEP particle (protons and heavy ions) energy spectra for E>30 MeV are best approximated by a power law function of particle momentum (per nucleon) or, in the case of protons, rigidity. 5. At E<30 MeV the spectra are drooped (or in some cases, due to arrival of additionally accelerated by chock particles the spectra became softer)
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Nymmik R.A., 1993.Averaged Energy Spectra of Peak Flux and Fluence Values in Solar Cosmic Ray Events, Proc. 23rd ICRC, Calgary, v.3, p.29, Nymmik R.A., Models describing solar cosmic ray events, Radiation Measurements, 26(3), 417420, 1996 Nymmik R.A., The Statistical and functional analysis of the characteristics of the energy spectra of the solar energetic particles (1
5.1 The spectral indexes for E>30 Mev ­ are distributed according to a log-normal function, the mean spectral indexes do not depend on the event size. 5.2 The additional droop spectral index for E<30 MeV range depends on event size and on spectral index for E>30 MeV.
The solar energetic particle (proton and heavy ion) peak fluxes and cumulative fluence models have been used in a large number of calculations of the space particle impact. This is reflected in the following publications: N.V.Kuznetsov and R.A.Nymmik , Radiation single event upsets in spacecraft microelectronics caused by solar cosmic rays, Cosmic Research 35(5), 434-446, 1997. N.V.Kuznetsov and R.A.Nymmik, Single event upsets of spacecraft microelectronics exposed to solar cosmic rays, ESA Symposium Proceedings on "Environment Modelling for Spacebased Applications", ESTEC, Noordwijk, 18-20 Sept. 1996. V.F.Bashkirov, N.V.Kuznetsov and R.A.Nymmik, An analysis of the SEU rate microcircuits exposed by the various components of space radiation, Radiation measurements 30, 427-433, 1999 N.V.Kuznetsov, R.A.Nymmik and Sobolevski, Estimates of radiation effect for a spacecraft on the Earth-Mars-Earth route, Adv. Space Res. 30(4), 985-988, 2002. A.V. Dementjev, N.M.Sobolevswky and R.A.Nymmik, Secondary protons and neutrons generated by galactic and solar cosmic ray particles behind 1-100 g/cm2 aluminium shielding, SAdv. Space Res. 21(12), 1793-1796, 1998. N.V.Kuznetsov and R.A.Nymmik, Prediction of the Absorbed doses for spacecraft irradiated by particle fluxes of solar cosmic rays, Cosmic Research 41(6), 585-589, 2003.

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Kuznetsov N.V., Nymmik R.A., Panasyuk M.I. , Sobolevsky N.M., Equivalent dose during longterm interplanetary missions depending on solar activity level, American Institute of Physics Conference Proceedings, Mohamed S., Spinger-Verlag, NewYork, V. 552, 9, 2001, 1240-1245.
The solar energetic particle model fluxes were recalculated to: Interplanetary routes near-Earth satellite orbits and the Earth's atmosphere Nymmik R.A., The problems of cosmic ray particle simulation for the near-orbital and interplanetary flight conditions, Radiation Measurements, 30, 669-677,1999. Nymmik R.A., Predicting the solar and galactic cosmic ray fluxes influencing to the upper atmosphere: dependence on solar activity level, Adv. Space Res. 22(1), 143-146, 1998. Kuznetsov N.V., Nymmik R.A., Panasyuk M.I., The balance between SEP and GCR particle fluxes in Interplanetary space depending on solar activity level, American Institute of Physics Conference Proceedings, Mohamed S., Spinger-Verlag, NewYork, V. 552, 9, 2001, 1197-1202 Kuznetsov N.V., Nymmik R.A., The dependence of solar energetic particle fluxes in the EarthMars-Earth route on solar activity period, Advances in Space Research, V. 30, 4, 981- 984, 2002. Kuznetsov N.V., Nymmik R.A and Sobolevsky N.M, Estimates of radiation effects for spacecraft in the Earth-Mars-Earth route, Advances in Space Research. V.30, 4, 985-988, 2002. This version of the ISO Draft Standard with the 3 supplements ­ Memorandum, Calculation Code (Software - Fortran) and SEP events database (Part 1 ­ 1974-1985 on board of IMP-8 spacecraft measured and Part 2 - 1985-2003 on board of GOES spacecraft measured events) is prepared according to the International Standard Organization Technical Committee 20 (Aircraft and space vehicles), Subcommittee SC 14, )(Space systems and operations) Working Group 4 (Space Environment) 18th - meeting (Toulouse, France, September, 2003) resolution No 166. The work was supported by INTAS grant No. 00-629.

The version "October"of this Memorandum was corrected according to the comments of Prof. G.Bazilevskaya (Russia), Dr. A.Hilgers (ESA), and DR. B. Quaghebeur (Belgiun).

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8. References
Bazilevskaya G.A., Vashhenyuk E.V., Ishkov V.N., et al Catalogue of Energy Spectra of Solar Proton Events of 1970-1979, IZMIRAN, Moscow, 1986. .Bazilevskaya G.A., Vashhenyuk E.V., Ishkov V.N et al., Solar Proton Events, Catalogue for 19801986, Inter-agency Geophysical Committee, Moscow, 1990. Ellison D.C., Ramaty R., 1985, Shock acceleration of electrons and ions in solar flares, Ap.J., 298, 400-408. Ellison D.,C., 1984, JGR 90, 29. Feynman J., T.P.Armstrong, L.Dao-Gibner, and S.Silverman, A New Interplanetary Proton Fluence Model, Journal of Spacecraft and Rockets, 27(4), 403-410, 1990a. Feynman J., T.P.Armstrong, L.Dao-Gibner, and S.Silverman, Solar proton events during solar cycles 19, 20, and 21. Solar Physics 126, 385-401, 1990b. Feynman J., Spitale,G., Wang,J. and Gabriel,S: 1993, Interplanetary Proton Fluence Model; JPL, Journal of Geophysical Research 98, A8,1328,1991. Feynman J., G.Spitale, asnd J.Wang, Interplanetary Proton Fluence Model: JPL 1991, JGR, 98(A8), 13281-13294, 1993 Feynman J., Ruzmaikin A., Berdichevsky V., The JPL proton fluence model: an update, Journal of atmospheric and solar-terrestrial physics, Forman, M.A., 1981, Adv.Space Res., 1, 41. Gabriel S.B., Feynman J.: 1996, Power-law distribution for solar energetic proton events, Solar Physics 165, 337-346. Gleghorn T.F. and G.D.Badhwar, Comparision of the SPE model with proton and heavy ion data, Radiation Measurements 30, 251-250, 1999. Goswami J.N.,.McGuire R.E,.Reedy R.C,.Lal D, and Jha R., Solar flare protons and alpha particles during the last three solar cycles, JGR, v.93, No.A7, pp.7195-7205, 1988. Internet GOES: http://spidr.ngdc.noaa.gov Internet IMP: http://hurlbut.jhuapl.edu/IMP/cpme ISO 15390, Model of Galactic Cosmic Rays, accepted by ISO, 2003, 1. January (document in press). King, J.H.Solar Proton Fluences for 1977-1983 Space Missions, Journal of Spacecraft and Rockets, v.11, No.6, pp.401-409, 1974. Kurt Victoria, and.Nymmik R.A, 1997, The >30 MeV proton fluence size distribution of SEP events, Space Research, v.35(10), 598-609. .Kuznetsov N.V, Nymmik R.A..Popov V.D, Khamidullina N.M., 1999, Predictions of space radiation environment and electronics serviceability in the "Earth-Mars-Earth" spacecraft trajectory, in Proceedings of CREW99 conference, Farnborough, England, September 1999. Kuznetsov N.V. and Nymmik R.A., 2002, The dependence of solar energetic particle fluxes in the Earth-Mars-Earth route on solar activity period, Advances in Space Research, 30(4), 981- 984. Kuznetsov N.V., Nymmik R.A. and Panasyuk M.I.,2001a The Balance Between SEP and GCR Particle Fluxes in Interplanetary Space, Depending on Solar Activity Level, in American Institute of Physics Conference Proceedings, 2001b., 552, 1197-1202, N.Y.: Spinger-Verlag, (Proceedings of conference "Space technology and Applications International Forum 2001", 11-14 February 2001, Albuquerque, New Mexico, USA). Kuznetsov N.V., Nymmik R.A. and Panasyuk M.I., 2001b,The balance between fluxes of galactic cosmic rays and solar energetic particles, depending on solar activity, in Proc. of ICRC2001, 3193. Lee, M.A., Fisk L.A., 1982, Space Sci. Rev. 32, 205. Lingenfelter R. E. and H. S. Hudson, Solar particle fluxes and ancient sun, in Proc. Conf. Ancient Sun,. Edited by. Pepin R.O., J. A. Eddy and R. B. Merril, pp.69-79, 1980. Lockwood J.A., Webber W.R. and Hsieh L., 1974, Solar flare proton rigidity spectra deduced from cosmic ray neutron monitor observations, JGR, V. 79, No. 28, 4149-4155.
82


Lockwood J.A., Debrunner H., FlÝckiger E.O., and GrÄdel H., 1990, Proton energy spectra at the sun in the solar cosmic-ray events on 1978 May 7 and 1984 February 16, ApJ., 355, 287-294. Lovell J.L., Duldig M.L., Humble J.E., 1998, An extended analysis of the September 1989 cosmic ray ground level enhancement, JGR, 103, A10, 23,733-23,742. Lu E.T ., Russel J., Hamilton J., McTiernan J.M., Kenneth R. Bromund, 1993, Solar flares and avalanches in driven dissipative systems, Ap. J., 412, 841-852. Kuznetsov N.V., Nymmik R.A., Popov V.D., Khamidullina N.M., Predictions of the Radiation Environment and Electronics Serviceability in the "Earth-Mars-Earth spacecraft trajectory, Space Radiation Environment Workshop, Farnborough, England, 1-5 Nov., CDROM. 1999. Kuznetsov N.V., Nymmik R.A., Panasyuk M.I., The balance between SEP and GCR particle fluxes in Interplanetary space depending on solar activity level, American Institute of Physics Conference Proceedings, Mohamed S., Spinger-Verlag, NewYork, V. 552, 9, 1197-1202, 2001. Kuznetsov N. V., R. A. Nymmik, M. I. Panasyuk, Models of solar energetic particle fluxes: the main requirements and development prospects . ­ Invited report on the 34th COSPAR Scientific Assembly, Houston, 2002, Unpublished invited report on the 34th COSPAR Scientific Assembly, Houston, Oct. 2002. Paper is available on the website http://srd.sinp.msu.ru/nymmik/, 2002. Mazur J.E., Mason G.M., Klecker B., McGuire R.E., 1992, The energy spectra of solar flare of Hydrogen, Helium, Oxygen, and Iron: evidence for stochastic acceleration, Ap.J., 401, 398410. Mazur J.E., Mason G.M., Klecker B., McGuire R.E., 1993, The abundance's of Hydrogen, Helium, Oxygen, and Iron accelerated in large solar particle events, Ap.J., 404, 810-817. Mottl D.A., and R.A.Nymmik, Solar activity and solar energetic particle events, Izvestiya Akademi Nauk, ser. Phys. 65(3), 313-316, 2001. Mottl D.and R A.Nymmik, Databases for solar energetic particle models: methodical uncertainities and technical errors, Unpublished invited report on the 34th COSPAR Scientific Assembly, Houston, Oct. 2002. Paper is available on the website http://srd.sinp.msu.ru/nymmik/, 2002. Mottl D.A., and R.A.Nymmik, Errors in the particle flux measurement data relevant to solar energetic particle spectra, Adv.Space Res. 32(11), 2349-2353, 2003. Mottl D. and R A.Nymmik, The standard energy spectra for solar energetic particle models, Unpublished invited report on the 34th COSPAR Scientific Assembly, Houston, Oct. 2002. Paper is available on the website http://srd.sinp.msu.ru/nymmik/, 2002. Mottl D.A., Nymmik R.A., Sladkova A.I., Spectra of solar energetic protons derived from statistical analysis of experimental data on large set of events, in Proc. of ICRC2001, 3185, 2001a Mottl D.A., R.A.Nymmik and A.I.Sladkova, Energy spectra of high energy SEP event protons derived from statistical analysis of experimental data on a large set of events, "Space Technology and Applications International Forum 2001", Albuquerque, NM, Ed. Mohamed S. El-Genk, American Institute of Physics Conference Proceedings, Vol. 552, 1191-1196, Springer-Verlag New York, 2001b. Niehuss K.O. Euler H.C., and Vaughan W.W., Statistical technique for intermediate and long-range estimation of 13-month smoothened solar flux and geomagnetic index, NASA Technical Memorandum 4759, 1996 Nymmik R.A., 1993.Averaged Energy Spectra of Peak Flux and Fluence Values in Solar Cosmic Ray Events, Proc. 23rd ICRC, Calgary, v.3, p.29, Nymmik R.A., 1995, Behavioural Features of Energy Spectra of Particle Fluences and Peak Fluxes in Solar Cosmic Rays, Proc. 24th ICRC, Roma, v.3., pp.66-69,. Nymmik R.A., 1997, Statistical and functional analysis of characteristics of the energy spectra of the solar energetic particles, Izvestiya Akademi Nauk, ser. Phys. 61, 6, 1058-1061 Nymmik R.A., Relationships among Solar Activity, SEP Occurrence Frequency, and Solar Energetic Particle Event Distribution Function, Proceedings of the 25th ICRC V.6, pp. 280-283, 1999a. Nymmik R.A., 1999b., SEP event distribution function as inferred from Spaceborne measurements and Lunar rock isotopic data, Proceedings of the 26th ICRC, Salt Lake City,
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Nymmik R.A., (1999c) Probabilistic Model for Fluences and Peak Fluxes of Solar Particles, in Radiation Measurements 30, 287-296. Nymmik R.A., 1999d, Some problems of the Solar Energetic Particle probability model development. Sent to Radiation Measurements in May 1999, no any response from Referees. Nymmik R.A., The main characteristics of the solar energetic particle events relevant to solar activity, 27th International Cosmic Ray Conference, 07-15 August 2001, Hamburg, Germany, ED. W.Droege, H.Kunow, M.Scholer, Copernicus Gesellschaft, 2001, V.8, 3197-3200. Nymmik R.A. and Kuznetsov N.V.,2000, About the dependence of SEP fluxes in the Earth-MarsEarth route on solar activity period, COSPAE Scientific Assambly, Warssaw, 2000, to be published in Adv. Space Res. . Nymmik R.A., Panasyuk, M.I., and Suslov A.A., Galactic cosmic ray flux simulation and prediction", Adv. Space Res. 17, (2)19-(2)30, 1996 Price, P.B., Chan, J.H., Crawford, H.J., & Sullivan, J.D., 1973, in proceedings of 13rd ICRC, 3, 1479. Reames, D.V., Kahler S.W., & Ng, C.K., 1997, Spatial and temporal invariance in the spectra of energetic particles in gradual solar events, Ap.J., 491, 414 Reedy R.C., Constraints on Solar Particle Events from Comparisons of Recent Event and MillionYear Averages, Solar Drivers of Interplanetary and Terrestrial Disturbances, Astronomical Society of the Pacific Conference series, v.95, 1996, pp.429-436. Sauer, H.GOES Observations of Energetic Protons E>685 MeV: Ground-Level Events from October 1983 to July 1992, Proc. 23rd ICRC, Calgary, v.3, p.254, 1993. Sauer H., Preliminary Solar Cycle 22 Event Fluences, to be published. Sladkova A.I., Bazilevskay G.A, Ishkov V.N., et al., Catalogue of Solar Proton Events, 19871996, Ed. Yu.I.Logatchov, Moscow University, (1998). Smart D.F., and M.A.Shea, Solar proton events during the past three solar cycles, J. Spacecraft, 26(6), 403-415, 1989. Shea M.A. and Smart D.F., Patterns of solar proton events over four solar cycles, Proceedings of 26 ICRC, Solt Lake City, 6, 374-377, 1999. Xapsos M.A., G.P.Summers, P.Shapiro, E.A. Burke, New techniques for predicting solar proto fluences for radiation effects applications, IEEE Trans. on Nucl. Science, 43(6),27722777,1996. Xapsos M.A., Summers G.P., Burke E.A., Extreme value analysis of solar energetic proton peak fluxes, Solar Physics 183: 157-164, 1998a. Xapsos M.A., Summers G.P., Burke E.A., Probability model for peak fluxes of solar proton events, IEEE Trans. on Nuclear Science, 45(6), 2948-2953, 1998b. Xapsos M.A., Summers G.P., Barth J.L., Stassinopoulos E.G., Burke E.A., Probability model for worst case solar proton event fluences, IEEE Trans. on Nuclear Science, 46(6), 1481-1485, 1999a. Xapsos M.A., Summers G.P., Barth J.L., Stassinopoulos E.G., Burke E.A., Probability model for cumulutive solar proton event fluences, Proceedings of the RADECS-99, session A-27, 1999b. Xapsos M.A., Barth J.L., Stassinopoulos E.G., Messenger S.R., Walters G.P., Summers G.P., Burke E.A., Characterizing Solar proton energy spectra for radiation effects application, IEEE Transaction on Nuclear Science, 47(6), 2218-2223, 2000. Tylka A. J., Cohen C.M.S., Dietrich W.F., Maclennan C.G., McGuire R.E., Ng, C.K., and Reames D.V., 2001, Energy spectra of very large gradual solar particle events, in Proc. ICRC 2001, 3189. Zwickl R.D., GOES energetic particle correction algorithm, in http://www.ngdc.noaa.gov/stp/GOES/goes_legenda.htm

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