METHOD OF GLOBAL SURVEY (GSM) AND CORRESPONDING TOOLS FOR DATA PREPARATION

Eroshenko1 E., Belov1 A., Abunin1 A., Abunina1 M., Oleneva1 V., Yanke1 V., Papaioannou2,3 A., Mavromichalaki2 H.1 Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation (IZMIRAN) of the Russian Academy of Sciences, Moscow, Russia

2 Nuclear and Particle Physics Section, Physics Department, National and Kapodistrian University of Athens, Zografos3 IAASARS, National Observatory of Athens, Greece

One of the versions of the global survey method (GSM) is developed by IZMIRAN and is used for the calculation of the cosmic ray parameters, beyond the Earth atmosphere and magnetosphere, based on the data of world wide neutron monitor (NM) network. Due to this technique the main characteristics of 10 GV cosmic rays (density and anisotropy) were obtained for each hour over the history of the cosmic ray observation – more than 60 years. This allow us to carry out correlation analysis of various parameters of the space environment (characteristics of the Sun, solar wind, interplanetary magnetic field) with the cosmic ray parameters and study their relationships in the solar-terrestrial space. But before using this method, it is necessary to appropriately prepare the data of neutron monitors. The essence and practical use of the global survey method as well as the tools of the preliminary preparation of data are considered in this work.

ABSTRACT

Method of global survey (GSM)Actually, GSM applied to the data of NMs is a combination of three methods: a method of coupling functions, trajectory calculations of the particle movement in a magnetic field and a method of the spherical analysis. Coupling functions allow carrying out transition from variations of CR in a point of observation to the expected variations on the border of the atmosphere [8-12]. The second component is the method of particles trajectory calculations in the magnetic field of the Earth, which works as a kind of spectrometer. Owing to the change of the Earth’s magnetic field, first, the effective thresholds of the cut off rigidity and, secondly, the effective asymptotic directions of NM stations, change. Trajectory calculations for particles of various energies arriving at different points of the globe are executed for all NM stations of the world network [16,17,21], and allow us to consider the influence of the magnetosphere on primary CR through the reception coefficients [19,22]. Reception coefficients include the influence of the atmosphere, thus, their use incorporates the possible transition from the variations of a detector’s counting rate to the variations of an extraterrestrial origin, reflecting the influence of structure and dynamics of the heliosphere. The third part of GSM is the method of the spherical analysis (e.g., [3,4,7,14,15,18]) which allows to detect spherical harmonics, significant for a specific objective. For example, isotropic and anisotropic variations of the CR intensity outside the magnetosphere in any time intervals. Intensity of CR, as well as any function, can be presented as the expansion in terms of the spherical harmonicas (see, e.g., [22]).

The need to have the global parameters of cosmic rays (CRs) independent of the location of the point of observation on Earth, led to the creation of special methods ("Methods of global survey"- GSM) which use data from as large as possible number of NM stations distributed on the globe. In fact, in all options it is a method of the spherical analysis where expansion of the CR variations in terms of spherical harmonics is used. But the world wide network of neutron monitors registers secondary particles generated in the Earth’s atmosphere due to the interaction of it with the falling primary space radiation.To consider the movement of particles in Earth’s magnetosphere, cascade processes in the atmosphere and properties of detectors, the reception coefficients and coupling functions were invented for each NM station allowing to carry out transition from the variations of the secondary CRs recorded on Earth to the intensity outside the magnetosphere [1,6,13,14,18,22]. In the beginning of the seventies, a modification of this method was developed in IZMIRAN [3,4] and then was changed and improved with the purpose to receive the simplified, but more reliable and convenient method for applications. This option became the basic one, and with its help we gradually processed data of the world network of NMs over the whole period of observation (>60 years).

Introduction

where m – is the number of unknowing parameters of model (m = 5, if to limit by zero and the first harmonicas), and n – is the number of used stations.

The behavior of the reception coefficient for the isotropic component (С00) reflects the ability of each station to register the CR modulation. Additional information about this is presented in Fig.2, where the distribution an expected isotropic variation on the operating now NMs is presented for two power rigidity spectra of primary CR variations. The greatest such ability stations in the range of cut off rigidities Rc from 0.5 to 3.5 GV possess (Mount Washington, Calgary and Climax), and the smallest response to modulation of CR has recently opened Thailand station (Princess Sirindhorn ). The first harmonica of the CR anisotropy

The greatest responses to solar - daily modulation (A11) are recorded at stations at a latitude of about 50° and a cut off rigidity of about 1 GV (Calgary). However, here aren’t present obvious leaders and almost all stations of the world network are capable to observe a solar-diurnal variation, and all together give unique information on the angular distribution of CR. For other rigidity spectrum of the anisotropy a distribution of the amplitude and phase of a solar-diurnal variation can significantly change. And at high-altitude stations with the maximum sensitivity to solar- daily anisotropy these changes are small, and at middle and low-latitude stations which reception cone will extend on longitude, they are much more [22]. It is middle and low-latitude (Rc>3.5 GV) stations that are especially important for definition of a rigidity spectrum of anisotropy

Fig.1.Reception coefficients for zero harmonic calculated by the formula (6) for γ = 0.5. Points depict NMs at the sea level, triangles – in the mountain NMs. Blue crosses are the approximation for the stations absent in the Table

Where Pnm– are attached Legendre functions, θ and φ latitudinal and

azimuthally asymptotic angles in the chosen coordinate system (in particular, it may be the geographic system), n – is a number of harmonic, and m – is a number of component for chosen harmonic. Almost in all cases the CR variations in any point of observation are possible to be presented as the sum of zero and the first two spherical harmonicas of Fourier expansion. In turn, the counting rate variation for i – station can be written down through the reception coefficients as:

Practical use of the Global Survey Method

Here – the contribution of the zero harmonic in to CR variations (isotropic part): A0 – amplitude of the zero harmonic, γ – indexes of the spectra of the variation, which in particular may be defined as A0R-γ– and with which a dependence of reception coefficients on С0(γ) is being achieved; Ax, Ay, Az – three components of the first harmonic of the CR anisotropy, Ci

0(γ), Cix, Ci

y, Ciz

correspondingly, reception coefficients for each component [2].The system of the equations (1) is solved by LSM of minimization of the sum of squares of residuals relatively unknown parameters, characterizing a spectrum variations of primary CR intensity (A0 and γ), and also components of the vector of anisotropy, Ax, Ay, Az. These characteristics are derived in the geographical coordinate system connected with a zero meridian. For transition to the system of coordinates connected with the Sun it is necessary to execute turn on a corner φh = 2π/24(hour + 1/2) [20]. Reception coefficients of the zero harmonic are calculated relatively simply:

Fig. 3. Dependence of the reception coefficients of the first harmonic of anisotropy on the cut off rigidity Rc at the spectra index γ=0.5: (а) С10 North-south component; (б) A11, (в) P11.- solar diurnal component. Points are the NMs at sea level, triangles – at the mountain level, blue crosses- results of approximation

0 0

)(sinsincos),,(n

n

m

mn

mn

mn PmbmaRJ

Here Ak – is the amplitude of the component of the anisotropy at fixed a cut off rigidity R0, and Vk

i – are reception coefficients of the k-component in i-point of observation (station), which may be described as:

Rc

Rc niikik

dRddNRW

dRddNRWRfRRFV

2

0

2

0

2

0

2

0

sin),()(

sin),()(),()),,(),,,((

where λ and ψ – are the latitude and longitude of the point of observation in the geographic coordinate system; θ and φ – the zenith and azimuthal angles of the incoming particles (asymptotic directions); W(R) – the coupling functions of a detector; N(λ,ψ) – directional diagram of a device (i.e., sensitivity of a device to the particles incoming at different angles). Depending on that, the number of necessary harmonics as well as the number of reception coefficients for each station will change. For example, for a zero harmonic one reception coefficient (k=0) is necessary, for the first – three reception coefficients (k=1-3), and for the second harmonic – already 5 reception coefficients are needed for each station [5]. To various k correspond various angular functions Fk(θi(λ,ψ,R), φi(λ,ψ,R)), defining a share of the particles coming to this point under a certain angle (λ, ψ) from the possible asymptotic directions Fk(θi,φi). For the calculation of the reception coefficients it is also necessary to define a type of the spectral function fn(R,β), where β is a vector of a spectral characteristic: in case of a power spectra it is simply a spectra index, and in more difficult cases – a set of parameters.To derive an optimum set of the ak and βk, parameters, defining variations of the primary CR, the least square method (LSM) is usually used, minimizing the following expression taken for each of n stations:

Being limited to the zero and first harmonic (isotropic part and three components of the first harmonic of the anisotropy), the variations of CR expected on Earth can be written as a system of equations for each point of observation of i at h height with rigidity of geomagnetic cutoff of Rc, in t time:

)1(000

ierrz

izy

iyx

ix

ii

i

ACACACCANN

dRRhRWRC ci

R

Rc

iu

),,()(0

where Wi(Rc,h,R) are the coupling functions for the variations of primary and secondary CR for a device i, located at the level hi in the point with cut off rigidity Rc. Calculation of reception coefficients of the first and higher harmonics is very labor-consuming as it is necessary to consider not only the interaction of CR with the atmosphere of the Earth (involving coupling functions of Wi(Rc,h,R)), but also the influence on CR of the Earth magnetosphere, using the directions of the CR movement outside the magnetosphere – asymptotic (see, e.g., [17,21]). We use reception coefficients calculated by a group of Japanese authors for minimum and maximum solar activity. In [22] tables of reception coefficients for a large set of the stations, calculated for various indices of a spectrum γ (-1.5,-1.0,-0.5, 0.0, 0.5, 1.0) and values of the top threshold of energy of Ru above which anisotropy disappears (30, 50, 100, 200, 500, 1000 GV). All these coefficients are entered in the base of the working GSM program and are used at the appeal to various stations during the calculations. Reception coefficients calculated for all stations of the NM network may be retrieved at ftp://cr0.izmiran.ru/GSM/CCn.Calculations of coupling functions and reception coefficients for the isotropic part of CR are carried out at each account depending on the number of stations and the chosen period. At realization of GSM there are often stations used for which reception coefficients are absent in the tables of [22]. In such cases interpolation of the available reception coefficients is performed.

Fig. 2. Distribution of the expected isotropic CR variations on the operating now neutron monitors for two power rigidity spectra R-γ of the primary variations with indexes γ=-1.0 (left) and γ=-0.5 (right).

1. Altuchov A.M. et al. / Proc. 11-th Int. Cosmic Ray Conf., 1969. V. 4. P. 457-460.2. Asipenka A.S. et al. / Adv. Space Res., 2008. V. 43. P. 708-716.3. Belov A.V. et al. / Proc. 13-th Int. Cosmic Ray Conf., 1973. V. 2. P. 1247-1255. 4. Belov A.V. et al. / Izvestiia AN USSR, 1974. V. 38. P. 1867-1875.5. Belov A.V. / Dissertation, IZMIRAN, 1980. 181 p.6. Belov A.V. and Eroshenko E.A. / Proc. 17th Int. Cosmic Ray Conf., 1981. V. 4. P. 97-100.7. Chirkov N.P. et al. / Geomag. and Aeronomy, 1967. V. 7. N. 4. P. 621-631.8. Clem J.M. and Dorman L.I. / Space Sci. Rev., 2000, V. 93. P. 335-359.9. Dorman L.I. / M.: Gostechteorizdat, 1957. 492 p. 10. Dorman L.I. and Yanke V.G. / Izv. USSR, 1971a. V.35. N. 12. P. 2556-2570. 11. Dorman L.I. and Yanke V.G. / Izv. USSR, 1971b. V.35. N. 12. P. 2571-2582.12. Dorman L.I. / M.: Nauka, 1972. 211 p.13. Dorman L.I. / Springer Science+Business Media B.V., 2009. 800 p.14. Krimsky G.F. et al. / M.: Nauka, 1966. С. 105 p.15. Krimsky G.F. et al. / Geomag. and Aeronomy, 1967. V. 7. N. 1. P. 11-15.16. McCracken K.G. et al. / Technical report, 1962. N. 77. P. 77 p.17. McCracken K.G. et al. / IQSY instruction manual, 1965. N. 10. 183 p.18. Nagashima K. / Rep. Ionosphere Space Res., 1971. V. 25. P. 189-211.19. Nagashima K. et al. / Nuovo Cimento C, 1989. V. 12. N. 2. P. 173-209.20. Russell C.T. / Cosmic Electrodyn., 1971. V. 2. P. 184-196.21. Shea M.A. et al. / Can. J. Phys., 1968. V. 46. P. 1098-1101.22. Yasue S. et al. / Nagoya, 1982. N. 7. 225 p.

kk

ik

i

AVNN

00

min

2

1

2

0

mn

VaNNg

D

n

i

m

k

ikk

ii

iCA 00

Calculation of the parameters of the CR intensity I. Definition of the equatorial component of the first harmonic of the CR anisotropy using the data of high-latitude stations. For this step, only high-latitude stations at sea level (RC<3 GV, h> 800 mbar) are selected for which the system of the equations (1) is solved. As at the first stage the full model (5) is used, as a result in each hour the required parameters of GCR are obtained: Ax, Ay, Az – characteristics of the first harmonic of anisotropy of CR; a0 and γ for isotropic CR component. For the calculation of the variations of the NM count rate are used relatively a basic period (Ni/N0), which choice (as a rule, the days identical to all stations) plays an important role. Count rate of each concrete device is defined by a number of difficult accounted factors, and uniformity of the N0 is also certainly broken during the disturbed periods because of magnetospheric and extraterrestrial variations. It leads to false daily rotation of a phase of the equatorial component of the first harmonica of anisotropy, especially, if the calculated period is far from the basic one. In order to avoid this effect it is necessary to change several times the basic period (3-7 times in a month). This procedure isn't reflected in the level of Ax and Ay components, but the behavior of the a0 and Az components becomes multistage that does impossible use of these parameters for the analysis. Their definition is carried out at the second stage of the GSM program operation.II. Definition isotropic and North southern components of the first harmonica of CR variations. In the general list all stations for which reception coefficients of C00 were calculated are selected (RC<17 GV, h>600 mbar). On the basis of the data of Ax and Ay obtained at the first stage and reception coefficients from data of each station the equatorial component of the first harmonica of CR anisotropy is excluded on algorithm:

)2(00ierrz

iz

ii

i

ACCaDD

Further the system of equations (2) is solved relative parameters а0, γ and Аz. The use of more NM stations significantly increases the accuracy of the results obtained. In the course of working with GSM a number of offers, which are given below, are collected on improvement and more optimum use of a method1.Specification of model rigidity dependence of the isotropic part of the CR variations. 2.Replacement of power spectral function with more complicated ones that has to affect, first of all, big FDs.3.Introduction of the second harmonic of the CR anisotropy to the variation model.4.Account of the magnetospheric variations.5.The better choice of the basic periods.6.Definition of the rigidity dependence of the CR anisotropy and/or accounting of its changes (that is essential at large anisotropy). 7.Accounting of the changes of coupling function (and, consequently, of the reception coefficients) along the time.8.Improvement of quality of the input data. 9.Barometric coefficients refinement and recalculation corresponding corrections. Sometimes other atmospheric effects are important (for example, wind effect on sub polar and mountain stations, snow effect…). 10.Addition data of other detectors (first of all, muon) to the data of NMs. The easiest way – to add differences of variations from azimuthally directions of the same telescopes.

MODE of Manual EDITING DATAFor effective use of GSM and receiving reliable results it is necessary to have qualitative basic data. As NMs work in the continuous mode, for the long period of registration drifts and other deviations from normal work are natural. Variations of a hardware origin are extremely undesirable at data processing of a network. In fig. 4 the example of the most frequent and typical distortions of data which can meet at the stations is given. One can see three kinds of possible artifacts: points (1); graduate change of count rate (2), snow falling or graduate removing, drift in electronic sensivity…); sudden jump from current level during some interval (3), removing snow, exchange counters or electronic…). For amendment of such data we use DataEditor program.

Fig.4. Total view of the editing form in program DataEditor and examples of the data with false variations.

DataEditor allows correction of point errors: to edit its value or exclude this point, attributing it value 0. Artifact 2 – graduate decrease or increase of count rate. It is necessary to select right time interval and fix its left point by button combination "Ctrl + L". Then, correct edit line (by right end) until ratio coefficients in the base and editing intervals become equal (fig. 5). Artifact 3 – sudden up or low jump in the counting rate. In DataEditor we expand interval of editing and change count rate of ‘edit line’ by such a way for ratio ‘base line’ and ‘edit line’ in the basic interval was equal to ratio of the same variations in editing period.

For effective use of GSM and receiving reliable results it is necessary to have qualitative basic data. As NMs work in the continuous mode, for the long period of registration drifts and other deviations from normal work are natural. Variations of a hardware origin are extremely undesirable at data processing of a network. In fig. 4 the example of the most frequent and typical distortions of data which can meet at the stations is given. For amendment of such data we use DataEditor program.

This Form is divided on five areas. A – area of plotting of the CR variations at choose NMs. In the top right part there is a legend with a list of choosing stations and attributed numbers. In the area B ("CURSOR") an information on current location of the cursor is placed, or, about diapason of data editing. In the field of C ("BASE PERIOD") the user has to define base period relatively of which the CR variation will be calculated. In D area ("RATIO") the ratio of variations between basic and edited stations within basic and edited intervals is gone out. E ("HELP") contents the information on the button combination and corresponding commands.

yiyx

ixii ACACDD *

The remained data D*i practically contain a response to the isotropic

part of the primary CR and to a North southern component of the first harmonic of anisotropy:

Fig.5. Data of two NMs after correction

References