Barometer Coefficients of High Latitude Neutron Monitors

Barometer

Coefficients of Ｈ返ｈ Latitude Neutron Monitors

        Masahiko KuSUNOSE

Ｄｅｐａｒtｍｅｎt of Infoｒｍａｔｉｏｎ Ｓｃｉｅｎｃｅ, Ｆａｃｕlりｏｆ Ｓｃｉｅｎｃｅ      Ｋｏｃｈｉ Ｕａｉｕｅｒｓitｖ, Ｋｏｃｈｉ 780, Ｊａｐａ几

Abstract:The

cosmic ray monitor is used to measure

the primary

cosmic ray intensity･

The counting rate of neutron monitor is affected by the atmospheric

pressure variation.

The amplitude

of the variation in the counting rate caused by the atmospheric

pressure is

usually larger than that of the primary

cosmic ray intensity. It is very important

to derive

ａ certain approprヽiatebarometer

coefficient to make ａ reliable correction of the counting

rate for the barometric

pressure. To decide the barometer

coefficients of the neutron

monitors, it is necessary to separate the intensity variations caused by the primary

cosmic

ray itself and that due to the pressure variation. To this end, we

adopted

the spherical

harmonic

analysis using the neutron

monitor

data from

about twenty

stations located in

the high latitude region where

the geomagnetic

cutoff rigidity is below

2.３ GV. The

primary

cosmic ray variations are removed

from

the observed data, and thus the residuals

are derived. Through

the study of the correlations between

the derived residual and

the

daily mean

pressures, reevaluation of the barometer coefficients was made by using

twelve-years data from January 1966 to December 1977.

The re-evaluated barometer

coefficients for every year were tabulated. The result shows that the re-evaluated

barometer

coefficients at ａ few stations are considerably deviated from

the conventionally

used coefficients. Further

analysis is made

0n the data observed at the selected eight

stations, where complete twelve-years data were available. As ａ result,it is found that the

long-term

variation of the revised barometer

coefficientsis correlated in positive sense

with that of the cosmic ray neutron intensity levels. The barometer

coefficient depends on

the cosmic ray neutron intensity. The dependence in the solar quiet period is stronger than

that in the solar active period. Using

the -ｒiがdityspectrum

of the barometer

coefficient

and

the cosmic

ray

neutron

intensity at sea level,the dependence of the barometer

coefficient on the primary

spectrum

variation was

estimated by numerical calculation｡

 The result shows clearly that the variation rate of the barometer

coefficient against the

cosmic ray neutron intensity is influenced by the changes in the cutoff rigidity and in the

primary

spectrum.

Key

words : Cosmic

Ray, Neutron

Monitor,

Barometer

Coefficient.

      1.

Introduction

1 0

Res. Rep. Kochi Univ. Vol.46

Most

of the primary

cosmic rays are the galactic cosmic rays arriving onthe top of the

earth's atmosphere

from

outside the earth, while the secondary ones ａｒｅｿthose

produced in

the air through nuclear interactions between the primary 姉smic ｒａ沁∧andair nuclei. It is

well known

that most

parts of the primary

cosmicニ血y………jうarticles

wh:6砲ニhighest energy

amounts to the order of 1022 eV have their origins in the universe outside the solar system and ａ little ctﾆ)ntribution from the sun is recognized as the so-called solar cosmic rays with

energies of the order of 109 eV.       ∧       ‥        上

一〇ｎ the travelling iourney ofﾄthe primaryﾚcosmic rayくparticlesしfromﾚt畑･outside of the solar system toward the earth, they usually sufferイrom various kinds of modulations such as scattering, degradation and deflection owing to the ordered or disordered interplanetary

magnetic field as well as the earth's magnetic field. AS□ａ result, cosmic ray intensity

variations observed on the earth are influencedﾚby

Time modulations of the

primary cosmic

ray

several………typesof modulations.……

にinte邨沁y一include∧theニtransient and

long-term variations. The former is the Forbush decrease,ニsolar cosmic ray event. diurnal

variations and so on. The latter is the periodical fluctuations caused by the rotation of the

sun and the eleven-year solar activity change. These two kinds of modulations can be

detected easily on the earth's surface. Whdしwe observe……･t･he cosmic rayぺ……i･ntensityby………the

neutron monitor on the ground, the atmospheric and temperature effects on the secondary

cosmic rays are usually superposed on the primary cosmic ray modulations. It is very

important to discriminate the primary and secondary modulations as precisely as possible,

tｏ上show characteristics of the respective modulationsト……=J :=:1I=JII      し.････.････       .･･.

 Since the primary cosmicトray modulations are concerned with three dimensional

anisotorpic flows of cosmic ray particles in space, the spherical harmonic analysis is one

of the most useful methods to understand the physical ch征racters of the modulations. For

example, this analysis was applied by Yoshida ｅt al. (1971)上如＼the studies of the Forbush

decrease and also by Nagashima (1971) to the solar ａうd sidereal anisoｿtropies. For these

studies are essential the data from ａ network of cosmic ray stations distributed uniformly

over the globe.      ..

 In the earlier stage of cosmic ray modulation studieらくcontinuous monitoring of the

secondary cosmic ray intensity had started by∧using the∧畑皿zation chamber･that is one =of

the most simple and stable instruments to detect: the c（始血ic ray ｍｕｏｎﾉｾﾞomponent. After

that the precision ionization chamber was developed by Compton ｅt al.(1934) and four

sets of the identical chambers were installed at four different stations:

Huancayo, Cheltenham, Christchurch and Ｇｏ曲尽ｖｎ･. InJ如4れ，･five sets gfﾚthe Nishina-type ionization chambers had been constructed 拍ｒ the ai ｢毎卜establishing a =ねimilar network

system of observations during the period 1934 − 1941 (Ishii↓1944). Four Compton-type and one Nishina一七ype of chambers have been in satisfactory operation for more than 40 years (Ｋｕｓｕｎｏsｅand Wada, 1969). Muon data accumulated during such long period are usefulイor

the studies of the 11-year solar cycle modulations.  …………:ﾚし.･･.･.･    ･.=.･･･..     ･･犬

 Muon observations were further ･extended to ａ ｎｅｗ∧technique of multi- directional

telescopes using plural arrays of the Geiger-Miiuller counters and/or plastic scintillation counters. This observation method has made possible ＼ｎｏt＼only improvement of the

目０

】 ０ ０

９０

95

Barometer Coefficients of∇High Latitude Neutron Monitors (Kusunose) 11

statistical accuracy but also directional surveyり of modlｕ毎tions in space at aりtation.……  Another important component of the secondary cosmicしrays is theくnucleonic犬component

仇at has the energy response tｏ＼theprimary cosmic汁ays different from that of:the muon ｃｏポponent and it h乱S little effect of the atmosphericトtemperat計eレSimpson犬(1957)

developed the first standardized device for measuring this component↓一万which is called 曲ｅ

IGY-type (InternationalﾚGeophysical Yearレ1957卜↑958)△of neutronつmonitors〉ａれd has been

in operationしthroughoutへthe world. The dataﾄobtained by this deviceﾚ尽ｒむnow widelyコsed by many cosmic ray investigators through the二World Data Centers for Cosmic Rays.  Cosmic ray neutron data obtained by the neutron monitor have]been highlyしevaluated by improving the IGY-type ･into the IQSY-typeニ(Inter皿tionaト･Quiet ・Sun .･Year, 1964√1965)｡ using the largeしneutron ＣＯＵｎｌteｒ十Ｗ社hしdetection･sensitivity incr阿斗ng･ by an･orderトof

magnitude higher than that of IGY ･neutron counter (Carmichael, 1964)レThe number of

IQSY:neutron monitors being now in operation ａｍｏｕ緋s to about∧fifty. ‥‥‥‥‥‥‥‥

ヶFluxes O仁cosmic ｒａy∧nucleoれic componenトare modulated∧in the atmosphere. Counting

rates of the ground-basedトneμΓon ｍｏｎ辻ｏｒａｒe]very sensitive to the atmospheric pressure variations, therefore the monitor seems to beﾆa kind of barometer. As is shown in Fig. 1, the amplitude of n卵七ron intensity variations due to pressure variations exceeds usually the primary cosmic ray intensity variations, eχcept in cases of the Forbush decrease and the

   十  ・･．･．･･･  DEEP RIVER ＮＥＵＴＲＯＮＭＯＮＪＴＯＲ………NOVEMBER 1966ニ＝‥‥‥‥‥

  １ ･２ 3 4 5 ６ ７ 日・日ＩＯ□ １２ト１３ １４ ．１Ｓ･１６ｊｌフ･１日／1日･20 21 22･23 24･２５ ２６ ２７２日２Ｓ ３０

０Ｒ[⊃Inote: SCRLE Ｓ.０ PERCENT      ト  ト 尚 ‥‥‥‥‥ト  ･･    ，ト  ．．  ト

       ㎜     ・       ・        ・ ■■     ■Fig.l. Deep River neutron monitor intensity for November 1966. The upper curve shows the

    intensity before correction, the lower curve, the intensityﾄafter correction foratmospheric

 Ｔｈｅ即Ｕtrｏｎ皐面ltＱｒこisごａ（ｄeｖjc６ｔｈａt ldete収（仙（叫§面（ニ=IT功夕………レil収1面れ……=………Cｇｍ加面峠;／ｌt CO耶iStS<of＼an＼昨rayjo仁BF.3わropニor仏)n耐∇couh坤叫レニj・叫叶面面組∧叶ゾ…… Ｉ dQ仙加………琳妙叫こミ./6fＩ･−・・lle昧..d･．1nd 釦1ye仏y1e面（or十p=吋4哨n).……=Th。j nIQutrI6h 万串卵㈲礼j……毎面叫二叫尚尚4ダ……=j4―φ=ぐφれ44yyjII宍1 吋od如6d 1loむaｕｙ好＼1nニu巾a（坤;eract沁nｉノbotｗe卵………jIエ―tニれ.ニり.万I―万エJhjixjjぐIJIり―φれ.iIIりj―I―I―J―=2ぐニφ加袖呻叶Ta頑ケエ1叫d<卯巾iづ 1ｔ縦iｍ面tta牡ｔoダexc但dee面i坤h出 .e耳ta1―.―.=b.adk―gれ ｍ４tet伍佞加tSidｅｔｈ（ｍｏnit吋犬by▽the=面1ｙeth=yI面φニレ尚叫d―y―),怖緋……エ=ぐ .。φjJれ｀tニ4iIねI5ニ――j。―=41jれ.iIiと―れニわjφlラcφInI―tI芦ｇe―of

Barometer Coefficients of High Latitude Neutron Monitors (Kusunose) 13

neutron), being∼3820 barns （1 barn ＝10-28 ｢）ａt thermal ぽergies (l/40eV). As the

counter is operated in the proportional region, it is easy to discriminate large pulses caused

by me nucleus from somewhat small pulses produced by muons, electrons or gamma rays

passing through this counter. Alpha pulses thus detected have one-to-one correspondence to ･incident nucleons｡

 Around each counter there is an inner moderator, the function of which is to slow down fast neutrons to near thermal energies to facilitate their capture in the boron trifluoride. Surrounding the inner moderator, there is the producer in which the evaporation neutrons are produced. Besides, the entire device is enclosed by ａ reflector that reflects the neutrons also moderates them. The reflector has the additional function of absorbing and

reflecting unwanted low energy neutrons produced in the atmosphere and in materials close to the monitor.

2.2. The IGY

and NM64

monitor

 As shown

in Fig. 2，a full size of the standard IGY

type neutron monitor

contains 12

counters and usually is divided into ａ duplicate unit consisting of six counters each. The

total counting rates of the monitor is ∼ 24,000 counts/hour

at a high-latitude sea level

Table l. Comparison

of the dimensions and counting rates of various cosmic ray

     neutron monitor designs. (Hatton, 1971)

Number

of counters per channel

Ｃｏｕｎtｐ.ｒＲ

 Active length(cm)

 DiameterCcm)

 Pressure(cm Ｈｇ)

Ｉｎｎｅｒ

ｍｏｄｅｒａtｏｒ

 Average thickness(cm)

Ｐｒｏｄｕｃｅｒ

 Average depth(g ｃｍ-2)

 Area per channel(mO

 Length parallel to counters(cm)

Rｅμｅｃtｏｒ

 Average thickness(cm)

Ｃｏｕｎtｉｎｇｒａtｅ(1962)＊

Of a high latitude sea-level station  Per channel per hour

 Per ｍ２ of producer

Standard

  IGY

６ 86.4  3.8 45 3.2 153  0.94 102 28 ∼12000 ∼12800 leeds IGY ６ 41  5.1 40 3.3 153  0.72 76 28 ∼9000 ∼12000 Ottawa １ 69 6.35 56 5.4 285  0 61 17 13 ∼6000 ∼35000 NM64 ６ 191 14.8 20 2.0 156  6.21 207 7.5 ∼250000 ∼40000

The counting in 1962 has been adopted as representative of the average counting

rate over the solar cycle.

14 _{Res. Rep. Kochi Univ. Vol. 46 （19り7）犬Nat.}

station. Dimensions

of various types of the neutron monitors are summarized in

Table 1.

 Ａ radical change took place in the design of neutron monitors from

the need for ａ much

larger counting rate the order of 10" counts/hour

ｏｒ詐印加r), which leads to the improved

statisticaトaccuracy of neutron  monitorｹﾞ上data. TheﾔNM64 monitor犬was

designed

(Carmichael,

1964)

by

using large

(BP28)

BF3

pΓφ面巾onal counters

developed･ by

Fowler(1963).

Figure 2 shows its geometry.

The quanti蝉ｏ白°B in the effective volume

of

each counter should be approximately

2.1×１ＰａtｏｍＳ.犬

O…………= 50   し １ １１１１ １ １  CENTIMETERS

に7ご］POLYETHYLENE . EEI LEAD

      NM ６４ MONITOR      し IGY  Ｍ●ＯＮＩＴＯＲ

Fig.2. Plans and elevations of ａ ｓiχ-counter一一unit of………ド:M64neutron:……monitor and ＼ｏｆ ａ     twelve-counter unit of IGY neutron monitor. Incidentｿﾞ五ｕｃ］earparticles interact ｗ社ｈthe     lead target yielding evaporation neutrons that are moderated in the inner polyethylene     sheath (paraffin for ＩＧＹ）ａｎｄcaptured in the gas of the counters. The drawinＳＳ show     the structure of the NM64 and IGY neutron monitors on the same scale.

    （ＩＧＹ:Simpson, 1957 and NM64: Ｃａｒ血1chae1，1964y‥‥‥‥‥‥ ‥‥万

 An innovation in the NM64 monitor design was the………useof polyethylene in place of

paraffin as the inner moderator. This alternation enabled the counter with ａ moderator to be manufactured as ａ single assembly. Paraffin:wax ａＵｄ∧polyethylene are both composed of carbon ａｎｄごhydrogen, and essentially theﾀﾞcarbon∠hydrogen ratios are the same. The use of polyethylene reflector has also been ableくtｏ･ｍａｋ=ｅ･（.くconvenienti.面･tallation that the producer of lead could be placed directly on the lower ｐ皿tion of reflector. A full-size of

Barometer Coefficients of High Latitude Neutron Monitors (Kusunose) 15

counters each. The counting rate of one unit of 18-NM64

1s ∼750･,000 counts/hour

at a

high latitude seaしlevels七ation.

2.3. Multiplicity and total counting rate

 Multiplicity means the number of neutrons produced in a single nuclear reaction. Cosmic ray nucleus interacting in the lead ･’･producer of the neutron monitor result in 曲e multiproduction of evaporated neutrons within the short time interval of about 1 μsec.  The total counting rate yｖ is given by the product of the intensity 7， the interaction probability ？， the mean multiplicity of neutrons 771, and the detection probability ｅ . Thus

      十      N=IPm A,      (2.2)

where A is the effective area of the lead in the monitor.

 Multiplicity measurements have been performed for the IGY neutron monitor (Bachelet

 屹 ｢･, 1964, 1965; Kent ｄ al, 1968; Dyring and Sporre, 1966a, 1966b) and the NM-64

neutron monitor (Griffiths ｄ aL, 1968; Blomster and Tanskanen, 1969;Agrawal ｄ  ｢.，

1969; Smirnov and Ustinovitch, 1969;Lockwood and Singh, 1969).        ．.

 Hughes and Marsden (1966) suggested that the detected multiplicity spectrum would

reflect the energy dependence of the primary cosmic radiation. The spectral response functions were determined experimentally by latitude surveys carried out at different phase of solar cycle (Kodama and Inoue, 1969).

The neutron multiplicity distribution depends upon the geometry of the neutron monitor, for instance, the arrangement of the monitor pile, or the number of operated neutron counters (Hatton and Carmichael, 1964; Fujii有心よ1972).

 According to Kodama and Inoue (1970), it is known that the barometer coefficients and the magnitudes of intensity variations as observed in the solar proton and Forbush decrease events are decreasing ｗ此h the increasing multiplicity, while no significant multiplicity effect is recognized in the diurnal variation.

 It is expected that the time variations in the rates of the detected multiplicities will reflect the characteristics of the primary energy spectrum of the cosmic radiation, and then this matter will be useful in the study of the various time-dependent phenomena of the

cosmic ｒａy･

2.4. Contributions made

by the various components

 Cosmic

ray neutron monitors

are sensitive to the secondary

components

of the nucleon

cascade, which are generated in nuclear interactions throughout

the atmosphere.

Many

authors

have made

the quantitative estimations of

the contributions of the secondary

components

to the total counting rates obtained by the neutron monitor (Simpson

ｅtｄ.，

1953; Hughes

and Marsden,

1966)｡

 Hatton

(1971) made

ａ certain significant improvement

on the calculations of Harman

and Hatton

(1968) to incorporate more recent data of the various parameters required. The

results are given in Table ２ for both

the IGY

and NM64

monitors,

where the fractional

!6 Res. Rep. Kochi Univ. Ｖ 46 Nat.

counting rate of ａ neutron counter is in general due to se帥りdary neutrons, protons, muons captured in the detector. The daily counting rate from each componeni, Ｎｉ,was calculated under the assumption that the various components makeﾄthe sa皿e fractionalΛcontribution to the interactions in the moderator and surroundings as that in the producer｡

 The contributions made by the various components are found上to be comparable for the

two monitors, although those are not identical.………yl:naddition, because the uncertainties in those contributions are not independent for the two monitors, the differences are important and may be interpreted in terms of the ﾄreducedニreflectorﾄthickness in the NM64 monitor.

Table 2. The contributions made

by secondary componentsｻﾞto the counting rate

      of

the IGY

and NM64

monitors. (Hatton,二1971) し   ：

Component

Neutrons

Protons

Pions

Stopping muons

Interacting muons

Background

 Daily counting･   rate 161200  15200  2530  9150  4800  2000

   ％ 犬

Contribution

 Daily 皿 ･一一rate ｻ 4 8 5 7 0 0 0 4 2 3 0 0 0   ・ 5 8 0 0 0 … … 2 1 2 0 0 0 : I レ 1 1 8 0 0 0 ／   6 0 0 0 0

   ％

Contribution

85.2±2 犬7.2土t.0  1.0±0.3  3.6土O･･.7 2.0土O=.4  1.0 Predicted total Observed total 194880 216000 83.6±2ト］  7.4土1.0  1.2±0.3  4.4士0.8  2.4士0.4  1.0 5 7 2 8 0 0 0 6 0 0 0 0 0 0

 The contributions given in･Table 2 are applied如 a high latitude s6ぷlevel station with a thin roof above the monitor. It may be expected :that they will vary slightly at individual stations dependinぼ･ upon the thicknessトlhd一一material 0fしthe roof. They areトalso average values for the solar cycle. During the 1954-65 solar cycle the total intensity of a high latitude sea-level neutron monitor decreased by "ヽ･18% while that of ａ muon monitor

decreased by ∼5％.       づ

      3. Spherical Harmoりjc Analysis      ト

 As

a first approximation

the external magneticトfield of the earth can be represented by

ａ dipole located in the center of the earth. The

fiｒ昨geophysicaトapplication

of

the

spherical harmonic

analysis was Gauss's

analysis of the potential of geomagnetic

dipole

field (Gauss,

1839), and since then spherical harmonic

analysis has been used for various

studies that must

represent geophysical quantities∧asfunctionsﾚ吋spherical coordinates. In

the present section, the spherical harmonic

analysis is aうplied to the cosmic ray intensity

variations observed by the worldwidりnetwork

of上前ｏｕr!dﾚbased

neutron monitorsに

Barometer Coefficients of High Latitude Neutron Monitors∧(Kusunose) 17

3｡1. Cutoff rigidity       ∧  十        二    ト 1  ｡１

 Ａ charged particle is characterized by the rigidity R=pc/ふぃwhere ふ is the charge and

p the momentum of ａ particle, and c the velocity o卜light. The rigidity R is usually

expressed in unit of [ＧＶ]. It has been shown〉=by Stormer (1955) that particles with any rigidity less than ａ critical value Ro (cutoff rigidity), are unableくto reach a specificｻﾞpoint

ｏｎ丿he earth's surface, The cutoff rigidity Re is given by ‥十一.j………

R｡∠器cos'

B,

(3.1)

where n is :the radius of the earth,θ the geomagnetic

latitude of: the point ａｎｄへM the

dipole moment

of :the spherical harmonic

expansion of the magnetic potential 0f the earth.

 To have ａ full knowledge

of the cutoff rigidit如sat different geographic locations on the

earth is O仁great importance

in the study of the energy spectrum and

modulations of

primary

cosmic ray intensity.      ＼  ＜     /

3.2. Asymptotic directions of approach    ∧    ト      ＼   ＝ ＼

 Information耳bout the directions of propagation of a cosmic ray particle in the

interplanetary space before they enter to the vicinity:of the geomagnetic field is required for the study of the spatial dependen叩of primary cosmic rays. The cosmic ray particles that arrive at any point on 怖ｅ earth's surface haveコbeen deflected in尚the geo皿agnetic field.  To relate the time variations of cosmic ｒａyこintensities observed on the ground to the time variations and anisotropy of the primary 6(沁耳lierays in the interplanetary space, it is essential for the analysis of the data to take into: account these deflections.・..   ..  Suppose that cosmic ray particles having a rigidity R arrives from仙ｅ vertical direction｡ in average, at a location on the earth surface, where the geographic latitude and longitude

are <p, and λ Γespectively. Those cosmic ray particles aｒe∧deflやctedin the geomagnetic field as shown in Figへ3. Let us refer the direction of approach before their entering into

− ｊ（Ｒ沁八）

     StationLongitude       ＼ 犬      ＼． ＼ 十      ＼

Fig.3. The trajectory of a charged particle through the geomagnetic field. Illustration of the      def毎毎on of the asymptotic direction ｏｆトapproach. (MoCracken et al., 1965).

18

￣￣Ｚ￣'￣ｌ'･･． ・   ． ･･・ ．・   ．  ･･･ふ   ・･･・．・ ･･．･･･一一 ･．・．･･．：･■■■■■ ■■■

Malmfors (1945)☆皿d Brunb雨Jﾚand Dat:ｎ:eｒ=員9卵卜水卜=聯y=j万作（毎牡皿ﾉ卵s/如eh……1･nvestigated

by Stormer (1955), Jory (1956), and Lus卜部dy……拍血㈱れ=j……(1957)………〉ヶﾆ:………1………∧:ﾉ…………:万…………几……=………＼……万

 Thド：orbit 0仁a negatively charged partic:↓･e･ ･I血.:φ々.･1り倉･=･J=.:j.J.゜.φ.ji,ｷﾒ

the earth i乱dentical:with th･e ･･･.･orbi･t･of a･posit･ﾊﾟ/e･･=:=うj4が.t:1･(う万l･0..:j･::万of:･,..･0.φj･･４

earth脂om the outside andく蛍t血ately arri対噌…………at the………皿垣ｅ/……location.………Pro･･ぽｒla･ms･and

methods尚曲at use the differential equationいｏ仁面水皿ﾉ……ｿﾞ………ﾄ∧◇〉):･し万………I.………＼･＼………:･:………)＼‥‥‥‥‥‥‥

tｏし畑ｃ垣りth白皿thくof aｿparticleﾀﾞofy･charge∧q and →... ･･･.･･ ･･･ .･.･.･･

B by numericalトintegration, have been

   ｇ         Ｗ  ．●一一    ●四    ・・･･･  ・ ・

and the references there in):. In theうreseねtxyφおく:､lにtwo t

mainly in the即och of 1955し[McCracken it etｹﾞ皿ｿﾞﾚ……]坤65)一万j巨面万.:･p･artl一 琵琵∧aLに1983) wereトused:………I………犬………=､1…………/∧:∧ﾄ……1:……〉:………/j……呂……1万jj

3jレMethod of the∧spherical har ｢onic analysiﾚ4=/………1………=:ﾚｽ……＼………=＼=｀ﾌﾟｿﾞ…………￨………ﾌ…………=･＼宍･.･にI･.:  Here, Ｈｅ呻ﾝﾚwe we describe thedescribe the method十〇卜‥‥ ‥‥∧ﾚﾅﾚ∧＜ﾉ…………=:ﾉ=宍ヶｿ…………ｹ…………ﾉﾉ……1………:ﾚ…………method∧ｏＬト

analysis aceぱd垣gしto Yoshida入沁/禅屁

(1971):ﾚA functioれイ(θレφ)しdefined on

ａ･spherical ｓｕ球収e/ in .･termsユof the∧∧

うolar coordinates θ and ψ，=卵胞own

加F収一 六

4, is expa卜ded into ａ serie:s of

theﾚ印herica卜harmonic functions as… ……:

  プ(（φ＝Σダ=(肌φ)………(抑)○………  へ∧ ＜，･1-0   11    .1 ‥‥‥ where      ダ ‥‥‥‥‥‥ ‥‥ ‥   ‥‥‥‥ ΥλOi〉φ)=トＣｉＰ.(０√(p)＝ …… ………… ．：．・ ．･： ■■ ■ ･．Ｚ． ･．       ‥ ．･ ･ ……ｊ … ………=ｊ°十万jΣ{A＼･}じｏｓｍ＜p………I……    ヤ    ペ批=●l ･･    ･. 尚･ ．･ ∧≒   ………=‥‥‥デÅ'"'･' sin 171'φ}戸戸COSの……… ‥‥‥万‥‥‥‥ ‥‥‥‥万  犬 ダ(3.4) ﾚ ｿ ﾞ ﾉ … … … … : … … … = = … … … ゛ : ( 3 . 2 ) 皿:4………ａね夕｀φかotic ダ:幽目……epoぐれ, of ７￡ φ etic field ･.√1983, direct如ns, 1975 (Inoue

1cし

n of

Ｙ ｅ ｎ ｏ Ｉ Ｐ １ ０ −︱ 稗1如t沁丿如こordinate･gｙ叫:ems. itude,〉latitude

Barometer Coefficients of High Latitude Neutron Monitors (Kusunose) 19

 In the above equation, Al""^,召呻，ａｎｄ

Ｇ are harmonic

coefficients.The sum

of the terms

ｕpトto the second order of 1=2, is given as   十十       △

y(０. <p)＝ ゛ ｀ ’ ２▽ 乙 ＝ _{n（０, <p）} where       ∧    :      し  ‥‥‥‥‥      ‥‥‥‥j   十 十   ･ｙo(θ，妁＝Ｇ几加sθレ……1   ∧       ニ ニ       ｎ(肌炉)＝ CiPi(ｃｏsθ)十(ぶ1)qｏ岬十ろび)sｉｎｍ武)晋(ｃｏsθ)，      ＝

＼        ｙ2(０バ))＝ＧＲ(cosθ)ご十(洵1)co岬十召び' sin mcp)月(cosθ)ニ   ）     ＼      十(湘2)eQs収)十召Pjsin恥)月(co･Ｊ). 上 ‥‥‥‥‥ ‥  Further, the associated Legendre functions 戸戸･(cosθ')up to the order of Z，碍 ＝ﾚ0

2 are expressed as in the next table, where Z＞ｍ∧ａｎｄ丿,(coφ)＝戸(cosθ). /

(3.5) (3.5a) (3.56) (3.5c)  1√

l/m.

Isotropic/zonal

component

0

First harmonic

component

1

Second harmonic

component

2

０

１

２

1 COSθ ￢ y(cos2θ−1)

sinθ

3sinθcos.θ

3sin2θ

Now, we express the asymptotic direction of the i-th station specified by the polar

coordinates 6i and (Pi, which are given with｡････・ ･.   ･.・ .・  .･.・    ..  ・･･

respect to the earth's axis and the direction toward the sun, respectivelyトAs shown in

Fig. 4 and 拘ｇレ5, the polar coordinates (仇，

(み)ａｒe related to the asymptotic latitude 仇

and longitudeλi as follows:上   ト

θ,＝π／2−(pi and 仇＝ω(￡−12)十λべ3.6) レ

where ￡ denotes UT (Universal Ｔ.ｉｍｅ)／ａｎｄ

 ωis the angle velocity of the earth's self

rotation (ω＝π／12ｒad／hoｕｒ).

 Nine harmonic coefficients up to the second order, Co, d, d,ぶ1)，屈1)，刈1)，瓦1レ人2)油d務2).. are determined every one hour from the data of cosmic ray intensities亘6i, </>i)at stations,

≠(ﾌﾞ)ﾌﾟﾔ……＼＼………

:

ﾉ……

…＼:

.

￨￨

ﾉ

千ﾉﾔＨ

SENSE OF ROTATION OF THE EARTH ψi＝ω(t−13)十λ，

where

i° 1，

2・

3・…・″･by

the least  Fig.5……ｐｅれれing

the angles employed

to specify

squarりfitting method,

which is to minimize

theasymptotic direction 6f viewing an

 20 ＼……… Res. Rep. Koohi Univ.仁ｙ皿ｿﾞ俳ﾄ(1997)く･ﾄＮ貼……I………=･上白………万………

minimize the totaトsums of square devia蝉)面騨雨声如軋ﾉ町レ彫Ｖ〉………I……=……:＼＼＼………

  ………J:･ 二万……:………ａ＝･Σ皿/［y昧ﾚ   :･ レ．・･．･･   ．・     ．･  ｉ＝１  ･．

where the mean countingぴte at十an t-th･

stａtiohｓご‥‥‥‥‥‥‥‥‥‥‥‥ ‥‥‥‥‥‥‥

T如ﾀﾞcoeff姐咄tﾄＣ｡it) i･s t臨入isotropic ＼(ｗQｒ岫

ぶ1)](￡)＼knd………5P,(after thi臨bbrev姐佃d……:as A ａｎｉ帥■tropicぐompone皿∧The二coeff池谷nt ｡已くj asymmetric (latitudinal)ﾚcomponen卜血dﾚ=伽

longitudinalﾚasymme:try. The

maximum〉nhχ

l………ﾌﾟヶ町ｹﾞ……j=1万･=皿:4ねd:万j:nis theかamber ofﾚ 加如皿丿面4▽らﾉ(り, together with

)∧6φ面七姐lies the first……order of

harmonic

terms comes

from一the asymptotic longitude give

itude………of………the north一台outh ﾃﾞ=排)リノ＼/前面……that of the 丿6皿瞬緋図………by the:first ｕ り ９ り ､ y i i i j j L u b i し l U l 卜 ５ ・ ･ ｌ ･ ! そ : Ｑ ｐ ･ ﾖ . ､ ･ ６ 万 考 V C i i … … … 1 J J … … … … ト し . ∧ 1 ○ ‥ ‥ ‥     ‥ ‥ ‥       ＝   φ 牛 ｔ ａ ｎ ダ 1 ( 且 ／ Å 八 十 ( ￨ ご 万 … … … = 〉 宍 = … … … … 1 … … … j = j … … … …I = j ﾉ ｹ . 1 = 宍 … … … ∧ … … … ＼ ＼ j = … … … ﾄ … … … j … … I I ¨ = し ∧ へ ＼ … … : ･ j ( 3 ｡ . 8 )

One also〉ｃａｎ:definりthe threeトdimensioれal quantitie球〉…………J………:ﾚ………万………1…………1=……二………:………j= 1

 ■ ■  ■  ■■ ■      wい/･jn･.ﾏﾍnl.･/り6ゝ1･  ？ ヨ ( Å 1 十 狸 ＋ ａ ) イ , = j … … … : … … … j … … … … = : ﾚ … … … … ∧ ◇ ト … … … … ﾉ … … … : … … … 1 < … … … = ﾚ … … ∧ … … = = … … …./Qﾄ･．･･．．･．．．･･Ｊ･．･･：．／．．．･･， ．．・ し．．･一一

車 止 t ａ ｎ ソ { C 1 ／ { Å 1 ＋ 屈 ｙ イ } 1 / . =

, y ＼ ﾉ … … … ｹ ﾞ ﾉ … … ∧ = … … = 〉 1 … … … … j … … … ∧ ＼ ﾚ ﾉ … … = ﾉ … … ＼ ﾌ ﾟ … … … …

The quantity P gives the maxi㈲i皿

asymptotic direction specified by the relationsくare illustrated犬in Fiヒ6レダ

Ｘ Å 1 Ｃ φ ∧＼    ‥‥‥  ‥万Ｗ≠t:ａｎヤ{CI／(j Fig.6……Illustration of coeffiぐients Ａ:1=:゜， / ＼▽Jm4×imum anisotropicしcompon:り asymj〕totic directiりｎ:ぼivenby longitudeΦ.く………万  Ｉ

flux

ﾔ(3.9) (3↓:10) m an

Barometer Coefficients of Latitude Neutron Monitors (Kusunose) 21

 The

stations where data are used in the analysis are given in Table 3. For each station,

the vertical cutoff rigidity, the asymptotic

direction (cOiand λi), and

the mean

counting

rates (Wi) are given. The vertical cutoff rigidities for every station can be seen to be less

than 2.3 GV,

whicりis close to the atmospheric

cutoff value.しThegeographic distribution of

the stations is shown in Fig. 7.      ト

 It is assumed

as theトfirstapproximation

that the mean

rigidity of primary

cosmic ray

particles arriving at every station is almost ｅqﾘal t0 9.５GV.

This assumption

is based on

the fact that the effective asymptotic

latitudes obtained for 11 stations (except for

Sｕ!phur Mt.)

agree within accuracy of ±5°十with the asymptotic

latitudes obtained by

McCraeken

it ｄ al. (1965) for the rigidity value ｄ ９.５GV

(Nagashima

it et al, 1968)｡

 Figure 6 shows

the geographic distribution of 仙ｅ asymptotic

directions for rigidity 9.5

GV

at ＵＴ＝O for all the stations where data are used in this analysis.･Ａ･geographically

uniform

distribution of stations is essential for making

an accurate spherical harmonic

analysis.

22 90ﾚ4

Geographicﾚｹﾞ

HI仙工dt↓tu

Neutron十M6｢4

◇Ｖ心卜刈ｿﾞﾚ（ 万喜7･Geographic distribution吋:high … ………sphericalharmonic analysis.〉

90E

90W

Barometer Coefficients of High Latitude Neutron Monitors (Kusunose)

180

０

O

Northern

(D S･outhern

Hemisphere

Hemisphere

Geo･graphic Asymptotic Direction

of Neutron ･MonitorjS‥‥‥‥‥

23

90E

Fig.8. Geographic distribution ｏ卜the asymptotic directioりs (for rigidity 9.５ＧＶ）    of high latitude neutron monitor町used in止e spherical harmonic analysis.

24 NO.STATION 1 2 3 4

 …………Res. Ｒ面｡Kochi Univ………ｿﾞＶ挺4肩汗(四97)………Nat.……＼ｽ…………]ﾉ………ﾄ……

Taり1e 3. List of the high lati皿萌………万々:osm如………=姐y………neutr皿……mon･itor･り一万･｡･

ＨＥＩＧＨＴプVERTICAL  コ :･ニ=1  =ＣＵＴＯＩＦＦ ■■■■   :. RIGIDITY ALERT (S)く ＡＰＡＴＩＴＹ(Ｓ) ＣＡＬＧＡＲＹ(Ｓ) ＣＡＳＥＹ▽  ‥ ５ ＣＨＵＲＣＨＩＬ(Ｓ)ト 6 DEEP RIVER(S) ７へDURHAM(S) ８／Ｇ００ＳＥＢＡＹ(Ｓ) ９トHEISSIS‥‥‥‥ 10.･ＨＯＢＡＲＴ…… 1i………ＩＮＵＶＩＫ(S)＼ 12 KERGUELEN(S) 13. KIEL(S)犬 ‥‥‥‥ １４ ＫＩＲＵＮＡ(Ｓ)し １５……ＬＥＥＤＳ(Ｓ)  ／ １６▽ＭＡＧＡＤＡＮ(Ｓ)上 17＼ＮＡＷＳＯＮ  上一 １８＼ＭＣＭＵＲＤＯ(Ｓ)＋ 19犬MT.WASHINGTON'ト 20しＮＯＲＩＬＳＫ(Ｓ)ニ ２１ OTTAWA  ＋ ２２ OULU(S)………J° 23 RESOUTE ＢＡＹ(S) ２４ ＳＡＮＡＥ(S)＼ ＋ 25 SOUTH POLE ２６＼ＳＵＬＰＨＵＲMT.(S)ﾀﾞﾚ 27しＳＶＥＲＤＬＯＶＳＫ(S) ２８ SWARTHMORE(S) 29 TERRE ADELIE(S) ３０ ＴＨＵＩＬＥ(S) ニ 31 TIXIE ＢＡＹ(Ｓ) ３２ UPPSALA 犬〉 ３３ ＶＩＣＴＯＲＩＡ(Ｓ)…… ３４ WILKES ３５＼ＹＡＫＵＴＳＫ  〉  ……ＹＡＫＵＴＳｋ(Ｓ) ト (ｍ) 一 犬57 177 ８Ｌ９５Ｌ６０ＬＩＬ４０２ＬＬ８ ｍＳ３14Ｓ４２Ｓ２Ｓ5407ＳＳ４ 1909 Ｌ７Ｌ７ＣＯ O ＣＯ Ｑ︶ｒｏｑ゛１ｒD8228       CV] ＣＯ :300 ∧80 lO O ＬＬＩＬ55 426ＳＳ７Ｓ1010 /(ＧＶ) 0.0し 0.65 寸.09 0.01△ 0.21 L02 L41 0.52 0.10 ↓.89 0.18 1.19し 2.29 0.54 2.20∧ 2,10 0j2犬 0.01 上24ト 0.63…… 1.08 0.81 0.0 1.02 0.11 1.14 2.30 1.92 0.01ニ 0.0 ト 0.53 L34 1 1.86 0.01 ＼ ↓.70＝ L70ﾀﾞ

NUMBER OF STATIONS USED IN THE

HARMONIC ＡＮＡＬＹＳＩＳニニ (MAXIM

（Ｓ）：ＮＭ＋６４ＭＯＮＩＴＯＲ，０ＴＨＥＲＳ ：IGY

（＊）：:NOT USED IN THE SPHERICAL］

t / j … … … ｿ ﾞ 犬 : … … ト 1 1 . 0 6 … … … … 万 … … … … 1 1 , 1 0 ㎜   % ･ ％     ・   ･ ■ ■ ■   ■ ■ ■ ■ ゝ … … … : ･ . . ■ ■ ■ ■   : ﾐ ﾐ ㎜ 23 1 9 6 8 一 二 6 . 7 9 1 . 9 7 … … … 1 0 . 7 0 2774  8552  1  630 一 622358 一 75236607 1305 一 2439 一 ９ 一 384  751319  292258410 一 一 Ｉ   Ｉ − 一  一   Ｉ   一 一 Ｉ   一 一 一 − Ｉ 一   Ｉ 一 一 一 Ｉ Ｉ ∼ 一 71946  0675  6  0只︶Ｉ  132127  33470400 21 ／26.Ｔ22

Barometer Coefficients of High Latitude Neutron Monitors (Kusunose) COUNTING RATES 1969

   6.68

，  3.87

1970 -6.68 1971 -7.15 4.65   (105／ｈ) 1972   1973 7.46    7.43 4.72    4.73 10.48   10.57   11.22   11,71 0.39  十〇.40    −    − ･7.01   1 7.05    7.53    7.66 19.05   19.18・  20.51   20.86 3.53 6.43  − 0.27 6.35 7.19 5.83  − 6.64  − 0.35 8.75 一   一 1.73 3.47 2.12 1.32 2.09 3｡54    4.84 6.46コ つ6.87  一    一 0.28 6.39 7.26 5.86 6.52 6.27  − 0.35 8.79 1.36  − 1.76 3.49 2.12 1.33 2.09 85 一 7 79 一 ７ 3｡20 3.84 4.16 6.59 0.55 6,23 0.39 0.18  − 25-20  24 3.23 3.88 4.19 6.55 0ｊ6 一 一 一 一 22  0.29  6.80  7.76  6.23 6,96  6.23  4.92  0.38  9.43 1.443  3.50  1.92  3.75   −  1.42  2.23 ８ Ｑ Ｕ ４ ４ ４一４０４ 6.76 0.58 一 一 一 1.48 ･5.83 6.98  − 0.30 6.90 7.90 6.31 7.09 6.31 5.00  − 9.61 1.46 3.33 1.95 1974    1975 二  1976 7.33    7.49    7.52 4.64   4.77   ｡4.77 一 一  7.50 20.90 ト5.84 98 一 Ｒｙ 0.29 6.91 7.88 6.29 7.11 6.29 4.99  − 9.56 1.45 3.34 3.79    3.82  − 1.43 2.25 Ｏ  CTi ＣＯ CD 8一４２５ ＱＵ  ＱＵ４４ 6.33 一 一 一 一 1.50 1.48 2.25  − 5､81 一 一 一 20.55  5.77  6.88 一 ︸81 7.79 6.20 6.99 6.20 4.97  − 9.46 1.42 3.30  − 3.77  − 1.46 2.19  − 5.61 一 一 一 一 一 一 31.07   21.21 5.8｢i    5.70  7.01   7.04 一   一 6.96 7.96 6.32  − 6.32 5.06  ･− 9.69 1.46 3.36  − 3.85  − L46  −  − 5.78 一   一 6.98 7.99 6.35  − 6.35 5.10  − 9.74 1.48 3.37  − 3.88  − 1.47  −  − 5.81 4 0 5 ≪ 3 L O Ｃ Ｏ L O   一   一   Ｉ Ｑ ｕ ４ ４ り 乙 ︷ ｈ ︸ り ｎ ｙ L O Ｏ Ｏ L O   i   。   ． Ｑ Ｕ ４ ｔ ４ Ｌ Ｏ L O Ｃ Ｏ ４ １ ４   一   一   Ｉ ｎ ｊ ４ ４ ０ ０ T -Ｈ Ｌ Ｏ ４ Ｃ Ｎ ] L O   一   一   一 Ｑ ｕ ４ ４ 6｡87  − 一 一 一 1.49 2.19 一 一 一 一 1.46 2.26 一 一 一 一 1.46 4.00 一 一 一 一 25 1977 -7.48 4.75 一 一   − 21.13  5.86  7.00 一 一 6.94   1 7j8  ト 6.34  − 6.34   ぺ 5.03 一 7 3 5 0   Q ■ ⋮ 1 -( 3.36   ・ 3.86   ＞  − 1.47 1.17   :  − 5.79 3.53  −  − 3.09 一 一 一 -1.46    1.46 25-21  24-21  24-21  22-20ト 20-20  20-18  19−18

26 Res.く狸ｅｐﾝｹKochi Univ.………Ｖ皿ｻﾞ研(1997)ﾊﾟﾂﾞｹ……Ｎ組･=･∧j=………I,………∧に=ﾉ……

………ト………4、Atmospheric Eff如ts on the Neutron Monitoりごjﾚ）‘j…………ノ………:…………＼………/IJ………:

The countingプate of a neutリｎ＼陽ｏ皿tor is囃bj皿鋤d/:丿o…………､皿（枇如ぱ似耐＼ﾚ好防氷上〇f六大･t･1!e

4.1. Barometer effeCt‥‥‥‥‥‥‥ト  ソ ＼

□The barometer:effect〉is associated with

The close correlation between the cosmicﾄ組夕=･一万J:=･. discovered byﾚMyssowsky八姐d･Ｔｕ･ぺffiva ･(1926)∧7Jﾌ

isコtaken as ａ measure of十thiレmass ａｎｄﾚ=t･h･6］

attenuation and/or barometer coefficienレβ,/Ty

the cou削血g (/うrincipalﾌﾟparts of 昨皿ﾚﾉ皿十仙e ground jt………above the°ni:onit〇ｒ. 如spheric pressure………糞ａs e recorded at a station 了如t所レknown白臨ノthe 4｡2. Temperature effeとt 犬 ∧   〉。 十The工如untingトrate皿（尽｡, ｐ， t）6fトａ＼

written for the seco姐町y七〇mpone肩丿

where Re and p axe

ｹﾞqｕ:纏以tﾀﾞﾀﾞｙ(凡φ)

cosmic…… 二in.･the……

べ（ｙ（㈲で早牛ｹ

the cu仏ff rigidity and

レthe gross specific

generated fromﾚ仙e

primary

p町tidりsトwith

primary

･ ｀ ゛ ゛ ｀ 4 ゛ Ｊ ･ . ゛ ゛ ｀ ゛ ゛ . ゛ . ｀ ゛ J - . ゛ 4 ゛ j . . “ ￡ , J . V A ‘ ゛ Ｊ   ｀ J ｒ ゛ ｀ ゛ ゛ 4 ゛ ^ や ｀ 4 = ゛ ･ . ｀ 4

differer巾峠rigidity spectrum

at a tii

゛ ･ f “ ‘ 7 1 . : . ｒ ぺ … … … : I T h e a t m o s p h e r i c : p a r a m e t e r a p p e a r i : n g e x p l i c 縦 元 半 ﾚ 面

correction for t恥∧atmospheric effects is to

to ･瓦……value･at a･.･蔀j1むcted standard depth………

cascade procおりproduφng theぶompo面nt

i in

1φng in compari噌with the time d :･flight∧･一行6毎ｿﾞ  ■■■㎜■㎜㎜㎜  ㎜   ａ  -･･    Ｊ   ・八-i■-- --･ ･■■■■■■■■

This situation is not always

fulfilledfor

11佞七1耳le of a･3ﾄＧＶ=皿ｕｏｎし1sroughly ｅq皿トt9ﾄ

sea level. The muon intensity at sea level is t臨 temp皿出ire distribution throughout the atmos componentけａ significan卜depen:dence on柿e尽t:l pjoかlink in the nucleo『cascade. Owing to theﾚ

is too small如励ａ土印mewhat

jgねificant

帥（皿りね1如r at亙timｅ t,is usually ﾄﾞｹﾞ1皿白面融lﾚし如p如如ね皿球屈＼ﾉ……… 了ぴ∧ハ……。4:ｐﾄ＜し1………1＼:l=∧ﾄ………:l= 犬∧………１ W ■ ■ ■     ㎜     ■ ■ ■   ■ ■     ■   ■ ) ｹ … … … d R … … … : : : 呂 … … … J : … … … ∧ … … … ： ト ( p 坤 s 尚 尚 √ 袖 印 り 直 祐 水 Λ Υ h e r … … … ∧ 曲 ( ･ ･ ＼ 心 り c l o : i ＼ ) l 柿 （ ＼ 面 面 坤 如 寸 ( 日 √ ∧ ﾉ ) … … I i s : t h e .しThe depth 〉翁=jく如s縦陣（卯之f面△as……the

s whose life time is enough

jねxample,ｽthe relativistic

）有6血the 100∧mb level士to

佃姐面t……血……the density and

可＼七he low energy〉ｎ:如!eon

し面（面i白面………ｏれ=1y七hrouだh°ａ

contribution

宮姐鋤de will

  ■ ■■     ■■ ■ ■     ■    W   ■■  ■■■㎜■■■■■ ■■■ ■■■■        ■■ ■

Barometer Coefficients of High Latitudむ Neutron Monitors (Kusunose) 27

 The median energy of the primaries detected by sea level high latitude neutron monitors is about 20 GV. We note that this energy isﾚdivided roughly equally at the first interaction

in the atmosphere （ａt ａ mean depth of ぺ=60ﾄg／耐）しbetween fast nucleons and two or

more charged pions with average enerぱies of」ess than ５ GV.       尚   し 〉

 If r n is the probability of pion decay per unit……time and the l≒ 曲e probability of

nuclear ･interaction,･then ・       ▽･.･･ ..･･ .･･.      .・ ・.･.

Γ。＝

 ｌ

ら几

白骨

(4.3)

where F ;, is the pion energy in units of rest mass, r , is the pion lifetime of 2.5×10-8

sec, p is the atmospheric density at a deptれof 60 1g／ ･ａｎｄλ, is the interaction ｍ･叫n

free path. Thus, it follows that     十        尚    ニ      し

呉/二旦nn^n

..ヽ･12.5r。ρ (4.4)

for p∼109 gm／ 氓≠獅 ７ .=35(∼５ GeV), I≒／Γカ∼0.045. This meansﾄthat about 4 ％

or less O仁the energy of the nucleonic cascade is transmitted through ａ pion ｌｉ皿 at the first interactionレSince p changesしby about -0.5% per 1.゜C,十the effect of the te血perature change on the fluxes∧of the nucleonic component near the top of the〉atmos油ere is d the order of -0.02％／゜Ｃ or less. In typical cases大目uch an order尚of the temperatureニeffect can be neglected.       ＼       し＼  .･    一一 ＼

 Although the nucleon component has little atmospheric temperature effect, ａｎ:appreciable contribution of muons to the counting rate of a S6aしlevel neutron monitor introduces a significant temperature dependence. Since the muons involved there are found トnear the termination of their flight range, their negative temperature effect is considerably larger than for the muon flux alone. As a result the neutron temperature effec卜becomes large. Dormanで1958) has calculated the temperature coefficients toニ卵ply to the correction of

neutron monitor data.      レ    ‥‥‥‥‥‥‥‥   ‥‥‥ ‥‥‥‥:

 Kaminer et al. (1965) have investigated the: annual∧temperature effect by むomparing neutron:counting rates at 乱 station in the Northern∧Hemisphere几with that at the

geomagnetically むorresponding station in the SouthernしHemisphere. They find an annually

seasonal wave of Ｌ２％ in amplitude from c6・parativeヶstudies between the Hobart and

Chicago neutron data, being about 1.8 times the∧value theoretically obtained by using Dorman's temperature coefficients. Thus the atmosphericユemperature effect on neutron =iS

found as small as one fifth of that of muons.  レ       尚 ………  １   ∧

4.3ンEquation for the barometer coefficientし =＼………:.・.･ ・ . =.･・..･..・ .・ ・ ･.･ ・. ・  .･. ･･

 Let us consider how the mass absorption coefficient o仁neutronsニdepends on the

atmospheric depth, the cutoff rigidity and the⊃primary∧spectrum. The∧subscript トin

eq.(4.2) will 1beしfrom now on omitted for treating mainly neutron CO･mponentsト 犬 プ

28

where

The expressionβ'=(瓦:ｐ)うsﾄtheトdifferentialﾄab如

from the primaries叩沁hしａ specific∇うμd雨に菰〉飢二

on theうrimarダ:spectrumバ凡イ) whereas･β……4=り･p.･

It is evident from eq√(4.5) that the barometer柏耐恥尚尚………異ﾉ鋤畑面目:)面微……the:shape ｑ.･f:

the……primary尚spectrum. In general｡……any・6佃1:姐血]征子(瓦宍………ﾉ=)…………袖八面……in:.･:gre:ater extent 飢

lower rigidities than……ａ.tしhigher rigidities,しand alsoΛ皿e coeffic如牡く………βt･ends･to decrease as:

the intensity decreases, sinceぐthe coeffi･雨聯βｿ｀',ｿﾞ鋤やreases with……鋤皿臨白営ﾚenergy∧十＼………

The spectrumニdependent changes of･β＼毎町e firs卜pointedｹ･り似=ﾚこ.ﾉﾚ町=万ﾉﾚMcCracken a･うd▽Johns

(1959). They noted十曲ａト2=％大助crease inβご似………皿油j………1=j

Forbush:decrease of 10% in amplitude occurred……)……＼……=Iﾔ…………ﾚﾚｹﾞjﾄ･=＼yj･･.･ﾄ………=ﾉ……j………万……土入………1………

4.4. Inf:luence of the high winds ／ …………ﾚﾚ.十ﾉｻlﾚ＼………＼………=……:……＼ﾚ………:＼-=………J…………:………ﾚ……

In applying corrections for the barometr細大奸佞ct to………=･曲（鋤帥面面y………com如面皿/㈲･asured a

possiblや･. difference between the air mass二八b卵り………ﾉ仙ｙyj節姐叫佃（臨社1∧ｊ励………ﾚreading of………the

barometei≒when strong wind blow should上恥]＼如■ted.………j狐半＼d社印rence･,し･面面:i噌……:ft6㎡/t如

Sφ-called Bernoulli'心effect, is▽proportiona卜如く皿谷ﾚし.ﾉ面姐緋……万……=胚二万t㈲∧面皿)ﾀﾞ＼y.･･velocity. In･=.･ａ

ｈroｍetcr

.希ｈeｎ∧叫roｎg

ｗjｎd b1oｗ＝Sｂｏｕ誹ケ畑Tノ面佃jd,―………jΥ垣（I4j;μ9r昨加√面isニiれgj……ニft6ｍ十t徊

Sφーqal1Qd Be印ouni'ノ白＼effed。iS▽propo竹iohaI＼縦ノ怖谷レづ.ノ亘面加]……万……=奸レゾt㈲∧面面)ダ＼yIII面1oぐi竹。・＼=万Ih―I=.―a

pra雨ceバhe Iinf1uen坤ｏfthむｗ沁dニtｏ伴いi叫紅叫＼φ叫加坤吋ニ……ノ畑………=d―o縦i面吋＼加励n=thQケ和面

continuous observations of cosmic ray neu

neutron mo ｢tｏｒ尚sin叩入February!9卵∧Ｕs･1μg………tl)゜4

March 1971, possible deviation of thO〕b佃如ed]

investigated in typical 8 e姐mples of ･hi帥∧Ｗ如

 It is∧shown that thむ pressure deviation inferredｿﾞ

reduced byコuse of ａ specially designed barometr紅白

amounts

to about

4 mb

in maximum

whe元二:th6……:l:

deviatic〕n is still higher by one order血sトcompared ■>

theニwind tunneトexperime緋thatしhad beenくｃ如西浦=

Figure 10 shows……an example of仇ｅへeffectｹﾚj･l:Iφ.･･f=.･jl=一一一一§

correction for atmosp!aerie pressure：observedﾄ万町jﾌﾟ=7･4

sensor at Syowa

Station.

(=ﾌﾟ面ingthe二12-NM64

years up to

h winds were

k. 9.十＞

･condition. トi緋ensity barometric

＋１  Ｏ り    ２ ﹃    ４ ︵％)   ｕｏａ：＾ｎ＾Ｎ  ｊｏ  Ａ：；Ｔｓｕａ::mＨ −5

Barometer Coefficients of High Latitude Neutron Monitors (Kusunose)

       ト wind Velocity (m/sec)

Fig.9. The relation between the neutron monitor intensity deviation and the      pressure deviation caused by high wind observed at Syowa station      （Ｋｕｓｕｎｏｓｅand Kodama, 1972) CVJ ︱ 十  十 29 ︵ ︵ ︷ 日 ︸ aｊｎｓｓａｊｃｄ  ＯＴａｓｔ［ｄｓｏｕｉｑ.ｖ Ｉ  ２  ３  ４  ５  ６ atmospheric  Antarctica.

 As

has been reported by Kawasaki

(1966, 1972),

there are two

problems

in neutron

observation at Mt.

Norikura (36.11ON, 137.55OE, cutoff rigidity: 11.4 GV,

altitude: 2770

m):

(1)

Barometer

coefficient of

Mt.

Norikura

neutron

monitor

is 0.64 ％／mb(＝0.85

％／ｍｍＨｇ)，ｗhichis extraordinary lower than that expected from

the values obtained at

other stations, and

(2)the

time variations of the barometer

corrected intensity frequently suggest abnormal

pattern compared

with the data

of other stations, specially with

those at Tokyo that

should show

almost

the same

variations.

  The barometer

readings at the mountain

observatory

that are affected by h址h winds

through

the dynamic

pressure effect are corrected reasonably by the free air pressures that

are estimated from the interpolations of radiosonde data of corresponding altitude

(Kawasaki,

1979; Kawasaki

d

al., 1983; Kawasaki

and Wada,

1983).

3 0 ＳＥ︶３ｄｎＳＳ３ｄｄ  ３ｉｙ３ＨｄＳ０ＷｌＶ つｇ︶ ＡｌｌｓＺ］トＺ一 ＺＯｔトコ山Ｚ 9９０ ９8０ ９７０ ９６０ ９５０ ９４０  ○ ○ ○ ○ ○     ︲ ２ ３ ４ (ＶＥ) ＡｌＩｕｏＪ］ン         ＱＺ一Ｓ

Res. Rep. Kochi Univ. Vol. 46 Nat.

((】)

(b)

(c)

(d)

 。    

ﾉ∩ダ

[

L

−（ｅ）       −        ∼ −    （Ｏ        − ∼        ＝ −        ●      ●

AUG.14

AUG.15

AUG.16,1969

Fig.10. An example of the effect of strong十windダon the neutron intensity correction for      atmospheric pressure observed at Syowa Station. (a) Apatity, (b) Oulu. (o) Syowa 犬   Neutron intensity corrected for the wind velocity coけected十atmospheric pressure, (d)      Syowa Neutron intensity corrected for the wind velocity uncorrected atmospheric      pressure, (e) Syowa atmospheric pressure. Dotted line means correction for wind

Barometer Coefficients of High Latitude Neutron Monitors (Kusunose)

5. Examination of the Barometer Coefficients

31

 As described in the previous section, the barometric correction of the observed counting rates of ground based neutron monitor is important and unavoidable process. The purpose of the present section is to examine the barometer coefficients of high latitude neutron monitors that are used for barometric correction of data. Barometer coefficients that are used for the barometric correction are usually determined by individual observatories. It is not easy to examine the value of the barometer coefficient in use at each station. At a single station, the successive differencing method (Lapointe and Rose, 1962) and the autoregressive method (Martinelle, 1968) have been proposed. However, it is not proper to

examine the baromむter coefficient in the earth's scale. Through the study of the

correlations between the daily mean pressures and the residuals of the observed data from which the composed intensities were removed, re-evaluation of the barometer coefficients

have been performed. (Ogita ｄ ｢｡, 1973; Kusunose ｄ ｢｡, 1981; Kusunose, 1984)

 In eq. (4.1), the barometer coefficient β is determined statistically from the linear regression analysis between the neutron intensity and the barometric pressure. Our first objective is to examine whether the barometer coefficients used in the existing cosmic ray stations are appropriate or not. We evaluate how large in the order of magnitude is the residual variation that is ａ possible pressure-dependent term still remained in 七he pressure

corrected neutron intensity data supposedly caused by improper coefficients. The observed counting rates of incident particles depend upon the characteristi叩 inherent to the

observational apparatus and environment.

 Therefore, the counted number of particles coming from the apparatus aiming direction must be transformed into that for unit area, unit solid angle and unit time. However, in studying the time variations of cosmic ray intensity, use of the relative intensity is convenient. Using the relative intensity, one can disregard the differences due to the size of apparatus. The pressure corrected neutron intensity 7＼/｡｡。is transformed into percentage values L｡,rrelative to the mean value. After this we use the relative percentage values in place of counting rates.

 To eliminate the longitudinal component, the daily mean values are used. We define the composite neutron intensity to be

       −

       ｙ（φ）＝Co十Cisinφ       (5.1)

whereφ＝π／2−θis the geographic asymptotic latitude. The harmonic coefficient Co

       −and c, were obtained in Section 3. The function ｙ（φ）is the composite neutron intensity for the cosmic ray station at asymptotic latitude φ .

 The composite intensity ｙ is derived from the analysis by using data from nearly twenty stations, so the effect of improper barometer correction at some stations is reduced to about ａ tenth of the pressure corrected neutron intensity variation at each station. The       −difference△7 between L｡t and ｙ（φ) for ａ neutron monitor located at an asymptotic latitudeφ, that is,

32 _{Res. Rep. Kochi Univ. Vol.46 (1997) Nat.}

   ト       △7＝Ｌ−ｙ（φ）,∧……… ……＼    ‥‥‥   ‥‥‥‥  (5.2)

minimizes the effect of the intensity variations of the primary cosmic rays outside the

magnetosphere. In this way, the remaining small pressure好和ct that 皿ａy be included in

the pressure corrected data becomes apparent by inspection of plots on the diagram of ∂7

 against the barometric pressure｡

 Ｔｈｅ｡residual barometer coefficient △βis obtainedｹﾞ卵a 11叩町regression coefficien七from

the correlation between the atmospheric pressure p and the residual in七己nsity variation △7

 defined by eq. (5.2). Thus derived values of △βfor the period from 1966 to 1977 are

presented in Table 5.1. The errors of coefficients in Table 5.1 stand for the stａ回教d errors

of the linear regression coefficients derived from this analysisﾚThe barometer coefficients

 βΓeported at each station are also given｡

 Figure 11 (a) and (b) are examples of the corr出所on between the pressure corrected

neutron intensity L･r and the barometric pressure p, at (a)尚Deep River, 1968 and (b)

Kerguelen, 1968. There appears no indicative of any correlation bewtween L｡。and p as seen

in two figures√Figure 12（ａ）ａｎｄ（b）shoｗ the c面relationくbetween the residual neutron

intensity△7 and the barometric pressure p, at (aドDeep Ｒｉｖ:er,1968 and (b) Kerguelen,

1968. There is no correlation between △/ and p in Fig｡12(a), but the correlation is seen

clearly in Figト12 (b). It seems necessary that the barometer coefficient at ＼Kerguelen

Station in 1968 should be re-corrected.       ･･

○    ５     ０     ５        一 ︵％ ) ＡｉｌｓＺ３にＬＺ一 Ｚ︵︶叱﹂にｎ３Ｎ   ’””Ｉ ○

DEEP

RIVER I

968

    １．  １   １● ．  １      ●    ・１  １ １１  １   1-     ≒ Ｉ ・１･ヅヅ     ・●   1 11 111 ，. 一一‥1･ 3    1 11 1 1 ・ 1 11･ 3･1211 11 1      11  t 11 11 15211 2･222 111   1 .11 λ1 44 43 1131.2 1 *3321211     1.1 121 1 1413121 }23Z2 4232H↓212U .1.2...X..i..3・..2311..11112.，λ14531212211・.   ・   1 1 1 1 . １   １   ， １ １ １ １   １ １ 1 1 1 . １ ([]) ．   1 1 2 1 2 1 1 1 2 1 2 2 ● １ １   １ １ i m ２１ ･ ， ． １   λ   ↓ １ １   １ １ ・ ２ １ ２ 二 3 1 a i l ･ １ ． ２ １ ． １ = ． ， ． １   ２ ｋ ﾝ ． ･ 1 . 2 2 2 i n 1 . 1 ･ ３ ２ １ ･ ． ２ ・ １ ノ ド . １ . ﾊ ﾟ ・   １ １   １     １ １ ． ･ λ １ λ １ ･ ト ２ ２ １   ・ ． ／ ・ ， λ １ ．   ・ ●   ． ・ ● １   Ｌ   １ ● ● ● ○ -3０ ０ ｜○ _{２０ ３}       BAROMETRIC PRESSURE ( mmHgﾚ）  ………=   ノ Fig.ll. The relation between the cosmic ray neutron monitor intensity and barometric

︵ｇＴ″︶にＩωｚ］に［ｚ一   き   Ｑ 卜 卜 ' 『

Barometer Coefficients of Ｈ址ｈ Latitude Neutron Monitors (Kusunose) 33

５ ○       ５       一 Ｚ〇ｙ.［Ｄ］Ｚ ＩＩＩ４・Ｉ      ５         ０         ５ ︵ｇ︶メヒ∽Ｚ３にＬＺ一 ＺＯ叱トＤ］Ｚ 1.0

KERGUELEN 1968

︱ Ｉ Ｉ あ Ｉ ！           ︱ 1 1 ! 1   1 1 1   1 1 2 . 5 1 1 . . ︱λ ＩＩ自ＳＩＩＩａ １ ， １     1 1 1 1 a ｓ 自 １ １       １         − １     １           ４ ￡           ５ 一       １ １ １   １ ︱   ︱ ＩＩＩａ∼Ｉ一一ＳＩ141ＳＩＩ ０   １ １ １ ． ｄ：１・ 1111 ｌｌｌ  １３Ｕ   １１１  1111   3112 ３ 3 2 1 l . H     2 2 2 . 1 1 １ １ ４ １ １ １ 11 1 1   l ｔ ｌ １ １   − Ｕ ２ １ ・     １    １   １１ １      １２ １ Ｌ２１１Ｕ １ １    i H 1 Ｕ ｌｊ︵ ｉ一１一 −  １１ −︱・11119 ０   ． １   １ ． １   １ １ １ １ ･   ． １ １ ． １ 。 ○ 1 1 (b) ２０ ２０ ３０ (0) ３０ ● ● ● ● 丿 ● ・ ● ● ● ・ ● ● ● ●   ・   １ ● ● １ １ ︱ ︱   Ｕ １ １ ● １ ●   １ １ ２ ．     ． ２ ２ . 1 . 1 ・ λ   １ ， １ 11111 １ １ 1 -３０ −２０ −｜○       日AROMETRIC PRESSURE ( mmHg) Fig.ll. The relation between the cosmic ray neutron monitor intensity and barometric      pressure, (b) Kerguelen, 1968 ○‥‥‥‥‥

DEEP

RIVER

１ -３０ −２０

I 968

一一︱ＩＩ欄 ＩＩ ． １    ．1    1  11 1. 1 ．１    ．工 - ○ １ １ １ ● ● Ｉ ● ・ ● ・ .. 1 . .   ． １   １   ． ２ ･ １ １   ． １ Ｌ ． ２ Ｕ ２ Ｌｋ 11 . 1   ２ １ 。 １ １ １ ２ １ ２ １１１ １ １ １ １ ３ １２ ！       ３ １ １ １ １ ２ 。 3 2 1 3 1 1 I 2 1 I 2   。 ２ １ I l l 2 1 １ １ １ １ １ ｊ １ １ ２ １１ I l l 2３   １   J . 1 . . 1 １ １  ｎ Ill 13      １ １ ●１  １     １● 1 １ １   i l ｊ １     . L 1 1 1 H . i . U 2 1 l - . 1 . 1 . 1 1 1 1 . 3 1 2 2 1 1 . 1     １ ２   １ １ X 1 5 3 2 ２ １ 3 1 1 1 2 3 １ ２１ ２ １ ２ ２ １２ ２ １ １ ２１ １ １   １ １ ２ １   Ｌ 2 : ^ . 2 2 2   １ １ Ｉ Ｉ Ｉ   ︱   ｔ Ｌ Ｉ １ 2     1 . 1 1 1 1 1   ・       １   。  11 11  １１ ｜○ １ １   １       BAROMETRIC PRESSURE ( mmHg)

Fig. 12. The relation between the residual △/ of cosmic ray neutron intensity and the      barometric pressure ｐ. (a) Deep River, 1968

34 ︵％ ) ＡｌｌｓＺ３に一にＺ一 ○ ０．５ ０。０･       Ｏ Ｚ〇ａｉｎａＺ 卜η ５ :

KERGUELEN

−￨．０：……    -３０ −２０

Fig. 12. The relation between       barometricpressure p

1968

１４１ １ １ １ ２ １ 。 (1997) Nat. Ｓ Ｉ Ｉ Ｉ Ｉ ∼ ︱ 1 1 1 1 − １ １   −   ︱ 1・ 2・●・，･1・･:･●･･i    1 1･･;･･.   ･.･･. 1 1 1 1 １ １ １ １ １ ． 1     1 1 1 1 1     1 1 1 ･ ． 】 1 2 1 1 ・ １ ． １ Ｌ ２ １ ‥       １ ● １   １ Ｚ １ ． １ … …     I 1 1             1 1 1 1 1 1 1 ∼ Ｉ Ｉ Ｉ 1 1 ･ ･ ● ●   ３ １   ， ． ･       ． １ １１ １ １ ・ ｌ ・ ・ ・ ・ ・ ・ ● ・ ・ ・ ・ ● ・ ● ・ (b)   i , I 1   1 1 . 2 １ １ ， １ ･ １１ １ ・ Ｉ Ｉ Ｉ ● ● ． Ｉ ● ・ . . . .. 1 , . . 1 - . ･ ･ ● ･ ● I ● I ● ● ･ ● ●     ト       ｜ ○ ● ● ● ・ ● ● ● ● ● ●       ●   ．   ●       ●       丿       ● ３０ ． ２   Ｚ 1 11 1   。１１  ２･   １２ １ １ ４       １ ・ ． ●   χ       ● １ １     ， １       ２     ２ ト ， 1 ト ２ ２ １ ２ ． Ｅ Ｉ ． １ ‥ ‥ ‥ ‥ １   ･ ．   1 1 I I 1 ･ ４ ↓ １ ２   1 1 １ １     １   1 1 1 1         １ 2 2 1 1 ２   ４ ･ ２ １   １ １ ．   I1 1 1 1 U l   ． １ １   １   １ ２   １   ・ １ １ １   ２ 1 3 . 3 ２   １ １ １   １ １ １ １ ． ・ ・ . . 1 1 . . 1 . - 1 1 1 1 3 . し １ ｄ ． パ . 1 ・ ・ ・ ・ ・ 1 ・ ・ ・ 丿 ● ・ ・ ● ・ ・ ・       １ ･ 2 . 21 1 二 し １ １     ･ ･ ･ ．   I 1 2 U   ． ４ １   １ １   ト ･ ･     ・ ． 1       1 1 1 2 1 . I H 2   1     1 ． ・   １     １ １ １ １ １   1 . 7 1 1 1 １ １   １     １ ，     １ ｔ １   ･ ， １     １     １   １ ． １ .1111 ２ １ １ １ 1 11 .1  1．１ 111 111  １ ． １ Ｚ ･ ｜○ 1 . . 1 １   １ １   １ ２ １ ２０ ０   日AROMETRIC :PRESSUREﾆ( mmHg)

the residual △7o卜＼ｃｏｓmiと∧肺ｙ neutronうntensity and the

 (b) Kerguelen, 1968 1=･..･.   .･:･   ｙ   ･･

 Figure 13 (a) shows the relation between the reported barometer coefficient β and the used standard pressure p･ヽAs seen in the figure the reported barometer coefficients of individual stations scatter widely even at an identical st紅臨ｒdﾆpressure. Two curves are

observed barometer coefficients （％／ｍｍＨｇ）of the nucleonic component as a function of

atmospheric depth (mmHg), for stations at:cuto拝ﾚrigidi牲ﾚ ｢2∧GV.       ＝

 Those curves are obtained by the different two ﾚworks (BA: Bachelet et al｡, 1965, CB:

Carmichael and Bercovitch, 1969). From the reported barometer coefficient β and the

residual barometer coefficient △β, the corrected pressure coefficients i｡

         ：      β。＝β十△β｡  ‥‥‥‥‥‥‥‥‥‥‥‥   (5.3)

 The dependence of the corrected pressure coeffic加財sβ｡９ on the pressure is presented in Fig. 13 (b). Scattering of the points in (b) is much smaller than in （ａレThis suggests that

the newly derived values of β。are evaluated to be more accurate than β.

 Table 4 is the list of cosmic ｒａy犬stations fro血which neutron data ＼are used in the

present analysis. Two stations, Mt. Washington and Sulphur Mt. are excluded from the

spherical harmonic analysis because they are ｍｏ!jntain stations, but 攻ｒeapplied to the examination of barometer coefficients.

︵｀エＥＥ／％) ｉＵｄ＼Ｏ＼ＵＢＯＯ Ｊ９４９ＥｏＪｏｇ  ９'-ぺ □l 工_{ＥＥ／％)ｉＵ９!Ｏ!ａ９００} ﹄９１９ＥｏＪＤＱ

ヅ

Barometer Coefficients of High Latitude Neutron Monitors (Kusunose)

１．０ｑ 1.02 1.00 0.98 0.96 ５００ １．０ｑ 1.02 1.00 0.98 ○。９６ 50０

Po

− Ｐ 5５０      ６００    Atmospheric ５５０

_{‥  ６００}

Atmospheric

６５０ ７００

Pressure

(mmHg)

6５０      ７００

Pressure

(mmHa)

35 ７５０ ７５０

Fig. 13. Barometer coefficient and atmospheric pressure. Figures attached to marks correspond     to those in Table 5.1. Curves are reproduced from the papers, ＢＡ: 1962-1963, Bacheletei     al. (1965). CB: 1965, Carmihael and Bercovitch (1969).

 （ａ）β:thebarometer coefficients of the neutron monitors and p: the standard atmospheric     pressure, those are reported from respective stations.

   −

 （b）β．:the mean barometer coefficients corrected by the present analysis. Error bars mean        −

     the standard deviations. ρ:mean pressure. The period of averages correspond to their      respective analyzed years as given in Table 5.1.