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3.4.ThemodelsforthemeasuredandnaturalSEP uxes.Theiceberge ect

Fromtheabove,itfollowsthatthemethodsforrecordingandanalyzingtheSEP uxesmayintroducesu cientdistortionsintotheexperimentaldatasetand,hence,intothedescriptiveexperimentaldatamodels.ThedistortionsarevalidforalltheSEPmodelsbasedonthecumulative uencedistributionmethod(Feyn-manetal.,1990a,b,1993,2002;Tylkaetal.,1997).ThisisduetothecharacteristicfeaturesoftheprobabilisticnatureoftheSEPevents,namely,duetothe uctuationsoftheSEPeventsizeandduration(causedbydispersionoftheeventpeak uxsizesfortheeventswiththesame uencesize),aswellasthe uctuationsoftheenergyspectrumrigidity.RandomdispersionoftheSEPchar-acteristics,whencombinedwiththegalacticbackground(whichvariesoversolaractivitycycle)orwiththearti -ciallyintroducedselectioncriteria,leadstoselectionofafractionoftheeventswithcertaincharacteristics.

Thus,thelognormaldistributionofmedium-energy(<40MeV)particles,thoughitaccountsforthecontri-butionofrelativelylargeeventstotheradiationenviron-ment,stilldisregardsthenear-orunderthresholdevents,whichcanmakeasubstantialcontributiontotheparticle uxesofthesaidenergies(comparedwithgalacticparticles)inthespaceduringshort-termspacemissions,orduringlowsolaractivity.

Thecaseisevenworsefor>40MeVparticle uxes.Ifthelognormaldistributionisusedtodescribetheparti-cles,thecharacteristicsofthedistributiongetdistorted,sotheparticle uxmodelsbasedonthisapproachover-estimatethe uxes.Sincealltheprocessesofinelasticinteractionsofprotonsandnucleiwithmatteroccurat>30MeV/(nucleon),themodelsdevelopedbasingon

thelognormaldistributionapproachprovetobeinade-quateandcannotbeused(withoutadditionalcommentsandlimitation)todescribesecondaryradiatione ectsinducedbySEPeventsandtocalculatedosesbehindP1g/cm2shieldings.

Allthee ectsillustratedbytheproton uxexamplesshouldbeinherenttoevenalargerextenttorecordingheavy-particle uxesandtodevelopingthemodelsforthembecausethevariationsoftheparticleenergyspec-trumcharacteristicsareaccompaniedbyvariationsinthecompositionoftheeventparticles.Inthecaseofheavyparticles,obviously,theSEPeventsenrichedwithheavyparticlesarerecorded rstofall,whichshouldleadtoanevenstronger(ascomparedwiththeprotoncase)overestimationoftheir uxesbythemodelsbasedontherecordsofthethreshold-exceedingSEPparticle uxes.

TheSEP uxesaresomewhatsimilartoaniceberginthatasigni cantfractionofthe uxesareunobservablebecauseofthegalacticbackground(seeFig.3,SEP uxesbelowgalacticbackground),justastheunderwa-terpartofanicebergcannotbeobservedvisually.Like-wise,justasitisimpossibletohaveanideaoftheicebergpropertiesbasingondescriptionofitsabove-waterpartonly,anyobjectiveSEP uencemodelcanhardlybeconstructedusingthefractionoftheSEP uxesobservedabovethegalacticbackground.3.5.TheSEPeventdistributionfunction

Themeasurementprocedureswereshownabovetodistortthesmall-sizeSEPeventdistributionfunction.Now,weshalldiscusstheroleofthefunctionintheSEPmodelsintermsoftheimpactonanobjectiveap-praisalofradiationenvironment.

Thedistributionfunctionformde nesthefollowingtwoaspectsofestimatingandpredictingtheradiationhazard.

Inthecaseofsmall-size(U3<106protons/cm2)eventsrecordedintheEarthÕsorbit,twocompetingviewsofthedistributionfunctionformleadtoverydif-ferentconclusions.

Ifthefunctionforsmall-sizeeventsisabranchoflog-normaldistribution,whilethenumberofeventsde-creaseswithdecreasingtheeventsizeintheEarthÕsorbit,thenthesizeoftheeventswillincreasewhenmov-ingfromtheEarthtotheSun,whereasthenumberoftheeventswillremainconstant.

If,astheeventsizedecreases,thedistributionfunc-tionis(andremains)apower-lawfunctionwithacon-stantspectralindex,then,whenmovingtotheSun,theoccurrencefrequencyoftherecordedgiven-sizeeventswillincrease.Duringhighsolaractivity,there-fore,thesmall-sizeeventswillfolloweachotheraftersosmalltimeintervalsthattheSEP uxeswillconstitutethequasi-stablebackgroundoflow-energy(<10

MeV)