Ionospheric characteristics

Transcription

1 Rec ITU-R P RECOMMENDATION ITU-R P434-6 ITU-R REFERENCE IONOSPHERIC CHARACTERISTICS AND METHODS OF BASIC MUF, OPERATIONAL MUF AND RAY-PATH PREDICTION * (Questios ITU-R 212/3 ad ITU-R 223/3) Rec ITU-R P434-6 ( ) The ITU Radiocouicatio Assebly, cosiderig a) that log-ter referece ioospheric data ad propagatio predictio ethods are eeded for HF radio-circuit desig, service plaig ad frequecy bad selectio, recoeds 1 that for the predictio of ioospheric characteristics, use should be ade of the forulatios cotaied i Aex 1; 2 that for the predictio of basic ad operatioal MUFs, use should be ade of the forulatios cotaied i Aex 2**; 3 that for the predictio of ray paths, use should be ade of the forulatios cotaied i Aex 3 ANNEX 1 Ioospheric characteristics 1 Itroductio Expressios are provided for the evaluatio of the othly edia of fof2, M(3000)F2, foe, fof1, h F ad h F,F2 ad of the othly edia, upper decile ad lower decile of foes ad fbes Also icluded are represetatios of the percetage of occurrece of spread-f These forulatios yield values for ay locatio, oth ad tie-of-day for differet solar epochs I the case of foe ad fof1, epirical forulae i ters of solar-zeith agle are preseted For the other ioospheric characteristics a uerical appig techique based o orthogoal Fourier fuctios is applied * Coputer progras associated with the predictio procedures ad data described i this Recoedatio are available fro the ITU (see 9 of Aex 1 ad 8 of Aex 2); for details see the ITU/BR Catalogue of Software for Radio Spectru Maageet ** For defiitios, see Recoedatio ITU-R P373

2 2 Rec ITU-R P Mappig fuctios The geeral for of the uerical ap fuctio, Ω (λ, θ, T) is the Fourier tie series: H Ω (λ, θ, T ) = a 0 (λ, θ) + j = 1 [a j (λ, θ) cos j T + b j (λ, θ) si j T] (1) Ω : ioospheric characteristic to be apped λ : geographic latitude ( 90 λ 90 ) θ : east geographic logitude (0 θ 360 ) (θ i degrees East of the Greewich eridia) T : uiversal tie (UTC) expressed as a agle ( 180 T 180 ) H : the axiu uber of haroics used to represet the diural variatio The Fourier coefficiets, a j (λ, θ) ad b j (λ, θ), vary with the geographic coordiates, ad are represeted by series of the for: K a j (λ, θ) = U 2j,k G k (λ, θ), j = 0, 1, 2,, H (2a) k = 0 K b j (λ, θ) = U 2j 1,k G k (λ, θ), j = 1, 2,, H (2b) k = 0 The particular choice of the fuctios, G k (λ, θ) is deteried by specifyig the itegers k (k 0, k 1, k 2,, k i,, k ; k = K), where i is the order i logitude Therefore, a uerical ap ca be writte ore explicitly i the for: K Ω (λ, θ, T ) = k = 0 H U 0,k G k (λ, θ) + j = 1 K cos j T k = 0 K U 2j,k G k (λ, θ) + si j T U 2j 1,k G k (λ, θ) (3) k = 0 U 2j,k ad U 2j 1,k i equatios (2a), (2b) ad (3), ca be writte as U s,k, where s is either 2j or 2j 1 I the uerical appig techique, the odified agetic dip: X = arc ta I cos λ has bee used, where I is the agetic dip ad λ is the geographic latitude Sice X is a fuctio of both geographic latitude ad logitude, the foral expressio of Ω (λ, θ, T), equatio (3), is uchaged Table 1 shows the geographic fuctios, G k (λ, θ)

3 Rec ITU-R P TABLE 1 Geographic coordiate fuctios G k (λ, θ) (X is a fuctio of λ ad θ, is the axiu order i logitude) q 0 = k 0 ; q i (i = 1,) = k i k i k Mai latitude variatio k First order logitude k Secod order logitude k th order logitude 0 1 k cos λ cos θ k cos 2 λ cos 2 θ k cos λ cos θ 1 si X k cos λ si θ k cos 2 λ si 2 θ k cos λ si θ 2 si 2 X k si X cos λ cos θ k si X cos 2 λ cos 2 θ k si X cos λ cos θ k si X cos λ si θ k si X cos 2 λ si 2 θ k si X cos λ si θ k 0 si q 0 X k 1 1 si q 1 X cos λ cos θ k 2 1 si q 2 X cos 2 λ cos 2 θ k 1 si q X cos λ cos θ k 1 si q 1 X cos λ si θ k 2 si q 2 X cos 2 λ si 2 θ k si q X cos λ si θ A odel of the Earth s agetic field for epoch 1960 based o a sixth-order spherical-haroic aalysis is eployed i order to deterie odified agetic dip ad gyrofrequecy required i the evaluatio of the uerical aps The 1960 epoch ust be used, rather tha soe other epoch of iterest because it is that which is used i geeratig the values of the uerical coefficiets The agetic iductio F x, F y ad F z i gauss alog the geographic orth, east ad vertically dowwards directios respectively, is give by: 6 F x = = 1 = 0 x g cos θ + h si θ R + 2 (5a) 6 F y = = 1 = 0 y g si θ h cos θ R + 2 (5b) 6 F z = = 1 = 0 z g cos θ + h si θ R + 2 (5c) x = d d ϕ (P, (cos ϕ)) y = P, (cos ϕ) si ϕ z = ( + 1) P, (cos ϕ) (6a) (6b) (6c)

4 4 Rec ITU-R P434-6 with: ϕ : P, (cos ϕ) : orther co-latitude (= 90 λ), where λ is the geographic latitude i degrees (orth positive, 90 λ 90 ) associated Legedre fuctio defied as: P, (cos ϕ) = si ϕ cos ϕ ( ) ( 1) 2(2 1) cos 2 ϕ + ( ) ( 1) ( 2) ( 3) (2) (4) (2 1) (2 3) cos 4 ϕ + (7) g ad h : R : uerical coefficiets for the field odel i gauss height-depedet scalig factor give as: R = h r (8) h r : height at which the field is evaluated (take as 300 k) The total agetic field, F, is give as: F = F 2 x + F 2 y + F 2 z (9) The agetic dip, I, ad gyrofrequecy, f H (MHz), are deteried fro: I = ta 1 F z F 2 x + F y 2 (10) ad: f H = 28 F (11) 3 Predictio of fof2 ad M(3000)F2 The F2-layer uerical aps are based o vertical icidece soudigs of the ioosphere at a large uber of groud statios all over the world The sets of uerical coefficiets defiig the diural ad geographical variatios of the othly edia of fof2 (Oslo, 1966) ad M(3000)F2 are based o a liear relatioship with solar activity The coefficiets are the values of U s,k (see equatios (2) ad (3)) that defie the fuctio Ω(λ, θ, T), of the uerical ap of the give characteristic for the idicated oth ad level of solar activity The coefficiets are available for each oth of the year, ad for two levels of solar activity, R 12 = 0 ad R 12 = 100 R 12 is the twelve oth ruig ea value of the othly suspot ubers ad is used as a idex of the level of solar activity For ost purposes it is adequate to assue a liear relatioship with R 12 for both fof2 ad M(3000)F2 However, the relatioship betwee fof2 ad R 12 becoes o-liear at a level of solar activity which is a fuctio of geographic locatio, tie of day ad seaso The ost oticeable departure fro liearity is for values of R 12 above approxiately 150 For values of R 12 greater tha 150, the error is reduced by assuig that higher values are effectively 150 The relatioship of M(3000)F2 with R 12 is effectively liear over the etire rage of values of R 12

5 Rec ITU-R P Predictio of foe The ethod for predictig the othly edia foe is based o all published data over the years fro 55 ioospheric statios foe (MHz) is give by: (foe) 4 = A B C D (12) A : solar activity factor, give as: A = (Φ 66) (13) B : Φ : othly ea 107 c o solar radio-oise flux expressed i uits of W 2 Hz 1 For predictio purposes, it is appropriate to approxiate Φ by a estiate of Φ 12, the twelve-othly soothed value seasoal factor, give as: B = cos N (14) N = λ δ = 80 for λ δ < 80 for λ δ 80 λ : δ : geographic latitude ad is take as positive i the Norther Heisphere solar decliatio ad is take as positive for orther decliatios The expoet is a fuctio of geographic latitude, λ: or: = cos λ for λ < 32 (15a) = cos λ for λ 32 (15b) C : ai latitude factor, give as: C = X + Y cos λ (16a) X = 23, Y = 116 for λ < 32 (16b) or: X = 92, Y = 35 for λ 32 (16c) D : tie-of-day factor 1st Case: χ 73 D = cos p χ (17a) where χ is the solar zeith agle i degrees For λ 12, p = 131; for λ > 12, p = 120 2d Case: 73 < χ < 90 D = cos p (χ δχ) (17b) δχ = (χ 50) 8 degrees (17c) ad p is as i the 1st Case

6 6 Rec ITU-R P rd Case: χ 90 The ight-tie value of D, for χ 90, is take as the greater of those give by: D = (0072) p exp ( 14 h) (17d) or: D = (0072) p exp ( χ) (17e) where h is the uber of hours after suset (χ = 90 ) I polar witer coditios, whe the Su does ot rise, equatio (17e) should be used p has the sae value as i the 1st Case The iiu value of foe, is give by: (foe) 4 iiu = 0004 ( Φ) 2 (18) where Φ ay be approxiated by a estiated value of Φ 12, the twelve-othly soothed value At ight, if foe, whe calculated by equatios (12) to (17e), is less tha that calculated by equatio (18) the latter value should be take Tests of the accuracy of the predictio ethod give for a data base of over hourly coparisos for the 55 statios a edia rs deviatio of 011 MHz 5 Predictio of fof1 Expressios for othly edia fof1 are based o data recorded fro 1954 to 1966 at 39 ioospheric statios located i both heispheres fof1 (MHz) is give by: fof1 = f s cos χ (19) f s = f s (f s100 f s0 ) R 12 f s0 = λ λ 2 f s100 = λ λ 2 = λ λ R 12 ad where λ, the value of the geoagetic latitude i degrees take as positive i both heispheres, is give by: λ = arc si [si g 0 si g + cos g 0 cos g cos (θ 0 θ)] g : geographic latitude of positio of iterest g 0 : geographic latitude of N geoagetic pole (take as 783 N) θ : geographic logitude of positio of iterest θ 0 : geographic logitude of N geoagetic pole (take as 690 W) The axiu solar zeith agle at which the F1 layer is preset (see also Figs 1 ad 2) is give by the followig expressios: χ = χ (χ 100 χ 0 ) R 12 degrees (20) χ 0 = λ χ 100 = λ

7 Rec ITU-R P FIGURE 1 Variatio of χ with geoagetic latitude ad R χ 30 R 12 = N 90 S Geoagetic latitude D01 FIGURE 1[D01] = 8 CM D02-sc FIGURE 2[D02] = 15 CM

8 8 Rec ITU-R P Predictio of foes ad fbes A set of uerical coefficiets defiig the diural, geographical ad othly variatios of the edias ad upper ad lower deciles of the foes for a year of iiu ad oe of axiu solar activity, ad a set of uerical coefficiets defiig the variatios of the edias ad upper ad lower deciles of the fbes (blaketig sporadic-e) for a year of iiu solar activity have bee derived 7 Predictio of h F ad h F,F2 Nuerical aps have bee developed o a othly basis for years of axiu ad iiu solar activity of othly edia h F, which is the iiu observed virtual height of reflectio of vertical icidece sigals fro the F regio (geerally fro the F2 layer at ight ad fro the F1 layer i the daytie) Nuerical aps have also bee developed for years of axiu ad iiu solar activity of h F,F2 h F,F2 is the cobiatio of the iiu observed virtual height of reflectio of vertical-icidece sigals fro both the F layer at ight ad the F2 layer i the daytie 8 Predictio of the percetage of occurrece of spread-f The percetage occurrece of spread-f has bee deteried fro the ioospheric data fro the world etwork of vertical-icidece ioosode statios o a othly basis for a year represetative of high solar activity ad for a year of low solar activity, ad values have bee represeted uerically by eas of a appig techique 9 Available coputer progras ad referece data The ITU/BR Catalogue for Radio Spectru Maageet lists available progras ad referece data for evaluatio by icrocoputer of the ioospheric characteristics oted above The progra WOMAP displays for locatios i a specified geographic area, the values of the chose ioospheric characteristic, for a give Uiversal Tie, oth ad solar epoch The copleetary progra HRMNTH displays the chose ioospheric characteristic for a give locatio ad year, as a fuctio of the Uiversal Tie, for each oth ad the associated solar epoch ANNEX 2 Predictio of basic ad operatioal MUFs 1 Itroductio Epirical forulae are preseted for the evaluatio of the othly edia basic MUF for the propagatio path This MUF is estiated as the greatest of the basic MUF values for the propagatio odes appropriate to the path legth beig cosidered The relatioship betwee the operatioal MUF ad basic MUF is give ad a coputer progra is described leadig to estiates of path basic MUF, operatioal MUF ad optiu workig frequecy o a poit-to-poit propagatio path of ay legth

9 Rec ITU-R P Mode cosideratio The odes cosidered are: 1F2 Higher order F2 odes 1F1 1E 2E 0 to d ax beyod d ax k k k where the axiu groud rage d ax (k) for a sigle hop F2 ode is give by: with: d ax = ( / x / x / x 6 ) (1 / B 0303) B = M(3000)F [M(3000)F2] si 7854 x ad x = fof2/foe, or 2 whichever is the larger Ioospheric characteristics for the id-poit of the great-circle path are used 3 Predictio of F2-layer basic MUF 31 Groud distace D up to d ax The F2-layer basic MUF is give by: F2(D)MUF = 1 + C D C 3000 B 1 fof2 + f H 2 D 1 d ax f H : appropriate gyrofrequecy (see Aex 1) ad: C D = 0591 Z 0424 Z Z Z Z Z 6 with Z = 1 2D/d ax C 3000 : value of C D for D = k where D is the great-circle distace (k) The above forulae apply for the basic MUF for the x-wave at zero distace, for the o-wave at d ax ad beyod ad for soe coposite waves at iterediate distaces The correspodig o-wave basic MUF is give for all distaces by deletig the last ter i f H fro the first forula 32 Groud distace D greater tha d ax Values of F2(d ax )MUF are deteried for two cotrol-poit locatios at d 0 /2 fro each terial alog the coectig great-circle path where d 0 is the hop-legth of the lowest order F2 ode The path MUF is the lower of the two values 4 Predictio of F1-layer basic MUF Ioospheric propagatio via the F1-layer is iportat for trasissio distaces i the k rage at id ad high latitudes durig the suer oths For these trasissio distaces the F1-layer basic MUF is take as the product of the id-path value of fof1 (see Aex 1) ad the M factor M F1 This M factor was derived fro ray-tracig calculatios o electro desity versus height profiles obtaied fro represetative oo ioogras recorded at id ad

10 10 Rec ITU-R P434-6 high latitudes It is assued that these factors are applicable for all solar zeith agles The M factor ca be deteried fro the followig uerical expressios: M F1 = J ( J 0 J 100 ) R 12 J 0 = D D 2 J 100 = D D 2 ad where R 12 is betwee 0 ad 150 ad D represets the great-circle distace i kiloetres i the rage of k 5 Predictio of E-layer basic MUF 51 Groud distace up to k Ioospheric propagatio via a sigle reflectio fro the E-layer is iportat over distaces up to k The E-layer basic MUF of a particular ode ay be estiated as the product of the id-path value of foe (see Aex 1) ad the M factor M E This M factor based o ray-path calculatios for a parabolic odel E-layer with he = 110 k, ye = 20 k, whe effects of the Earth s agetic field are eglected, is give by: M E = x 170 x x x 4 x = D ad D represets the great-circle distace (k) 52 Groud distace betwee ad k The 2E MUF, for rages betwee ad k, is take as E(2000)MUF expressed i ters of the id-path foe 6 Predictio of the operatioal MUF For predictio purposes the operatioal MUF (see Recoedatio ITU-R P373) whe deteried by a F2-ode is expressed i ters of the basic MUF for differet seasos, ties of day ad trasitter radiated power as show i Table 2 Use of etries appropriate to id-path coditios is suggested Whe the operatioal MUF is deteried by a E or F1 ode it is take equal to the correspodig basic MUF TABLE 2 Ratio of the edia operatioal MUF to the edia basic MUF for a F2-ode, R op Suer Equiox Witer Equivalet isotropically radiated power (dbw) Night Day Night Day Night Day > Predictio of the optiu workig frequecy The FOT (Recoedatio ITU-R P373) is estiated i ters of the operatioal MUF usig the coversio factor F l set equal to 095 if the path basic MUF is deteried by a E or F1 ode ad as give i Table 3 if the path basic MUF is deteried by a F2 ode

11 Rec ITU-R P TABLE 3 Ratio F l of FOT to operatioal MUF whe deteried by a F2-ode a) R 12 less tha 50 as a fuctio of seaso, id-path local tie t ad id-path geographic latitude λ (North or South of equator) λ t W i t e r E q u i o x S u e r b) R 12 greater tha or equal to 50 ad less tha or equal to 100 as a fuctio of seaso, id-path local tie t ad id-path geographic latitude λ (North or South of equator) λ t W i t e r E q u i o x S u e r Witer: Suer: Equiox: Noveber, Deceber, Jauary, February i the Norther Heisphere ad May, Jue, July, August i the Souther Heisphere May, Jue, July, August i the Norther Heisphere ad Noveber, Deceber, Jauary, February i the Souther Heisphere March, April, Septeber, October i both heispheres

12 12 Rec ITU-R P434-6 TABLE 3 (cotiued) c) R 12 greater tha 100 as a fuctio of seaso, id-path local tie t ad id-path geographic latitude λ (North or South of equator) λ t W i t e r E q u i o x 089 S u e r Witer: Suer: Equiox: Noveber, Deceber, Jauary, February i the Norther Heisphere ad May, Jue, July, August i the Souther Heisphere May, Jue, July, August i the Norther Heisphere ad Noveber, Deceber, Jauary, February i the Souther Heisphere March, April, Septeber, October i both heispheres 8 Coputer progra The procedures described i this Aex are ipleeted i the coputer progra MUFFY, which predicts basic MUF, operatioal MUF ad optiu workig frequecy as a fuctio of tie of day, for give propagatio path, oth ad suspot uber ANNEX 3 Predictio of ray path For a siplified estiatio of oblique ray paths, reflectio ay be assued to take place fro a effective plae irror located at height h r I the followig: x = fof2 / foe ad H = with: M = ad y = x or 18, whichever is the larger 018 y ( R 12 25) M(3000)F2 + M 316

13 Rec ITU-R P a) For x > 333 ad x r = f / fof2 1, where f is the wave frequecy h r = h or 800 k, whichever is the saller h = A 1 + B 1 24 a for B 1 ad a 0 = A 1 + B 1 otherwise with A 1 = ( H 47) E 1 B 1 = ( H 17) F 1 A 1 E 1 = x r x r 2 06 x r + 06 F 1 is such that: F 1 = 1862 x 4 r x 3 r 3203 x 2 r x r 1091 for x r 171 F 1 = x r for x r > 171 ad a varies with distace d ad skip distace d s as a = (d d s ) / ( H + 140) d s = (H + 43) G G = 2102 x 4 r x 3 r 6315 x 2 r x r 4473 for x r 37 G = 1925 for x r > 37 b) For x > 333 ad x r < 1 h r = h or 800 k, whichever is the saller h = A 2 + B 2 b for B 2 0 = A 2 + B 2 otherwise with A 2 = ( H 47) E 2 B 2 = ( H 24) F 2 A 2 E 2 = Z Z F 2 = 0645 Z Z Z = x r or 01, whichever is the larger ad b varies with oralized distace d f, Z ad H as follows: b = 7535 d f d f d f d f + 1 d f = 0115 d Z ( H + 140) or 065, whichever is the saller c) For x 333 h r = H J + U d or 800 k, whichever is the saller with J = y y y ad U = ( H 80) ( y 22 ) H y 36