- Email: [email protected]
Anomalous ionospheric reflection during solar eclipses
Journal of
Atmosptwricand Terrestrial
Plwica, 1969, Vol. 16, pp. 93 to 98. Pergamon Press Ltd. Printed in Nortlwml Ireland
Anomalous ionospheric reflection during solar eclipses W. L. PRICE Radio Research Board (Sydney Laboratory), Commonwealth Scientific and Industrial Research Organization, Electrical Engineering Department, University of Sydney Abstract-The appearance of complexities in ionosonde records has been ascribed by MUNRO to multiple reflections from inclined isoionic surfaces. Further extension of this work by MUNRO and HEISLER has suggested that irregularities appearing on ionosonde eclipse records and affecting consequent interpretations may be due to a similar cause. In this paper a necessary relation between height and curvature of the reflecting isoionic surface to produce complexities is deduced. It is further shown by calculating a typical set of isoionic contours for solar eclipse conditions that the necessary height curvature relation is satisfied at aert,ain regions within the erlipe zone so thd complexities can occur. 1. INTRODUCTION HORIZONTAL variation
of ionospheric ionization has aroused increased interest in recent years, and records of ionosonde and fixed frequency sounding equipment (h’j, h’t) have been examined for evidence of such gradients. These supply measurable information about some physical properties of the upper atmosphere; such as the large scale travelling ionospheric disturbances (T.I.D.) described by MUNRO (1949, 1950, 1953), MUNRO and HEISLER (1956), and HEISLER (1958). In recent papers MUNRO and HEISLER (1956, 1957) have shown that many of the ionospheric effects caused by solar eclipses (BEYNON and BROWN, 1956) produce irregularities in records which closely resemble those of T.I.D. and that the irregularities in both cases probably result from reflections by inclined isoionic They point out that in all cases allowance should be made for the surfaces. possibility of such tilts when analysing the records. The travelling eclipse disturbances (E.I.D.) cover a considerably larger area than T.I.D. so that inclination of the layers is in general correspondingly smaller. This paper shows how sufficient warping of the contours to account for the anomalies in records can occur. 2. OCCURRENCE IN RECORDS OF COMPLEXITIES DUE TO NON-VERTICAL REFLECTIONS
The appearance at any instant on an h’f record of more than one ordinary (or extraordinary) ray trace except those due to multiple reflections will be referred to (after MUNRO) as a complexity. Certain necessary conditions for the simultaneous reception by a station of rays from two separate parts of a reflecting layer are given in Section (2.1.1) or in Section (2.1.2) and in Section (2.2). 2.1.1. The layer may be a continuous surface ACDBA (Fig. 1) whose slope varies but is everywhere continuous and whose normal nowhere makes an angle greater than 90’ with the vertical (in practice never greater than about 10’). The station at S receives rays from areas A and B. Continuous lines such as ACDB can be drawn in the surface and every small element CD (ds) lies in a plane OCD normal to the surface. 0 is the centre of curvature of CD relative to the earth and CD’ (ds’) is 93
Then C) must be sometimes above li and sometimes below the earth. (This follows from the fact that ds’ ~--o anti I1.4 that, t,he sense of ds’ changes when 0 moves across the earbh’n boundary as tts moves continuously from A to R.) This result is equivalent! bo saying that there must be lines in the continuous contour whose radius of curvature R relative tc) the earth is less than the sla,nt height of the layer h.. the intercept
on the (flat) earth by W ‘, ()I).
/, /
0
dS’
2.1.2. The isoionic surface has an effective discontinuitZ>r. or a discontinuit,g of slope; then a complexity may’ occur as in Fig. l(b) and Fig. l(c). 2.2. The equipment must be able t’o resolve the complexit?;. Especially. the transmitted beam must be wide enough Do fall on both reflecting surfaces and each surface must reflect enough radiation to record a trace on t#he film. The optical shadow cast on the surface of the earth by a t&al eclipse is approximately a circle of radius 2,500 km; the time from first to last contact is about 2 hr. The ionospheric region affected extends behind the shadow because of the lag due to a finite rate of recombination. This “tail” is more pronounced in t,he higher layers where the recombination is slower. Consider now the maximum curvature relative to the earth, occurring when the curvature changes symmetrically throughout and uniformly in each part, being zero at the ends and maximum in the middle and having inflections at the quarter points. Suppose the distance apart of the quart%erpoints 2% = 3000 km. and the elevation above them of the centre d = 20 km. Then the radius of curvature
Anomalous ionosphericreflection during solar eclxpses
h? N x2/3&2i 38,000 km. This is much greater than the height of the layer so that a complexity cannot occur if the curvature changes uniformly through the eclipse. There is the possibility however that some contours might change rapidly in height over a small part of the eclipse. To examine this possibility a set of consul has been calculated using probable vaIues of recombination coefficient (x and day-time (initial) electron densit,ies2\7. tcx 1O1o cm*/electronset
N x IO6 electron/cm3
Fig. 2. Assumed variation of CLand of initial iV with h.
3. C~LoufrATnm AND
ANALVSE~ 0~ THE CBNT~URS
The cr-h and initial X-4 curves are plotted in Fig. 2. X.4 has been made parabolic for each layer (E, 31, _B’Z)excepting for sections between E and P1, and Pl and P2 where iV is assumed to be oonstant. It is probable that N does remain large in these “unseen” parts (JACKSON, 1956); the presence of small fluctuations there would be unimportant to our main conclusions. The actual magnitudes of h,, N, and the Iayer thickness Y, are considered typical for day-time and mid-latitude and medium intensity distribution. No allowance is made for the zenith angle changing during the 2 hr duration of the eclipse. It seems feasible that the electron loss function is “effectiveIy” recombination (a) for E and P2 and effectively attachment (8) above about 250 km. We have assumed that a falls by a factor of about 3.5 from h,E to &Fl, remains sensibly constant for 20-30 km and then falls rapidly by a factor of about 50 from there to h,PZ at 250 km (MMXA, 1952; SZ~~DREI and _~c~~HI~~Y, 1956). This variation agrees with the idea first advanced by BRADBYJRY (1938)that PI and P2 are produced by the same band of solax radiation. The electron density N through the centre’ of a total eclipse was eaIe~Iated 95
curves of N/X, as a function of time for various \ulues of a paramet,rr z := N,crt, given by RYDBECK and WILHELMSSOP; (1954) where X0 is the initial value of ion density. It has been assumed that apparent diameters of sun (d) ant1 moon (D) are equal and that the eclipse duration 2, is equal to X000 sec. The results are plobted in Fig. 3 as vert,ical sections of the cont,ours of constant S, t,aken along the eclipse patch. The maxima of electron densit,?: X,E, N,,EI. S,,Ir’2 are shown by broken lines. ‘I’htk horizontal and ~c~rticnl scales are equal so that angles between intersecting lines appear undistortctl. Horizontal dista#nces :I 1.8 cont’racted are measured from 0: the centre of the eclipse. ‘lYlest? (liSt&llCW by the “flat earth” representation b>r MI amount whioll it~c~reascsw&h height Ijut1the angles between intersecting lines RR’ not. appreciabl,v changed. ‘Vhe contours are all horizont,al of course just2 before and sornet,ime aft,cr t,hc eclipse. When the electron density is decreasing wit,h t.ittl(b;L given contour rises ilrasimum of S. or falls according to whether it, is helow 01 ab0vV t’he ittljM3~~Ilt The fact that 0: decreases with height causes the rise to occur mor(’ rapid1 y t haI1 the corresponding fall so that’ the heights of maxima ot’ S in(:reasc while S,:,, The slopes near 1-h<-beginning al~tl cud of tSlir eclipse are’ decreases in magnitude. very small and unimportjant and only t’hft uentjral part of’ t ho eclipse is show11. Here however certain contours show nluch steeper slopes ant1 also rliscont,illuities giving rise to complexi&s. This o(~curs as follows: Where AT originally has t,he same va)lue above and below a n1aximum t*he two contours with this value sometimes merge and cross thtl tnaximum line. This 2% km and -+ 414 kul iti the E- and F.5layers respectively, tha ca,n be seen at positions being indicated by arrows. A4gain where A’ origina’lly has a given value helow a tltitSiullirkl only, the11 as _Y,,, decreases. the contour with this value Inay cross the maximum and continue -GOkm. .It. is easily seen that. (III above it,, as for instance in the F’I-layer at c:omplexities can occur in either of these cases. For example the (h’f) curve for a &ation S at, 470 km would show t’he ordinary ray trace like t’hat in Fig. 4 with t,wo branches in the Pl-section. One hrauch produced by rays reflected as at A gocrs to infinite virtual height M.IIAII cl%ical reflection occurs at the level marked X,,,Ir’.l; it then continues until infinite virtual height again occurs at 7Q’Z. The ravs for the second branch are reflected at pointIs such as 11. The trace for this branch is a spur, ending when the reflect’ing area H becomes so small that the radiation reflected is insufficient to form a visible record. Had a maximum existed between h,,,,.Fl and h,,F2. which was originall_c obscured by h,Fl, the gradient’ in the recombination rate could result in it being revealed. The result would be t,o divide E’2 int)o t,wo. as showy by the dotted line, as if another layer had been formed. The general sequence of events will be reversed when the ionization is increasing with time. It is clear t,hat there is an asymmetry in the positions and times of occurrence of the anomalies because of the lag caused by a finit’e M. Two further points may be noted: Bending of the rays due to refraction is negligible because the rays are all lbearly normal to the strata. Focusing may occur at reflection because the station is sometimes near the cent,re of cnrrature of the reflecting surface so that h = R.
from
Anomalous ionospheric reflection during solar eolipsos
I I I I I I
I
I ! I
Analysis of electron densities during an eclipse shows that while the slopes and curvatures of the strata are mostly very small, effective discontinuities occur and the slopes are sometimes large enough to produce complexities in the records of ionospheric sounding equipment. These complexities are due t’o rays reflected along paths inclined to the vertical.
/
/
1
2
/
,3
f,
/
I
4
5
/
6
1
7
I
8
MC/S
Fig. 4. I!“ormof the ordinary rap trace which would be recorded when the station was :tt 470 km (Fig. 3). A complexity appears due to rays I-eflectedfrom surfaces B. The dotted part shows the effect if a maximum, originally not seen, was between h,,Pl and h,PZ.
Acknowledgements-This work has been carried out as part of the programme of the Radio Research Board of the Commonwealth Scientific and Industrial Research Organization and is published with the permission of the Executive. The author wishes to thank Dr. G. H. MUNRO for suggestion of the problem and both him and Mr. L. H. HEISLER for helpful discussion. REFERENCES BEYNON
W. J. G. and HItowN
(:.
M.
1956
BRADBURY N. N. HEISLER L. H.
193X
MUNRO G. H. MUNRO C. H. MUNRO G. H. MUNRO G. H. and HJXISLE~ L. H. MUNRO G. H. and HEISLER L. H. RYDBECK 0. E. H. and WILHELMSSON H. SZENDREI M. E. and MCELHINNY M. W.
1949 1950 1953
195x 1956 1952
1956 19.57 1!154 1956
!)H
Pergamon Press, London. Terr. Magn. Atmos. Elect. 43, 55. -4ust. J. Phys. 11,79. .J. G’eophys. Res. 01,120. The Upper i2tmoaphere. The Asiatic Society, Calcutta. Nature, Lord. 168, 81%. Proc. Roy. Boc. A B&$ 208. Proc. Roy. Rot. A 219, 447. Aust. J. phys. 9, 343, 359. .I. Atmoapplh. Terr. Phys. 12, 57’. Chalnaers Tek. Hiig8k. Handl. 149. J. Atm.osph. Terr. Phys. 9, 118.
Atmosptwricand Terrestrial
Plwica, 1969, Vol. 16, pp. 93 to 98. Pergamon Press Ltd. Printed in Nortlwml Ireland
Anomalous ionospheric reflection during solar eclipses W. L. PRICE Radio Research Board (Sydney Laboratory), Commonwealth Scientific and Industrial Research Organization, Electrical Engineering Department, University of Sydney Abstract-The appearance of complexities in ionosonde records has been ascribed by MUNRO to multiple reflections from inclined isoionic surfaces. Further extension of this work by MUNRO and HEISLER has suggested that irregularities appearing on ionosonde eclipse records and affecting consequent interpretations may be due to a similar cause. In this paper a necessary relation between height and curvature of the reflecting isoionic surface to produce complexities is deduced. It is further shown by calculating a typical set of isoionic contours for solar eclipse conditions that the necessary height curvature relation is satisfied at aert,ain regions within the erlipe zone so thd complexities can occur. 1. INTRODUCTION HORIZONTAL variation
of ionospheric ionization has aroused increased interest in recent years, and records of ionosonde and fixed frequency sounding equipment (h’j, h’t) have been examined for evidence of such gradients. These supply measurable information about some physical properties of the upper atmosphere; such as the large scale travelling ionospheric disturbances (T.I.D.) described by MUNRO (1949, 1950, 1953), MUNRO and HEISLER (1956), and HEISLER (1958). In recent papers MUNRO and HEISLER (1956, 1957) have shown that many of the ionospheric effects caused by solar eclipses (BEYNON and BROWN, 1956) produce irregularities in records which closely resemble those of T.I.D. and that the irregularities in both cases probably result from reflections by inclined isoionic They point out that in all cases allowance should be made for the surfaces. possibility of such tilts when analysing the records. The travelling eclipse disturbances (E.I.D.) cover a considerably larger area than T.I.D. so that inclination of the layers is in general correspondingly smaller. This paper shows how sufficient warping of the contours to account for the anomalies in records can occur. 2. OCCURRENCE IN RECORDS OF COMPLEXITIES DUE TO NON-VERTICAL REFLECTIONS
The appearance at any instant on an h’f record of more than one ordinary (or extraordinary) ray trace except those due to multiple reflections will be referred to (after MUNRO) as a complexity. Certain necessary conditions for the simultaneous reception by a station of rays from two separate parts of a reflecting layer are given in Section (2.1.1) or in Section (2.1.2) and in Section (2.2). 2.1.1. The layer may be a continuous surface ACDBA (Fig. 1) whose slope varies but is everywhere continuous and whose normal nowhere makes an angle greater than 90’ with the vertical (in practice never greater than about 10’). The station at S receives rays from areas A and B. Continuous lines such as ACDB can be drawn in the surface and every small element CD (ds) lies in a plane OCD normal to the surface. 0 is the centre of curvature of CD relative to the earth and CD’ (ds’) is 93
Then C) must be sometimes above li and sometimes below the earth. (This follows from the fact that ds’ ~--o anti I1.4 that, t,he sense of ds’ changes when 0 moves across the earbh’n boundary as tts moves continuously from A to R.) This result is equivalent! bo saying that there must be lines in the continuous contour whose radius of curvature R relative tc) the earth is less than the sla,nt height of the layer h.. the intercept
on the (flat) earth by W ‘, ()I).
/, /
0
dS’
2.1.2. The isoionic surface has an effective discontinuitZ>r. or a discontinuit,g of slope; then a complexity may’ occur as in Fig. l(b) and Fig. l(c). 2.2. The equipment must be able t’o resolve the complexit?;. Especially. the transmitted beam must be wide enough Do fall on both reflecting surfaces and each surface must reflect enough radiation to record a trace on t#he film. The optical shadow cast on the surface of the earth by a t&al eclipse is approximately a circle of radius 2,500 km; the time from first to last contact is about 2 hr. The ionospheric region affected extends behind the shadow because of the lag due to a finite rate of recombination. This “tail” is more pronounced in t,he higher layers where the recombination is slower. Consider now the maximum curvature relative to the earth, occurring when the curvature changes symmetrically throughout and uniformly in each part, being zero at the ends and maximum in the middle and having inflections at the quarter points. Suppose the distance apart of the quart%erpoints 2% = 3000 km. and the elevation above them of the centre d = 20 km. Then the radius of curvature
Anomalous ionosphericreflection during solar eclxpses
h? N x2/3&2i 38,000 km. This is much greater than the height of the layer so that a complexity cannot occur if the curvature changes uniformly through the eclipse. There is the possibility however that some contours might change rapidly in height over a small part of the eclipse. To examine this possibility a set of consul has been calculated using probable vaIues of recombination coefficient (x and day-time (initial) electron densit,ies2\7. tcx 1O1o cm*/electronset
N x IO6 electron/cm3
Fig. 2. Assumed variation of CLand of initial iV with h.
3. C~LoufrATnm AND
ANALVSE~ 0~ THE CBNT~URS
The cr-h and initial X-4 curves are plotted in Fig. 2. X.4 has been made parabolic for each layer (E, 31, _B’Z)excepting for sections between E and P1, and Pl and P2 where iV is assumed to be oonstant. It is probable that N does remain large in these “unseen” parts (JACKSON, 1956); the presence of small fluctuations there would be unimportant to our main conclusions. The actual magnitudes of h,, N, and the Iayer thickness Y, are considered typical for day-time and mid-latitude and medium intensity distribution. No allowance is made for the zenith angle changing during the 2 hr duration of the eclipse. It seems feasible that the electron loss function is “effectiveIy” recombination (a) for E and P2 and effectively attachment (8) above about 250 km. We have assumed that a falls by a factor of about 3.5 from h,E to &Fl, remains sensibly constant for 20-30 km and then falls rapidly by a factor of about 50 from there to h,PZ at 250 km (MMXA, 1952; SZ~~DREI and _~c~~HI~~Y, 1956). This variation agrees with the idea first advanced by BRADBYJRY (1938)that PI and P2 are produced by the same band of solax radiation. The electron density N through the centre’ of a total eclipse was eaIe~Iated 95
curves of N/X, as a function of time for various \ulues of a paramet,rr z := N,crt, given by RYDBECK and WILHELMSSOP; (1954) where X0 is the initial value of ion density. It has been assumed that apparent diameters of sun (d) ant1 moon (D) are equal and that the eclipse duration 2, is equal to X000 sec. The results are plobted in Fig. 3 as vert,ical sections of the cont,ours of constant S, t,aken along the eclipse patch. The maxima of electron densit,?: X,E, N,,EI. S,,Ir’2 are shown by broken lines. ‘I’htk horizontal and ~c~rticnl scales are equal so that angles between intersecting lines appear undistortctl. Horizontal dista#nces :I 1.8 cont’racted are measured from 0: the centre of the eclipse. ‘lYlest? (liSt&llCW by the “flat earth” representation b>r MI amount whioll it~c~reascsw&h height Ijut1the angles between intersecting lines RR’ not. appreciabl,v changed. ‘Vhe contours are all horizont,al of course just2 before and sornet,ime aft,cr t,hc eclipse. When the electron density is decreasing wit,h t.ittl(b;L given contour rises ilrasimum of S. or falls according to whether it, is helow 01 ab0vV t’he ittljM3~~Ilt The fact that 0: decreases with height causes the rise to occur mor(’ rapid1 y t haI1 the corresponding fall so that’ the heights of maxima ot’ S in(:reasc while S,:,, The slopes near 1-h<-beginning al~tl cud of tSlir eclipse are’ decreases in magnitude. very small and unimportjant and only t’hft uentjral part of’ t ho eclipse is show11. Here however certain contours show nluch steeper slopes ant1 also rliscont,illuities giving rise to complexi&s. This o(~curs as follows: Where AT originally has t,he same va)lue above and below a n1aximum t*he two contours with this value sometimes merge and cross thtl tnaximum line. This 2% km and -+ 414 kul iti the E- and F.5layers respectively, tha ca,n be seen at positions being indicated by arrows. A4gain where A’ origina’lly has a given value helow a tltitSiullirkl only, the11 as _Y,,, decreases. the contour with this value Inay cross the maximum and continue -GOkm. .It. is easily seen that. (III above it,, as for instance in the F’I-layer at c:omplexities can occur in either of these cases. For example the (h’f) curve for a &ation S at, 470 km would show t’he ordinary ray trace like t’hat in Fig. 4 with t,wo branches in the Pl-section. One hrauch produced by rays reflected as at A gocrs to infinite virtual height M.IIAII cl%ical reflection occurs at the level marked X,,,Ir’.l; it then continues until infinite virtual height again occurs at 7Q’Z. The ravs for the second branch are reflected at pointIs such as 11. The trace for this branch is a spur, ending when the reflect’ing area H becomes so small that the radiation reflected is insufficient to form a visible record. Had a maximum existed between h,,,,.Fl and h,,F2. which was originall_c obscured by h,Fl, the gradient’ in the recombination rate could result in it being revealed. The result would be t,o divide E’2 int)o t,wo. as showy by the dotted line, as if another layer had been formed. The general sequence of events will be reversed when the ionization is increasing with time. It is clear t,hat there is an asymmetry in the positions and times of occurrence of the anomalies because of the lag caused by a finit’e M. Two further points may be noted: Bending of the rays due to refraction is negligible because the rays are all lbearly normal to the strata. Focusing may occur at reflection because the station is sometimes near the cent,re of cnrrature of the reflecting surface so that h = R.
from
Anomalous ionospheric reflection during solar eolipsos
I I I I I I
I
I ! I
Analysis of electron densities during an eclipse shows that while the slopes and curvatures of the strata are mostly very small, effective discontinuities occur and the slopes are sometimes large enough to produce complexities in the records of ionospheric sounding equipment. These complexities are due t’o rays reflected along paths inclined to the vertical.
/
/
1
2
/
,3
f,
/
I
4
5
/
6
1
7
I
8
MC/S
Fig. 4. I!“ormof the ordinary rap trace which would be recorded when the station was :tt 470 km (Fig. 3). A complexity appears due to rays I-eflectedfrom surfaces B. The dotted part shows the effect if a maximum, originally not seen, was between h,,Pl and h,PZ.
Acknowledgements-This work has been carried out as part of the programme of the Radio Research Board of the Commonwealth Scientific and Industrial Research Organization and is published with the permission of the Executive. The author wishes to thank Dr. G. H. MUNRO for suggestion of the problem and both him and Mr. L. H. HEISLER for helpful discussion. REFERENCES BEYNON
W. J. G. and HItowN
(:.
M.
1956
BRADBURY N. N. HEISLER L. H.
193X
MUNRO G. H. MUNRO C. H. MUNRO G. H. MUNRO G. H. and HJXISLE~ L. H. MUNRO G. H. and HEISLER L. H. RYDBECK 0. E. H. and WILHELMSSON H. SZENDREI M. E. and MCELHINNY M. W.
1949 1950 1953
195x 1956 1952
1956 19.57 1!154 1956
!)H
Pergamon Press, London. Terr. Magn. Atmos. Elect. 43, 55. -4ust. J. Phys. 11,79. .J. G’eophys. Res. 01,120. The Upper i2tmoaphere. The Asiatic Society, Calcutta. Nature, Lord. 168, 81%. Proc. Roy. Boc. A B&$ 208. Proc. Roy. Rot. A 219, 447. Aust. J. phys. 9, 343, 359. .I. Atmoapplh. Terr. Phys. 12, 57’. Chalnaers Tek. Hiig8k. Handl. 149. J. Atm.osph. Terr. Phys. 9, 118.