- Email: [email protected]
Mapping monthly quantiles of ionospheric electron content and foF2
Phys. Chem. Earrh (C), Vol. 24, No. 4, pp. 359-363, 1999
0 1999 Elsevier Science Ltd All rights reserved 1464-1917/99/$ - see front matter
Pergamon
PII: S1464-1917(99)00012-4
Mapping Monthly Quantiles of Ionospheric Electron Content and foF2 R. Leitinger and G. Hochegger
Institut
fiir Meteorologie
Received
24 May 1998;
und Geophysik, accepted
Universit2t
7 September
Monthly
quartiles
of electron
Graz, Austria
appear. It turned out that the minimum is 7 x 7 Fourier coefficients. Examples are shown in Fig. 1 (mapping of lower quartiles) and in Fig.s 2 and 3 (maps for medians and quartiles from 7 x 7 Fourier coefficients).
2
TEC quantiles from relative quantiles of peak electron density
From several European ionosonde stations F2 layer peak electron density data from foF2 are available from a long time interval. Therefore these data can be used to model monthly quantiles of peak electron density down to deciles. Since the variabilities of both electron content (TEC) and peak density are much higher than the variability of “Equivalent Slab Thickness” which is electron content divided by peak density, it makes sense to use the relative quantile ranges to calculate TEC quantiles from N?Tl Fig. 4 shows the slab thickness values calculated from TEC(SIRIO-Graz) and iV,(Roma) for 0 LT and 12 LT. Juantiles. The proposed procedure can be checked by means of data for individual months. An example is shown in Fig. 5 where quantiles of peak electron density N,,, from Roma, Italy (41.9 “N, 12.5”E), are compared with quantiles of electron content from Faraday observations made at Graz on the VHF beacon of the geostationary satellite SIR10 (latitude of the ionospheric point: 42.5”N). The data are from 1981.
content
The European data base of electron content derived from the Differential Doppler effect on the signals of the polar orbiting satellites of the (US) Navy Navigational Satellite System (NNSS) allows to gain monthly and bi-hourly medians and quartiles. Mapping procedures have been constructed and used for the medians (see, e.g., Feichter and Leitinger , 1997). One of these has been adopted for COST 238 (PRIME) and is based on 5 x 5 Fourier coefficients for the annual and for the diurnal variation (Leitinger , 1995). An equivalent mapping procedure for the quartiles leads to numerical difficulties: under some conditions negative lower quartiles Correspondence
1; A-8010
1998
Abstract. Monthly quantiles of ionization parameters are important information for system planning and to assess one aspect of ionospheric variability. For ionosonde parameters the data base is probably large enough to allow mapping of deciles. For electron content the situation is not so good: at least for Europe the data base only allows to construct maps for the upper and and the lower monthly quartiles. We present mapping procedures and maps for monthly quartiles of electron content and of foF2 based on experiences with mapping procedures for monthly medians. It turned out that for the lower quartiles it is necessary to to use more coefficients for the quartile maps than for the median maps. We discuss possibilities to gain decile information for electron content from foF2. For a few selected months and locations deciles can be gained from the Faraday effect on the signals of geostationary satellites. These selected cases are used to check on procedures to use foF2 experience to construct electron content deciles. 0 1999 Elsevier Science Ltd. All rights reserved. 1
Graz, HalbPrthgasse
3
Conclusion
Since slab thickness (TEC divided by peak density) is a very stable quantity and has only a small day to day variability (when compared with the day to day variability of both N,,, and TEC) one is justified to estimate the relative TEC quantiles by means of the relative N,
to: R. Leitinger 359
360
R. Leitinger and G. Hochegger: Mapping Monthly Quantiles of Ionospheric Electron Content and foF2
lower
LSA
quartile,
24
24
22
22
20
20
18
18
16
16
14
14
12
12
10
10
8
8
6
6
4
4
2
2
0
0 JFMAMJJASOND
JFMAMJJASONO doto
reconstruction
24
24
22
22
20
20
18
18
16
16
14
14
12
12
10
10
8
8
6
6
4
4
2
2
from
5x5
Fourier
coefficients
9x9
Fourier
coefficients
0
0
JFMAMJJASOND
JFMAMJJASOND reconstruction
from
7x7
Fourier
coefficients
reconstruction
from
Fig. 1. Example for mapping of lower quartiles of electron content from observations of the Diff. Doppler effect on NNSS signals. Low solar activity (0 < ii 5 40 - iz: monthly mean of sunspot number), data from 1984-1986 for 50”N. Contour lines of electron content in units of 10’5m-2 over a season (months) vs. local time (hours LT) system. Upper left: original quartiles;.upper right: map from 5 x 5 Fourier coefficients; lower left: map from 7 x 7 coefficients; lower right: map from 9 x 9 coefficients.
R. Leitinger and G. Hochegger: Mapping Monthly Quantiles of Ionospheric Electron Content and foF2 24 22
24 22
20
20
18
18
16
16
14
14
12
12
10
10
a
a
6
6
4
4
;
2 0
361
JFMAMJJASOND
JFMAMJJASOND lower
lower
quartile
24 22
24 22
20
20
16
18
16
16
14
14
12
12
10
10
6
6
6
6
4
4
quartile
2 0 JFMAMJJASOND
JFMAMJJASOND
median
median 24 22
24 22
20
20
18
16
16
16
14
14
12
12
10
10
8
6
6
6
4
4
2 0 JFMAMJJASOND
JFMAMJJASOND upper
quartile
Fig. 2. Example for maps of lower quartiles,
medians and upper quartiles of electron content. NNSS derived TEC data for low solar activity (0 5 w 5 40 - ??: monthly mean of sunspot number), selected months from 1984-1986 for 50’N. Contour lines of electron content in units of 10’sm-2 over a sesson (months) vs. local time (hours LT) system. Top: lower quartiles; middle: medians; bottom: upper quartiles. All maps constructed from 7 x 7 Fourier coefficients.
upper
quartile
Fig. 3. Example for maps of lower quartiles, medians and upper quartiles of electron content. NNSS derived TEC data for high solar activity (130 5 li 5 170 - ?i: monthly mean of sunspot number), selected months from 197&1982 for 50°N. Contour lines of electron content in units of 10’5m-a over a season (months) vs. local time (hours LT) system. Top: lower quartiles; middle: medians; bottom: upper quartiles. All maps constructed from 7 x 7 Fourier coefficients.
R. Leitinger
362
and G. Hochegger: Mapping Monthly Quantiles of Ionospheric Electron Content and foF2
Sirio-Groz
/
Roma,
1981,
00
quantiles. (Relative quantile: quantile divided by the median.) For this purpose the combination of two models is needed: A model for TEC medians and a model for relative N, quantiles. The following construction procedure can be applied for TEC quantile mapping: Step 1: Use the monthly and hourly quantiles (e.g., from the COST data base). Use a quadratic dependence on R12 to calculate quantiles for three selected levels of solar activity (low: R12=35; medium: R12=85; high: R12=135). “Normalized quantiles.” Step 2: Apply two dimensional Fourier decomposition to the normalized quantiles. 12 x 24 Fourier coefficients are obtained. Step 3: Cut the number of Fourier coefficients to obtain smoothing but to preserve the large scale structures in season vs. local time. A number of 7 x 7 coefficients seems to be appropriate for the quantiles. Step 4: Combine the relative quantile maps with an equivalent (7 x 7 Fourier coefficients) map of TEC to obtain the quantile maps.
LT
400
T 5 E 5 .j -D ;
300
200
100
ok
j
J
F
M
A
M
J
JASOND
References
months
Sirio-Groz
/
Romo,
1981,
12
LT
400[
0; J
F
M
A
M
J
JASOND
months
Fig. 4. Annual variation of equivalent slab thickness for 1981 from the combination of vertical electron content (TEC), measured by means of the Faraday effect on the VHF signal of SIRIO, received at Graz (latitude of ionospheric point 42.5’N) and peak electron density N,,, from the ionosonde data of Roma (41.9 ON, 12.5”E). Upper panel: 0 LT, lower panel: 12 LT.
Leitinger, R., The PRIME recommended long-term mapping method. Part of Section 9 of PRIME Final Report (Ed.: P.A. Bradley). pp. 70-84 of Advance Issue, ECSC-EEC-EAEC, Brussels, 1995 Feichter, E., Leitigner, R., The regional TEC model developed in Graz - a progress report. Acta Geod. Geoph. Hung. 32, 343354, 1997
363
R. Leitinger and G. Hochegger: Mapping Monthly Quantiles of Ionospheric Electron Content and foF2
Roma,
1981,
00
LT
Roma, i
120 1 0’0m-3 z 100 .= u c 0 (I.$ 80 x 5 ?i E
300 1 0’0m-3
\
2
150
40
5 E E
100 / -
‘Z
20
CI JFMAMJJASOND
JFMAMJJASOND months
SIRIO-Graz,
1981,
r
months
00
SIRIO-Graz,
LT
1981,
12
LT
1000
10’5m-2
10’5m-2
f
800
300
Pi i+ g
~
5c , -
0
.z
LT I
60
400
12
G 250 .X c 6 3 200 c
E
Z
1981,
600 200
6 E g t
100
0 IFMAMJJASOND months
JFMAMJJASOND months
Fig. 5. Comparison of peak electron density N,,, from foF2 with electron content. Ionosonde station Roma, Italy (41.9 ON, 12.5”E), electron content from Faraday observations made at Graz on the VHF beacon of SIR10 (latitude of the ionospheric point: 42.5”N). Data from 1981. Monthly quantiles for 0 LT and 12 LT. From bottom to top: lower deciles, lower quartiles, medians (heavy lines), upper quartiles, upper deciles.
0 1999 Elsevier Science Ltd All rights reserved 1464-1917/99/$ - see front matter
Pergamon
PII: S1464-1917(99)00012-4
Mapping Monthly Quantiles of Ionospheric Electron Content and foF2 R. Leitinger and G. Hochegger
Institut
fiir Meteorologie
Received
24 May 1998;
und Geophysik, accepted
Universit2t
7 September
Monthly
quartiles
of electron
Graz, Austria
appear. It turned out that the minimum is 7 x 7 Fourier coefficients. Examples are shown in Fig. 1 (mapping of lower quartiles) and in Fig.s 2 and 3 (maps for medians and quartiles from 7 x 7 Fourier coefficients).
2
TEC quantiles from relative quantiles of peak electron density
From several European ionosonde stations F2 layer peak electron density data from foF2 are available from a long time interval. Therefore these data can be used to model monthly quantiles of peak electron density down to deciles. Since the variabilities of both electron content (TEC) and peak density are much higher than the variability of “Equivalent Slab Thickness” which is electron content divided by peak density, it makes sense to use the relative quantile ranges to calculate TEC quantiles from N?Tl Fig. 4 shows the slab thickness values calculated from TEC(SIRIO-Graz) and iV,(Roma) for 0 LT and 12 LT. Juantiles. The proposed procedure can be checked by means of data for individual months. An example is shown in Fig. 5 where quantiles of peak electron density N,,, from Roma, Italy (41.9 “N, 12.5”E), are compared with quantiles of electron content from Faraday observations made at Graz on the VHF beacon of the geostationary satellite SIR10 (latitude of the ionospheric point: 42.5”N). The data are from 1981.
content
The European data base of electron content derived from the Differential Doppler effect on the signals of the polar orbiting satellites of the (US) Navy Navigational Satellite System (NNSS) allows to gain monthly and bi-hourly medians and quartiles. Mapping procedures have been constructed and used for the medians (see, e.g., Feichter and Leitinger , 1997). One of these has been adopted for COST 238 (PRIME) and is based on 5 x 5 Fourier coefficients for the annual and for the diurnal variation (Leitinger , 1995). An equivalent mapping procedure for the quartiles leads to numerical difficulties: under some conditions negative lower quartiles Correspondence
1; A-8010
1998
Abstract. Monthly quantiles of ionization parameters are important information for system planning and to assess one aspect of ionospheric variability. For ionosonde parameters the data base is probably large enough to allow mapping of deciles. For electron content the situation is not so good: at least for Europe the data base only allows to construct maps for the upper and and the lower monthly quartiles. We present mapping procedures and maps for monthly quartiles of electron content and of foF2 based on experiences with mapping procedures for monthly medians. It turned out that for the lower quartiles it is necessary to to use more coefficients for the quartile maps than for the median maps. We discuss possibilities to gain decile information for electron content from foF2. For a few selected months and locations deciles can be gained from the Faraday effect on the signals of geostationary satellites. These selected cases are used to check on procedures to use foF2 experience to construct electron content deciles. 0 1999 Elsevier Science Ltd. All rights reserved. 1
Graz, HalbPrthgasse
3
Conclusion
Since slab thickness (TEC divided by peak density) is a very stable quantity and has only a small day to day variability (when compared with the day to day variability of both N,,, and TEC) one is justified to estimate the relative TEC quantiles by means of the relative N,
to: R. Leitinger 359
360
R. Leitinger and G. Hochegger: Mapping Monthly Quantiles of Ionospheric Electron Content and foF2
lower
LSA
quartile,
24
24
22
22
20
20
18
18
16
16
14
14
12
12
10
10
8
8
6
6
4
4
2
2
0
0 JFMAMJJASOND
JFMAMJJASONO doto
reconstruction
24
24
22
22
20
20
18
18
16
16
14
14
12
12
10
10
8
8
6
6
4
4
2
2
from
5x5
Fourier
coefficients
9x9
Fourier
coefficients
0
0
JFMAMJJASOND
JFMAMJJASOND reconstruction
from
7x7
Fourier
coefficients
reconstruction
from
Fig. 1. Example for mapping of lower quartiles of electron content from observations of the Diff. Doppler effect on NNSS signals. Low solar activity (0 < ii 5 40 - iz: monthly mean of sunspot number), data from 1984-1986 for 50”N. Contour lines of electron content in units of 10’5m-2 over a season (months) vs. local time (hours LT) system. Upper left: original quartiles;.upper right: map from 5 x 5 Fourier coefficients; lower left: map from 7 x 7 coefficients; lower right: map from 9 x 9 coefficients.
R. Leitinger and G. Hochegger: Mapping Monthly Quantiles of Ionospheric Electron Content and foF2 24 22
24 22
20
20
18
18
16
16
14
14
12
12
10
10
a
a
6
6
4
4
;
2 0
361
JFMAMJJASOND
JFMAMJJASOND lower
lower
quartile
24 22
24 22
20
20
16
18
16
16
14
14
12
12
10
10
6
6
6
6
4
4
quartile
2 0 JFMAMJJASOND
JFMAMJJASOND
median
median 24 22
24 22
20
20
18
16
16
16
14
14
12
12
10
10
8
6
6
6
4
4
2 0 JFMAMJJASOND
JFMAMJJASOND upper
quartile
Fig. 2. Example for maps of lower quartiles,
medians and upper quartiles of electron content. NNSS derived TEC data for low solar activity (0 5 w 5 40 - ??: monthly mean of sunspot number), selected months from 1984-1986 for 50’N. Contour lines of electron content in units of 10’sm-2 over a sesson (months) vs. local time (hours LT) system. Top: lower quartiles; middle: medians; bottom: upper quartiles. All maps constructed from 7 x 7 Fourier coefficients.
upper
quartile
Fig. 3. Example for maps of lower quartiles, medians and upper quartiles of electron content. NNSS derived TEC data for high solar activity (130 5 li 5 170 - ?i: monthly mean of sunspot number), selected months from 197&1982 for 50°N. Contour lines of electron content in units of 10’5m-a over a season (months) vs. local time (hours LT) system. Top: lower quartiles; middle: medians; bottom: upper quartiles. All maps constructed from 7 x 7 Fourier coefficients.
R. Leitinger
362
and G. Hochegger: Mapping Monthly Quantiles of Ionospheric Electron Content and foF2
Sirio-Groz
/
Roma,
1981,
00
quantiles. (Relative quantile: quantile divided by the median.) For this purpose the combination of two models is needed: A model for TEC medians and a model for relative N, quantiles. The following construction procedure can be applied for TEC quantile mapping: Step 1: Use the monthly and hourly quantiles (e.g., from the COST data base). Use a quadratic dependence on R12 to calculate quantiles for three selected levels of solar activity (low: R12=35; medium: R12=85; high: R12=135). “Normalized quantiles.” Step 2: Apply two dimensional Fourier decomposition to the normalized quantiles. 12 x 24 Fourier coefficients are obtained. Step 3: Cut the number of Fourier coefficients to obtain smoothing but to preserve the large scale structures in season vs. local time. A number of 7 x 7 coefficients seems to be appropriate for the quantiles. Step 4: Combine the relative quantile maps with an equivalent (7 x 7 Fourier coefficients) map of TEC to obtain the quantile maps.
LT
400
T 5 E 5 .j -D ;
300
200
100
ok
j
J
F
M
A
M
J
JASOND
References
months
Sirio-Groz
/
Romo,
1981,
12
LT
400[
0; J
F
M
A
M
J
JASOND
months
Fig. 4. Annual variation of equivalent slab thickness for 1981 from the combination of vertical electron content (TEC), measured by means of the Faraday effect on the VHF signal of SIRIO, received at Graz (latitude of ionospheric point 42.5’N) and peak electron density N,,, from the ionosonde data of Roma (41.9 ON, 12.5”E). Upper panel: 0 LT, lower panel: 12 LT.
Leitinger, R., The PRIME recommended long-term mapping method. Part of Section 9 of PRIME Final Report (Ed.: P.A. Bradley). pp. 70-84 of Advance Issue, ECSC-EEC-EAEC, Brussels, 1995 Feichter, E., Leitigner, R., The regional TEC model developed in Graz - a progress report. Acta Geod. Geoph. Hung. 32, 343354, 1997
363
R. Leitinger and G. Hochegger: Mapping Monthly Quantiles of Ionospheric Electron Content and foF2
Roma,
1981,
00
LT
Roma, i
120 1 0’0m-3 z 100 .= u c 0 (I.$ 80 x 5 ?i E
300 1 0’0m-3
\
2
150
40
5 E E
100 / -
‘Z
20
CI JFMAMJJASOND
JFMAMJJASOND months
SIRIO-Graz,
1981,
r
months
00
SIRIO-Graz,
LT
1981,
12
LT
1000
10’5m-2
10’5m-2
f
800
300
Pi i+ g
~
5c , -
0
.z
LT I
60
400
12
G 250 .X c 6 3 200 c
E
Z
1981,
600 200
6 E g t
100
0 IFMAMJJASOND months
JFMAMJJASOND months
Fig. 5. Comparison of peak electron density N,,, from foF2 with electron content. Ionosonde station Roma, Italy (41.9 ON, 12.5”E), electron content from Faraday observations made at Graz on the VHF beacon of SIR10 (latitude of the ionospheric point: 42.5”N). Data from 1981. Monthly quantiles for 0 LT and 12 LT. From bottom to top: lower deciles, lower quartiles, medians (heavy lines), upper quartiles, upper deciles.