The state of the art in D-region IRI modelling

0273—1177184 $0.00

8, 1984 Adv. Space Red. Vol.4, No.1, pp.71—7 Printed in Great Britain. All rights reserved.

+ .50 Copyright © COSPAR

THE STATE OF THE ART IN D-REGION IRI MODELLING K. Rawer and Y. V. Ramanamurty* Albert-Ludwigs- Universität, D-7800 Freiburg, F.R. G.

ABSTRACT While describing the formulation of IRI—79, in so far as it is applicable to the sub E—peak electron density profile, an attempt is made to compare its predictions with the available experimental evidence. The improvements needed for 0—region electron density modelling are summarized. The current D—region IRI modelling effort is illustrated with a typical example. INTRODUCTION Beginning with the COSPAR Conference at Konstanz in 1973, the International Reference Ionosphere (IRI) was first presented, and the scientific community was invited to suggest an improved description of the main plasma parameters of the ionosphere. The latest published version, IRI—79 is contained in GAG Report 82 /1/. 0—REGION Ne MODELLING EFFORT Modelling of the 0—region electron density (Ne) distribution is based purely on observational evidence. There are statistical models which are also based on observations, theoretical aeronomy models which rely on the chemistry of the D—region, and models which use experimental Ne profiles also as one of the inputs and use the chemistry to arrive at neutral nitric oxide density distribution. D—REGION IRI

1979

—

The electron density Ne at a particular height h is described as a function of (local) time, solar zenith angle (X), (smoothed Zurich) sunspot number (R 12), latitude (LAT) and month: Ne(h)

f(X, R12, LAT, MONTH)

=

(1)

Details of the formulation of the 0—region model were described by Bilitza Ill. About 40% of the then measured rocket profiles showed a characteristic inflection point whose location (H~) and electron density value (N5~) could be described by 2~7X) NMD/m—3 = F(R 8 (O.1/cos 12) . 10 e (2) F(R12)

6.05

=

+

0.088 R12

(3)

Different scale heights were used below and above the inflection point and these are interrelated through FP1 which is defined as d(lo FP1

)

N dh

=

e

(4)

The 0—region profile is connected to the E peak (HNE) through the relation Ne(h)

=

N~

.

exp(—D1

.

(HME_h)K) for MDX

*Permanent address: National Physical Laboratory, Hillside 71

<

h ~ HME

Road, New Delhi, India.

(5)

72

K. Rawer and Y.V. Ramanamurty

where Dl and K involve the height derivatives and HDX is the height where Ne as compared to NMD increased by a factor of e(2.718). Below HMD the profile is extrapolated down to 65 km through the use of the scale height S (the height difference between HMD and the height where Ne has dropped to NMD/e) and FP 1 Ne(h)

=

f(1-IND, FP3, S) for 65 km

NMD

2+ S2/2

FPI

—

.

S

—

h

MDX

1)S3

(6) (7)

FP3 = (FPI A different scale height Sa is used to model the region between MMD and HDK where Ne increased by a factor of e: Ne(h)

=

NMD

.

2 Fp3a

=

f(HND, Fp +

—

3a, Sa) (FF1 . Sa)

(8) +

1)/Sa3

(FPI

About 80 Ne profiles available at that time showed the characteristic inflection point and these were used to deduce the following values for FF1 and MMD ypi

= = =

HHD

= =

0

—

0.02 0.05 0.05 81km 88 km

day, low latitudes day, mid/high latitudes night, all latitudes day night

REGION IRI VERSUS RADIO OBSERVATIONS

The Collision Frequency Problem En the determination of Ne profiles either by rocket or ground based (0 — region) radio experiments, the mono—energetic transport collision frequency (Om) is only very rarely simultaneously measured. In such cases, a collision frequency profile has to be assumed in order to obtain the electron density profile. The direct rocket measurements indicate the existence of a proportionality factor between ~m and the atmospheric pressure measurements incorporated in reference atmosphere models such as CIRA — 72 /2/ through a relation of the type: Vm=K~P

(9)

where 2p is the pressure. The magnitude of the constant K (values ranging from 5.8 to 9.9 m N~s~were reported in the literature) depends upon the atmospheric model and the seasonal dependence assumed when the CIRA—72 model is used; it is implied that K depends upon season/month and latitude. There were indications that (indirectly) measured (lower) E—region collision frequencies, apart from pressure, 0m is at were least dependent a function on solar of latitude activity and as well season and,can of therefore course, height /3/. One write in general that =

f(MONTH, TAT)

(10)

The apparent discrepancies, if any, between radio wave absorption and the available rocket measurements of Ne profiles must be viewed therefore in the context of (simultaneous) collision frequency measurements and their modelling effort in the first instance. In this connection, rocket um measurements at different places and seasons, especially those that are carried out simultaneously with We measurements, have special significance. The same value of ‘m is used as in the Sen—Wyller generalization of the magnetolonic theory for vertical incidence, and is based on the assumption that the electron collision cross— section o is proportional to the relative velocity between the neutrals and the electrons: 0=

where B is a constant.

B~o~

(ii)

However recent laboratory measurements (4) have suggested that (12)

where 0Te is the average (thermal) velocity of the electrons, and that the magneto—ionic theory ought to incorporate Eqn (12) including the term A. Many important aspects concerning the interpretation of observations, particularly those in the region below 70 km (such as MF rocket radio propagation measurements, rocket probe results, ground—based VLF/LF/MF radio ref lection/propagation measurements) depend upon the correct assessment of the collision frequency problem from the experimental and theoretical points of view.

0—Region IRI Modelling

73

For the intercomparison of radio observations made at different places and seasons, ~ must be based on the same atmospheric model, preferably the mean reference atmospheric model CIRA—72, /2/, which may be used (until its new version becomes available) apart from cases where simultaneous vm measurements were available. The relation between K (CIRA—72) and the actual K value used in data reduction may be indicated. Shape and Absolute Values The shape of 0—region IRI models, as well as the absolute value of electron density, should agree with the rocket propagation measurements (controlled by probe measurements wherever possible). The rocket measurements are the primary data base. The ground based (radio) measurements extending over a wide frequency spectrum (from ELF to HF) could be used to establish the solar zenith angle, solar activity, latitude and seasonal dependencies of Ne, and also the diurnal variation of Ne profiles. Solar Zenith Angle (X) Dependence In IRI—79 /1/ the dependence of Ne on X on a particular relation (Eqn 2). NMD

Const

=

day is introduced through the

2~7~

.

e(005

The solar zenith angle control of the D — region is thus mainly introduced in the NMD parameter. The X control at a given height is usually expressed as Ne(h)

N

=

0 cosnX (Aeronomy,

or by

N(h)

A

=

absorption models)

(13)

B cos X (Statistical models)

+

(14)

The statistical models, e.g. /5,6/, are fitted to a set of observed profiles and have the form: Ne(h)

Const. term

+

B cos X

F(magnetic activity

+

CLAT

term)

+

+

DR

+

E

(seasonal tern)

+

Residual standard deviation

(15)

(McNamara /5/) Ne(h)

=

A

+

B (L

+

Lo) (Torkar at al. /6/, Riometer absorption).

(16)

In Eqn(16) A is a constant independent of X, L is the absorption usually measured in dE and 0~7(X) by day Lo/dB

= =

0.6 Ch 0.028

(X

<

98.75°)

by night (X

>

98.75°)

B/m3 dB~/ is the part that varies with X during daytime and Ch is the Cha~tranfunction (approximately sec X). The main difficulties met when incorporating the statistical model due to McNamara /5/ directly into IRI are: (i) it is based on all the Ne profiles reported from all techniques (ground based and rocket borne) whereas IRI gives more weight to rocket measurements checked with simultaneous rocket propagation measurements. (ii) The reliability of the technique as a function of height is not taken into account while formulating the statistical model. The statistical model due to Torkar et al. /6/ has limited applicability (high—latitude particle controlled 0—region). A comparison of the results of the IRI—79 Ill approach with those from statistical models shows up the following differences. No constant term independent of solar (electromagnetic radiation) control is included in IRI—79 which attempted to describe the lower ionosphere using one parameter (R 12) to describe solar activity, and three terms (X, LAT, MONTH) to describe the terrestrial dependence. There is, however, considerable experimental evidence for the influence of parameters of non—solar origin (e.g. cosmic rays at middle/high latitudes; cosmic X—rays at low latitudes)

and of other factors not covered in earlier work

on models (e.g. nitric oxide variability). If the influence of these factors is not taken into account in IRI, it is possible that the true nature of the control by X and R12 may not be discernible.

74

K. Rawer and Y.V. Ramanamurty

The absorption (Al, A3) values could equally well be represented either by L=A+Bcos or by

L

X

(17)

0x

(18)

0 cos

=

Both Eqns(17) and (18) contain two constants A and B or D and n. In Eqn (18) n is dependent on the latitude which determines the range of the variation in X. Torkar et al. /6/ encountered negative values of A at heights below 100 km (daytime) and this ought to be re—examined. Equation (~4)may be used to find the terms not controlled by the solar zenith angle from the rocket Ne profiles. The height dependence of the x control pointed out by Mitra and Somayajulu /7/, as well as the latitudinal influence on the diurnal variation of Ne, could then be adequately taken into account. If the IRI representation of X control, Eqn (2), is put in the form of Eqn (18), the value of n (Fig. 1) is greatest (about 3) at 65 km and approaches the value of 0.5 expected for a Chapman layer near 100 km. At E—region heights the value of n predicted by IRI agrees with the values deduced from rocket and jonosonde observations. However, the height variation of n in the 0—region is not the same (in fact opposite variations appear between 65 to 85 km) as the one predicted by the statistical model /5/, but it agrees in general with the semi— empirical model /7/. The value of the constant term in Eq. (15), as in the McNamara model /5/, is also shown in Fig. I. It is interesting to note that the magnitude of this constant term increases with height in the 55 to 90 km range.

10

110

20

30

I

~

-

~

I

I

0~2

I

(1979)

~I

I

0.4

O~6

I

0~8

FO

b Fig. 1. Dependence of D—region electron density on solar zenith angle X /5/. The diurnal index n obtained from IRI—79 is compared with the prediction from the statistical model (circles, abscissa on top) Dependence on Sunspot Number The IRI profiles show (Fig. 2) that dependence of Ne on sunspot number is stronger at lower heights, and this is difficult to reconcile with (indirect) observational evidence. The ratio of the Ne values for R = 100 and R = 10 varies from 2.1 at 65 km to about 1.4 at 110 Tan. This dependence is the same from the equator up to South Gist (570) for heights below 100 km. At 95 km, Ne increases by a factor of 2.3 as shown by the rocket observations /8/ at Wallops Island (38°N) whereas the IRI prediction is about 1.7. Taubenheim and Singer /9/ mentioned that the ratio was about 1.6 at 80 km. A value of unity at 70 km may therefore not be unrealistic. The effect appears to vanish at 55 km, as in the statistical model /5/. Latitude Dependence While the variations due to the geographic latitude should be taken into account by the solar zenith angle term, a latitude dependence of Ne (in the lower 0 region) is expected because of the established latitude dependence of measured cosmic ray intensities. The statistical analysis of Ne /5/ shows marked dependence of Na on geomagnetic latitude, the effect being more significant at 60 km. The cosmic ray dependent latitude factor in the lower 0—region could be introduced in future IRI models through the geomagnetic latitude parameter.

geomagnetic/magnetic azimuth plays an important role in VLF/LF propagation phenomena.

The

D—Region IRI Modelling

DEPENOENCE oc Me 014 SCLAR AC1IV1TY

110 ~

x oui~DEss

c~.

•

ALL DATA

QL~TD4~S

•

ALL DATA

-.

OEPE~~NC~ CF Nq C14 L~mJj~

(19791

•~~ 90 .

lob

75

a

~

CONSTANT TERM 0

1EOATCNd’~

2 SOUTH

:~

A 60

>)

( •/1

XT&S(9] OMEcHTLYET:L(19721

I

o

~4 0 2 d

12

I

I

IS

II

I

20

2

FACTOR(F)

I

4

6

I

I

8

C

I

25

15

35

0

Fig. 2. IRI prediction of solar activity dependence compared with the statistical model /5/. Dependence on Season and Winter Anomaly The statistical analysis (Fig. 3) by McNamara /5/ shows the effect of season to be the smallest in comparison with the other effects discussed above. The effect is greatest between 80 and 90 km, and there is some evidence of magnetic activity dependence related to season. There is substantial evidence for a seasonal effect from a variety of radio observations (e.g. the so called November effect observed on VLF/LF field—strengths). There is the winter anomaly phenomenon, which appears to vanish at latitudes less than 35°N, and also the equatorial A 1 absorption anomaly. As discussed in a scientific report /10/, the height (range) in which such effects are important, the change of Ne per day in the case of the (regular) winter anomaly and the change of Ne per degree of latitude in the case of suggested equatorial anomaly in Ne must be ascertained if these phenomena are to be incorporated in IRI. The sensitivity of the measuring technique at different heights and the errors of observation must also be taken into account.

90

-

X—X QUIET DAYS ALL DATA 180-

~

:I I I -~~O8 —04

SEASONAL EFFECT I 0

I

I I •Q4

e

I I ~08

I I ~I2

I 16

1

Fig. 3. Seasonal influence on 0—region Ne based on the statistical model /5/.

76

K. Rawer and Y.V. Ramanamurty

I8~R0VE~NTNEEDED IN 0—REGION MODELLING The 0—region Ledge based identification of the inflection point/ledge and its variability is to be obtained by making use of the existing reliable experimental profiles below the E peak.

Profile

Night—time N

5

8m~is recommended for NMD corresponding to the height HND(= 88km) at all latitudes for all solar activity conditions. Some input based on LF/MF A constant value and of 41O absorption observations is already available /9/. Merging of Daytime Ne to Night—Time Ne through the Twilight Periods The merging of daytime Ne to night—time Ne and vice versa could be achieved preferably by using X as the variable instead of (local) time (t). In IRI—79 /1/ the transition periods DI, 02 are taken as Dl = 02 = I h. There are several interesting twilight phenomena (e.g. sunrise effect at VLF/LF) which depend critically on the pre—sunrise solar zenith angle. A critical value of X 980 could be used in future to demarcate the (ionospheric) day/night/ day transition periods and for the merging of the daytime and night—time conditions. The latitude factor is already taken care of when X is used instead of t. Some difficulties have already been encountered /12/ when the LF/MF absorption data is compared with the IRI—79 profiles. During the twilight periods it is best to use the Chapman function Ch(X) or better the Swider function. Matching with Radio Observations As discussed in the previous sections, the variations with height of (i) the solar activity influence, (ii) the cosy exponent and (iii) the latitude factor can be adequately taken into account by matching the experimental Ne profiles with the IRI description. The current effort in this direction is outlined in the next section. The C—Layer

When modelling the region below 70 km, provision or otherwise for a C—layer, based on the existing experimental evidence and especially the VLF/LF observations, is to be incorporated. Some efforts in this direction have already been described elsewhere /13,14,15/. CURRENT D—REGION IRI (Ne) MODELLING EFFORT

The backbone of any modelling effort is a convenient and flexible mathematical representation of the electron density profile. In the new IRI description it is proposed /16/ to replace IRI—79 with a description similar to the one originally proposed by Booker /17/ but with modifications needed for the reasonable matching of the experimental profiles with the Epstein functions. The whole ionosphere would be visualized as consisting of the top, middle and lower ionospheres. The topside description remains the same as before, except for a correction for high solar activity (see /10/ for more details), because Epstein functions have already been used. The middle ionosphere would be described by a combination of specialised Epstein functions, each peaking at F 2 maximum, and a similar procedure is envisaged for the lower ionosphere with the peak at E—layer maximum /10/. The results of trial calculations for the 0—region profile are as follows. Comparison with Booker’s Approach An experimental electron density profile shown in Fig. 4 is considered. This model depicted by McNamara /18/ represents the rocket electron density distribution discussed by Mechtly etal. /19/ and refers to low solar activity (R=70) noon—time conditions at 32°S,308°W. The profile shows the characteristic inflection point; it has a minor perturbation (C—layer) between 60 and 65 km and it extends up to 101.3 km. The inflection point is located at 83.14 km whereas IRI—79 predicts HMD as 81.0 km. There is thus a difference of about 2 km in this test example. Further, in the absolute value of Ne (at MMD) there is a difference of about 86% between the measurement and the IRI—79 prediction. The results of the calculation of the fit parameters based on Booker’s approach and followed by Gulyaeva (1980) for middle ionospheric modelling (based on ionograms) are shown in Table I.

D—Region IRI Modelling TABLE I

77

Adjustable Parameters of N

5(Z) Profile

Z

LOGION

SLOPE

Z—TRANS

LOGION5

HSMOOTH

65.0 68.0 71.0 73.0 76.0 79.0 81.0 85.0 89.0 91.0 96.0 99.0 110.0

8.074 8.264 8.522 8.619 8.757 8.852 8.869 9.581 10.060 10.273 10.690 10.798 11.058

.060115 .00622! .056364 .045815 .044718 .000000 .041418 .159645 .160952 .125912 .049635 .023301 .02386!

68.171 66,219 7L500 76~66O 78.110 80.575 80.382 211.346 87.911 93.214 97.447 104.520 110.000

8.265 8.253 8.550 8.787 8.852 8.852 8.844 29.75! 9.884 10.552 10.762 10.927 11.058

.238 .241 .215 .626 .246 .166 .283 .778 .17! .377 .269 3.193 .000

Given (input) values in the first in the last three columns.

three columns, those of an adapted model

Large values of the slope between 85 and 91 km, a very high transition height associated with a large smoothing scale (HSMOOTH) are some of the features of the calculation. The first and second (height) derivatives (DERI and DER2) calculated at 5 km intervals from 65 to 110 km are shown in Table 2, TABLE 2 Z

LOGION

65. 70. 75. 80. 85. 90. 95. 100. 105. 110. 115.

DERI

7.94 8.33 8.58 8.73 9.45 10.17 10.66 10.83 10.95 11.06 11.17

.000367 —.003687 .047049 .026897 .160953 .125903 .050318 .023413 .023602 .023776 .02384!

—20 I

0 I

20

I

40

I

I

I

.001314 —.000151 —.000108 .075552 .000000 —.000039 —.001737 .000020 .000044 .000023 .000006

60 I

I

MISFIT (%)

BOOKER [17) X ~N~M0RA

DER2

[51

~

I

los ELECTRON

Fig. 4. profile.

a’

3

o10

DENSITY (rn)

Illustration of IRI matching of an experimental 0—region

id

78

K. Rawer and Y.V. Ramanamurty

Based on IRI—79, the E—peak is assumed to be at 110 km, but the profile—based extrapolated value of Ne at 110 km is taken as EmaxE. The final representation of the analytic function of log~ 0N~ based on Booker’s approach /17/ is also shown in Table 2. This profile, as well as the statistical model described by McNamara /5/, is shown in Fig. 4 for comparison. The agreement between the two approaches is good in this particular case. The percentage misfit at each (experimental) data point based on the new proposal /16/ is also shown in Fig. 4. The mismatch changed sign in the height range considered because the intention was to look for minimum least—square error over the entire height region. A maximum disagreement of 74% is obtained at the inflection point. The new proposal appears to be better than IRI—79 /1/, but the matching process must be applied for all the available experimental profiles before firm conclusions are drawn. ACKNOWLEDGEMENT

One of us (YVR) wishes to express his thanks to the Deutsche Forschungs Gemeinschaft, FRG, and to the Council of Scientific & Industrial Research, India for the opportunity provided to him to work in close cooperation with Professor K. Rawer at Albert—Ludwigs—UniversitMt, Freiburg, FRG. REFERENCES

1.

K. Rawer (Chmn.), J. Virginia Lincoln and R.O. Conkright (eds.), International Reference Ionosphere — IRI—79, Rep. UAG—82, World Data Center A for Solar Terrestrial Physics, NOAA, Boulder, Co., USA (1981)

2.

COSPAR International Reference Atmosphere (CIRA), 1972 Akademie Verlag, Berlin

3.

D.M. Schlapp, S. Atmos. Terr. Phys.,

4.

M. Friedrich and K.M. Torkar, High latitude plasma densities and their riometer absorption, J. Atmos. Terr. Phys. 44 (1983) in press

5.

L.F. McNamara, Statistical

6.

K.M. Torkar, M. Friedrich and W. Riedler, Collection of D— and E—region plasma densities (processed at the Technical University Graz), Internal Report TNW 8211, Institut fur Nachrichtentechnik und Wellenausbreiturg, Technische UniversitEt, Graz, Austria (1982)

7.

A.P. Mitra and Y.V. Somayajulu, Space Res. XIX, 269 (1979)

8.

E.A. Mechtly, S.A. Bowhill and L.G. Smith, S. Atmos. Terr. Phys. 34,

9.

5. Taubenheim and It. Singer, Paper presented at this Workshop and discussion that followed

16, 340 (1959) relation to

model of the D—region, Radio Sci. 14, 1165 (1979)

1899 (1972)

10.

Y.V. Ramanamurty, Scientific Report, Oct. 17, 1983 (Manuscript)

11.

A.P. Mitra, J. Atmos. Terr. Phys.

12.

W. Singer, S. Taubenheim and S. Bremer, 0— and lower E—region electron density profiles compared with LF and ME absorption data, UAG Report 88, 1—8 (1983)

13.

Yu. K. Chasovatin, A.D. Danilov, S.M. Demykin, T.L. Gulyaeva, V.1. Ivanov, V.G. Khriukin, A.A. Nikitin, L.L. Sukhacheva, V.B. Shushkova and S.P. Tikhomirov, Comparison of IRE with electron density profiles obtained below 200 km by different methods, Report IJAG—88, 38 (1983)

14.

Y.V. Rainanamurty, Report UAG—88, 9 (1983)

15.

Y.V. Ramanamurty, Adv. Space Res. 2 (10), 205 (1983)

16.

K. Rawer, Adv. Space Res. 2 (10), 183 (1983)

17.

H.G. Booker, S. Atmos. Terr. Phys. 39, 619 (1977)

18.

L.F. McNamsra, Report UAG—69 (1978)

19.

E.A. Mechtly, K. Seino and L.G. Smith, Radio Sci. 4, 371 (1969)

20.

T.L. Gulyaeva, Geomagn. Aaron. 22, 919 (1982)

43, 737 (1981)