Winter anomalous D-region over Sardinia (40°N)

PIon&. Space Sk. Vol. 27. PP. 1333-1342. Pereamon Press Lxd.. 1979. Printed in Northern Irefand

WINTER

ANOMALOUS

D-REGION

B. S. N. PRASAD*

OVER SARDINIA

(4O”N)

and S. MOWANTY

Department of Physics, Utkal University, Bhubaneswar-751004,

India

(Received 2’7 March 1979) Abstract-A simplified D-region model consisting of Oa’, NO’ and their respective cluster ions grouped as Zo*+ and Z,, t is used to reproduce the available rocket data on positive ion relative composition and effective ciustering rates for the height range 70-90 km. The resuhs of this analysis for a winter anomalous day (Sardinia, 4O”N) are in good agreement with the presently known ideas on NO densities, 0,” production rates, mesospheric temperature, negative ion to electron density ratio and effective loss coefficient for electrons. Mesospheric nitric oxide density and temperature profiles from this study are in excellent agreement with the findings of Zbinden er al. (1975) and Hidalgo (1977) for the-anomalous day at &dinia.

INTRODUCTION

scheme for computing

Rocket data on D-region ion densities for a winter anomalous day (Sardinia, 40”N) have been analysed by Zbinden et al. (1975) to obtain NO densities and 0,’ production rates for the height range 8090 km. Hidalgo (1977), using the same rocket data has derived the temperature profile for the height range 73-86 km. The above finding are in general agreement with the current ideas about these parameters for a winter anomalous D-region. We have analysed the above mentioned rocket data to obtain a comprehensive knowledge about the NO densities, Oz* production rates, mesospheric temperature, effective electron loss coefficient + and negative ion-electron density ratio A for the height range 70-90 km. The method of analysis is to adjust the input parameters of the simplified D-region model (Prasad and Mohanty, 1978) so as to obtain a satisfactory agreement with the positive ion relative composition and effective clustering rates from the rocket data. From the input data on ion production and clustering rates for the model, we calculate the NO densities, Ozi production rates and mesospheric temperature. We also obtain JI and A from the analysis. Our results are in good agreement with the results of Zbinden et al. (1975) and Hidaigo (1977).

the lumped parameters

C,

B,,*+ and I&,+. In this model all cluster ions de-

rived from the precursors 0,’ and NO’ are grouped as Zo,+ and Z,,+ respectively and retained separately. The cluster formation reaction chain is terminated with the formation of initial hydrates O,“*H,O and NO’-H,O. Individual cluster ions H’(H,O),, n = 1,2,3 etc. are not calculated but the tota cluster ion density [Z’] = [Zo,+] + [Z,o-] is calculated. Positive ion relative compositions are calculated and compared with the corresponding rocket measurement. The main considerations for adopting this approach are:

The simplified D-region model used in our study is shown in Fig. 1 and Fig. 2 shows the reaction

(a) Simplicity and ease with which D-region parameters are obtained without invoking lengthy calculations. (b) Individual reaction paths for the formation of many of the experimentally observed hydrated ions are not yet identified (see Reid, 1977; Chakrabarty et al., 1978). Thus the results from any elaborate model involving these reactions may not represent the true situation at D-region heights. (c) Due to collisional breakup of heavier water cluster ions into smaller ions during rocket sampling (Goldberg and Aikin, 1971; Johannessen and Krankowsky, 1972), the experimental data may not indicate the true ambient distribution of positive ions. On the other hand even with collisional dissociation of large clusters, the total cluster ion density relative to primary ions 02* and NO’ remains unaltered.

* On leave of absence from the Department of Physics, Mysore University P.G. Centre, Mangalagango~ 574152, India.

The height variations of [Z+]/[N+] or [Z’l/([N0+1-1-~0~‘& where [N’]=[Z”]-t-[O,+J+ [NO’J, are indicative of cluster ion cut off level and show marked variations with D-region

SIMPLIFIED MODEL

1333

1334

B. S. N. PUSAD and S. MOHAN~ TABLE 1.

dd(zo;)

F~EACTIONRATECOEFRCIENTSANDRECOMBINATION COEFFICIENTS

*Rate coefficients

References

k, = 6.3 x 10~~‘”

Fehsenfeld and Ferguson (1972) Ferguson et al. (1965) Fehsenfeld and Ferguson (1972) Payzant et al. (1973)

k, = 1 x 10-l’ k, = 2.8 x lo-= k, = 2.6 x loo=’ (300/T)=

k, = 3 x lo-lo

[N+]=[Z’] +[NO+]+[O:] ,

A=([N+]/[e])

-1

FIG. 1. SIMPLIFIED D-REGIONMO~ELWSEDINTHISSTUDY.

(a)

ps:(::$

k, = 1.8 x lo-= (308/T)4.7 k, = 2 x 1O-31(300/T)4.4 k_, = 1.5 x lo6 T-5.4 exp(-2450/l k,,= 1~10-~ k,, = 1 x 1OW k,, = 7 x 1O-3”(300/T)3 k_,, = 3.1 x lo4 T-“ exp(-4590/T) k,,=l~lO-~ a d(o,+j=

1.6x 1O-7 (300/T)“.55

~‘,(~o+)= 4 x lo-’ (300/T) q,(- = 3 x 1O-6 (300/T)“.5 ~d(z,,+) = 8 x lo+ (300/T)“-5

(b)

Fehsenfeld and Ferguson (1972)

k, = 1 x 10-l” k, = 2.2 x 10m9

Reid (1977)

Torr et al. (1976) Biondi (1969) Estimate Estimate

*cm6 s-l for three body and cm3 s-’ for two body reactions.

I I

I

I

I

I

_ K,,CWI

I

POSITIVE ION REACTIONS (a) C, (b) BO+ ANO (Cl EN,+ 2

FOR

FIG. 2. POSITIVE ION REACTIONS SCHEME.

See Table 1 for reaction rate coefficients.

conditions such as PCA event, eclipse condition etc. (see Mitra, 1975; Danilov, 1975). Table 1 lists the reaction rate coefficients and recombination coefficients used in our computations. Since NO’ as precursor ion is known to yield heavier clusters 55’, 73’ etc., whereas 0,’ gives lighter dusters 19’, 37’ etc., we have used a larger

value of (Y~(~~,,+) than (Y~(~~;). The neutral density data used here are [0,] and [NJ (CIRA, 1972), [CO,] (constant mixing ratio of 3X 1O-4 n[M], [M] = neutral density), [H,O] (Hunt, 1973) and [0] (Thomas and Bowman, 1972). We have used the temperature data for 40”N for December from Groves (1971) but as discussed later our model study shows a widely different mesospheric temperature for the anomalous day. The reaction rate coefficients used here are the ones usually adopted in D-region model studies (see Ratnasiri and Sechrist, 1975; Spjeldvik and Thorne, 1975; Thomas, 1976; Nath and Sethy, 1976). We have not checked the effect of the variations in individual rate coefficients or neutral densities on our results. For example, the rate coellicient k, has an uncertainty of 30% and the equilibrium rate coefficient k = kg/k_, has an uncertainty of SO%(Johnsen et al., 1975). This variation if considered would alter the computed value of BNo+. Similarly the rate constant k,(O,+ + N2k2-

NO+ + NO)

Winter anomalous D-region over Sardinia (40”N) has not been observed in the laboratory and only upper and lower limits are quoted (see Spjeldvik and Thorne, 1975). Omission of this term would reduce the value of C and hence the required NO’ production rate would be slightly increased with a consequent reduction in 0,’ production rate. Other reactions of 02+ with N and NO, are not considered here as their contribution to C is negligible. We have also found the charge transfer reaction involving the production and destruction of H,O,’ as proposed by Arnold and Krankowsky (1974) does not contribute significantly to C. The temperature dependence of rate coefficients (Table 1) is taken from literature. Where data on temperature dependence are not available we have assumed (l/T)‘.’ law for two body reactions and (1/T)‘-5 law for three body reactions. It is probable that the two body reactions are independent of temperature. We have computed the values of B,?+ and BNO+ with and without the (l/T)‘.’ dependence for two body reactions. The difference in these values for B,,,is less than 5% and negligible for &o+. We have not taken into account the possible errors in the rocket data on electron and positive ion densities. The probable errors in the various

FIG. 3. “Low

1335

laboratory and rocket data will not affect substantially the computed results of this study.

METHOD

OF ANALYSIS

Expressions for positive ion densities, effective clustering rates and recombination coefficients are given in the appendix and equation numbers used in the text refer to those in the appendix. These are derived from the continuity equations for positive ions under steady state conditions. In this study positive ion relative compositions [Z’]/[N’] and [NO’]/[N’] have been computed with the input parameters qo2+, qNO+, C, Bo,+, BNo+, electron density and the dissociative recombination coefficients (Table 1). Since the ion-ion recombination coefficient (Y, is of the order of 1 x lo-'cm3Y1 for the height range 70-90 km (Smith and Church, 1977) and A is small at these heights (Fig. 6), the loss terms due to dissociative recombination of O,‘, NO’CO,, NO’.N, and of total negative ions are negligible. Computed vaiues of C, Bo,+ and B,,,+ are shown in Fig. 3. BNo+ shows marked variation with temperature (see Fig. 10 for summer and winter temperatures). Seasonal variation of C (not shown in Fig. 3) is similar to that of Bo2+. Further, BNO+ is larger

COMPUTED VALUES OF

C,B,,+

AND

Bo2+.

qo,+” se&Ion of the graphs in this figure and in Figs. 4, 5, 7, 9 and 10 have been obtained “LOW qO,+” values shown in Fig. 8 (see text).

using

B. S.N. PRASAD and S.MOHANTY

1336

than B,,+ above 80 km. At lower heights where B,,+ is larger than BNc,+, we find C comparable to B,,+ and so the cluster formation proceeds chiefly through the NO’ chain. The required variation in the input parameter B,,+ for obtaining a satisfactory agreement with the experimental values of B can thus be related to mesospheric temperature for the anomalous day. The initial value of qo2+used in the analysis is the sum of (a) solar U.V. radiations ionising O,(‘A,), calculated from O&A,) concentration and the formula given by Paulsen et al. (1972); (b) solar X-ray ionization for solar maximum conditions and the appropriate zenith angle taken from Swider (1969); (c) cosmic ray ionization for the geomagnetic latitude of SO” taken from Webber (1962); and (d) ionization due to particle precipitation for middle latitudes from Tulinov (1970). The initial value of qNo+ due to solar Ly-a ionizing NO is calculated using the NO profile of Meira (1971), photon flux of 3 X 10” cm-’ s-l, absorption cross-section of 9 x 10ezl cm2 for 0, (H&man, 1969) and ionization cross-section of 1.9 x lO_” cm2 for NO (Watanabe et al., 1967). The initial quantities qNo+, qo,+ and B No+ (winter values, Fig. 3) are varied in suitable steps to find a satisfactory agreement between the computed values and the rocket data. In this pro-

0

RESULTS

POSITIVE

0

POSITIVEIONFLELATIVECOMPOSITIONS

I 0.6

0.4

ION

AND DISCUSSION

Upleg rocket data (70-90 km) are used here since downleg data appear to be approximate (Zbinden et al., 1975). The latter are also shown for comparison. There appears to be a difference in the water cluster cutoff level (-1 km) between the upleg and downleg data (Figs. 4 and 5). Rocket data on electron density only is available for the height 70 km. In Figs. 4, 5 and 6 we have shown the results of positive ion relative compositions, B and A. Points marked “Low qozi” refer to Fig. 8 and its significance is discussed later. In Fig. 4, water cluster cutoff level is around 77 km for the anomalous day and this height is around 82 km for the normal day (see Mitra, 1975). Reid (1977) has discussed this lowering of the cluster cutoff level in terms of electron production and loss rates for disturbed days. Error bars at 90 and 88 km refer to similar

I 0.2

Frc.4.

cess we make sure that the quantity A= ([N+]/[e]) - 1 from the computations is kept within reasonable limits of its value from the rocket data and as reported by others for normal and disturbed D-region conditions (see Fig. 6).

RELATIVE

08

COMPOSITION

[Z+]/[N+] and [NO+]/[N+] FORTHEANOMALOUSDAY.

Winter anomalous D-region over Sardinia (40”N)

I6 FIG. 5. B, (Ye

IOC IO-1 B ANO tidcz+)[e](cm3scr?) [e] .~ND~FOR~EANOM.~L~~SD.~~.

Plain broken curve refers to B using equation (1 l), for upleg rocket data.

A FIG.~. A VALUESFORNOFZMALANDDISTUFUSEDDAYS.

1337

1338

B.S.N.PRASAD

ION DENSITY

&ITI"E

i

c

i

,4’

/

.*.

ION PRiiDUCTION

FIG.%

Km-‘,

[NO+] AND [O,+] FORTHEANOMALOUSDAY.

FIG.~. POSITIVEIONDENSITIES[Z+],

qe-i

and S.MOHANTV

RATES

(cm-’ set-I)

IONPRODUCTIONRATE3FORTHEANOMALOUSDAY.

Winter

anomalous

D-region over Sardinia (40”N)

variations shown in Figs. 7 and 8 while B is held constant at these heights. Experimental B values (Fig. 5) obtained from expressions (11) and (12) are markedly different. Mesospheric winter temperature is taken in expression (11) through BNO. and Bo2+ and a,(=+) = 1 x 1Om5cm’ ss’ is assumed for (12). As will be seen later. anomalous day temperature is vastly different from the assumed temperature whereas adCzV) from this study [expression (9)] is 9-10 X lo-” cm’s’. Hence we have compared the experimental value of B from expression (12) with the computed value [expression (1 l)] when the input BNoi is varied. These adjusted BNOi values are used for deriving the anomalous day temperature profile. In Fig. 5 the computed values of 0~~~~‘) [e] is seen to be smaller than B in the cluster dominated region. It is clear that the linear relation between the total ion production rate and electron density q = [e] is not valid at these heights (see Haug and Landmark, 1970). Our A profile (Fig. 6) is well within the limits of this parameter for daytime conditions and also our A values are in good agreement with the experimental values below 76 km. Low A values from this study justify our assumption in neglecting the loss terms due to ion-ion recombination. Below 74 km A values for anomalous day are smaller than the normal day values of Ratnasiri and Sechrist (1975). This reduction in A is the result of increased electron detachment rate which is caused by the enhanced [0] and [O,(‘A,)] (0, + hv --P 0 + O,(‘A,), see Zbinden et aE. (1975). Enhanced electron densities at the lower heights are now known to be due to modifications in the negative ion chemistry of the winter anomalous D-region (see Abdu and Angreji, 1974; Mitchel et al., 1972). In Fig. 5, electron loss coefficient (Ir=q/[e]’ is seen to be smaller than that for the normal day at middle D-region heights. We find 9 = (ad +ha,) (1 +A) to hold good at all heights. Thus the parameter 4 calculated from production rate and ion composition methods (see Mitra, 1975) is identical in our simplified D-region model. We have shown [Z’], [NO’] and [02’] in Fig. 7. At 90 and 88 km [Z’] is not significantly altered with the variation in [O,‘] and [NO’] as indicated by error bars. Large discrepancy between our values and rocket data is seen at 90, 88 and 86 km. Rocket data for these heights give [N’] < [e] so that A is negative which is unrealistic and so this has been excluded in our computations. The positive ion densities shown refer to the lowest positive value of A and also satisfy the positive ion relative

1339

composition and B (Figs. 4 and 5). We have shown in Fig. 8 0,’ production rates due to various sources used as initial values and also qoz+ from our model. Assuming that the inrate for the anomalous crease in 02+ production day is due to enhanced O,(‘A,) (Zbinden et al., 1975) we estimate the concentration of O&A,) for the anomalous day by comparing the qo,(la,, values for the anomalous and normal days. We note that O,(‘A,) is increased by more than an order of magnitude on the anomalous day with a minimum around 83 km. However, this procedure cannot be adopted for heights below 78 km since the normal day qo,cla,) for x = 64” is negligibly small at these lower heights. Enhanced particle precipitation which can contribute significantly to 02+ production at these lower heights is ruled-out by Zbinden et al. (1975). It is not certain if the normal day 0,’ production due to precipitating electrons can be larger than that used in this study for the latitude of Sardinia (see Larsen et al., 1976). Downward transport of ionization can also account for this enhanced 0,’ production at lower heights (see Mitchel et al., 1972). Also “Low qo>+” values at these heights (see Fig. 8) do not reprcduce rocket data on positive ion relative composition or effective clustering rate (Figs. 4 and 5). The NO profile for the anomalous day (Fig. 9) is derived by comparing the qNo+ for the anomalous day with the normal day values. In Fig. 9, the height at which minimum in NO density occurs is the same for all the profiles except for that of Zbinden et al. (1975) for which it is 1 km higher than for other profiles. By moving the NO profile of Zbinden et al. (1975) downwards by 1 km we find excellent agreement between this and our NO profile. The corrected NO profile of Meira (1971) is taken from Tohmatsu and Iwagami (1976) who have discussed the reasons for this correction. Meira’s profile measured on a day of winter anomalous absorption (see Mechtly et al., 1972) shows enhanced NO densities compared to other normal day profiles but not as high a value as the profile for Sardinia. The electron densities for the two cases also show marked differences. Gnanalingam and Kane (1973) have reviewed Ly-a data for solar maximum and minimum conditions and a value of 3.3 x 10" photons crtC2s-’ is found to be appropriate for solar maximum conditions. With this value of Ly-a flux our NO profile would be reduced by about 10%. Mesospheric temperature profile deduced from the BNo+ values for the anomalous day (see Fig. 3) is shown in Fig. 10 and this is in agreement with the

B. S. N. F~ASAIIand S. MOHANTY

1340

I

I

I

10' NITRIC

!?IG. 9. NMRICOXIDE

DENSITY

OXIDE

PROFILES

HiC&LGO(IP7?~

-

I

8

&WY

FOR NORMAL

109

I

[cm-‘) AND WINTER

ANOMALOUS

DAYS.

results in increased B,o+ and also Box+. It is possible that more than one factor might be con~buting to the observed changes in the clustering rate for the anomalous day. Even then the temperature profile would retain its wave-like nature but the magnitude of the mesospheric temperature would be different. We note that winter temperature profile (Fig. 10) has been used in calculating B,,+ and dissociative recombination coefficients whereas the anomalous day temperatures are different from the initially used temperatures. Thus it would be more appropriate to find out a mesospheric temperature profile by the method of iteration. This we have not attempted since B,+ variation with temperature (Fig. 3) is not as marked as that of BNO+ and the dissociative recombination coefficients differ by less than 10% from their initial values when the initial temperatures are replaced by the anomalous day temperatures. CONTUSIONS

FIG.

10.

MESOSPHERIC NORMAL

TEMPERATURE

AND WiNTE.R ANOMALOUS

PROFILES

FOR

DAYS.

profile deduced by Hidalgo (1977). Observed varia. . tion m BNo+ for the anomalous day may also be due to changes in neutral constituents like water vapour (Zbinden et al., 1975). Increase in I-I,0

Transport of minor neutral constituents like NO, OS, O,(‘AJ, 0, etc. and energy dissipation due to gravity waves have been suggested as causing the enhanced electron densities and sharp temperature gradients of the winter D-region (see Zbinden et al., 1975; Hidalgo, 1977). Our results for a winter anomalous day from a simplified model are in good

Winter anomalous D-re :gion over Sardinia (40”N) agreement with the known D-region processes. These are (i) increase in the density of NO and O,(‘AJ, (ii) reduction in effective loss rate for electrons, (iii) reduction in negative ion to electron number density ratio, and (iv) enhanced mesospheric temperature with a wave-like nature. Although the magnitude of these changes could be slightly different depending on the input data on neutral densities, ionizing flux, etc., the qualitative nature of our results would remain the same. Laboratory data on reaction rate coefficients and the reaction scheme for cluster ion formation used in this study are justified by the close agreement of OUT results with the prevalent ideas about the winter anomalous D-region. A~knowZedgeme~~-We are thankful to the University Grants Commission of India, New Delhi for financial assistance.

REJ?RRENCES Abdu, M. A. and Angreji, P. D. (1974). The role played by ozone in the lower D-region electron density variations in winter. J. geophys. Res. 79, 649. Arnold, F. and Krankowsky, D. (1974). Measurement of H,O,’ in the D-region and implications for mesospheric H202. Geophys. Res. Left. 1, 243. Biondi. M. A. (1969). Atmospheric electron-ion and ionion recombination processes. Can. .l. Chem. 47, 1711. Chakrab~ty, D. K., Chakrabarty, P. and Witt, G. (1978). An attempt to identify the obscured paths of water cluster ions build-up in the D-region. J. atmos. fen. Phys. 40, 437. CIRA (1972). COSPAR International Reference Atmosphere. Akademie-Verlag, Berlin. Danilov, A. D. (197.5). Konization-recombination cvcle of the D-region. J. atmos. ten. Phys. 37, 885. Fehsenfeld. F. C. and Fereuson. E. E. (1972). Recent laboratory measurements of b- and ‘E-region ionneutral reactions. Radio Sci. 7, 113. Ferguson, E. E., Fehsenfeld, F. C., Goldman, P. D. and Schemeltekopf, A. L. (1965). Positive ion-molecule reactions in the ionosphere. J. geophys. Res. 70,4323. Gananalingam, S. and Kane, J. A. (1973). A study of electron density profiles in relation to ionization sources and ground-based radio wave absorption measurements-I. Report X-625-73-355, Goddard Space Flight Centre Greenbelt, Maryland, U.S.A. Goldberg, R. A. and Aikin, A. C, (1971). Studies of positive ion composition in the equatorial D-region ionosphere. J. geophys. Res. 76, 8352. Groves, G. V. (1971). Atmospheric structure and its variations in the region from 25-120 km. AFCRI-710410. Air Force Cambridge Res. Labs. Bedford, Mass., U.S.A. Hidalgo, M. A. (1977). Winter anomaly in ionospheric absorption and the D-region ion chemistry. Planet. Space Sci. 25, 1135. Huffman, R. E. (1969). Absorption cross-sections of atmospheric gases for use in aeronomy. Can. J. Chem. 47, 1823.

1341

Hunt, B. G. (1973). A generalized aeronomic model of the mesosphere and thermosphere including ionospheric processes. J. atmos. ten. Phys. 35, 1755. Johannessen, A. and Krankowsky, D. (1972). Positive ion composition measurement in the upper mesosphere and lower thermosphere at a high latitude during summer. J. geophys. Res. 77, 2888. Johnsen, R., Haung, C. M. and Biondi, M. A. (1975). The formation and breakup of NO+ N, clusters in N, at low 1_ temperatures. J. chek Phys. 63,3374. Larsen, T. R., Imhof, W. L. and Regan, J. B. (1976). L-dependent energetic electron precipitation and midlatitude D-region ion pair production protlles. J. geophys. Res. 81, 3444.

Mechtly, E. A., Bowhill, S. A. and Smith, L. G. (1972). Changes in lower ionosphere electron concentrations with solar activity. .I. atmos. terr. Phys. 34, 1899. Meira, L. G., Jr. (1971). Rocket measurements of upper atmospheric nitric oxide and their consequence to the lower ionosphere. J. geophys. Res. 76, 202. Mitchell, J. D., Hale, L. C., Olsen, R. O., Randhawa, J. and Rubio, R. (1972). Positive ions and the winter anomaly. Radio Sci. 7, 175. Mitra, A. P. (1975). D-region in disturbed conditions, including flares and energetic particles. J. atmos. ten. Phys. 37, 895.

Nath, N. and Setty, C. S. G. K. (1976). The D-region ion composition. J. pure appl. Geophys. 114, 891. Paulsen, D. E., H&man, R. E. and Larabee, J. C. (1972). Improved photoionization rates of Oz(‘AZ) in the Dregion. Radio Sci. 7, 51. Payzant, J. D., Cunningham, A. T. and Kebarle, P. (1973). Temperature dependence of the rate constants for the third order reactions 0,’ + 20, -+ O,+ + 0, and 0,‘+20,+0,‘+0,. J. &em. Phys,J9, 5615. Prasad, B. S. N. and Mohantv. S. (19781. Electron loss mechanism at D-region heights on days of normal and anomalous winter absorption. Indian. J. Radio Space Phys. 7, 224.

Ratnasiri, P. A. J. and Sechrist, C. F., Jr. (1975). An investigation of the solar zenith angle variation of Dregion ionization. Aeronomy Report No. 67, Dept. of Electrical Engng. Univ. of Illinois, Urbana, Illinois, U.S.A. Reid, G. C. (1977). Production of water cluster positive ions in the quiet daytime D-region. Planet. Space Sci. 25, 27.5. Sechrist, C. F., Jr., Mechtly, E. A., Shirke, J. S. and Theon, J. S. (1967). Coordinated rocket measurements on the D-region winter anomaly-I. Experimental resuits. J. atmos. terr. Phys. 31, 145. Smith, D. and Church, M. J. (1977). Ion-ion recombination rates in the Earth’s atmosphere. Planet. Space Sci. 25, 433. Spjeldvik, W. N. and Thorne, R. M. (1975). A simplified D-region model and its application to magnetic storm after-effects. J. atmos. terr. Phys. 37, 1313. Swider, W. (1969). Ionization rates due to the attenuation of l-100 A non-flare solar X-rays in the terrestrial atmosphere. Reu. Geophys. 7, 573. Thomas, L. (1976). Mesospheric temperatures and the formation of water cluster ions in the D-region. J, atmos, terr. Phys. 38, 1345. Thomas, L. and Bowman, M. R. (1972). The diurnal variations of hydrogen and oxygen constituents in the mesosphere and lower thermosphere. J. atmos. ten.

1342

B. S. N.

PRASAD

and S. MOHANTY

Phys. 34, 1843. Torr, D. G., Torr, M. R., Walker, J. C. G., Nier, A. C., Brace, L. H. and Brinton, H. C. (1976). Recombination of O,+ in the ionosphere. J. geophys. Res. 81, 5578. Expressions for C, Bo, and B,o+ (Fig. 2) Tulinov, V. F. (1970). The role of Lyman-a radiation in C = k,ENGl+ k,EN,I, ionization of the lower ionosphere. Space Res. 10,689. Ulwick, J. C. (1972). Effective recombination coefficients k,k,[G,P&Gl and lumped parameters in the D-region during solar BoZ+= M-WINI+ k,Wl+ k&$(lAg)I + k,[H@l particle events. AFCRL-72-0474, p. 571. Special Report No. 144. Air Force Cambridge Res. Labs. BedB,,+ = k,[H,Cl[N,I ford, Mass. U.S.A. k&,,PJJ21H,01 Watanabe, K., Matsuraga, F. M. and Sakal, H. (1967). + k_@J+ h&W+ k&WI Absorption coefficient and photoionization yield of NO in the region 580-1305A. Appl. Optics 6, 391. Webber, W. (1962). The production of free electrons in the ionospheric D-layer by solar and galactic cosmic rays and the resultant absorption of radio waves. J. x ( k&.%lCW \ geophys. Res. 67, 5091. k,k,,[N,12[C0,1 Zbinden, P. A., Hidalgo, M. A., Eberhardt, P. and Geiss, +k_9[N~l+k~O[CO~1+k~t[H,01 J. (1975). Mass spectrometer measurements of the positive ion composition in the D- and E-regions of the ionosphere. Plunet. Space Sci. 23, 1623. OLd(Zo;) 1+ ad(Z’l

i :;g+;)

= 1

od

APPENDIX

Expressions for positiue ion densities [&‘I = [NO+] =

%m+Qdtzo2’,[No+l ’ Bo,+%tz,,+i-0z+l

@‘I

[NO+] t 1-+o,@,+)#, [pi’]

=“dcZ+‘,fi+adWO

B=Vh,+cp+Bo2+);

2 a,~,i,[e3+~~bo~++*~i[el 4No+-+ao,+l ~d(,o”,lel+B,o++~~i[e]

+

’ ’

(1) (2)

We also have the following:

B,,,ING+] E&o+1 = (LdfZ,+~~e]+

’

(4)

EC%‘1’

[z+l B =f”ff d
(3) ~Z+l=~Zo;l+[Z,,-l, [N+]=[Z+]+[O,+]+[N+], h = ([N+]~[e~ - 1.

(6) (7)

(8)

(9)

(lo)

PJNO+l

1+cp

(5)

(11) 1179