The diurnal variation of atomic hydrogen

686

RESEARCH

NOTES

Arknowkdgements-We wish to express our many thanks to the Assistant Director, Ionospheric Prediction Service, Bureau of Meteorology, Sydney, Australia, and the Magnetic Observatory, C.S.I.R., Hermanus, Republic of South Africa, for providing geoalerts essential for this programme; to the Wave Propagation Laboratory and Fritz Peak Observatory, NOAA Environmental Research Laboratories, Boulder, U.S.A.; to Professor Syun-Ichi Akosufu. Professor Keith D. Co!e and Professor Manfred H. Rees for all their valuable comments leading to interpretation of the reported events. University of Botswana, Lesotho and Swaziland, Roma, Lesotho University of Rhodesia, S~~isbury, ~~sia

E. H. CARMAN M. P. HEERAN R. W. H. STEVBNSON

L. K., MAROVICH,E., MEGKLL,L. R., f&s, M. H., RBUBECK, L. 1. CRUZ, J. E., DAVIES, R., DROPPLEMAN, and ROACH, F. E. (1965). NBS Tech. Note No. 308. 2. HOCH, R. J., MAROVICH,E. and CLARK, K. C. (1968). J. geophys. Res. 73,4213. 3. HOCH, R. J. and CLARK, K. C. (1970). J.geophys. Res. 75,2511. 4. ICHAKAWA,‘I’. and KIM, J. S. (1969). J. utmos. terr. Phys. 31,547. MAROVICH,E. (1966). ESSA Tech. Report, IER 164TSA 16. 2: ROACH, F. E , BARBIER,D. and DUNCAN, R. A. (1962). Annls Gtr,phys. 18,390. ROBLE,R. G., HAYS, P. B. and NAGY, A. F. (1970). Pkmet. Space Sci. 18,431. I: BARBIER,D. (1958). AnnIs Giophys. 14, 334. 9. BARBIER,D. (1960). An&s G&ophys. 16,544. CARMAN,E. H., HEERAN,M. P. and WILTSHIRE,V. (1969). Planet. Space Sci. 17,1073. :: NAGY, A. F., ROBLE,R. G. and HAYS, P. B. (1970). Space Sci. Rev. 11,709. 12: TOHMATSU,T. and ROACH, F. E. (1962). J.geophys. Res. 67,1817.

piaoct.Spsa Sd. 1973,Vol. 21, pp_686to 691. Perpamon Prtss.print&in Northcm Inlsnd

THE DIURNAL

VARIATION

OF ATOMIC

HYDROGEN

(Received injinal form 25 August 1972) Ah&a&-This note critically examines the relative importance of several effects which influence the diurnal variation of atomic hydrogen abundance near the critical level. It is pointed out that the neglect of exospheric hydrogen in a recent theoretical treatment causes an over~t~mat~on of the diurnal variation at high exospheric temperatures, and an ~de~timatioR at low exospheric temperatures. The fluxes due to lateral fiow are large compared to other fluxes only to the extent that the actual diumaf variation is very different from the diurnal variation corresponding to zero net lateral flow, which does not seem to be the case in the real atmosphere. Two effects which are probably important are charge exchange reactions with thermal oxygen ions, resulting in a diurnal exchange with the plasmasphere; and charge exchange reactions with high velocity protons, resulting in enhanced escape and diurnal variation. TIME DEPENDENT SOLUTIONS Hanson and Patterson, 1963 (hereafter HP), and Patterson (1966. 1970) have obtained an approximate solution to the diurnal variation of the number density n, at the critical level at geocentric distance r, by the equation

where f is time; N, is the cohmm density of hydrogen above the critical levet, given approximateIy NI - 2&a

by (2)

#,pois the constant upward &sx from the source re&n;

ff* is the scale height of atomic hydrogen at the

critical level, given by jJ# = kr, (3) mga wham Tdaudga are the temperature and gravitationa acceleration at the critical level, k and mare BoItxmann’s constmtt and the mass of the hydrogen atcm~ The term 4= is the flux of hydrogen due to them& excape at the critical level, and is given for example by Mcolet (1957) by +p = n, g Y&-‘tr(l ( 1 Df

+ I&jrJe-Vx

@I

&J - @G,3.

0

~ovid~ug fate& Bow at the exobase and ioss processes other than thermal excape have ~~lig~h~ effects. the solution to Eqwaticm (1) might be considered to be a good a~~roxi~tio~ to the diumaf variation of q at r,, However WaRace and Strobe1 (1972) fbereafter WS) have cast doubts on this approach, and drawn attention to the region between about 120 km and the critical fevel, neglected by HP who considered the region above So0 km accounted for most of the variation of hydrogen content. Pigum 1 is a plot of steady state altitude pro&s of atomic hydrogen for values of T, of 1000 and 1250 K, which represent typical minimum and maximum diurnal temperatures. The profiles were calculated according to the method of Kockarts and Nicolet (1962,1963). The critical level is at about SO0km, and the quantity of hydrogen above SO0km represealed by the difference between the NCvnlues for 1000 and 1250 K is shcwa by diagonal shading. This quantity af hydrogen acts as a ‘reservoir’ in smoothing the d.iumaI n, v;lsiation to considerably less than the factor of about 4 represented by the static profiles. The remainder of the ‘reservoir’ lies in the shaded region below 500 km. WS have solved for the smoothing ofdiurnal variations due to hydrogen in this region by integrating the time dependent continuity equation 34 $+F”O

0

I

HYDROGEN FM,

1. SWY

2

3

NUMBER

SrnrrJ ALTrmDE PiKxxES

OP AMD

@I

4

5

6

DENSITY.ln ATcwtC f250

lo4

7

8

atoms Cm-’

HYDROGEN

FOR

VALW

OP

r,

OP

loDo

K.

critical leei is S&m at So0 km. Nd.lbDB - MGIpmis the quantity of hydrogen above SQokm represented by the shaded area. 0pposhe shading indicates the corresponding quantity below 500 km. The thermal escape flux JbTtthe proton flux #+ the Rux of heated hydrogen &, and the flux of hydrogen from the 100 km level &, are schematkafiyindicated,

The

688

RESEARCH

NOTES

and the diffusion equation 4 =

(1 + a) aT -D(Z+[Tz++H

1

I)*

(7)

from 120 km to the critical level. The quantities n, z, $, D and a are the number density, height, vertical flux for transport by molecular diffusion, average diffusion coefficient and thermal diffusion factor for atomic hydrogen respectively. The upper boundary condition was the thermal escape flux & at the critical level. No treatment so far has included the effects of both regions, above and below the critical level, in determining the smoothing of the diurnal variation of n,. As would be expected, since the lower reservoir is smaller than the upper one, WS calculated greater diurnal variations than did HP for the same diurnal temperature range, except for minimum temperatures Tcsrn~,, below 750 K. At low temperatures the terms + 100and +T integrated over 12 hr become negligible with respect to N, and the only n, variation is due to scale height changes in the exosphere. Putting the RHS of Equation (1) zero yields N, = const, and from Equations (2) and (3) n, a l/T,. Putting R,, = nc,max/nc,m~n. representing the factor of diurnal variation from the solution to Equation (1) then R, tends to T,,msx/Tc,m~n at low temperatures. HP used To,,& WS repeated the HP calTc.min= 153, and their values of R Tn tend to this value at low temperatures. culation for T,.max/Tc,min = l-245, aiia their RTD values as expected tend to 1.245 at low temperatures. A treatment which included the effects of both reeions would be one in which Eauations (6) and (7) were integrated from say 120 km to an upper value gf say several thousand km, with the thermal escape inserted as a loss term at the critical level. Using Equation (7) in the exosphere in this way implicitly assumes a hydrostatic altitude profile which has constant density at infinity and neglects the spherical rather than plane parallel geometry. Corrections would have to be made for these effects. HP did so by use of Equation (2). A simpler approach would be to use as the upper boundary condition at the critical level the flux

This assumes that the column of hydrogen represented by N, responds instantaneously to changes in N. and T,. This is reasonably accurate since the time lag, corresponding to the ballistic flight time for one scale height is only about 15 min. A treatment with Equation (8) as the upper boundary should yield a low temperature asymptotic solution but slightly less. At all temperatures the treatment conabout the same as R, tending to T,.max/Tc,m~n sidering the whole protile should yield a solution for R,, less than the solution considering only the region above the critical level. OTHER EFFECTS Such a treatment is probably not warranted however. Lateral flow has been neglected, but probably what is more important is that the exchange of hydrogen with the plasmasphere, in the form of a proton flux +p which is upward in the daytime and downward at night, has been neglected. This effect was first considered by HP, but underestimated by them. The charge exchange reaction O++H+O+H+ (9) occurs sufficiently fast in the thermosphere that upward and downward fluxes of a few times the average I& can be sustained. This is according to observations of fluxes of a few times lo* cm-2 se& (Park, 1970; Schunk and Walker, 1972; Ho and Moorcroft, 1971), and the result of a survey of observations yielding hydrogen abundances consistent with the average $T equal to about 10Bcm-2 set-I, Tinsley (1971). Since the exchange fluxes can be as much as a few times the thermal excape flux, for periods of a few hours, they can thereby modify the diurnal variation, provided the temperature is not so low that the effects of changes in the fluxes are negligible compared to the effects of changes in the exospheric scale height, as discussed earlier. A third effect which has been neglected in the treatment of diurnal variations is the escape of hydrogen atoms by charge exchange collisions with hot protons in the plasmasphere, as suggested by Cole (1966). The charge exchange reaction yields neutral hydrogen atoms with the velocity of the proton. If the ion energy corresponded to the mean thermal velocity at a temperature of 5750 K (energy 0.63 eV) or greater, and the ion was moving upward, the neutral hydrogen atom produced would be able to escanc from the lower exosphere. Smaller en&gies are required at highe;altitudes: Measurements of ion temperature and density have been made bv Serbu and Maier (1970). who found temoeratures as low as 5300 K at 1.5 R, on the nightside and 7e K at 1.5 RE on the dayside, ranging up\;ard to 20,000 K at 3.6 R, on the2ayside. Ion densities were about 10’ cm-s at 1.5 RE on the dayside (these are somewhat higher than usually measured). A very rough evaluation of the excape flux is based on the integral

RESEARCH

NOTES

689

where K is the rate coefficient for Equation (9), taken from Dalgamo (1960); iU is a geometric factor to take into account that not all collisions produce outward moving atoms, (r/r,)* normal&s the escape flux to the critical level, n(r) and rip(r)) are the neutral and ion densities respectively. Using a n(r) altitude profile given by dlol, = 10scm-* se+, and the ion densities and temperatures of Serbu and Maier (1970), the integral of (10) outwards from 15 R, for the dayside yields an escape flux of about 4 x lo* cm-* set-I. This will be increased by fluxes from below 15 RE, from the region of diminishing ion temperature but increasing neutral and ion density. The flux obtained is larger than that from the source region, but would only be so for a restricted local time and latitude range. Also, the Serbu and Maier densities may be too high. For that part of the ion velocity distribution with less than escape velocity, collisions will result in heated hydrogen which will have some effect on the altitude profile and the diurnal variation by a sort of lateral flow. To evaluate the diurnal effect of this loss process, and of the production of heated neutral atoms, it will be necessary to use a global distribution of ion density and temperature from heights of about lOOO-15,000 km. Such a distribution is not available at present. OBSERVATIONAL DATA The best experimental evaluation (Roes)of the diurnal variation is that of Brinton and Mayr (1971) as noted by WS. A variation of RoBa = 1.7 was found at 350 km (close to the critical level), for the minimum temperature 800 K at the epoch of their measurements. There was a phase lag of about three hours compared to the Jacchia (1965) model diurnal temperature variation. This diurnal variation and phase lag is consistent with the 10 per cent or so difference in column abundance found by Tinsley (1970). when Balmer a intensities a few hours after sunset are compared with intensities a few hours before sunrise. The HP solution for RTD for i’&,,i,, = 800 K, as shown in Fig. 3 of WS is about 1.25 and is near the region of the asymptotic solution. EFFECTS OF LATERAL FLOW Lateral flow is the net horizontal transport of atoms in ballistic trajectories in regions across the exobase where temperature and density gradients are present. The temperature effect, manifested in larger thermal velocities and longer trajectories for the particles from hotter regions, drives a flux from hotter to colder regions. The density gradient thereby produced and enhanced by reduced escape rate in the colder regions, produces a compensating return flux. The plasmasphere exchange and effects of interactions with high velocity protons can also enhance density and temperature gradients. In a steady-state atmosphere with only temperature gradients (no escape or other fluxes) the lateral flow would decrease the density in the region of net outflow, and increase it in the region of net inflow. Given enough time a density distribution would be reached in which there was zero net lateral flux. This density distribution may be described as a zero net lateral flow solution specified by RzNLp = nc,max/nc,min. The effects of lateral flow may be qualitatively evaluated by comparing the solution for zero net lateral with the diurnal variation obtained in the real atmosphere, RoBo. If RzRW is greater than flow &RLF R OBS and the phases agree, then the effect of lateral flow is to tend to increase the diurnal variation with a net outflow from the minimum density region. If RZNLFis smaller than ROBS, and the phases agree, then the effect of lateral flow is to tend to decrease the diurnal variation with a net outflow from the maximum density region. There is no phase lag between temperature maxima and density minima and oice versa for ZNLF solutions. For the real atmosphere phase lags of up to three hours may be present. This is small enough not to affect seriously comparisons of RINLP and Ross. Of interest for the real atmosphere are the net lateral fluxes generated by a departure of the real density distribution from the ZNLF distribution. An indication may be obtained from the results of calculations presented by McAfee (1967 Figs. 6 and 8). For density normalisations corresponding to three times Kockarts-Nicolet (1962) abundances, hence mean & of about lOa cm-* secl, and for Tc maxand T&,rn 1000 and 700 K respectively, the diurnal variation corresponding to the steady state situation, R., was 1.45 x 10”/5.3 x IO”= 2*7.- The value of RsxIF was 156 x 10’/6.7 x 10’ = 2.3. Under these conditions the net lateral flow out of the maximum densitv region was about 2 x lo8 cm-l se@. To obtain an estimate of the lateral fluxes present at the time of th& Brinton and Mayr (1971) observations we need a value of R lNIY appropriate to that time, for comparison with RoBs. FIT TO ZERO NET LATERAL FLOW RATIOS A ZNLF solution for a Jacchia (1965) global model temperature variation has been given by Patterson (1970). Further calculations of ZNLF solutions have been made by Quessette (1972). The value of R,,,F was found to be a good fit to a linear function of the parameter Y, where

(11)

690

RESEARCH

NOTES

Since the value of RBNLrwas not unity when T,,max - T,,min was set equal to zero in the linear relation, as it must be for an isothermal atmosphere, a better variation is R ZNLF =l+orl*+bY.

(12)

With a and b set at -28.33 and 4376 respectively, the fit to Quessette’s results is even better than the linear relation and it can confidently be used for small Y. Quessette’s results agree closely with that of Patterson (1970). The value of RINLI for T,,,min = 800 K and T,.mar/To,m~n= 1.245 is 1.62 using (12). EVALUATION

OF OBSERVATIONAL

RESULTS

The observed diurnal variation R 088 = 1.7 is somewhat greater than the appropriate RaNw = 1.62. If the accuracy of these numbers is indeed such that it is true that the ZNLF variation is less than the ohserved variation, the lateral fluxes must be such as to tend to reduce the observed variation, not increase it, and hence cannot be invoked as a means of increasing the R,, variation of I.25 to the observed value. If the accuracy of R,,, and RBNLPis not such that the sign of the difference can be considered reliable, nevertheless the difference must be so small that judging by McAfee’s results, the net lateral fluxes must be not more than lOa cm-* se&. This is only comparable to the escape fluxes, and smaller than the estimate of the plasmasphere exchange fluxes and the fluxes from interactions with high velocity protons. Thus it becomes plausible that the effects of plasmasphere exchange fluxes and the effects of interactions with high velocity protons are sufficiently large to increase the diurnal variation which would otherwise be about 1.25, to about 1.7 at Tcsrnln= 800 K. The fact that there is a phase lag of about three hours in the observed density variation relative to the temperature variation is further evidence that lateral fluxes have not heen dominant over other fluxes in producing a near ZNLF variation. Acknowledgements-I wish to acknowledge useful discussions with Dr. W. B. Hanson. supported by NSF grant GA18767 and NASA Institutional Grant NGL 44-004-001.

This work was

BRIAN A. TINSLEY

The University of Texas at Dallas, Texas 75230, U.S.A REFERENCES BRINTON,H. C. and MAYR, H. G. (1971). Temporal

variations of thermospheric hydrogen derived from in situ measurements. J. geophys. Res. 76, 6198-6201. COLE, K. D. (1966). Theory of some quiet magnetospheric phenomena related to the geomagnetic tail. Nature 211, 1385-1387. DALGARNO,A. (1960). Low energy stopping power of atomic hydrogen. Proc. Phys. Sot. Lond. 75,374-377. HANSON, W. B. and PATTERSON,T. N. L. (1963). Diurnal variation of the hydrogen concentration in the exosphere. Planet. Space Sci. 11, 1035-1052. Ho, M. C. and M~~RCROFT, D. R. (1971). Hydrogen density and proton flux in the topside ionosphere over Arecibo, Puerto Rico, from incoherent scatter observations. Planet. Space Sci. 19, 1441-1455. JACCHIA,L. G. (1965). Static diffusion models of the upper atmosphere with empirical temperature profiles. Smithsonian Cont. Astrophys. 8,215-257. KOCKARTS,G. and NICOLET,M. (1962). Le probleme aeronomique de l’helium et de I’hydrog&ne neutres. Annls Giophys. l&269--290. KOCKARTS,E. and NICOLET,M. (1963). L’helium et l’hydrogkne atomique au tours d’un minimum d’activitt solaire. Annls GPophys. 19,370-385. McAFE~. J. R. (1967). Lateral flow in the exosphere. Planet. Space Sci. 15,599-609. NICOLET; M. (1957): The aeronomic problem df helium. An& Gbophys. 13, I-21. PARK. C. G. (1970). Whistler observations of the interchanee of ionisation between the ionosuhere and the I proionosphere. j. geophys. Res. 75,4249-4260. y PATTERSON,T. N. L. (1966). The diurnal variation of the atomic hydrogen concentration at the base of the exosphere. Planet. Space Sci. 14,425-43 1. PAWERSON, T. N. L. (1970). Diurnal variations in thermospheric hydrogen. Rev. Geophys. Space Phys. 8.461-467. QUESSETTE,J. A. (1972). Atomic hydrogen densities at the exobase. J. geophys. Res. 77.2997-3000. SCHUNK, R. W. and WALKER, J. C. J. (1972). Oxygen and hydrogen ion densities above Millstone Hill. Planet. Space Sri. 20.581-589. SERBU,Ci. P. and MAIER, E. J. R. (1970). Observations from OGO 5 of the thermal ion density and temperature within the magnetosphere. J. geophys. Res. 75, 6102-6113.

RESEARCH

NOTES

691

T~NSLEY,B. A. (1970). Variations of Balmer a emission and related hydrogen distributions. S’uce Research, Vol. X, pp. 582-590. North-Holland, Amsterdam. TINSLEY, B. A. (1971). Hydrogen in the upper atmosphere. Trans. Am. geophys. Wn. 52; U.S. National Report to IUGG 510-513. WALLACE, L. and STROBEL,D. F. (1972). Diurnal variation of atomic hydrogen in the thermosphere. Planet. Space Sci. 20,521-531.

P&met. Space Sci. 1973 ,Vol. 21, PP. 691 to 692. Permttton Press. Printed in NorthernIreland

DISCUSSlON ON GEOMAGNETIC DISTURBANCES IN THE POLAR CAP: Sap AND BP-2 BY K. KAWASAKI AND S. -1. AKASOFU (Received 1S August 1972) In a recent article Kawasaki and Akasofu (1972) examined the geomagnetic and aurora1 data in the polar cap and concluded that it is not necessary to invoke DP 2 as a new mode of the distlirbance field that is distinct from the polar substorm. The purpose of this note is to point out a logical difficulty in the argument that has led them to the above conclusion. In their article two types of the observational material are employed to testify to their thesis that DP 2 is nothing but the polar substorm. The first is the amoral-zone magnetogram data as represented by the AL index and the second is the aurora all-sky camera film. Using the AL index they argued that DP 2 is identical to substorm since AL varies in synchronism with DP 2, and using the all-sky data they argued the same on the ground that the aurora] break-up is observed during DP 2. Although they did not state it explicitly, the above argument is based on the very important premises; namely, (1) any disturbance field that influences the AL is the polar substorm, and (2) no other disturbance fiefd can exist when the aurora] break-up is in progress. In order to prove these premises, one is forced to assume, among other things, that DP 2 does not exist. If DP 2 does exist, it would be registered by the aurora]-zone magnetograms and would contribute to AL, since DP 2 is defined as a global disturbance phenomenon encompassing the aurora1 zone (Nishida, 1971), and the variations seen in AL cannot be attributed uniquely to the substorm. Also, if DP 2 exists as a disturbance field that can occur superimposed on the substorm (Nishida, 1971), the occurence of the aurora1 break-up cannot immediately exclude the possibility that another mode of the disturbance is simultaneously present. Thus the argument of Kawasaki and Akasofu for the non-existence of DP 2 is based on the premise that requires the non-existence of DP 2 for its validity. In other words, their conclusion that DP 2 does not exist is built in their argument from the start. Their paper therefore cannot be taken as a valid proof for the non-existence of DP 2. As we have emphasized repeatedly in earlier articles (in particular in Nishida and Kokubun, 1971), it is extremely difficult to distinguish DP2 and substorm by the high latitude data alone. Above the aurora]-zone latitude the spatial ~hamcteristi~s of these two modes of the distur~nce field is much alike and it requires a careful quantitative analysis to separate them. In the lower latitudes, however, the disturbance vectors of the two modes have characteristically different directions, and it is from the analysis of these low-latitude records that we have been led to suggest the existence, often simultaneous, of two elementary modes of the disturbance field. The disturbance fields that have different spatial distributions on the ground should be associated with different current systems. (It may be worthwhile to note that the above method of separating the disturbance fields requires no assumption on the actual location of these current systems.) The coherence is merely one of the several check points we have employed. Toward the end of the paper Kawasaki and Akasofu briefly quote another paper concerned with the base line level at the dip Equator. This problem has been discussed in Nishida (1971) and the possibility of the presence of long-period DS type disturbance is suggested. The finding of the enhanced daily variation inside the polar cap during DP 2 days by Kawasaki and Akasofu may be a support to the above suggestion, although much remains to be examined. In any event, the analysis that led to the separation of DP 2 is immune to the problem involved in setting the proper base line (Nishida, 1971). Institute qf Spare and Aeronautical Science University of Tokyo, Tokyo 1.53, Japan

A. NISEUDA