PARAMETERIZATION OF THE HEATING IN THE MIDDLE STRATOSPHERE DUE TO SOLAR
WIND INDUCED ELECTRIC CURRENTS
L.N. Makarova, A.V. Shirochkov, A.P. Nagurny,
Arctic and Antarctic Research Institute, Saint - Petersburg 199397, Russia
E. Rozanov and W. Sсhmutz
Physikalisch-Meteorologisches Observatorium, Davos, CH-7260 Davos Dorf, Switzerland
ABSTRACT
A new mechanism of the thermal heating in the middle stratosphere by the solar wind induced electric currents is
proposed. This process occurs mostly at 20-30 km altitude where a permanent layer of heavy ion-clusters is
produced by the galactic cosmic rays and by some other sporadically occurring sources. The currents in this layer
control the electric fields in the stratosphere. Numerical estimation of the possible atmospheric heating rate due to
this process shows that such heating could reach (1-2) K/day that is comparable to the heating due to the absorption
of the solar UV radiation. Thus, the electric fields and currents induced by the solar wind energy are candidates for
producing relevant additional heating in the middle stratosphere (altitudes 20-30 km). This process may alter the
thermal structure of the polar stratosphere and the structure of the polar stratospheric vortex, and as a result, the
global climate/weather system. In this paper we describe the parameterization of this heating suitable for the
application in climate and general circulation models.
Keywords: solar wind, stratosphere, electric current, rate of ionization, Joule heating
1. Introduction
Most studies of the solar effects on the Earth’s atmosphere and climate paid attention to the radiative energy
variations connected with 27-days and 11-year solar cycles [Baker, 2000]. The effects of the energetic particle
precipitation induced by the solar wind disturbances on the middle atmosphere composition and dynamics have been
considered also as a part of the solar output [Callis, 1999]. These processes can affect the ozone and other
radiatively active atmospheric species and can be detected mostly in the upper and middle stratosphere.
_____________________________________________________________________________
Corresponding author**: L.N. Makarova, Arctic and Antarctic Research Institute, 38 Bering Street, Saint-Petersburg
199397 Russia. Phone: 7-812-352-06-01 FAX: 7-812-352-26-88; E-mail: shirmak@aari.nw.ru
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Analysis of the experimental data as well as theoretical considerations revealed that the solar wind energy could be
transferred into the Earth’s atmosphere also by the electric fields [Callis, 1999; Makarova and Shirochkov, 2000].
A high correlation between the solar wind activity and different atmospheric parameters suggests a strong coupling
of these parts of the near-Earth space [Makarova et al., 1997, 1998; Makarova and Shirochkov, 2000]. A new view
on the global electric circuit proposed by Makarova et al. [1998] and Makarova and Shirochkov [2000] could help to
explain this close coupling. According to this approach the main source of energy controlling the global electric
circuit is the Electromotive Force generator located at the dayside magnetopause of the Earth’s magnetosphere and
driven by the solar wind energy. The passive elements of the circuit are the conducting regions in the ionosphere, a
layer of heavy ion-clusters in the middle stratosphere and conducting parts of ground surface. Existence of the
conducting ion layer in stratosphere at altitudes of the primary ozone maximum (around 23 km) seems to be an
important factor in the atmosphere thermodynamics and electrodynamics. This layer is a channel for electric current
at stratospheric heights, which is induced by electric fields produced by the solar wind. Electric current in the
stratosphere will undoubtedly influence the atmospheric parameters. This paper is devoted to analysis of the
interactions between the solar wind and the global electric circuit as a possible mechanism of the solar wind
influence on the Earth’s atmosphere. We are using the approach of Alfven and Falthammar [1963] to evaluate the
electric currents effects in weakly ionized plasma.
2. Evaluation of the effects produced by the electric currents in the middle atmosphere
Let us suggest that the density of the charged particles with charge e k and mass mk in atmosphere is equal to nk. An
electric field of strength E will move these particles with an averaged drift velocity u k.
uk = bk E
(1)
where bk is a constant, which can be called mobility in a case of weak fields. If the values of mobility of all
atmospheric gases are known it is possible to calculate intensity of electric current I and of conductivity of
atmosphere  since I = E. Alfven and Falthammar [1963] give equations for the current (I) and conductivity () in
the following form:
I =  nk ek uk=  nkekbk E
(2)
 =  nkekbk
(3)
An electrical resistance of the atmosphere R can be calculated as:
R = 1/= 1/ nkekbk
(4)
We evaluate the effects of electric currents in the atmosphere with a simplified method based on concept of “particle
free path length”. The result of our calculations will depend on the parameters involved whose values are difficult to
evaluate exactly. Among these the frequency of ion-neutral collisions and the concentration of the charged particles
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are poorly known. “Particle free path length” approach assumes that the charged molecules undergo instant
collisions while between the collisions they move with acceleration under the influence of electric field.
Alfven and Falthammar [1963] defined the mean velocity uk of a particle moving in the direction of electric field by
the “particle free path length” method as:
uk = ( ekk/2mk Vk) E
(m/s),
(5)
where k= Vk /k is a particle free path length; V k is a mean thermal velocity of ions ; k - is ion-neutral collision
frequency.
Then the mobility of a particle follows from (1) as
bk = uk /E =  ekk/mk Vk =  ek/mk k (m/s),
(6)
where  is a dimensionless coefficient.
Values of  vary in the range between 0.5 and 1.0. An accurate calculation of the mobility taking into account
statistical distribution of the velocities and the free path lengths gives the expression similar to equation (6) but with
 = 1 [Alfven and Falthammar, 1963]. Inserting these values of mobility into the expressions for current intensity
and resistance we obtain
I = ( nkek2 E)/ mk k (A/m)
(7)
R = 1/( nkek2 )/ mk k
(8)
= mk/( nkek2 tk) ( m).
The charged component of the middle atmosphere consists of the electrons as well as positive and negative ions. As
a rule, these particles are in the state of electric equilibrium when the concentrations of positive and negative
particles are equal. In the equations (7) and (8) the summation should be made for negative (mainly electrons) and
positive particles separately. The mass of the electron (me =1.6 10-31 kg) is much less than mass of the ion
(mi=M mp=M 1.6 10-27kg, where M is a mean mass number of ions). Their ratio me/mi is equal to 1.57 10-6 for
M=400 at stratospheric heights [Brasseur and Chatel, 1983]. In this case the part of the equation for electron
component of the current is a dominant in expression for current (7) while ionic component is a main part in
expression for resistance (8).
The amount of Joule heating produced by current I is
dQ/dt = I2 R (J /m3 s).
(9)
Inserting (7) and (8) into (9) yields
dQ/dt= n e2 E2 mi/ me2 (J /m3 s).
where n=ni = ne – total concentration of the charged particles for electrodynamic equilibrium conditions.
(10)
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The external parameters, which determine amount of the Joule heating dissipated by the electric currents in the
atmosphere (equation 10) are the following: electric field strength E, charged particle concentration n, collision
frequency , and ion mass weight mi.
3. Evaluation of the external parameters
Accurate values of these parameters are difficult to evaluate. In this section we attempt to collect as much
information as possible from different sources.
3.1. Strength of the electric field in the stratosphere.
There are very few reliable measurements of the stratospheric electric field strength. E. Bering [1995] performed
one of them by using the special long-lived balloons in summer seasons of 1988-1989 over South Pole Station in
Antarctica. The range of the measured electric field values was 0.1 - 0.35 V/m. We have sorted these data in
accordance with the solar wind disturbances taken as the subsolar distance between the Earth and dayside
magnetopause position expressed in the Earth radius units Re [Makarova and Shirochkov, 2000] and got the
following empirical relation between these two parameters
E = (527.01 – 31.5 Re) 10-3 (V/m).
(11)
This relation was derived for 40 experimental values of stratospheric electric field. Correlation coefficient between
the magnetopause positions and stratospheric electric field values turned out to be rather high – 0.78.
This equation is to be used for the calculation of electric field parameters. This choice is explained by the lack of
other reliable measurements of stratospheric electric fields and must be considered as the first approximation of the
global electric field distribution in the stratosphere.
The magnetopause position is determined from an empirical
model developed in by Shue et al. [1997]. The input parameters of this model are the solar wind density n sw ,
velocity Vsw as well as the magnitude and orientation of the interplanetary magnetic field (IMF) vertical component
Bz. These parameters are given in the NASA periodic publications [King, 1993]. The magnitude of the solar wind
impact on the Earth’s atmosphere is maximal at the dayside of our planet during 06-18 hours local time [Makarova
et al., 1998]. Physical processes responsible for the interaction between the solar wind and the near-Earth space on
the Earth night side (18-06 local time) have not been investigated properly yet. Therefore, the magnitude of the
electric field strength induced by the solar wind on this part of the Earth could not be determined from the equation
(11) and at the moment only very rough estimations could be made. These estimations show that the magnitude of
stratospheric electric field on the Earth’s nightside is of about 40 percent of the corresponding daytime value.
3.2. Concentration of the charged particles in the middle atmosphere
Concentration of the charged particles in the middle atmosphere (18-40 km) is formed by many sources. The main
source is the galactic cosmic rays (GCR), which permanently ionize this part of the atmosphere at all latitudes from
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the pole to the equator. Concentration of the free ions in the atmosphere is determined as proposed in [Webber,
1962]:
ni = [q/eff]1/2 ,
(12)
where ni is the ion density in m-3; q is the rate of ionization in ion/m3s; eff is the effective recombination coefficient
in m3s-1. In general the latter parameter depends on altitude and the solar irradiance, but according to [Webber,
1962] we put it equal to 1.10-9 m3s-1.
Ionization rate (q) produced by the GCR fluxes could be calculated by the equation from [Heaps, 1978]:
q= (A+B sin4) nа ,
(13)
where  is the geomagnetic latitude; A and B are dimensionless coefficients depending on the solar activity level; na
is the concentration of neutral molecules in the atmosphere. A is a constant coefficient equal to 1.74 10 -18, B is a
coefficient equal to 1.93 1017 for the years of maximum solar activity and equal to 2.84 10 -17 for the years of
minimum solar activity. The solar cosmic rays, the solar X-rays and aerosols are able of producing an anomalous
ionization at these altitudes, only sporadically though. The rate of ionization by the GCR depends on geomagnetic
latitude (it increases from the equator toward the pole) and on the solar activity (it is highest/lowest during the solar
activity minimum/maximum).
The vertical distribution of the charged particles in the atmosphere obtained from the experimental data has been
presented in [Kohl et al., 1996]. The appearance of the secondary ionization maximum at 24 km altitude presumably
consisting of the heavy ion-clusters is clearly seen. Its density is about 3.0 109 m-3. Another experimental data
confirming the presence of similar layer in the stratosphere can be found in [Brasseur and Chatel, 1983]. Thus, there
are solid reasons to suggest the existence of a charged particles layer at stratospheric altitudes for any level of solar
and geomagnetic activity. It is a very important point for the present investigation.
3.3. Frequency of the ion-neutral collisions
Frequency of the ion-neutral collisions (k) is an important parameter of the middle atmosphere determining
electrodynamics of this region. In general form it could be calculated by the following equation [Webber, 1962]:
k = 4.4 10-15 (T/300) nа (s-1)
(14)
where T is the atmospheric temperature in K; nа is the density of the neutral molecules in the atmosphere in m-3 .
There are few experimental measurements of this parameter at altitudes 18-40 km [Webber, 1962] which gave the
value of k equal to 1.5 109 s-1 at the 30 km altitude.
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3.4. Mean mass of ions.
One of the main points of our investigation is the established fact of existence of a layer of heavy ions at altitudes
~25-35 km [Brasseur and Chatel, 1983; Kohl et al., 1996]. This layer consists of the cluster ions with the mean mass
weight of around 400. This value is taken as universal parameter in further studies.
4. Numerical estimation of the heating rate in the middle atmosphere produced by the electric current
Using the parameterization of all components in the final equation (10) it is possible to make a numerical estimation
of thermal effects produced by the electric currents in the atmosphere. For this calculation we have applied
moderately disturbed conditions in the solar wind. For this particular case we can take the following values of the
controlling parameters:
=
1.6 10-27 kg;
=
9.1 10-31 kg;
=
1.6 10-19 C
E
=
3 10-1 V/m
T
=
220.0 K
ni
=
4 108 m-3
M
=
400

=
1.51 s-1
mp
(proton mass)
me
(electron mass
e
(charge of electron)
k
)
By substituting these values into the equation (10) we can obtain the amount of Joule heating equal to 1.8 .10 -4
J/m3s. For the unit of volume (if we take cp = 240 kal/kg K and  = 4. 10-2 kg/m-3) we got dT/dt = 3. 10-2 K/hour.
It is known that similar impact of the solar UV radiation on the ozone layer produces dT/dt = 0.5 10 -2 K/day [Kohl et
al., 1996]. If the maximal value of the charged particles density in the stratosphere (n i = 3.0 109 m-3) is used in this
calculation we get dQ/dt = 3.0 10-4 (J/m3s). It means that the temperature tendency due to proposed mechanism
would be equal to dT/dt =1.2 K/day. The latter value is comparable with correspondent atmospheric heating due to
solar UV radiation [Ginzburg et al., 1989]. Results of the similar calculations for various situations showed the same
order of Joule heating due to the solar wind dynamics as those described above.
Figure 1 illustrates zonal mean distribution of the Joule heating rate. The calculations were performed for January
and for moderate level of solar and interplanetary activity by using the method described above. The geographical
distribution of the Joule heating rate at 10 hPa surface due to the solar wind dynamics is shown in Figure 2. The
heating rate increases monotonically from the equator to the poles in accord with the ionization rate (see equation
13). The heating rate reaches its maximum over high latitudes of the summer hemisphere (Antarctica) since density
of the neutral atmosphere is higher under such circumstances than in the winter. The both ionization rate and
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frequency of ion-neutral collisions crucially depend on this parameter (see equations 13 and 14). As one can see the
magnitude of the Joule heating given in Figures 1 and 2 are about 3 times lower than the corresponding maximum
values indicated earlier. This difference is explained by a moderate level of solar activity adopted for the
calculations with correspondingly smaller ionization rate and density of the neutral atmosphere. The most important
result of these calculations is that even these values of the Joule heating caused by the solar wind dynamics are
comparable with correspondent atmospheric heating rates due to solar UV radiation at these heights [Ginzburg,
1989].
5. Conclusions
Numerical estimations presented in this study show that the energy of the solar wind could be transferred into the
Earth atmosphere through the electric fields induced by the solar wind disturbances. This process could be effective
up to stratospheric altitudes 20-25 km where the ionized layer produced by the galactic cosmic rays and by some
other sources exists. The electric currents induced by the electric fields are able to heat the atmosphere at altitude
~25 km up to 5.10-2 K/hour (1-2 K/day). It means that the stratospheric warming could be produced not only by
dynamical factors but also by a local heating of the atmosphere by electric current. The latter phenomenon could be
especially effective in high-latitude region. Several rough approximations have been made in the above calculations,
which nevertheless did not prevent to get realistic results. The aim of the further studies is to elaborate more
accurate values of the parameters involved in these calculations.
The preliminary calculation of the global Joule heating fields allows to conclude that the proposed method of the
Joule heating rate parameterization is physically correct and meaningful. The obtained magnitude of the Joule
heating is comparable with atmospheric heating rate due to solar UV radiation even and should be taken into
account in climate models.
The direct consequences of such warming could be the changes in dynamics of the stratospheric polar vortex, global
ozone concentration and also climate/weather pattern. All these processes could only be accurately evaluated using a
global scale 3D chemistry-climate model and the parameterization for the additional heating presented and
explained here.
Acknowledgement. This research is supported by INTAS grant 2001-0432. Valuable advices of Prof. Dr. I.L. Karol
in process of the paper preparation are appreciated.
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Figure 1. Zonal mean heating rate (K/day) averaging over all longitudes for every value of latitude due to solar wind
induced electrical currents in the middle stratosphere. The heating rates have been calculated using the
parameterization and input data for January 1996.
Fig. 1
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Figure 2. Geographical distribution of the heating rate (K/day) due to solar wind induced electrical currents at 10
hPa surface. The heating rates have been calculated using the parameterization and input data for January 1996.