The

Global Atmospheric Electric Circuit

Colin Price

Department of Geophysics and Planetary Sciences

Tel Aviv University

Israel

cprice@flash.tau.ac.il

Historical Background

1752 Lemonnier discovered

that in fair weather regions

there is a persistent E-field

of ~100 V/m pointing

downward

Why do we not get electric shock? (200 V between head and ground)

1920s: There exists a diurnal variation of the atmospheric

electric field, which is independent of location and local

time, but dependent only on universal time:

~100V/m

“Carnegie Curve”

Long Term trends in surface Potential Gradient (E)

Implication of E-field Earth has a negative charge of ~500,000 C

Charge of the Earth

Q = 4 πR2 εo E = R2 Eo / k

= 4.5 x 105 Coulomb

εo= permittivity of free space (electric const.)

= 8.85x10-12 F/m

- - - - - - - - - - - - - - - - - - -

450,000 Coulombs

The conductivity of the atmosphere is determined by

the concentration of ions in the atmosphere. The

amount of ions increases

with altitude since the

main source of ionization

is cosmic and solar radiation

from outside the Earth's

atmosphere. The mobility

of ions increases with

decreasing density.

1887 Linss discovered ions in the atmosphere, implying that

air had a finite conductivity

Ionosphere

100km

j = σ E

Conduction

Current

σ x E

Conduction Current

J(R) = o E(R) = 2 x 10-12 Amp/m2

σ(R) =σo = 3x10-14 Siemen/m [S/m]

{1 S = Ω-1}

The conduction current

varies little with altitude

up to z~50 km

Globally, i = J(R) 4πR2

~ 1000 Amp

1900 CTR Wilson measured the air-Earth current which has

a value ~2x10-12 A/m2

+ + +

+ +

+ +

+ +

+ +

+ + +

Due to the high conductivity of the Earth, the

Earth-ionosphere represent a spherical capacitor

Volt

Meter

+

-

-+ - - + - + - - +

-- + + - + - + -

- + + - + - - +

ions

Earth

- - - -

- -

- - - -

ionosphere

However,

because of the

ions in the

atmosphere,

the capacitor

discharges

slowly (leaky

capacitor)

(i) ~10-5 S/m

(o) ~1 S/m

(air) ~10-14 S/m

Ionospheric Potential

The potential difference between the ionosphere (height h) and

the Earth’s surface, known as the ionospheric potential, is :

V = - E(r)dr = - E(r)dr

since E=0 for r> R+h (or z>h).

Most measurements show values of V~ 3x105 Volt (300kV)

Resistance of Atmosphere (fair weather)

From here we can also see that the total resistance between the

Earth and ionosphere is

RΩ = V/i = 3x105/1000 ~ 300 Ω

R

R+h

R

ground

ionosphere

Vi

0 3 6 9 12 15 18 21 24

Capacitance of the Earth

C = Q/V ~ 4x105C/3x105V ~ 1 Farad

The typical time scale for the discharging of the capacitor is

τ = RΩ C = 300 sec! (5-10 minutes)

Conclusion: Without a source of charging of the Earth-

ionosphere capacitor, the charge on the Earth would decay

nearly immediately (few minutes). What is the source of

this atmospheric charging? What is the battery in circuit?

+ -

1920 Wilson suggested

the generator was global

thunderstorms

1929 Whipple showed that

the diurnal variations of

the fair weather field

matches the diurnal

variations of global

thunderstorms

+ -

Q ~ -500,000 C

300Ω 300 kV

PG ~ -100 V/m

I ~ 2 pA/m2

DC – Direct Current

Global Circuit

The Global Atmospheric Electric Circuit

Rycroft et al. (2000)

Where are the batteries?

~1000 thunderstorms

Latitudinal

Distribution

Longitudinal

Distribution

Diurnal

Distribution

There is also an AC component to

the Global Electric Circuit

50-100 flashes per second

Generation of EM waves

Trapped in Earth-ionosphere waveguide

Standing Waves

(Hz) nVFrequency=

L

Bell 1 Bell 2

ELF- Schumann Resonances

2a …. Hz 20 , 14, 8~ nc ~ nf

(Schumann, 1952) Extremely Low Frequency (ELF) Range

F < 100 Hz

ELF

Waveguide Cutoff

Earth

Ionosphere

ELECTRIC FIELD MAGNETIC FIELD

Lightning Discharge

14 Hz

8 Hz

Ez

Hx,y

Hx,y

Ez

Schumann Resonance Modes 1 and 2 n c F ~

40,000km

02

0)1(1

cos12)1(

4n

ncr

nn

Pni

ha

ME

Theory

1

1

)1(1

cos12

4n

nc

nn

Pn

ha

MH

ω = angular frequency

Θ = great circle angle from lightning to the observer

ε0 = vacuum permittivity;

a = radius of the Earth;

h = the height of the Ionosphere;

Pn(cos θ) and Pn1(cos θ) are Legendre and associated Legendre functions

of degree n and order 0,1 respectively

, the modal eigenvalue related to the propagation constant of the

Earth-Ionosphere spherical-shell cavity

Mc(ω) is the vertical charge moment of the lightning ground flash.

f=8 Hz 14 Hz 20 Hz 26 Hz

n c F ~

40,000km (Schumann, 1952)

EW

NS

Magnetic Field detectors

Mitzpe Ramon

Electric Field Detector

-2

-1

0

1

2

0 1 2 3 4 5 6 7 8

Ma

gn

eti

c F

ield

Am

pli

tud

e(V

olt

s)

Time (seconds)

0

2

4

6

8

10

12

10 20 30 40 50

Pow

er (

Rela

tive U

nit

s)

Frequency (Hz)

8Hz

14Hz

20Hz

27Hz

33Hz39Hz

Negev Desert

Israel

0.2

0.3

0.4

0.5

0.6

0.7

0.35

0.4

0.45

0.5

0.55

0.6

0.65

50 55 60 65 70 75

Isra

el S

R A

mp

litu

de

Ca

liforn

ia S

R A

mp

litud

e

Julian Day 1998

r=0.9

Time Series

Spectrum

4pm 4pm

4pm

Rycroft and Harrison (2011)

Huge Range of Horizontal and Vertical Scales

Rycroft and Harrison (2011)

Huge range of Temporal Scales

Global Circuit and

Climate Change

T

Williams (1992)

Tropical

Temperature

Anomaly

Schumann

Resonance

0.007

0.008

0.009

0.01

0.011

0.012

300.5

301

301.5

302

302.5

303

303.5

304

02/11/98 16/11/98 30/11/98 14/12/98

1800

UT

Ligh

tnin

g Ac

tivity

ove

r Sou

th A

mer

ica

(SR

rela

tive m

agni

tude

)

1800 UT Surface Temperature over South Am

erica

(K)

Date

SR

Ts

r=0.57

Price and Asfur (2006)

Tem

pera

ture

(K)

Africa

S. America

Mag

neti

c F

ield

In

ten

sit

y

(au

)

Upper Tropospheric Water Vapour

Upper Tropospheric Water Vapour

0.04

0.045

0.05

0.055

0.06

0.065

0.07

0 10 20 30 40 50 60 70

0.0007

0.00075

0.0008

0.00085

0.0009

Afr

ica

n L

igh

tnin

g A

cti

vit

y

(SR

Ma

gn

eti

c F

ield

)

Day from 20 October 1998

Sp

ec

ific H

um

idity

(kg

/kg

)

r=0.91

Lightning Activity vs. Specific Humidity (300mb) +24hours

26% SR change => 0.1 g/kg change

Price and Asfur (2006)

Harrison (2002)

Harrison and Usoskin (2010)

Solar Influences

on the Global Circuit

Atmosphere

Nuclear Testing

DC Circuit

297.6 297.8 298.0 298.2 298.4

-20

-10

010

20

Year day

dB

z (

nT

)

297.6 297.8 298.0 298.2 298.4

-20

24

68

10

Year day

sd B

z (

nT

)

01

23

45

6

Bz of IMF from ACE

Jz SD of GEC in Israel

Jz SD of GEC in Israel

Bz SD of IMF from ACE

24 October 2011

ACE

Jz

Satori et al.

(2005)

AC Circuit

Monthly averaged Frequency for NS and EW components

7.60

7.65

7.70

7.75

7.80

7.85

7.90

96ר-ואנ י

96לי-יו

97ר-ואנ י

97לי-יו

98ר-ואנ י

98לי-יו

99ר-ואנ י

99לי-יו

00ר-ואנ י

00לי-יו

01ר-ואנ י

01לי-יו

02ר-ואנ י

02לי-יו

03ר-ואנ י

03לי-יו

04ר-ואנ י

04לי-יו

05ר-ואנ י

05לי-יו

Hz

NS

EW

NS, EW frequencies (yearly averaged)

7.65

7.70

7.75

7.80

7.85

1996 1997 1998 1999 2000 2001 2002 2003 2004

Hz

-9.0

-8.0

-7.0

-6.0

-5.0

-4.0

-3.0

X r

ay

flu

x (

W/m

^2

), lo

g. s

ca

le

NS

EW

X rays (0.5 - 4 A)

X rays (1 - 8 A)

NS and EW frequencies with

Log. ( X Ray Flux (1-8A)),

R(NS,1-8A)=0.941, R(EW,1-8A)=0.953

y = 0.0488x + 8.0577

y = 0.0495x + 8.1003

7.65

7.70

7.75

7.80

7.85

-8.0 -7.5 -7.0 -6.5 -6.0 -5.5 -5.0

X ray flux (W/m^2), log. scale

Hz

NS

EW

Linear (NS )

Linear (EW )

Frequency of first SR mode (~7.8Hz)

Monthly mean values

Hz

Hns

Hew

Annual Mean Values (SR and X-rays)

r=0.941 r=0.953

1996 2006

Month/Year

27-day solar rotation

effects on SR frequency

NS frequency (SAO) and X Rays (background flux) 01-03,2005

7.7

7.75

7.8

7.85

7.9

7.95

01/0

1/2

005

08/0

1/2

005

15/0

1/2

005

22/0

1/2

005

29/0

1/2

005

05/0

2/2

005

12/0

2/2

005

19/0

2/2

005

26/0

2/2

005

05/0

3/2

005

12/0

3/2

005

19/0

3/2

005

26/0

3/2

005

Day

Hz

0

10

20

30

40

50

60

70

SS

N

NS Freq. av

SSN (Belgium) av.

NS frequency (SAO) and X Rays background, 01-03, 2005

7.6

7.65

7.7

7.75

7.8

7.85

7.9

7.95

01/0

1/2

005

08/0

1/2

005

15/0

1/2

005

22/0

1/2

005

29/0

1/2

005

05/0

2/2

005

12/0

2/2

005

19/0

2/2

005

26/0

2/2

005

05/0

3/2

005

12/0

3/2

005

19/0

3/2

005

26/0

3/2

005

Day

Hz

-9.00

-8.50

-8.00

-7.50

-7.00

-6.50

-6.00

-5.50

-5.00

X r

ay f

lux (

W/m

^2),

lo

g. scale

NS Freq. av

Log Xrays, av

January-March 2005

Hns freq. and SSN Hns freq. and X-rays

[Füllekrug and Fraser-Smith, 1996]

30day

SR Spectral Power Variation

f1=8 Hz

f2=14 Hz

Solar Flares - X rays

15 Oct-15 Nov 2003

Ez, 8 Hz, Goes 10 - 8A, 4A

7.5

7.7

7.9

8.1

8.3

8.5

15/10

/03

20/10

/03

25/10

/03

30/10

/03

4/11/0

3

9/11/0

3

Day, 2003

Freq.

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

X - ra

ys

Freq. 8Hz

Goes 10 X rays 8A

Goes 10 X rays 4A

Ez, 14 Hz, Goes 10 - 8A, 4A

14.0

14.2

14.4

14.6

14.8

15.0

15/10

/03

20/10

/03

25/10

/03

30/10

/03

4/11/0

3

9/11/0

3

Day, 2003

Freq

.

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

X - r

ays

Freq. 14Hz

Goes 10 X rays 8A

Goes 10 X rays 4A

Ez, 20 Hz, Goes 10 - 8A, 4A

20.0

20.2

20.4

20.6

20.8

21.0

15/10

/03

20/10

/03

25/10

/03

30/10

/03

4/11/0

3

9/11/0

3

Day, 2003

Freq

.

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

X - r

ays

Freq. 20 Hz

Goes 10 X rays 8A

Goes 10 X rays 4A

8Hz

14Hz

20Hz

X Rays and NS Ampl, PKD , 04/11/03

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

18:0

0

18:3

0

19:0

0

19:3

0

20:0

0

20:3

0

21:0

0

21:3

0

22:0

0

22:3

0

23:0

0

23:3

0

Time

W/m

^2

2E-10

3E-10

4E-10

5E-10

6E-10

7E-10

8E-10

9E-10

pT

X-rays:

Ampl.

What do all these changes mean?

Changes in thunderstorms?

Changes in waveguide?

Changes in conductivity?

Data from 1866-1932

(Brooks, 1934)

Solar Cycle in Thunderstorm Frequency?

Stringfellow (1974) showed similar relationships for UK from 1930-1973 (4 solar cycles)

Schlegel et al. (2001)

European Thunderstorms

(Austria and Germany)

Data from ground networks

April-September

Takahashi et al. (2009)

27-day Periodicity in Clouds

Global Lightning Clouds

What have we learned?

The global atmospheric electric circuit is made up of both a

DC component and AC component

The DC circuit depends on global thunderstorm activity (area

coverage, intensity) and atmospheric conductivity (ions,

aerosols)

The AC circuit depends on global lightning activity (intensity

and number of flashes) and ionospheric parameters (D-layer

reflection height, ionospheric conductivity profile)

There is evidence that solar variability (solar cycle, solar rotation,

solar flares) influence both DC and AC circuit parameters

These Solar impacts may result from changes in

the Earth-ionosphere cavity, and/or even changes in cloud and

thunderstorm activity itself.

The GEC may also be a sensitive tool to study climate change.