On Planning and Exploiting Schumann Resonance Measurements for Monitoring the Electrical Productivity of Global Lightning Activity

On Planning and Exploiting Schumann Resonance Measurements for Monitoring the Electrical Productivity of Global Lightning Activity Vadim MUSHTAK, Earle WILLIAMS Massachusetts Institute

On Planning and Exploiting Schumann Resonance Measurements for Monitoring

the Electrical Productivity of Global

Lightning Activity Vadim MUSHTAK, Earle WILLIAMS

Massachusetts Institute of Technology, Parsons Laboratory, Cambridge, MA 02139 USA

2010 AGU Fall Meeting, San-Francisco, USA

1 Presenting an algorithm for monitoring worldwide lightning activity from electromagnetic observations in

the Schumann resonance (SR) frequency range.

2 Choosing a method of processing SR observations and analyzing the applicability of its results to the monitoring

procedure.

3 Choosing an optimal inversion algorithm for the

monitoring procedure

4 Testing the monitoring procedure on the basis of actual observations from a world-wide net of ELF stations

GENERAL CONCEPT OF MONITORING

PROCEDURE

The power spectrum of an electric/magnetic component F ( UT f ; ) of the background natural ELF electromagnetic field is formulated via the distribution of lightning sources ( UT; ) as





 



 





















) (

2 0

1 ( )

2 0

2 0

| ) ,

; (

| )

(

| ) ,

; (

| )

; (

| )

;

; (

|

UT

M

m

m

M

m UT

m

m

d f

P UT

A

d f

P UT

UT f

(1)

where m are the symbolically limited territories of the major global thunderstorm “chimneys”, P( f ;0,) is the propagation factor for the given component observed at a station with a location 0 (all locations are formulated in the spherical coordinates {a,,} of a temporally

dynamic system whose pole coincides with under-the-zenith point on the Earth’s surface r  a), and the sought-for factor

A m(UT) | QdS |2 N m(UT) [C2 km2 / s ]

is the change in the integrated vertical electric charge moment over the territory of the given “chimney” (for short, the “chimney’s” electric

activities) expressed via the statistically averaged charge moment of an individual lightning source | QdS |2 and the average number of

lightning discharges N m (UT) occurring per 1 second over the

“chimney’s” territory

In this formulation, the general concept of the procedure is to

monitor the spatial (the geographical coordinates) and temporal (the UT variations of activities) dynamics of the major thunderstorm “chimneys” from the background electromagnetic fields within the Schumann

resonance frequency range observed at a global network of ELF stations

The initial observational material presents continuous

electromagnetic time series recorded at a world-wide net of ELF stations with working frequency bands limited by or including the SR range In this study, use has been made of magnetic observations from five stations shown by blue-yellow pentagrams in Figure 1: BLK = Belsk, Poland; MOS = Moshiri, Japan; RID = Rhode Island, USA; SHL = Shillong,

India, and SYO = a Japanese-team-operated station in Antarctica Due to diversity of recording conventions at different stations, the initial time series have been reformatted to a unified format: 120 of 12-minute

periods per day (Figure 2A) In order to clean the data from

non-background elements (of impulse or man-made nature), each period has been divided into 144 of 5-sec segments, each segment’s power spectrum and a 5 to 29 Hz energy content (EC) have been computed The energy

contents for the given 12-min period have been presented as sampling distributions for the east-west (EW) and north-south (NS) magnetic

components (Figure 2B), from which sampling mean values (shown by red pentagrams) and standard deviations (SD; red triangles showing 1 to

5 SDs) of the ECs have been calculated From the distributions it can be seen, for instance, that in period #3 observed on January 1, 2009 at the MOS station, the EW segments with ECs exceeding 65 pT2/Hz do

certainly contain non-background elements (seen clearly in Figure 2A) and their contributions are not be added to the period’s spectrum In this way, after an additional median filtering against narrow-band

interferences, rectified EW and NS spectra for each period have been

constructed (Figure 2B)

While the standard procedure at the RID station is to approximate

a background power spectrum by a N-mode Lorentzian functional

2 1

2

1 2

1

) (

; )

(



































n n

n n

N n

n

f

f Q

P f

L L

f L

via the modal frequencies fn , intensities Pn , and quality factors Qn , it

was found that some modes at some stations are irrevocably spoiled by interferences that are neither identified by the rectifying procedure nor effectively removed by the filtering one For this reason, it was decided

to present the SR observations, instead of the full Lorentzian’s L2( f ) ,

by the modal characteristics of isolated Lorentzian terms (I-Lors, for

short) L2n( f ) approximating the spectra in the vicinities of corresponding modes (Figure 3)

Some examples of the diurnal variations of the SR characteristics are shown in Figure 4 (modal frequencies) and Figure 5 (modal intensities)

In this material, it can be seen signs of both stability (reflecting the

general dynamics of global lightning activity, which allows for

constructing its general models) and variability (due to the activity’s day-to-day individual patterns, which makes it sensible to monitor it for the patterns’ details) Since along with rather regular behavior on the 24-hour scale, both frequencies and intensities show certain, sometimes

significant, variations within 5 periods of each hour, the periodical

diagrams of the kind presented in Figures 4 and 5 has been recalculated into hourly mean values and standard deviations of the SR characteristics (Figure 7), which material has been actually exploited in the monitoring procedure

PROPAGATIONAL MODEL

Since some preliminary simulations had shown that the major –

day/night – electrodynamic non-uniformity of the Earth-ionosphere

waveguide plays a significant role in monitoring efficiency, in this study

use is being made of the two-dimensional telegraph equation (TDTE) [1]

 

1 sin

sin

2

2 2

































ст C

L

H

U

















sin

) (

) (

)

0

0

a

f P







where the pole of the spherical system of coordinates O {a,,}

coincides with the solar zenith, the source’s location is S {a,S ,S},

a is the Earth’s radius, P0( f ) is the source’s spectral dipole moment, the

proper propagation parameters are two complex frequency-dependent characteristic ionospheric altitudes H C and H L [1], and the

electromagnetic field’s components are expressed via the potential

) ,

;

) (

1 )

(

)

( )

(

~ )

;

O H

S H

S

H f

ifP O

S f

E

C C

L

)

; ( [

)

; (

1 )

; (

)

; ( )

(

~ )

;













O S

f

U O

f H S f H

S f H f ifP O

S f

H

L C

)

; ( [

)

; (

1 )

; (

)

; ( )

(

~ )

;













O S

f

U O

f H S f H

S f H f ifP O

S f

H

L C

The model’s propagation parameters – tested in other studies - have been constructed basing on the results of both recent research [2] and still

actual full-wave computations presented in the classical monograph by Galejs [3]

INVERSE PROCEDURE

Generally, the inverse procedure is based on an iterative

minimization of some metrics of discrepancies between the set of

experimentally determined modal SR characteristics E  { Ek} [k=1,

…,K] and analogous characteristics T ( ρ )  { Tk ( ρ )} theoretically

computed via a propagational model in dependence on the set ρ  { n}

[n=1,…,N] of the source model’s parameters - the positions and electric

activities of the modeled global “chimneys”

This general concept has been realized in two versions:

NELSON’S (linear, deterministic) ALGORITHM [4] is based on a

linearized presentation





















N n

n i

n

k i

k

i k

1

) ( )

ρ ρ

ρ

of the deviations Λ(ρ) E  T(ρ) as dependent on the changes in the model’s parameters n i

i n

 1 between iterations i 1and i Assuming ( 1 ) 0





i

ρ

Λ , the next iteration is obtained as

) ( ) (

ˆ 1

i ρ D ρ Λ ρ



via the theoretically computed sensitivity matrix with elements

i n

k i

n k

T

ρ

ρ ρ







 ( ) )

(

GOLTZMAN’S (quadratic, statistic) ALGORITHM [5] is based on a

quadratic presentation

1 1

2

1

2

1 )

( )

( )

N

n

k N

n

n i

n

k i

k

i

































ρ

ρ

ρ

of the function (ρ)  [E T(ρ)]T Rˆ [E T(ρ)] (the function of

maximum likelihood) with a subsequent application of Le Cam’s

suggestion to average the second derivatives over the random

realizations of experimental data via a covariance matrixRˆ In this case:

) ( ) (

ˆ 1

i ρ G ρ g ρ



where

i n n

T i

n

ρ T R

ρ T

(









n

T i

n(ρ ) [ T (ρ) Rˆ {E T(ρ)}]ρ





INVERSION: TESTS

At the previous stage of this project, it was shown [6] that a

monitoring procedure exploiting the modal frequencies fn (  n 1 , , 4 )

alone localizes the global African and American “chimneys” in a

reasonable agreement with general knowledge about global activity’s

properties, which cannot be told about the Maritime “chimney” At the present stage, the modal intensities are incorporated into the sets of the measured E and T characteristics, though not directly, but – due to

some calibration problems yet to be solved – as their ratios rm  Pm / P1

(m  2 , 3 , 4 ) to the first modal intensity As at the previous stage, the set

of estimated parameters ρ includes the geographical coordinates of two

most active at the given time “chimneys”, the pair being selected on the basis of a general geophysical information (Figure 8) (The activities

themselves, the ultimate objective of this project, are to be included into the set at the next stage)

The relative stabilities of the two above inversion algorithms have been tested as their abilities to provide the same positions of the modeled

“chimneys” by various initial conditions The results of the test are

shown in Figure 9 (Nelson’s algorithm) and 10 (Goltzman’s algorithm) Not surprisingly, the more sophisticated – and statistically founded –

quadratic algorithm turns out to be much less vulnerable to the danger of local minima than the linear one For this reason, Goltzman’s algorithm (with a diagonal covariance matrix) has been exploited in the actual 24-hour inversions

INVERSION: RESULTS AND DISCUSSION

The hour-to-hour results of the application of the above-selected

inversion algorithm to the data recorded by 5 ELF stations on January 1,

2009 are shown in Figures 1 (global map) and 11 (continental areas).

Not surprisingly, the results for the African “chimney” look most

consistent with general geophysical knowledge: this region is directly (let it be remotely) circled by 4 stations and being “serviced” much better than the other two

The Maritime “chimney” is in a less benign position, but still shows rather a compact dynamics (the 12UT “confusion” yet to be carefully

inspected) A possible shortcoming here is the obvious westward shift of the active area in comparison with the general knowledge, which could

be the result of complicated along-the-terminator propagation to one of two most informative – for this area - stations, MOS, without enough

support from other stations

The American area is being “served” mostly by the RID station

alone, and the along-the-terminator propagation definitely plays its not too friendly role here, too The 16Ut and 17UT accidents could be

interpreted as results of American activity being “masked” by African one (see Figure 8) without enough support from other – too remote – stations Interesting scenarios are those at 06UT and 07UT: any one of

them could be considered as the inversion’s “confusion”, but their being close to each other looks like a reflection of some objective reality

INVERSION: PROSPECTS

The above considerations can be confirmed – or undermined – by exploiting a more sophisticated, better informatively founded inversion procedure The obvious ways to improve it are:

1) increasing the number of participating stations (good prospects); 2) incorporation of electric measurements where available (in

progress);

3) including the “chimneys’” activities into the set of estimated

parameters (next step);

4) constructing and exploiting the full covariance matrix instead of its

diagonal simplification (some research required)

We are extremely thankful to all – too numerous to be listed –

experimentalists who have provided their observations, knowledge, and expertise for this project in numerous discussions and continuous e-mail

REFERENCES

[1] Kirillov, V.V (2002) Solving a two-dimensional telegraph equation

with anisotropic parameters Radiophysics and Quantum

Electronics 45, 929-941.

[2] Greifinger, P S., V C Mushtak, and E R Williams (2007) On

Modeling the Lower Characteristic ELF Altitude from Aeronomical

Data, Radio Science, 42, RS2S12, doi:10.1029/2006hRS003500.

[3] Galejs, J (1972) Terrestrial Propagation of Long Electromagnetic

Waves Pergamon Press, Oxford-New

York-Toronto-Sydney-Braunschweig

[4] Nelson, P.H (1967) Ionospheric Perturbations and Schumann

Resonance Data, Project NR-37-401, Geophysics Laboratory,

Massachusetts Institute of Technology (PhD dissertation)

[5] Goltzman, F.M (1982) Physical Experiment and Statistical

Conclusions Leningrad State University, 192p [in Russian]

[6] Mushtak, V., E Williams, R Boldi, and T Nagy (2010) On

Estimation Strategies in an Inverse ELF Problem European General Assembly 2010, Vienna, Austria