Are small-scale irregularities ina predominantly non-linear state?

Evidence from Dynasonde measurements

Are small-scale irregularities ina predominantly non-linear state?

Evidence from Dynasonde measurements

N A Zabotin and J W WrightN A Zabotin and J W WrightCooperative Institute for Research in Environmental

Sciences (CIRES),University of Colorado, Boulder, Colorado, 80309-

0216

N A Zabotin and J W WrightN A Zabotin and J W WrightCooperative Institute for Research in Environmental

Sciences (CIRES),University of Colorado, Boulder, Colorado, 80309-

0216Results presented here have been obtained through support from the National Science Foundation, grant ATM0125297

Basic idea of the phase structure function methodBasic idea of the phase structure function method

Because the ionospheric plasma drifts, the radio sounding signal

encounters different realizations of the irregularity field even at only slightly

different times. The consequent phase fluctuations can be measured

by the dynasonde.

The temporal Structure Function

is a very appropriate statistical characteristic of the phase

fluctuations (see Zabotin & Wright, Radio Sci., 36, 757, 2001).

Because the ionospheric plasma drifts, the radio sounding signal

encounters different realizations of the irregularity field even at only slightly

different times. The consequent phase fluctuations can be measured

by the dynasonde.

The temporal Structure Function

is a very appropriate statistical characteristic of the phase

fluctuations (see Zabotin & Wright, Radio Sci., 36, 757, 2001).

2( )D t t

0 1 10 100ô, sec

1E-4

1E-3

1E-2

0.1

1

1E+1

1E+2

Str

uc

ture

fu

nct

ion

, ra

d2

f=5 M Hz; í =3; äR

=0.001;

Lm

=10 km ; z0

=50 km ; ã=0.2 rad;

ö =0.5 rad; è0

=0.2 rad

V=200 m /sec; ö0

=90 deg

V=200 m /sec; ö0

=80 deg

V=200 m /sec; ö 0=0 deg

V=200 m /sec; ö0

= -90 deg

V=50 m /sec; ö0

=90 deg

V=50 m /sec; ö 0=80 deg

V=50 m /sec; ö0

=0 deg

V=50 m /sec; ö0

= -90 deg

Theory (built for a power irregularity spectrum) and experiment both suggest that the small-lag part of the full-scale SF is well approximated by a log-log linear law:

log(D(φ)/rad2) = SIA+SIB·log(τ/sec).

Theory (built for a power irregularity spectrum) and experiment both suggest that the small-lag part of the full-scale SF is well approximated by a log-log linear law:

log(D(φ)/rad2) = SIA+SIB·log(τ/sec).

1

2

3

4

5

0 24 48 72 96 120

13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5

0.0001

0.001

0.01

0.1

= 8/3

October Local Date

Hours Since 2145 UT 12 October 1997

Irr

egu

lari

ty S

pec

tru

m In

dex

Irre

gu

lari

ty A

mp

litu

de

for

the

Sca

le L

eng

th1

km

IONOSPHERIC IRREGULARITY PARAMETERSBEAR LAKE UTAH DYNASONDE; Sequence Begins 97-10-12 2145 UT

Irregularity amplitude ΔN/N, gradients and GDIIrregularity amplitude ΔN/N, gradients and GDIF

reg

ion

F re

gio

nE

reg

ion

E r

eg

ion

SummarySummary

1. Small-scale irregularity spectrum is practically always approximated by power law.

2. There is not asymmetry between irregularity growth and decay.3. Irregularity amplitude never drops down to the thermal

fluctuations level.4. Average irregularity spectrum index is close to Sudan and

Keskinen’s 8/3.5. Horizontal gradients are not the main controlling factor for the

irregularity amplitude.

1. Small-scale irregularity spectrum is practically always approximated by power law.

2. There is not asymmetry between irregularity growth and decay.3. Irregularity amplitude never drops down to the thermal

fluctuations level.4. Average irregularity spectrum index is close to Sudan and

Keskinen’s 8/3.5. Horizontal gradients are not the main controlling factor for the

irregularity amplitude.

Practical ConsequencesPractical Consequences

When modeling evolution of the small-scale irregularities one should not assume “clean” initial state with thermal fluctuations only. It is useful to permit a possibility that initial state was already non-linear.

When modeling evolution of the small-scale irregularities one should not assume “clean” initial state with thermal fluctuations only. It is useful to permit a possibility that initial state was already non-linear.