Spatial Effects of Multiple Scattering of HF Signalsin the Ionosphere: Theory and Experiment

N. Zabotin 1,2, J.W. Wright 2, A. Gasiewski 1, G. Zhbankov 31 Univ. of Colorado at Boulder

2 Dynasonde Solutions Ltd., Longmont, Colorado3 Inst. of Physics, Southern Federal Univ., Russia

Introduction

The theory of multiple scattering of MF/HF radio waves by intermediate-scale (0.1-2 km) ionospheric irregularities, as developed earlier by the authors, predicts a very distinctive distribution of the integral intensity of a signal reflected from the ionosphere in the vicinity of a ground-based transmitter. In particular, it is significantly reduced within a distance of about several tens of kilometers. There then occurs a ring of enhancement at a greater distance. At still larger distances from the transmitter, effects of multiple scattering are weakened and the integral intensity returns to its undisturbed value. While there are experimental confirmations of the “anomalous attenuation” effect near the transmitter location, no attempt has yet been made to track the intensity features at the larger distances. An experiment of this kind is critical for confirmation of the theory, and its preparation is described in this paper.

Results of numerical investigation of properties of the above solution at the frequency of Platteville MF Radar (2.219 MHz)

The theory of radiative transfer should be used for characterization of such signalsThe spatio-angular distribution of signal intensity upon reflection from a plane ionospheric layer with random irregularities is described by the radiation energy balance equation which has the following analytic solution in the ‘SASIRC’ approximation, valid if the most probable difference between the “invariant” angles θ´,φ´ and θ,φ in a scattering act is small:

Details of the theory can be found in [Zabotin, Bronin, Zhbankov; Waves in Random Media, v.8, p.421, 1998].

Angular distribution of the sky radio brightness (ray intensity) for a receiver position shifted (here, Eastward) from the transmitter's magnetic meridian plane, for six shift distances, and for km-scale irregularity amplitude ΔN/N=0.005, at the latitude of Platteville Observatory. With increasing shift, the nearer-side maximum gradually becomes dominant, but the former central peak continues to play a noticeable role up to some distance. Characteristic two-maxima structure of the obliquely reflected signal suggests something like double refraction. This effect is not of magnetoionic nature; it is caused by multiple scattering. Calculations have been made at NCAR’s Supercomputing Center.

Distinction between Single Scattering and Multiple Scattering

In the case of multiple scattering the spatial redistribution of energy is described by a kind of radiative transfer equation. This treatment is quite different from conventional ray tracing based on geometric optics.

The ionosphere is a multiple-scattering medium for HF radio sounding signalsThe ionosphere is a multiple-scattering medium for HF radio sounding signals

Results by the phase structure function method: Typical irregularity amplitudes for the scale length 1 km are 0.3 - 3.0%; typical values of their power spectrum index are 2.5 – 3.

In vertical sounding of the ionosphere, the optical thickness for scattering by intermediate-scale (~100 m – 1 km) irregularities is frequently considerably greater than unity. This implies a multiplicity of scattering that leads to a spatio-angular redistribution of the radio radiation flux.

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z

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1P( z,ρ,θ,j)= d q P( q,θ,j) ×

2π

iqΦ( z ;θ,j,θ,j)×exp iqρ+ dz dθdj Q( z ;θ,j,θ,j) e -1 ,

The “Cowboy Hat” effect stated in the Introduction

Platteville MF Radar as a test bed for the theory (current NSF Project #0737625)

The Platteville MF Radar operates continuously, radiating pulse signals at the frequency 2.219 MHz, with repetition frequency 60 Hz. Here is how this signal has been observed by the Radio Vector Field Sensor in various conditions:

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008-06-11 5:28:59 UTBoulder Colorado (30 miles from Platteville Observatory)

In Longmont, CO(20 miles away)

In Boulder, CO(30 miles away)

7 multiples of the F-Region reflection can be seen

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Numerical results for the integral intensity of the ionospheric reflection as a function of

distance to Platteville MF Radar

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NCAR Supercomputing Center, 2008PROGRAM: /home/blueice/zabotin/sasirc/lin/intqn

PHYSICAL PARAMETERS: gama=23.5 f=2.219e+06 H=5e+06 h0=2e+07 l0=1e+06 R=100000 nu=2.7 y=0

Three different values for the irregularity amplitude at the scale length 1 km, were examined. Both strength of the “Cowboy Hat” effect and its spatial scale increase together with ΔN/N.

Experimental setup for measuring spatial effects of multiple scattering based on Radio Vector Field Sensor designed and

manufactured at the Swedish Institute of Space Physics

Magnetic and electric versions of Radio Vector Field Sensor…

…and its mobile setup.