IScatterSpectrum

IScatterSpectrum.jl

This package provides tools to calculate the incoherent scatter (IS) spectrum for a ionospheric plasma.

Facilities like EISCAT_3D and the Advanced Modular IS Radar form multiple beams, and so greatly increase the amount of data to process. The aim of this package is to develop and test software for calculating and fitting the IS spectrum using the high-performance Julia system and its parallel execution.

A reference is the article

Swartz, W. E. (1978), Analytic partial derivatives for least‐squares fitting incoherent scatter data, Radio Sci., 13(3), 581–589, doi:10.1029/RS013i003p00581.

and FORTRAN IV code written by the same author, iscatspe.for. If needed for testing and verification, ISfortran.jl shows how the reference FORTRAN code can be called from Julia. Presently only the functions and COMMON BLOCK addresses to call the plasma dispersion function are provided. In the FORTRAN code the plasma dispersion function is calculated following the prescription in the book

The Plasma Dispersion Function: The Hilbert Transform of the Gaussian, by Fried and Conte, Academic Press, 1961.

Over most of the part which is interesting for the IS spectrum the prescription integrates a differential equation, which does not lend itself easily to parallel execution.

In IScatterSpectrum.jl erfcx from the SpecialFunctions package is used. Also faddeeva using the method of

J.A.C. Weideman, "Computation of the Complex Error Function," SIAM J. Numerical Analysis, pp. 1497-1518, No. 5, Vol. 31, Oct., 1994

is provided for verification and experimenting. For physical constants the unregistered PhysicalConstants is required.

struct ScatterVolume precalculates parameters that change when processing along a beam or switching beams, but are constant in a fit. struct Plasma and struct CollisionalPlasma precalculate parameters that change in the fit (depending on N_e, T_e, T_i, ν_i, composition), but are constant at all the frequencies.

So far only the power spectrum can be calculated: pwrspec(freq, p::Plasma, s::ScatterVolume) and pwrspec(p::Plasma, s::ScatterVolume), the latter for zero frequency which requires special numerical treatment in the admittance formulation used here. The same functions are available for CollisionalPlasma.

plottest.jl (in the test folder) creates plots of some example spectra, using the PlotlyJS package.

To do

• add the Fourier transform to get ACFs. Swartz (1978) prefers a non-fast numerical integration (because only few ACF lags are needed, but many frequencies). But this seems not ideal for parallel execution. Several articles on methods for fast calculation of Fourier integrals have in the meantime been published.

• add the analytical derivatives with respect to N_e, T_e, T_i, ν_i, composition. The conclusion in 1978 was that numerical derivatives are roughly equally fast to calculate, but the analytical formulas seem still preferable, after they have been laboriously calculated.

• explore possibilities for parallel execution.

• add fitting to real data, with constraints from models, output of results etc.