In a previous post a wavelet-based analysis procedure was described and demonstrated with simulated inverse-power-law data http://chuckrino.com/wordpress/?p=464. The analysis procedure has been applied to a large number of C/NOFS high-resolution equatorial measurements during periods of strong ESF. The data are particularly well suited to wavelet-based analysis because large extent of the data sets (>1000 km) and the structure scale range. The analysis and results are described in a paper accepted for publication in Radio Science. URSIPaper2014.
Ionospheric diagnostics come from in-situ probes carried by rockets or satellites, forward propagation, and radar backscatter. This blog entry addresses in situ measurements and remote sensing via forward radio propagation from satellite to ground propagation paths. In situ measurements are time series generated the probe trajectory through the three-dimensional ionospheric structure. Propagation measurements are one-dimensional scans of a diffraction field that responds to the cumulative structure along the propagation path from the source to the receiver. The one-dimensional measurements are highly non-stationary with a very large range of contributing scale sizes. The unpublished manuscript PowerLawModelsMethodsREV1 reviews current stochastic models and presents a wavelet-based analysis procedure for identifying data segments that can be characterized by a generalized power-law structure model. A classifier finds a two-component power-law fit with a goodness-0f-fit measure using wavelet scale spectra.
As discussed in detail, wavelet scale spectra are particularly well suited for analyzing the class of non-stationary fractional Brownian motion (fBm) processes introduced by Benoit Mandlebrot. FBm processes have a self-scaling property akin to fractals that is often invoked to characterize the structure cascade associated with convective instabilities. The paper establishes a framework for data analysis and, ultimately, structure model improvement. This material updates and replaces earlier blogs that addressed the same material.
Tomographic reconstruction of ionospheric electron density profiles from GPS satellite measurement is being used extensively for global ionospheric monitoring. For the most part, the reconstruction process is a constrained iterative process. The results are sensitive to errors and initial conditions. To study these limitations and the possibility of high-resolution reconstruction two-dimensional simulations have been used. The simulation and analysis procedures are described in IntermediateScaleTomography, with the accompanying poster RinoPosterSA21B-2019(2).
To the extent that propagation disturbances can be approximated by an equivalent phase-screen, there are analytic models that allow computation of the power-spectrum of the intensity of the field as it propagates away from the phase screen. The analysis involves an integration to characterize the structure initiation as a phase perturbation and a second integration to propagate the structure to the observation plane. In real-world applications the integrations are two dimensional. However, the field-aligned structure in the ionosphere can be exploited to reduce the computations to one-dimensional integrations.
This motivated a revisit of early computations based on two-dimensional and one-dimensional phase screens. To test the numerical computations, which were performed by Charlie Carrano at the Boston College Institute for Scientific Research, analytic results for unconstrained inverse power-law spectra were used. Disparities between the computations and the analytic results motivated a careful look at the analytic results derived from complicated limiting operations. Some errors were found that clarified some long standing disparities between results by Victor Rumsey for isotropic structures and my own two-dimensional results, which should agree with the isotropic results if isotropy was assumed. The new results are summarized in PowerLawPhaseScreenHighlights, with computational details presented in a separate note. PowerLawPhaseScreenReview,
An updated book errata sheet can be found ScintTheoryErrata
The following attachment is the keynote talk presented at the Beacon Satellite Symposium, Bath England, July 8, 2013 KeynoteTalk
The following attachment was presented at the CEDAR workshop Friday 29 June at Boulder Colorado. CEDAR-Talk-Rino
The following attachment was presented at the International Center for Theoretical Physics, Tereste Italy, on May 14, 2013 GNSS_Rino
Chapter 4 of my book develops a computational framework for beacon satellite propagation. With a reference coordinate system centered at ionospheric heights, even small propagation angles lead to very large displacements in the observation plane. To avoid this problem, a continuously displaced coordinate system is used. The defining equation in Section 4.1 was in error, which combined with some other errors in the defining equations made it difficult to reconstruct the equation upon which most of the calculation in Chapter 4 is based. Equation 4.5 is correct. A revision of an earlier derivation is attached. I’m indebted to Harold Knight and Kshitija Despande for pointing out the inconsistencies. The errata sheet has been updated and placed on the book page.BookNotesNew
The blog entry Statistical Theory of Scintillation Update provides some background material.
In Chapter 3 of my book the system of differential equations that characterize the propagation of complex two-frequency field moments in irregular media were developed. The attached note reviews this material and its connection to the original and most cited source of the equations in the scintillation theory literature. A number of small but annoying errors in the equations have been corrected, and some definitions have been added for clarity. With recent updates and additions as of July 23, 2011, BookNotesCh3, fourth-moment-notes, ScintTheoryErrata
Revised May 30, 2011
Earlier blogs on this topic discussed the relation of The Theory of Scintillation with Applications to Remote Sensing, which uses the forward propagation method (FPE) , to optical methods based on the Huygens-Fresnel construction. The revised paper linked below presents a more cohesive development. There is a regime where wavelength does not dictate sampling requirements. In this common regime, identical computational methods can be used for optics, acoustics, and radio frequency applications. This regime includes the Fraunhofer diffraction limit. However, the FPE is formally unconstrained.
A case in point is ray optics, which is based on a wavelength independent geometrical construction. An example is shown in the Figure below. The problem is the omission of diffraction.
The paper uses Fourier domain methods to compute the evolution of the wavefront from the aperture stop where ray optics gives an accurate representation to the focal plane. The problem is that full diffraction computation requires wavelength scale sampling.
The figure below shows an example of Fraunhofer diffraction where computation at optical wavelengths is easily achieved.
The two figures below show the development of a focus at mm wavelengths where full-diffraction computations are feasible. The details are discussed in the unpublished paper submitted for publication in Antennas & Propagation Magazine linked below.
Updated June 17, 2011. OpticsDiffractionFPE2 Continue reading