A23D-0254: Analysis Procedures for Model-Based Interpretation and Extrapolation of High-Resolution ESF Measurements

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Maurice Walton
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1 A23D-0254: Analysis Procedures for Model-Based Interpretation and Extrapolation of High-Resolution ESF Measurements Authors: Charles L Rino 1, Charles S Carrano 2, Patrick A Roddy 3, John M Retterer 2 Author Institutions: 1. Rino Consulting, Menlo Park, CA, USA; 2. Institute for Scientific Research, Boston, MA, USA; 3. Space Vehicles Directorate, Air Force Research Laboratory, Albuquerque, NM, USA Abstract Although satellite and rocket probes can measure the structure of densities within a plume of equatorial spread F (ESF) irregularities from scales of hundreds of kilometers to tens of meters, few attempts have been made to employ analysis and modeling procedures that can accommodate full range of the ESF structure. This paper introduces and demonstrates wavelet-based analysis procedures that identify structured regions, classify the structured regions, and extract two-component powerlaw model fits where appropriate. High-resolution measurements from the Air Force C/NOFS satellite have been processed to demonstrate the procedures. The results are interpreted within the framework of fractional Brownian motion, which is well suited to both ESF structure and wavelet scale measurements. Full text can be found on

2 ESF Challenges Physics-based models reproduce the 3D large-scale dynamic structure evolution only to kilometer scales. Satellite probes produce 1D scans that subtend ESF scales from hundreds of kilometers to meters. Stochastic models necessarily guide analysis and data interpretation

3 PROCESSING High-resolution data extraction, editing, and interpolation to uniform spatial sampling To process highly inhomogeneous structure over large dynamic range it is necessary to identify homogeneous segments. Standard spectral analysis procedures must be modified to accommodate power-law structure with large dynamic ranges.

4 Wavelet Based Analysis Discrete Wavelet Transform performed over 20,000 km span sampled at ~15 m. Dyadic sampling identifies the largest scale that can be statistically characterized Segmentation partitions the structure and defines an analysis scale For the C/NOFS analysis uniform segments of ~240 km were used to compute Scale Spectra Segmentation Scale

SCALOGRAM Analysis Products Scale spectrum from each segment is

Parameters cs1, p1, cs2, p2 and break frequency are retained for

CLASSIFICATION Large Scale Break Small Scale NOISE LIMITED P1>p2

5 SCALOGRAM Analysis Products Scale spectrum from each segment is partitioned with power-lat fits to largeand small-scale regions. Parameters cs1, p1, cs2, p2 and break frequency are retained for summary analysis. CLASSIFICATION Large Scale Break Small Scale NOISE LIMITED P1>p2 NOISE FREE P1<p2 NON POWER LAW

6 Segment analysis summary for moderately disturbed data set Noise Free Noise Limited

7 285 consecutive C/NOFS data sets recorded 2011 day 246 through day ,449 segments analyzed, 62,512 (79%) achieved overall least-square errors less than 10, 59,849 segments noise-limited (p2<p1). Only 2663 noise free (p1<p2).

8 The noise-free small-scale population contains two sub populations, one with index values close enough to the large-scale index to be classified single component.

9 Two-component power-law structure applies to most highly disturbed regions Large-scale structure generally consisted with other intermediate-scale measurements Small-scale structure has smaller index than typically reported <= high C/NOFS sampling altitudes Break scale 500 to 600 m inferred Hypothesis: Structure development starts with single power law that evolves to two-component structure with dual cascade above and below 500 m input scale.

10 Analysis Details

11 Continuous Wavelet Transform Discrete Wavelet Transform Multi-Filtering Wavelet Scale Spectrum

12 Fractional Brownian Motion Scale Invariance => Power-Law SDF Wavelet Scale Spectrum => Power-Law Index

13 Power-Law Structure Model Summary Two-Component Model

Reconciling two-component power spectra

Reconciling two-component power spectra Charles L. Rino Institute for Scienti c Research, Boston College, Chestnut Hill, MA, USA and Charles S. Carrano Institute for Scienti c Research, Boston College,