XXII ISPRS Congress 2012: Technical Commission VIII

Shortis, M.; Shimoda, H.; Cho, K.

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Multivolume work

Persistent identifier:: 1663813779

Title:: XXII ISPRS Congress 2012

Sub title:: Melbourne, Australia, 25 August-1 September 2012

Year of publication:: 2013

Place of publication:: Red Hook, NY

Publisher of the original:: Curran Associates, Inc.

Identifier (digital):: 1663813779

Language:: English

Additional Notes:: Kongress-Thema: Imaging a sustainable future

Corporations:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Adapter:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Founder of work:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Other corporate:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Document type:: Multivolume work

Volume

Persistent identifier:: 1663822514

Title:: Technical Commission VIII

Scope:: 590 Seiten

Year of publication:: 2014

Place of publication:: Red Hook, NY

Publisher of the original:: Curran Associates, Inc.

Identifier (digital):: 1663822514

Illustration:: Illustrationen, Diagramme

Signature of the source:: ZS 312(39,B8)

Language:: English

Additional Notes:: Erscheinungsdatum des Originals ist ermittelt.; Literaturangaben

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Editor:: Shortis, M.; Shimoda, H.; Cho, K.

Corporations:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Adapter:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Founder of work:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Other corporate:: International Society for Photogrammetry and Remote Sensing, Congress, 22., 2012, Melbourne; International Society for Photogrammetry and Remote Sensing

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2019

Document type:: Volume

Collection:: Earth sciences

Chapter

Title:: [VIII/7: Forestry]

Document type:: Multivolume work

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Chapter

Title:: BIOMASS ESTIMATION USING VERTICAL FOREST STRUCTURE FROM SAR TOMOGRAGHY: A CASE STUDY IN CANADIAN BOREAL FOREST. E. Renaudin, B. Mercer, Q. Zhang, M. J. Collins

Document type:: Multivolume work

Structure type:: Chapter

normalised coherent sum of all contributions, can be formulated for a random distribution of scatterers, as shown in (1), where s; and s; are the complex signals received at either end of the interferometric baseline, * represents the complex conjugate and <...> is the expectation, in practise replaced by an averaging operation. h, ; ' Jr t js (ss) iis | (ze dz = eh gern, (1) (sis) (sas) Í f(z)dz' with 0 <7] <1 : In practice, the upper bound of integration is at z=z, +4, where the lower bound is at the reference datum, z= z,. The interferometer is then measuring a composite complex signal given by the weighted sum of contributions (taking into account phase). Before estimating the height using the phase to height relation ¢ = k,.h, , the sensitivity of the interferometers to height variation has to be defined using the vertical wavenumber factor k_ (Bamler, 1997): _ 4740 ios A 4zB, AsinO AsinQ' radians / meter (2) where A8is the incidence angle difference between the two antennas as seen from the target, Bis the spatial baseline between the two antennas, Ais the model forest height, B, is the normal baseline, A is wavelength of the radar system, and 6 is the incidence angle from one of the antennas. Equation (1) shows that there is a direct relationship between the observed coherence and the structural properties of the scattering. In the most widely used representation of the RVoG model, the structure function is assumed to have an exponential shape (Papathanassiou and Cloude, 1997). However in the PCT approach, a Fourier-Legendre polynomial decomposition is proposed to describe the structure function, f(z’), in terms of known basis functions with unknown real coefficients. It is important to notice that the structure function is bounded by the underlying ground phase and the vegetation height. Thus, it is critical to obtain good estimates of those elements prior to the profile estimation through the expanded Fourier- Legendre series. In the Legendre series development, n baselines provide 2n-1 terms of the series. Therefore, in the simplest practical application, a single baseline solution can provide the second order of the scattering profile.. In this special single baseline case (n=1), it allows determination of up to three terms of the series. The unknown coefficients a, (for the single baseline case) can then be estimated using a simple matrix inversion of equation (3): 1:0 0 || ay 1 0 —-ji 0a - Im(7,) |, (3) 0 0 fle Re(7,) - f, International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B8, 2012 XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia where f represents the Legendre polynomial parameter at order i, Ÿ,represents the polarimetrically optimised complex coherence for baseline-dependent Æ, and a,, are the (real) Legendre coefficients. It should be noted that the f£. terms are functions of the known quantities &,'h,. The evaluation of these coefficients is solved as a matrix inversion problem. The equation can be inverted in a simple manner as shown in 4): Ig» Il [Fla=g => ä=[F]'g (4) In the instance of two baselines, for instance, an improved vertical profile description at the second order is obtained by an expanded structure function now containing four unknown coefficients as shown in (5), where P; are the Legendre polynomials f) - Và Rz) * àP ) à, P (2) * à P). ) The main purpose of this work is to determine the structure function using this PCT approach applied to data from a ‘single-pass’ polarimetric InSAR system. Single-pass in this context refers to a single baseline with rigidly connected antennas such that temporal decorrelation effects are absent from the data. Therefore (3) and (4) are relevant in this case. 2.2 Tree Height and Ground Phase Estimation In this methodology, we use a ‘boot-strapping’ approach to obtain two of the unknown parameters, h, and à for the initial canopy boundary estimates. The height and ground retrievals are obtained by the use of a modified RVoG model, where another parameter is added to compensate for the "underestimation" of the RVoG. For that purpose, (Treuhaft et al., 2000) considered a fixed extinction assigned empirically to the radar. The mean extinction parameter allows computation of the canopy thickness. The fixed extinction coefficient compensates for both density and structure variations (Papathanassiou et al, 2003). In this two-layer model, the observed coherence is given by the formula: uL UA fet ums cO. An 6 di ge dicun -e [o pol (6) where ¢, is the ground phase relative to the reference datum, /,is the complex volume coherence and wis the ratio of effective ground surface to volume scattering. 7(w) refers to the normalized Fourier transform of the attenuated response from the vertical distribution of scatterers (z) and w represents the observed polarisation state. Equation (6) shows that by isolating the polarisation dependent terms (w), the resulting coherence lies in a straight line inside the complex coherence plane (Cloude et al., 2003). In our study, the results of the inversion coming from the RVoG were used as bounds for the vertical profiles reconstruction, Inte servin deriva study were | range coher coord 23 I A ‘st is thi equat wher stem on si facto Remc wher (Le obtai becor great when insta et al. seem in toj speci class appre this deriv 3.1 The airbc wint proo dem L-B: grou Aerc pres: Tab! fully

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