1. Introduction#

1.1 Context#

BIOMASS is ESA’s 7th Earth Explorer mission. The purpose of the BIOMASS mission is to reduce the uncertainty in the worldwide spatial distribution and dynamics of forest biomass to improve current assessments and future projections of the global carbon cycle. This objective will be achieved by implementing a P-band SAR mission, providing global maps of forest biomass stocks, forest disturbance, and growth.

The BIOMASS mission will also provide 3D views of forests through the “tomographic” phase and will also support additional science needs arising from the opportunity to explore the Earth for the first time with a P-band SAR system from space offering the possibility to “see” below the vegetated areas and in beneath bare soil or icy regions.

To achieve its challenging objectives, the BIOMASS requires a specific data processing strategy that combines different technologies and techniques at different processing level to generate the final Above Ground Biomass (AGB) global map.

1.2 Scope of the Document#

The purpose of this document is to provide the “Stack Processor Algorithms Theoretical Baseline Document (ATBD)” for the BIOMASS Processing Suite (BPS) project.

This document is organized as follows:

Section 2: Brief introduction about BPS and Stack Processor;
Section 3: Description of the Pre-processing algorithms;
Section 4: Description of the Stacking algorithms;
Section 5: Description of the Calibration algorithms;
Section 6: Description of configurable input parameters.

1.3 Acronyms#

Acronyms

Acronym	Description
AD	Applicable Document
AGB	Above Ground Biomass
ARESYS	Advanced Remote Sensing and Systems
AT	Along-track (e.g. along-track direction)
ATBD	Algorithm Theoretical Baseline Document
AUX	Auxiliary (e.g `AUX_PPS`)
AWGN	Additive White Gaussian Noise
AZF	Azimuth Spectral Filtering
BIODEMPP	Biomass DEM Prototype Processor
BPS	BIOMASS Processing Suite
CFI	Customer Furnished Items
CoSCS	Coregistered SCS
DEM	Digital Elevation Model
DSI	DEM Synthetic Interferogram
DTM	Digital Terrain Model
ESA	European Space Agency
FNF	Forest/Non-forest (e.g. mask)
FR	Faraday Rotation
InSAR	Interferometric Synthetic Aperture Radar
INT	Interferometric Phase
IOB	Background Ionosphere Removal (also Slow Varying Ionosphere Removal)
IODD	Input&Output Data Definition
L1a/b/c	Level-1 a/b/c product
L1M	Level-1 Monitoring product
L1S	Level-1 Standard product
LOS	Line-of-Sight
LUT	Look-Up Table
MB	Multi-baseline
MPMB	Multi-polarimetric Multi-baseline
MS	Multi-Squint (e.g. coherence)
MSC	Multi-Squint Calibration
PFD	Product Format Specification Document
RD	Reference Document
RFI	Radio-Frequency Interferences
SAR	Synthetic Aperture Radar
SB	Single-baseline
SCS	Single-look Complex Slant-range
SKP	Sum of Kronecker Products
SNR	Signal-to-Noise Ratio
SVD	Single Value Decomposition
TEC	Total Electron Content
TOM	Tomographic Phase

1.4 Applicable documents#

Code	Document
`[AD1]`	/

1.5 Reference documents#

Code	Document
`[RD1]`	BIOMASS DEM Product Processor Prototype, CoSCS Processor Algorithm Theoretical Baseline Document, BIODEMPP-CoSCS-ATBD-01, Issue 4.0, June 07th 2021.
`[RD2]`	BIOMASS Report for Mission Selection; SP-1341/1, May 2012
`[RD3]`	BIOMASS L2 Implementation Study, Integrated R&D Report. Report to ESA, 2018.
`[RD4]`	BIOMASS DEM Product Processor Prototype, DEM Processor Algorithm Theoretical Baseline Document, BIODEMPP-CoSCS-DEM-01, Issue 4.0, June 07th 2021.
`[RD5]`	BIOMASS DEM Product Prototype Processor, Critical review of CoSCS and DEM algorithms, BIODEMPP-TN-01, Issue of 07th of February 2020.
`[RD6]`	M. Liao, H. Jiang, Y. Wang, T. Wang, L. Zhang, “Improved topographic mapping through high-resolution SAR interferometry with atmospheric effect removal”, ISPRS Journal of Photogrammetry and Remote Sensing, Volume 80, 2013, Pages 72-79
`[RD7]`	Z. Hu, J. J. Mallorquí, G. Centolanza and J. Duro, “InSAR atmospheric delays compensation: Case study in Tenerife island,” 2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Fort Worth, TX, 2017, pp. 3167-3170.
`[RD8]`	M. Pinheiro, A. Reigber, R. Scheiber, P. Prats-Iraola and A. Moreira, “Generation of Highly Accurate DEMs Over Flat Areas by Means of Dual-Frequency and Dual-Baseline Airborne SAR Interferometry,” in IEEE Transactions on Geoscience and Remote Sensing, vol. 56, no. 8, pp. 4361-4390, Aug. 2018.
`[RD9]`	G. Gomba, A. Parizzi, F. D. Zan, M. Eineder, and R. Bamler, “Toward Operational Compensation of Ionospheric Effects in SAR Interferograms: The Split-Spectrum Method,” IEEE Transactions on Geoscience and Remote Sensing, vol. 54, no. 3, pp. 1446–1461, Mar. 2016.
`[RD10]`	S. Mancon, A. M. Guarnieri, D. Giudici, and S. Tebaldini, “On the phase calibration by multisquint analysis in TOPSAR and stripmap interferometry,” IEEE Transactions on Geoscience and Remote Sensing, vol. 55, no. 1, pp. 134–147, 2016.
`[RD11]`	S. Tebaldini, M. M. d’Alessandro, J. S. Kim, and K. Papathanassiou, “Ionosphere vertical profiling from biomass multi-squint InSAR,” in 2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), 2017, pp. 5866–5869.
`[RD12]`	R. Scheiber and A. Moreira, “Coregistration of interferometric SAR images using spectral diversity,” Geoscience and Remote Sensing, IEEE Transactions on, vol. 38, no. 5, pp. 2179–2191, 2000.
`[RD13]`	Tebaldini, Stefano, et al. “Phase calibration of airborne tomographic SAR data via phase center double localization.” IEEE Transactions on Geoscience and Remote Sensing 54.3 (2016): 1775-1792.
`[RD14]`	Bamler, Richard und Hartl, Philip (1998) Synthetic Aperture Radar Interferometry. Inverse Problems, 14 (4).
`[RD15]`	F. Gatelli, A. Monti Guamieri, F. Parizzi, P. Pasquali, C. Prati and F. Rocca, “The wavenumber shift in SAR interferometry,” in IEEE Transactions on Geoscience and Remote Sensing, vol. 32, no. 4, pp. 855-865, July 1994.
`[RD16]`	A. Reigber, “Range dependent spectral filtering to minimize the baseline decorrelation in airborne SAR interferometry,” IEEE 1999 International Geoscience and Remote Sensing Symposium. IGARSS’99 (Cat. No.99CH36293), Hamburg, Germany, 1999, pp. 1721-1723 vol.3.
`[RD17]`	Ferretti, A., Monti-Guarnieri A., Prati, C., Rocca, F., Massonnet, D. (2007). InSAR Principles: Guidelines for SAR Interferometry Processing and Interpretation. ESA Publications, TM-19. ISBN 92-9092-233-8.
`[RD18]`	[`BPS_AUX_FMT`] BPS Auxiliary Product Format, I/R 1/1
`[RD19]`	[`BPS_L1_PFD`] BIOMASS L1a/b/c Products Format Specification, I/R 1/1
`[RD20]`	BPS L1 SAR ATBD - Algorithms Theoretical Baseline Document
`[RD21]`	Miguel Arevallilo Herraez, David R. Burton, Michael J. Lalor, and Munther A. Gdeisat, “Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path”, Journal Applied Optics, Vol. 41, No. 35, pp. 7437, 2002
`[RD22]`	Laakso, Timo I., et al. “Splitting the unit delay [FIR/all pass filters design].” IEEE Signal Processing Magazine 13.1 (1996): 30-60.
`[RD23]`	S. Tebaldini, A. M. Guarnieri, and F. Rocca, “Recovering time and space varying phase screens through SAR multi-squint differential interferometry,” in EUSAR 2012; 9th European Conference on Synthetic Aperture Radar, Apr. 2012, pp. 16–19.
`[RD24]`	[`BPS_IODD`] BIOMASS Processors Input & Output Data Definition, Issue 3.0.5, February 2nd 2024.
`[RD25]`	[`BIOTOMEX_TN`] BIOTOMEX TN, Technical Note on Performance Analysis, Issue 1.1, November 26th, 2024
`[RD26]`	R. Lanari et al. “Generation of digital elevation models by using SIR-C/X-SAR multifrequency two-pass interferometry: The Etna case study.” IEEE Transactions on Geoscience and Remote Sensing (1996)
`[RD27]`	S. Tebaldini, F. Salvaterra, F. Banda, and M. Pinheiro, “Multi-layer ionosphere correction in low-frequency interferometric SAR: modeling, inversion, and application to BIOMASS”. Authorea Preprints (2025)