The ESA BIOMASS Mission

(Source: © ESA/AOES Medialab

https://www.esa.int/ESA_Multimedia/Images/2013/01/Biomass)

Carsten Pathe

In-situ measurements

AGB estimated from in-situ measurements of variables using an allometric model as a function of ρ as stem wood density of the focal tree, D as trunk diameter at breast height, and H as its total height:
To get AGB values at plot* level, tree-level AGB estimates are summed across trees and over the plot area
Errors due to the estimation of height, wood density, and choice of the allometric model usually result in a plot-based AGB uncertainty that is non-negligible.
- AGB is estimated with ~50% absolute error for a single tree
- When propagated at stand level, error is ~10% at the 1-ha scale

(Chave et al., 2019, Chave et al., 2014, Réjou-Méchain et al. 2014)

AGB=f(\rho,D,H)

AGB=f(\rho,D,H)

Errors / Uncertainties

* A plot is a parcel of woodland or forest

BIOMASAR I & II

BIOMASAR algorithm use of a Water Cloud model with gaps:

Forest backscatter = sum of:

Direct scattering from the ground through the canopy gaps, weighted by the percentage of ground seen through the gaps in the canopy expressed as (1 - ), where is the area-fill factor, representing the percentage of ground covered by vegetation
Ground scattering attenuated by the tree canopy attenuated by the vegetation layer
Direct scattering from the vegetation weighted by the area-fill factor and the two-way tree transmissivity

forest backscatter

direct scattering from ground

ground scattering attenuated by trees

direct scattering from vegetation

\eta

\eta

\eta

\eta

\eta T_{tree}

\eta T_{tree}

T_{tree}

T_{tree}

(Santoro et al., 2010, Santoro et al., 2011)

\sigma_{for}^0=(1-\eta )\sigma_{gr}^0+\eta\sigma_{gr}^0T_{tree}+\eta\sigma_{veg}^0(1-T_{tree})

\sigma_{for}^0=(1-\eta )\sigma_{gr}^0+\eta\sigma_{gr}^0T_{tree}+\eta\sigma_{veg}^0(1-T_{tree})

BIOMASAR I & II

For retrieval purposes it is more convenient to use the expression reported by Pulliainen et al. (1994), in which the two-way forest transmissivity has been expressed as , where V is the GSV and is an empirically defined coefficient expressed in :

ha/m^3

ha/m^3

\beta

\beta

e^{-\beta V}

e^{-\beta V}

(Santoro et al., 2010, Santoro et al., 2011)

\sigma ^0 _ {gr}

\sigma ^0 _ {gr}

\sigma ^0 _ {veg}

\sigma ^0 _ {veg}

= radar backscatter from ground

= radar backscatter from vegetation

Estimation of both parameters using MODIS VCF percent tree cover
Estimation of the parameter :
- Set equal to the mean value of the backscatter for pixels labelled as unvegetated within an estimation window centred at the pixel of interest (Santoro et al., 2011).
- Pixels = unvegetated if percent tree cover in MODIS VCF product < spatially adaptive threshold (15% up to 30%) within an estimation window
- VCF threshold have to satisfy requirement: at least 2% of pixels with a SAR backscatter measurement within the estimation window belong to class of unvegetated pixels!

https://modis.gsfc.nasa.gov/data/dataprod/mod44.php

Parameters:

\sigma ^0 _ {gr}

\sigma ^0 _ {gr}

1

(1)

\sigma_{for}^0=\sigma_{gr}^0e^{-\beta V}+\sigma_{veg}^0(1-e^{-\beta V})

\sigma_{for}^0=\sigma_{gr}^0e^{-\beta V}+\sigma_{veg}^0(1-e^{-\beta V})

BIOMASAR I & II

(Santoro et al., 2010, Santoro et al., 2011, Santoro et al., 2015)

Estimation of the parameter :
- Obtained from an estimate of the average SAR backscatter for dense forest (Santoro et al., 2013).
- Dense forest = pixels within a 200 × 200 pixels of estimation window with a MODIS VCF percent tree cover above 75% of the maximum value
- Estimation of requires: at least 1% of the pixels in the estimation window with a SAR backscatter measurement belong to dense forest class
- was then obtained by compensating for residual ground backscatter contributions by inversion of Eq. 1 (prev. slide) to express as a function of the estimates of , , (value representative of GSV in dense forest) and the coefﬁcient β (Santoro et al., 2013):

\sigma ^0 _ {veg}

\sigma ^0 _ {veg}

\sigma ^0 _ {df}

\sigma ^0 _ {df}

\sigma ^0 _ {df}

\sigma ^0 _ {df}

\sigma ^0 _ {veg}

\sigma ^0 _ {veg}

\sigma ^0 _ {df}

\sigma ^0 _ {df}

\sigma ^0 _ {veg}

\sigma ^0 _ {veg}

\sigma ^0 _ {df}

\sigma ^0 _ {df}

\sigma ^0 _ {gr}

\sigma ^0 _ {gr}

V_ {df}

V_ {df}

To finally obtain GSV estimate from a SAR backscatter measurement Eq. 1 (prev. slide) was inverted to express GSV as a function of a measured backscatter :

\sigma ^0 _ {meas}

\sigma ^0 _ {meas}

(2)

(3)

\sigma_{veg}^0=\frac{\sigma_{df}^0-\sigma_{gr}^0e^{-\beta V_{df}}}{1-e^{-\beta V_{df}}}

\sigma_{veg}^0=\frac{\sigma_{df}^0-\sigma_{gr}^0e^{-\beta V_{df}}}{1-e^{-\beta V_{df}}}

\widehat{V}=-\frac{1}{\beta}ln\frac{\sigma_{veg}^0-\sigma_{for}^0}{\sigma_{veg}^0-\sigma_{gr}^0}

\widehat{V}=-\frac{1}{\beta}ln\frac{\sigma_{veg}^0-\sigma_{for}^0}{\sigma_{veg}^0-\sigma_{gr}^0}

Parameter	Requirement
Instrument	P-band full polarimetric interferometric SAR
Instrument mass	215 kg
Power consumptiom	250 W
Data rate
Center frequency	435 MHz or 0.435 GHz (P-band, 70 cm wavelength)
Bandwidth	6 MHz (ITU allocation)
Near incidence angle	>23º (threshold); 25º (goal)
Spatial resolution (≥6 looks)	≤ 60 m (across-track) x 50 m (along-track)
Radiometric stability	≤ 0.5 dB (1σ)
Radiometric bias	≤ 0.3 dB (1σ)

Forest Biomass (AGB)

CASINO

(Ulander et al., 2021)

CASINO based on the assumption:

There is a relation between radar backscatter and AGB
In polarimetric data, HV is the channel with the highest sensitivity to AGB
Relation between HV and AGB can be modelled using a power function

(Source: https://de.wikipedia.org/wiki/Potenzfunktion#/media/ Datei:Potenzfkt.svg, Wikipedia, CC0)

Graphs of some power functions

y=x^a

y=x^a

A power function is a function with:

where a is a constant number.

f:x\mapsto y

f:x\mapsto y

Forest Biomass (AGB)

Ground cancellation technique:
- Uses two co-registered interferometric SAR (InSAR) data sets:
  - Ground-steered SLC master image (ground-steered = removed interferometric phase due to topography)
  - SLC slave image
- To form ground-cancelled SLC image :

(d’Alessandro et al. 2020, Soja et al., 2021)

Apply ground cancellation technique to isolate backscatter from forest canopy and minimize ground contributions

1

(Source: d'Alessandro et al., 2020, p. 6414)

Relation between AGB and radar HV polarization power

Ground cancelled power [dB]

SLC power [dB]

S_S

S_S

S_M

S_M

S_{GC}=S_S - S_M

S_{GC}=S_S - S_M

S_{GC}

S_{GC}

\sigma^0_{cnp}=c\langle |s_{GCE}|^2 \rangle cos\psi

\sigma^0_{cnp}=c\langle |s_{GCE}|^2 \rangle cos\psi

(1)

- Normalization of ground-cancelled and equalized backscatter intensity

|S_{GCE}|^2

|S_{GCE}|^2

(2)

Forest Biomass (AGB)

To describe the dependence of the forest canopy backscatter on AGB, power law model (PLM) is used:

(Soja et al., 2021)

Describe forest canopy backscatter dependence on AGB using a power law model (PLM)

2

(\sigma^0_{cnp})_{PQ}=A_{PQ}W^{\alpha_{PQ}}cos^{n_{PQ}}\vartheta

(\sigma^0_{cnp})_{PQ}=A_{PQ}W^{\alpha_{PQ}}cos^{n_{PQ}}\vartheta

scaling factor

exponent for incidence angle normalization

ground-cancelled and equalized backscatter intensity of forest canopy

\sigma^0_{cnp}

\sigma^0_{cnp}

A_{PQ}

A_{PQ}

with:

exponent for AGB

\alpha_{PQ}

\alpha_{PQ}

n_{PQ}

n_{PQ}

w

w

AGB in t/ha

(3)

Forest Biomass (AGB)

(Soja et al., 2021)

Describe forest canopy backscatter dependence on AGB using a power law model (PLM)

2

(\sigma^0_{cnp})_{PQ}=A_{PQ}W^{\alpha_{PQ}}cos^{n_{PQ}}\vartheta

(\sigma^0_{cnp})_{PQ}=A_{PQ}W^{\alpha_{PQ}}cos^{n_{PQ}}\vartheta

To fit the model to measured data, it is log-transformed:

S_{PQ}=l_{PQ}+ \alpha_{PQ}w+n_{PQ}c

S_{PQ}=l_{PQ}+ \alpha_{PQ}w+n_{PQ}c

(4)

The three model parameters , , and w are unknown
Only and c are observed quantities

l_{PQ}

l_{PQ}

\alpha_{PQ}

\alpha_{PQ}

n_{PQ}

n_{PQ}

S_{PQ}

S_{PQ}

Forest Biomass (AGB)

(Ulander et al., 2020, Soja et al., 2021)

Describe forest canopy backscatter dependence on AGB using a power law model (PLM)

2

To estimate w and the three model parameters an iterative technique is applied
The model (2) is fitted to measured data using a constrained non-linear minimization of a cost function J.
- Constrained:
  - Estimated values are constrained to lie in pre-defined ranges (see Table 1 in Soja et al., 2021)
- Cost function:
  - A function that measures how well a model performs for a given set of data by calculating the difference between anticipated and expected values
  - Total cost function J is sum of two cost functions and : one for calibration and one for estimation areas
    - Calibration areas: few areas with reference AGB values (preferably from in-situ measurements)
    - Estimation areas: large number of systematically distributed areas with unknown AGB

Iterative Estimation approach

J_{CAL}

J_{CAL}

J_{EST}

J_{EST}

Forest Biomass (AGB)

(Soja et al., 2021)

After the determination of the model parameters, the AGB can be estimated for any area by solving for w in (4)
This is done for each available polarization channel
Then they are combining them into a weighted average
Weights are calculated using the parameters , which represent the sensitivity of each channel to AGB.
- Represents the sensitivity of a particular polarization to the logarithm of AGB.
- The polarizations/stacks with better sensitivity to AGB will have greater contribution to the final estimate.

Final AGB Estimation

Use PLM to estimate AGB for each polarization channel and combine them into weighted average

3

\alpha_{PQ}

\alpha_{PQ}

Forest Disturbance

BIOMASS forest disturbance (FD) product:
- Aims at detection of high-intensity forest disturbance (eﬀectively forest clearance) occurring between satellite revisit times.
- Uses stack of polarimetric acquisitions for detecting temporal changes in the polarimetric covariance matrix
  - Bbased on the observation that changes in the polarimetric covariance matrix caused by deforestation are relatively large:
    - 5 dB change in for biomass decrease from 500 t/ha to nearly zero,
    - ~1 dB change in for AGB increase from 100 to 200 t/ha
- FD detection approach uses hypothesis testing:
  - Null hypothesis is that in a time series of polarimetric data, no change has occurred at a given position and up to a given time
  - A change is detected when this hypothesis fails at a given level of significance (assuming a Wishart distribution for the complex covariance data)

\gamma_{hv}^0

\gamma_{hv}^0

\gamma_{hv}^0

\gamma_{hv}^0

(Quegan et al., 2019, Ulander et al. 2021, Tebaldini et al., 2021)

Forest Disturbance

Polarimetric Stack

Average to 6 looks in Azimuth to form covariance matrix

Forest Mask time N

Update Forest Mask to

(Source: after Tebaldini et al., 2021, p. 785)

Flowchart Forest Disturbance (FD) Estimation Module

Test statistics: Is new cov. matrix different from previous ones?

Pixel is disturbed

Yes

No

Go to next time

F_N

F_N

F_{N+1}

F_{N+1}

previous covariance matrices

Forest Disturbance module

Input is a stack of polarimetric data
Averaged to 6 looks in azimuth to reach the 50 m target resolution
Then calculation of scattering statistics expressed by the covariance matrix
Process runs only for forest pixels at a given time N ; therefore initial run requires forest mask generated during the TOM phase)
Hypothesis testing:
- Assumes Wishart distribution for the complex covariance data
- Tests whether the new matrix is different from the previous n matrices at that pixel at a given signiﬁcance level
- If the null hypothesis (no change) is rejected, then assumption is that given pixel is disturbed
- This pixel then removed from the forest mask at time N + 1 (currently completed global cycle)

(Banda et al., 2020)

Ionosphere

Part of Earth's upper atmosphere ionized by the Sun
Starts above the Mesopause at an altitude of about 80 km and extends to a few thousand kilometres
Consists of ionized gas containing free electrons and positively charged ions
Peak density occurs at altitudes of about 400 to 500 km with a density of about electrons per cubic centimetre
Ionization
- Is caused by extreme ultraviolet and X-radiation from the Sun
- Depends on solar illumination and varies diurnally, seasonally and with latitude
- Is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons
- Can have a significant effect on the propagation of electromagnetic radiation in certain wavelength regions, including regions where SAR remote sensing takes place

(Source:
background: https://commons.wikimedia.org/
wiki/File:Earth_Horizon_(6143615821).jpg, CC BY 2.0)

Layers of the Earth's atmosphere with the ionosphere

\mathtt{5 \times10^5 - 10^6}

\mathtt{5 \times10^5 - 10^6}

(Woodhouse, 2017, Ulaby et al., 2014, Elachy & van Zyl 2006, Rees, 2012)

Ionospheric Distortions

Faraday rotation - Effects:

\Omega = \frac{ \left\lvert e^3 \right\rvert }{ 8\pi^2\epsilon_0m^2c } \frac{ B_{cos}[\psi] }{ f^2_0 }TECsec(\theta)

\Omega = \frac{ \left\lvert e^3 \right\rvert }{ 8\pi^2\epsilon_0m^2c } \frac{ B_{cos}[\psi] }{ f^2_0 }TECsec(\theta)

Ionosphere introduces a Faraday rotation to plane of polarization:

\mathtt{e = charge\:of\:an\:electron}

\mathtt{e = charge\:of\:an\:electron}

\mathtt{m = mass\:of\:an\:electron}

\mathtt{m = mass\:of\:an\:electron}

\mathtt{e_0 = permittivity\:of\:free\:space}

\mathtt{e_0 = permittivity\:of\:free\:space}

\mathtt{B = geomagnetic\:field\:intensity}

\mathtt{B = geomagnetic\:field\:intensity}

\mathtt{f_0 = radio\:frequency}

\mathtt{f_0 = radio\:frequency}

\mathtt{\psi = angle\:between\:radar\:beam\:and\:geomagnetic\:field}

\mathtt{\psi = angle\:between\:radar\:beam\:and\:geomagnetic\:field}

\mathtt{\theta = angle\:of\:the\:ray\:to\:the\:vertical}

\mathtt{\theta = angle\:of\:the\:ray\:to\:the\:vertical}

Faraday rotation is directly proportional to TEC (linear increase)
Radar wave pass twice through the ionosphere
Then plane of polarization is rotated by 2
If left uncorrected, extraction of geophysical parameters such will be significantly affected
for

\mathtt{\Omega>5°}

\mathtt{\Omega>5°}

(Rogers & Quegan, 2013)

\mathtt{\Omega}

\mathtt{\Omega}

\mathtt{\Omega}

\mathtt{\Omega}

1

The ESA BIOMASS Mission (Source: © ESA/AOES Medialab https://www.esa.int/ESA_Multimedia/Images/2013/01/Biomass ) Carsten Pathe

Campaign	Indrex-2
Objectives	Height retrieval in tropical forest; measurement of repeat-pass temporal decorrelation
Test sites	Sungai-Wai & Mawas, Borneo, Indonesia
Time	Nov 2004
Forest conditions	Tropical rain forest. Sungai-Wai: lowland, AGB ≤600 t/ha; Mawas: peat swamp, AGB ≤200 t/ha
Platform, Sensor, Operator	Do228 aircraft, E-SAR, DLR (Germany)
Acquired SAR data	Pol-InSAR data set in P & L-band
Outcomes	INDREX-II was a successful campaign in terms of experiment planning, radar data and ground measurement acquisition and radar data quality. All suggested experiments could be performed as described in the Experimental Plan submitted to ESA. The planned time schedule could be kept and no major technical problem occur during the INDREX-II campaign.
Website	https://earth.esa.int/eogateway/campaigns/indrex-2
Final Report	https://earth.esa.int/eogateway/documents/20142/37627/INDREX-II-final-report.pdf

Campaign	BioSAR-1
Objectives	Biomass estimation and measurement of multimonth temporal decorrelation
Test sites	Remningstorp, southern Sweden
Time	Mar - May 2007
Forest conditions	Hemi-boreal forest, low topography, AGB ≤300 t/ha
Platform, Sensor, Operator	Do228 aircraft, E-SAR, DLR (Germany)
Acquired SAR data	Pol-InSAR data set in P & L-band PolSAR data set in P-band
Outcomes
Website	https://earth.esa.int/eogateway/campaigns/biosar
Final Report	https://earth.esa.int/eogateway/documents/20142/37627/biosar-2007-final-report-no-synthesis.pdf

Campaign	BioSAR-2
Objectives	Topographic inﬂuence on biomass estimation
Test sites	Krycklan, northern Sweden
Time	Oct. 2008
Forest conditions	Boreal forest, hilly, AGB ≤300 t/ha
Platform, Sensor, Operator	Do228 aircraft, E-SAR, DLR (Germany)
Acquired SAR data	Pol-InSAR data set in P & L-band
Outcomes	The BioSAR 2008 campaign collected in-situ and airborne SAR data in support of decisions taken on satellite instrument configurations for the BIOMASS satellite mission. It provided an important database for the study of longer term mission concepts. While the BioSAR 2007 campaign collected data with the objective to investigate the effect of temporal decorrelation at P-band with 100MHz and 6MHz bandwidth in southern Sweden, BioSAR 2008 recorded data at boreal forests with strong topographic effects in northern Sweden to investigate the effect on forest height estimation and radar backscatter signal variation.
Website	https://earth.esa.int/eogateway/campaigns/biosar-2
Final Report	https://earth.esa.int/eogateway/documents/20142/37627/BIOSAR2_final_report.pdf

Campaign	TropiSAR
Objectives	Biomass estimation in tropical forest; temporal stability of coherence
Test sites	Paracou & Nouragues, French Guiana
Time	Aug 2009
Forest conditions	Tropical rain forest, AGB 300–500 t/ha, lowland and hilly terrain
Platform, Sensor, Operator	Falcon 20 aircraft, SETHI, ONERA (France)
Acquired SAR data	Pol-InSAR data set in P & L-band
Outcomes	Seven SAR flights were conducted with the SETHI system from ONERA during the 23 days of the SAR campaign, which lasted from 10 August to 1 September 2009. The selected waveform is characterized by P and L simultaneous acquisitions with a range resolution of around 1.5 m. During these flights, a temporal dataset characterised with a zero spatial baseline was acquired to allow the quantification of the temporal decorrelation, one key parameter for the performance evaluation of the PolInSAR technique in a single satellite configuration. A PolInSAR and tomographic database was also acquired with vertical baselines of 50, 100, 150, 200 and 250 feet.
Website	https://earth.esa.int/eogateway/campaigns/tropisar
Final Report	https://earth.esa.int/eogateway/documents/20142/37627/TROPISAR-FINAL-REPORT-2011-V2.1.pdf

Campaign	BioSAR-3
Objectives	Forest change and multi-year coherence relative to BioSAR-1
Test sites	Remningstorp, southern Sweden
Time	Sep 2010
Forest conditions	Hemi-boreal forest, low topography, AGB ≤400 t/ha (more high biomass stands than in BIOSAR-1)
Platform, Sensor, Operator	Falcon 20 aircraft, SETHI, ONERA (France)
Acquired SAR data	Pol-InSAR data set in P & L-band
Outcomes	The BioSAR 2010 campaign was planned and successfully implemented during the summer and fall of 2010 over the Remningstorp forest test site in southern Sweden. The planning and execution of the campaign was done with the aim to address all of the agreed primary objectives.
Website	https://earth.esa.int/eogateway/campaigns/biosar-3
Final Report	https://earth.esa.int/eogateway/documents/20142/37627/BIOSAR_2010_FinalReport_v1.0.pdf

Campaign	Tropiscat: Ground-based high temporal resolution measurement
Objectives	Measurement of long-term temporal coherence and temporal variation of backscatter in tropical forest
Test sites	Paracou, French Guiana
Time	Aug. 2011 - Dec. 2012
Forest conditions	Tropical rain forest, AGB ca. 400 t/ha
Outcomes	The overall results of this study prove that the 6 MHz bandwidth limitation is not critical concerning P-band SAR observations of tropical forests. However, in order to have a full assessment of the end-to-end performances, different types of noise sources still need to be considered. Those are for example the ionospheric disturbances, the seasonal effects (the TropiSAR data were acquired during the dry season), the temporal decorrelation. Reversely, some of the effects prevailing in airborne data will be less significant in space borne data. This is the case for example of the large variation of the incidence angle across the swath, the perturbations in the flight tracts of the aircraft.
Website	https://earth.esa.int/eogateway/campaigns/tropiscat
Final Report	https://earth.esa.int/eogateway/documents/20142/37627/TropiScat-Final-Report.pdf

Campaign	AfriSAR
Objectives	Biomass estimation in tropical forest; temporal stability of coherence
Test sites	Sites at Lopé, Mondah, Mabounie and Rabi, Gabon
Time	July 2015 (SETHI) Feb. 2016 (F-SAR)
Forest conditions	Tropical forest and savannah, AGB from 50 to 500 t/ha
Platform, Sensor, Operator	Falcon 20 aircraft, SETHI, ONERA (France), Do228 aircraft, E-SAR, DLR (Germany)
Acquired SAR data	Pol-InSAR and TomoSAR data set in P & L-band
Outcomes	During the AfriSAR campaign, shared between ONERA (dry season, July 2015) and DLR (wet season 2016), Pol-InSAR and TomoSAR airborne data set were collected over four test sites in Gabon (Africa), therefore covering different forest structures, biomass levels and disturbances. Although the interferometric / tomographic baselines were optimized for P-band acquisitions, L-band data were collected simultaneously as well.
Website	https://earth.esa.int/eogateway/campaigns/afrisar-2015
Final Report	https://earth.esa.int/eogateway/documents/20142/37627/AfriSAR-Final-Report.pdf

Campaign	Afriscat: Ground-based high temporal resolution measurements
Objectives	Measurement of long-term temporal coherence and temporal variation of backscatter in tropical forest
Test sites	Ankasa, Ghana
Time	July 2015–July 2016
Forest conditions	Tropical forest, low topography, AGB from 100 to 300 t/ha
Outcomes
Website	https://earth.esa.int/eogateway/campaigns/afriscat
Final Report	https://earth.esa.int/eogateway/documents/20142/37627/AfriScat-Campaign-Final-Report.pdf

Campaign	Borealscat: Ground-based high temporal resolution measurements
Objectives	Time series of backscatter, tomography, coherence and environmental parameters in boreal forest.
Test sites	Remningstorp, southern Sweden
Time	Dec. 2016, ongoing
Forest conditions	Hemi-boreal forest, spruce-dominated stand, low topography, AGB = 250 t/ha
Outcomes
Website	http://www.borealscat.se
Final Report