Feasibility of multi-temporal interferometric SAR data for stand-level
estimation of boreal forest stem volume
Jouni Pulliainen*, Marcus Engdahl, Martti Hallikainen
Laboratory of Space Technology, Helsinki University of Technology, Otakaari 5A, P.O. Box 3000, Espoo FIN-02015 HUT, Finland
Received 10 June 2002; received in revised form 23 December 2002; accepted 31 December 2002
Abstract
The feasibility of interferometric SAR (INSAR) coherence observations for stem volume (biomass) retrieval is investigated by applying
coherence data determined from 14 ERS-1 and ERS-2 C-band SAR image pairs. The image set covers a single forested test area in Finland,
and both summer (snow-free) and winter conditions are represented. The data set enabled (a) the study of stem volume retrieval performance
under varying conditions, (b) the analysis of the seasonal behavior of interferometric coherence, and (c) the determination of the accuracy
characteristics of empirical (nonlinear) coherence modeling. Additionally, a new technique to estimate forest stem volume from INSAR data
was developed based on constrained iterative inversion of the applied empirical model. The results indicate that the usability of winter images
with snow-covered terrain is superior to that of images obtained under summer conditions. The applied empirical model appears to be
adequate for describing the stand-wise coherence of boreal forest. Hence, a practical stem volume estimation method can be established based
on it. The highest correlation coefficient between the estimated stem volume and the ground truth stem volume showed values as high as
r = 0.9 and a relative RMSE level of 48% was obtained, respectively.
D 2003 Elsevier Science Inc. All rights reserved.
Keywords: Remote sensing of forests; Radar interferometry
1. Introduction
Forest stem volume is one of the key characteristics in
forest inventories. It is as well an essential characteristic for
forest and climatological research, as it is a figure directly
related to the level of total forest biomass. Satellite sensors
have shown to be useful for mapping forest stem volume for
large areas, but their accuracy for small areas, such as
individual forest stands with a typical size of a couple of
hectares, is poor. Possibilities to improve this handicap
include the use of high spatial resolution satellite data
(resolution in the order of few meters) and the use of
advanced measurement techniques, such as interferometric
SAR (INSAR), with a poorer spatial resolution (but con-
sequently with a larger imaging area).
Previous investigations have shown that the interfero-
metric coherence measured by a spaceborne INSAR sys-
tem is highly affected by the forest biomass (stem volume).
Especially, in the case of sparse boreal forests, INSAR
appears to be a promising data source, see, e.g. Askne,
Dammert, Ulander, and Smith (1997) and Koskinen, Pull-
iainen, Hyyppa, Engdahl, and Hallikainen (2001). How-
ever, problems arise due to the strong influence of weather
conditions. The sensitivity of interferometric radar response
to biomass can drop close to zero at its worst. Never-
theless, the results obtained in stem volume retrieval have
shown relatively good performances, comparable to those
obtained with optical satellite sensors, as multi-temporal
INSAR data are employed (Askne, Santoro, Smith, &
Fransson, 2002; Fransson, Smith, Askne, & Olsson,
2001; Koskinen et al., 2001; Santoro, Askne, Dammert,
Fransson, & Smith, 1999; Santoro, Askne, Smith, &
Fransson, 2002).
The modeling of interferometric coherence is a compli-
cated task as detailed models should describe both the
amplitude and phase of signals backscattered from the
forested terrain including the decorrelation of received
signals due to random phase shifts. These shifts are caused,
e.g. by volume scattering and by the movement of individ-
ual scatterers (the latter being the reason for temporal
decorrelation in repeat-pass interferometry), see, e.g. Treu-
haft and Siqueira (2000) and Zebker and Villasenor (1992).
0034-4257/03/$ - see front matter D 2003 Elsevier Science Inc. All rights reserved.
doi:10.1016/S0034-4257(03)00016-6
* Corresponding author. Tel.: +358-9-451-2373; fax: +358-9-451 2898.
E-mail address: [email protected] (J. Pulliainen).
www.elsevier.com/locate/rse
Remote Sensing of Environment 85 (2003) 397–409
However, recent investigations have indicated that rela-
tively simple empirical or semi-empirical models are fea-
sible to describe the average behavior of interferometric
coherence as a function of forest stem volume or tree height
(Askne et al., 1997; Koskinen et al., 2001). This makes it
possible to develop coherence model-based inversion tech-
niques to estimate the level of forest stem volume or
biomass.
The model by Askne et al. (1997) is a physically
detailed model describing the coherence as a function of
stem volume, (perpendicular) baseline length, and tree
height which can be expressed as a function of stem
volume. The model of Koskinen et al. (2001) is a simpler
formulation that only includes the effect of stem volume.
Both formulations are based on the semi-empirical model-
ing of forest canopy backscatter as a function of stem
volume, see, e.g. Pulliainen, Heiska, Hyyppa, and Hallikai-
nen (1994).
The methods used for the retrieval of stem volume
include empirical and semi-empirical (model-based)
approaches. Wagner et al. (2000) employed a nonlinear
empirical formula for relating the coherence to stem
volume in classifying Siberian forests into two stem
volume classes from a mosaic of single ERS-1/2 Tandem
INSAR images. Fransson et al. (2001), Hyyppa et al.
(2000), and Koskinen et al. (2001) applied simple and
multiple linear regression formulas for the determination of
stem volume from ERS-1/2 coherence (and intensity)
images. Askne et al. (2002), Santoro et al. (1999), and
Santoro et al. (2002) demonstrated semi-empirical stem
volume retrieval approaches based on the model by Askne
et al. (1997).
In this study, we introduce a novel stem volume retrieval
method that is based on the empirical backscattering–
coherence model presented by Koskinen et al. (2001). The
differences between the introduced technique and the non-
linear approach used by Santoro et al. (2002) include the
following aspects.
(a) The method used by Santoro et al. (2002) applies the
coherence model by Askne et al. (1997), whereas this
investigation uses the model introduced by Koskinen et
al. (2001). The underlying backscattering model has
some differences as well. The HUT boreal forest
backscattering model employed here has two empirical
parameters, whereas the model used by Santoro et al.
(2002) is a three-parameter formulation.
(b) The introduced method is based on the constrained
statistical inversion approach (Lehtinen, 1988) in which
the maximum likelihood of the stem volume value is
searched when multi-temporal observations are jointly
given. The approach by Santoro et al. (2002) separately
estimates the stem volume for each coherence image,
and linearly combines the estimates with specific
weighting factors (these factors are affected by the
residuals of model fittings).
The performance of the employed stem volume
retrieval method is analyzed by using a coherence data
set determined from 14 ERS-1 and ERS-2 C-band SAR
image pairs. For comparison, the stem volume estimates
are also determined with standard multiple linear regres-
sion approach. The applied image set covers a single test
area in Southern Finland, and both summer (snow-free)
and winter conditions are represented (1 year time span
from July 1995 to July 1996 is covered). The main
reference information includes ground-based forest inven-
tory data determined at stand level. The data set also
enables the analysis of the seasonal behavior of inter-
ferometric coherence and the investigation of the accu-
racy characteristics of empirical nonlinear coherence
modeling.
2. Methods and SAR data processing
This section describes the empirical backscattering–
coherence model and the inversion approach developed
based on the model. Additionally, the model by Askne et
al. (1997) is presented for comparison. The processing of
interferometric coherence data is also described in detail as
that issue is an essential factor regarding the quality of
interferometric coherence information. In practice, the accu-
racy of stem volume retrieval is highly affected by the
quality of data processing.
2.1. Empirical coherence modeling and model inversion
2.1.1. Modeling approach
The empirical coherence modeling is based on the HUT
boreal forest backscattering model that describes the C- and
X-band backscattering coefficient of forested areas as a
function of forest stem volume and takes into account the
effects of vegetation water content, top-soil moisture, and
the effective surface roughness (Koskinen et al., 2001;
Pulliainen et al., 1994; Pulliainen, Kurvonen, & Hallikai-
nen, 1999; Pulliainen, Mikkela, Hallikainen, & Ikonen,
1996). The model has been validated for conifer-dominated
boreal forests using C- and X-band airborne ranging scat-
terometer data and C-band spaceborne SAR observations,
especially ERS-1/2 SAR data. Observations used for model
validation were collected during the years 1992–1997 for
four geographical regions in Finland representing ecologi-
cally southern and northern boreal forests. The data repre-
sent both wintertime and snow-free summer conditions. The
detailed in situ reference data used for model validation
include field inventory data from a total of 1000 forest
stands, and from hundreds of smaller sample plots and
transects.
In case of ERS SAR observations (i.e. for C-band, VV-
polarized observations at 23j angle of incidence), the
average backscattering coefficient rj of forested terrain
can be approximately modeled ignoring trunk-ground and
J. Pulliainen et al. / Remote Sensing of Environment 85 (2003) 397–409398
other multiple scattering mechanisms (Koskinen et al.,
2001; Pulliainen et al., 1999) by
rjðV ; h;mv;can; rgroundj Þ ¼rcanj ðV ; h;mv;canÞþ t2ðV ; h;mv;canÞrgroundj
urcanjþ rfloorj ð1Þ
where rgroundj is the ground layer backscatter. The canopy
backscattering contribution rcanj is equal to
rcanj ðV ; h;mv;canÞ¼rV ðh;mv;canÞcosðhÞ
2jeðh;mv;canÞð1� t2ðV ; h;mv;canÞÞ
ð2Þ
and the two-way forest canopy transmissivity t2 is equal to
t2ðV ; h;mv;canÞ ¼ expð�2jeðh;mv;canÞV=coshÞ ð3Þ
In Eqs. (1)–(3), V is the total stem volume of forest
(forest stand), h is the angle of incidence, and mv,can is the
effective vegetation (forest canopy) volumetric water con-
tent. The forest canopy extinction and volume backscatter-
ing coefficients (je and rV, respectively) are the parameters
retrieved from scatterometer observations originally
(jefmv and rVfmv2).In this study, we can reduce the
influence of parameters je, rV, and rjground in Eqs. (1)–(3)
into two empirical coefficients that can be estimated based
on inversion algorithm reference (training) data that must be
available from the study region. Hence, the boreal forest
backscattering model (1) can be rewritten for the case of
ERS 1/2 SAR observations (absolute rj level determined
according to SLC image calibration coefficient data) as
rjðV ; hÞ ¼ 0:131acosh 1� exp �5:12� 10�3 aV
cosh
� �� �
þ bexp �5:12� 10�3 aV
cosh
� �urcanj þ rfloorj
ð4Þ
where parameter a is related to the volumetric vegetation
water content (under dry summer conditions a is close to 1)
and parameter bu rjground. Based on Koskinen et al. (2001)
the level of interferometric coherence as a function of forest
stem volume V is linearly dependent on the ratio rcano (V)/ro
(V) (note that h is omitted here and onwards for simplicity).
Hence, the interferometric coherence AcA can be modeled
by
AcðV ÞA ¼ c0 þ c1rcanj ða;V Þrjða; b;V Þ
� �ð5Þ
where c0 and c1 are empirical coefficients that have to be
determined from reference (training) data. As stated in
Koskinen et al. (2001) c0 corresponds to the level of
coherence for open areas, i.e. clear-cut or sapling areas
(V= 0 m3/ha), and c1 corresponds to the difference between
coherence levels of very dense forests and open areas.The
performance of the model (5) can be compared with that of
the model by Askne et al. (1997). The model (5) can be
rewritten as
AcðV ÞA ¼ c0rfloorj ða; b;V Þ
rjða; b;V Þ
� �þ ðc0 þ c1Þ
rcanj ða;V Þrjða; b;V Þ
� �ð6Þ
Similarly, the coherence model used by Askne et al. (1997)
and Santoro et al. (2002) can be expressed as
AcðV ÞA ¼ cgrrfloorj ða; b;V Þ
rjða; b;V Þ
� �þ ccan
rcanj ða;V Þrjða; b;V Þ
� ������ exp �j
4pBn
kRsinhðh� a�1Þ
� ����� ð7Þ
where cgr is the coherence level of ground and ccan is that ofthe forest canopy, respectively. j is the imaginary unit, Bn is
the perpendicular length of the interferometric baseline, R is
the slant range, k is the radar wavelength, h is the height of
forest canopy and a is the two-way attenuation of the forest
canopy (Askne et al., 1997). Based on the forest stand data
on stem volume (V) and mean tree height (h) of the present
test site (the Tuusula test site), the same relation between V
and h can be used here as that in Santoro et al. (2002), i.e.
h=(2.44V)0.46.One should note that Eq. (7) reduces to Eq.
(6) if Bn = 0 m.
2.1.2. Inversion technique
The developed inversion technique is based on the
statistical inversion approach (Lehtinen, 1988). In prac-
tice, a three-step minimization procedure is established.
The algorithm requires that ground reference data on
forest stem volume are available for training regions.
The actual minimization problems can be solved with
standard (constrained) iteration algorithms. In the case of
ERS INSAR data, the first step of the algorithm is the
fitting of backscattering model (curve as a function of V)
given by Eq. (4) to observed mean rj values of all
training regions with a and b as parameters to be
optimized
mina;b
XNi¼1
wiðrmodeledj ða; b;ViÞ � robserved;ij Þ2 ð8Þ
where rmodeledo is the backscattering coefficient predicted
by Eq. (4). Vi is the known value of forest stem volume
for the training forest stand number i. robserved,io is the
mean backscattering coefficient observed for the training
region i (mean value of the two intensity images used for
J. Pulliainen et al. / Remote Sensing of Environment 85 (2003) 397–409 399
the calculation). The total number of training regions is
N. The optional weighing factor wi is related to the
proportional area of the region i
wi ¼ Ai
XNi¼1
Ai
,ð9Þ
The second phase is the fitting of coherence model (5)
into interferometric coherence data by optimizing c0 and
c1. Again, this is performed for the training data set by
applying a and b values estimated at the first phase of the
algorithm. Let the estimated values of a and b be a and
b, then the minimization problem is stated as
minc0;c1
XNi¼1
wiðAcðc0; c1ÞAmodeled;i � AcAobserved;iÞ2
as Acðc0; c1ÞAmodeled;i ¼ Acðc0; c1;Vi; a; bÞA ð10Þ
The outcome of the nonlinear optimization procedure (Eq.
(10)) is the estimates c0 and c1.
The third phase of the algorithm is the estimation of
forest stem volume for any forest region, which can be
carried out using multi-temporal INSAR data (optimizations
according to Eqs. (9) and (10) are carried out separately for
each individual image). If the stem volume estimation is
carried out using a total of m images, the minimization
problem to retrieve forest stem volume for the forest region j
is given by
minVj
Xmk¼1
WkðAcðVjÞAmodeled;k � AcAobserved;k;jÞ2
such that Vjz 0 m3/ha as
AcðVjÞAmodeled;k ¼ AcðVj; c0;k ; c1;k ; ak ; bkÞA ð11Þ
where Wk is weight factor determined by the residuals of
model fitting (Eq. (10))
Wk ¼1
2VarðRkÞð12Þ
where Rk is the residual vector obtained for the training
regions of image k
Rk ¼�AcAk
modeled;1 � AcAkobserved;1 AcAk
modeled;2
� AcAkobserved;2 . . .AcAk
modeled;N � AcAkobserved;N
�ð13Þ
It can be shown that Eq. (11) yields a maximum like-
lihood estimate on forest stem volume given the radar
observations, if the error of model (5) has a Gaussian
distribution. Moreover, if the distribution of stem volume
is Gaussian around its mean value, the maximum like-
lihood estimate of stem volume is obtained based on
Bayes theorem by
minVj
Xmk¼1
WkðAcðVjÞAmodeled;k �AcAobserved;k;jÞ2
þ 1
2Varð½V1; . . . ;VN �ÞVj �
1
N
XNi¼1
Vi
!2
ð14Þ
such that Vjz 0 m3/ha.
Even though the forest stem volume does not typically
obey Gaussian distribution, the use of regulating sum term
can be useful, as it often reduces the retrieval bias by
shifting the estimates toward the mean value of the training
data set.
An important aspect of the multi-temporal inversion
technique is its ability to compensate for the random
fluctuations of individual observations. Even though the
observed coherence value for an individual stand may be
lower than the minimum modeled coherence values for the
highest stem volumes, the estimates determined from multi-
ple observations do not (typically) show unrealistically high
values. The bias term included in Eq. (12) emphasizes this
effect.
2.2. INSAR data processing
2.2.1. SAR data
The SAR data used in this study consist of 14 ERS-1/2
Tandem image pairs (28 SLC images in total) acquired with
the C-band SARs on-board the European Space Agency’s
ERS-1 and ERS-2 satellites. Table 1 summarizes the key
imaging characteristics and the weather conditions during
the image acquisition (all the images were acquired from
descending orbits). The imagery was acquired during the
ERS-1/2 Tandem mission in 1995–1996, when the two
satellites were flown in the same orbital plane so that ERS-2
imaged the same area on the ground 24 h after ERS-1. Due
to the relatively short temporal baseline of 24 h and the short
interferometric baselines, the image pairs collected during
the Tandem mission are useful in interferometric studies of
natural targets, which decorrelate quite rapidly in C-band.
The image data used in this study span a whole year from
the summer of 1995 to the summer of 1996.
2.2.2. Interferometric processing
Interferometric processing and geocoding of the SAR
image data were done using a software package described in
Wegmuller, Werner, and Strozzi (1998). Since the data were
from two different imaging geometries depending on the
track/frame combination, the images were processed in two
separate sets. First, a master image was chosen for both
geometries, and all images were co-registered to their
respective master image with sub-pixel accuracy that is
J. Pulliainen et al. / Remote Sensing of Environment 85 (2003) 397–409400
necessary for correlating images. Tandem interferograms
were generated from each Tandem pair by cross-correlating
the already co-registered images with each other. Common
band filtering (also called spectral-shift filtering) was ap-
plied before interferogram generation in order to minimize
the effects of the baseline geometry on coherence estimation
(Gatelli et al., 1994). At this stage, multi-looking (five
azimuth looks) was performed in order to improve on the
estimates of the interferometric phase and coherence. The
resulting 5-look interferograms were flattened using the
high-quality orbit information distributed by DLR (PRC-
orbits). The interferometric coherence was estimated using
square estimator windows with the estimator window size of
7� 7 pixels using Gaussian weighing of the samples. Also,
5-look intensity images were generated and radiometrically
calibrated for range spreading loss, antenna gain, normal-
ized reference area, and the calibration constant (Laur et al.,
1997).
2.2.3. Geocoding
After interferometric processing, all the processed images
were in the imaging geometries of the two master images.
This was accomplished by creating a simulated SAR image
from an INSAR digital elevation model (DEM) and using
the simulated SAR image to co-register the two image sets.
The simulated SAR image was created from an INSAR
DEM that was a weighed average of two INSAR DEMs
produced from the Tandem pairs 8 and 10 (see Table 1).
These wintertime pairs were chosen due to their high overall
coherence and usable baseline lengths. Averaging INSAR
DEMs reduces the effects of phase noise and possible
atmospheric artefacts. Images from track 179 were then
rectified into the geometry of track 408 using the simulated
SAR image. Now, when all images were in the geometry of
the master image for track 408, the INSAR DEM was again
used in orthorectifying the images to UTM projection. The
final registration to map coordinates was done using auto-
matically picked ground control points. Judging visually, the
image data from the two different tracks coincide perfectly,
which implies that sub-pixel accuracy was achieved. This
high-accuracy co-registration allowed us to use the methods
of temporal filtering and temporal averaging. The intensity
images were corrected for the true pixel size using the
INSAR DEM, which reduces the effect of terrain slope on
backscattered intensity.
2.2.4. Temporal filtering
Reliable estimation of the backscattering coefficient rjof a distributed target requires that the estimated number of
looks (ENL) is sufficiently large. In accurately co-registered
Table 1
ERS-1/2 SAR images and image acquisition characteristics
Image
pair no.
Image acquisition
dates (ERS-1/ERS-2)
Track/Frame Interferometric
perpendicular
baseline (m)
Air temperature
at 9.00 UTC (jC)Wind speed
(direction)
(m/s, deg.)
Snow
depth (cm)
Precipitation
between
images (mm)
1 17–18 July 1995 408/2385 � 2 19.5 8 (140) 0 3.4
17.1 5 (190) 0
2 21–22 August 1995 408/2385 � 72 17.1 3 (330) 0 0
21.1 5 (240) 0
3 9–10 September 1995 179/2385 � 28 11.5 6 (30) 0 14.9
10.3 3 (30) 0
4 25–26 September 1995 408/2385 239 13.5 8 (190) 0 1.2
11.7 10 (210) 0
5 14–15 October 1995 179/2385 � 221 8.6 6 (290) 0 0
6.2 1 (90) 0
6 30–31 October 1995 408/2385 � 49 5.2 2 (260) 0 0.1
� 1.7 5 (340) 0
7 8–9 January 1996 408/2385 � 29 � 6.5 2 (120) 13 0
� 5.0 3 (170) 13
8 12–13 February 1996 408/2385 85 � 14.9 5 (100) 16 1.4
� 10.8 1 (120) 19
9 2–3 March 1996 179/2385 � 76 � 4.2 4 (10) 32 0.1
� 5.5 3 (50) 32
10 18–19 March 1996 408/2385 80 � 3.2 3 (350) 39 0
� 4.4 1 (110) 38
11 6–7 April 1996 179/2385 37 5.5 4 (220) 38 (wet snow) 0
7.6 2 (130) 32 (wet snow)
12 22–23 April 1996 408/2385 � 58 14.7 5 (240) 0 0
10.0 3 (50) 0
13 15–16 June 1996 179/2385 48 15.6 7 (330) 0 0
14.9 6 (340) 0
14 20–21 July 1996 179/2385 188 16.0 4 (70) 0 0.1
14.6 5 (40) 0
All SAR observations were imaged at 10.35 UTC (12.35 local normal time).
J. Pulliainen et al. / Remote Sensing of Environment 85 (2003) 397–409 401
multitemporal data sets, it is possible to employ the techni-
que of temporal filtering, which can increase radiometric
resolution without degrading spatial resolution (increase
averaging by increasing effective number of looks). The
theory of temporal filtering is discussed in Lopes, Nezry,
Touzi, and Laur (1993), here we have used a simple
temporal filter which assumes that the filtered images are
uncorrelated. The simplified filter is defined as (Quegan, Le
Toan, Yu, Ribbles, & Floury, 2000; Quegan & Yu, 2001)
Jkðx; yÞ ¼hIkiN
Xmi¼1
Iiðx; yÞhIii
ð15Þ
Where (x,y) are the spatial coordinates in an image, J is the
set of temporally filtered images, I is the set of unfiltered
images, and < I> is a spatial estimate for I. Since a spatial
estimate for I is needed in Eq. (15), some loss of spatial
resolution is unavoidable.
2.2.5. Intensity images
The 14 ERS-1 and 14 ERS-2 intensity images (see Table
1) were filtered in separate sets with the temporal filter (Eq.
(15)). Filtering was done in separate sets because there are
significant correlations between the images in a ERS-1/2
Tandem image pair and the temporal filter assumes uncorre-
lated images. The spatial estimate needed in Eq. (15) was
acquired with a 5� 5 pixel k-nearest-neighbor-lee filter, see
Lee (1981). Judging visually, the temporally filtered images
have markedly diminished speckle with little or no reduc-
tion in spatial resolution. In fact, narrow linear structures are
more clearly visible in the filtered images than in the
unfiltered ones.
2.2.6. Coherence images
The 14 ERS-1/2 Tandem coherence images were filtered
with the temporal filter. A 5� 5 pixel median filter was used
for acquiring the spatial estimate. Judging visually, the
temporally filtered images display much less noise with
some degradation of spatial resolution. Narrow linear struc-
tures are well preserved, as in the intensity image case.
3. Test site and reference data
The selected test site, the Tuusula region in southern
Finland represents ecologically southern boreal forests. The
dominant tree species are Norway spruce (Picea abies) and
Scots pine (Pinus sylvestris). The employed reference infor-
mation includes ground-based forest inventory data deter-
mined at stand level. Meteorological observations from a
nearby weather station were also available. In this inves-
tigation, we particularly use the following in situ weather
data: (a) near-surface air temperature observed in a 3-h
interval for the days of each image pair acquisition, (b)
corresponding wind velocity observations averaged over 10-
min periods, (c) corresponding cumulative precipitation
measurements, and (d) corresponding snow-depth observa-
tions. Additionally, continuous wind velocity measurement
data were available for the days under investigation.
The total number of forest stands in the test region is 210
(total area of 506 ha). The data analysis was carried out for
the 134 stands that have an area larger than 1.5 ha (total area
of 432 ha). For these stands, the forest stem volume varies
from 0 to 539 m3/ha with a mean value of 174 m3/ha. Table
2 summarizes the stand characteristics, whereas Table 1
presents the weather conditions during the image acquisition
dates (together with the SAR image characteristics).
4. Results and discussion
4.1. Feasibility of empirical modeling
The feasibility of the empirical coherence modeling
approach was investigated by analyzing how well the model
given by Eqs.(4) and (5) explains the behavior of stand-wise
ERS-1/2 coherence observations under varying conditions.
In practice, the model was fitted into stand-wise ro and cobservations by estimating the empirical model parameters
(c0,k, c1,k, ak, bk) separately for each image pair k by
applying procedures (8)–(10). The obtained model param-
eter values for different occasions (image pairs) are listed in
Table 3. Additionally, Fig. 1 demonstrates how well the
backscattering model fittings according to Eq. (8) agree with
the experimental observations under typical summer,
autumn, and winter conditions. Even though the fluctuations
of stand-wise observations from modeled curves are high,
the average level of backscatter for different stem volume
classes is well described by model (4). Note that the listed
and depicted rj values determined from ERS SLC images
show systematically lower values than those obtained from
ERS PRI images. This is due to the difference in the
calibration constant of these two image data.
As the coherence data and model (5) describe the
interferometric coherence as a function of forest stem
volume (biomass), the obtained results also enable the
quantitative study of the matter on how largely the image
acquisition conditions affect the level of coherence, separat-
ing the contribution of ground and that of forest canopy
Table 2
Forest stand characteristics
All 210
stands
134 stands larger than 1.5 ha
(85.4% of the total area)
Mean stem volume (m3/ha) 155.5 174.4
Std. of stem volume (m3/ha) 160.3 176.1
Minimum stem volume (m3/ha) 0 0
Maximum stem volume (m3/ha) 539.3 539.3
Mean stand area (ha) 2.4 3.2
Std. of stand area (ha) 1.9 1.9
Minimum stand area (ha) 0.2 1.52
Maximum stand area (ha) 13.8 13.8
J. Pulliainen et al. / Remote Sensing of Environment 85 (2003) 397–409402
(vegetation layer). The estimated model parameters c0,k and
c1,k directly describe the coherence of ground layer and
vegetation, respectively, for each image pair k.
Fig. 2 shows the modeled behavior of coherence as well
as the actual stand-wise observations for all 14 INSAR
images. Also, the 70% prediction band of coherence mod-
eling is depicted for each case. The corresponding correla-
tion coefficients between the modeled coherence and
observed coherence are summarized in Table 4. The corre-
lation coefficients obtained between the data and model (7)
are also shown. The results in Table 4 confirm the con-
clusions of earlier investigations by indicating a high
temporal variability in correlation between the coherence
observations and stem volume, see, e.g. Fransson et al.
(2001), Koskinen et al. (2001), and Santoro et al. (2002).
According to Table 4, the model given by Eq. (5) describes
the behavior of interferometric coherence at the stand level
with a higher correlation than the model given by Eq. (7)
including the complex term. The lower correlation obtained
by model (7) is possibly caused by the inhomogeneity of
tree height inside individual forest stands.
Fig. 2 clearly indicates that the response of coherence to
increase in stem volume is nonlinear. This nonlinear behav-
ior is well described by the empirical models (4) and (5)
even though the scatter from the modeled (average) curve is
quite high at stand level.
4.2. Influence of weather-related factors on coherence
Fig. 2 indicates that the level of coherence is highly
dependent on seasonal conditions. The evident factors
affecting the level of coherence, and thereby parameters
c0,k and c1,k include the change in vegetation and soil/snow
moisture between the repeat pass SAR image acquisitions
and wind-induced changes in scatterer positions (absolute
positions of needles, branches, and tree tops). These aspects
can be investigated by analyzing the correlation between the
estimated model parameters (c0,k and c1,k) and weather
station observations-based indicators. The following quan-
titative indicators that are directly related either to changes
in vegetation and soil moisture conditions or changes in
(volume) scatterer positions are used here: (i) integrated
amount of precipitation between the moments of image pair
acquisition and (ii) averaged wind speed at about the
moments of image acquisition (refer to Table 1). The change
in temperature is used as a qualitative indicator as it is
essential especially when the temperature has varied above
and below the freezing point.
According to Fig. 2 and Table 4, the interferometric
coherence shows a low level, and consequently, has a low
correlation to biomass in five of the investigated images
(image pair nos. 1, 3, 4, 6, and 11). The precipitation andwind
speed data listed in Table 1 explain this behavior adequately
in four of the cases. In 17–18 July 1995 and 9–10 September
1995 (image pair nos. 1 and 3), considerable precipitation
occurred between the image acquisitions evidently causing
changes in the dielectric properties of the scene. For 25–26
September 1995 (image pair no. 4), the wind speed was high.
In the case of image pair no. 6, temperature was above the
freezing point in October 30 but below the freezing point in
October 31. This may have caused considerable changes in
the dielectric characteristics of the scene (refer to Table 3 for
backscattering model parameter values), which as well
decreases the overall level of coherence.
In one of the investigated interferometric images, the
image pair obtained for 6–7 April 1996 (image pair no.
11), the low level of coherence is not explained by the
temperature or precipitation behavior. During this image pair
acquisition, the scene was fully covered by wet snow.
Typically, the interferometric images obtained under snow-
covered conditions show very high coherence values. The
most probable reason decreasing the level of coherence for
the image pair no. 11 is the rapid melt of snow. The thickness
of the snowpack dropped about 6 cm between the image
acquisitions. As the drop in the snowpack thickness is a
spatially inhomogeneous phenomenon in a rugged forested
terrain (even at a small scale), it is possible that the low level
of coherence is directly caused by the snow melt: the
dominant backscattering mechanism from a wet snow layer
Table 3
Estimated parameters for backscattering model (4) and coherence model
(5): Backscattering model parameters for individual SAR images (a and b),
correlation coefficient between the backscattering model predictions and
stand-wise ro-observations, and estimated coherence model parameters (c0and c0 + c1)
Image
pair no.
a 10 log10 (b) Correlation
coefficient (r)
c0 c0 + c1
1 0.93 � 10.5 0.40 0.19 0.11
0.90 � 10.0 0.15
2 0.91 � 10.9 0.51 0.45 0.19
0.83 � 11.3 0.50
3 0.98 � 9.0 0.10 0.34 0.15
1.02 � 8.8 0.12
4 0.94 � 9.8 0.17 0.26 0.11
0.96 � 8.9 0.24
5 0.95 � 9.4 0.00 0.49 0.25
0.85 � 10.1 0.08
6 0.89 � 9.3 0.17 0.35 0.18
0.60 � 11.3 0.04
7 0.64 � 10.6 0.24 0.69 0.40
0.55 � 11.0 0.30
8 0.93 � 9.8 0.12 0.72 0.29
0.73 � 10.5 0.04
9 0.75 � 9.9 0.21 0.72 0.40
0.71 � 10.3 0.16
10 0.68 � 10.1 0.31 0.64 0.25
0.63 � 10.5 0.31
11 1.01 � 11.0 0.55 0.24 0.26
0.93 � 11.6 0.58
12 0.96 � 8.7 0.32 0.42 0.14
0.89 � 9.0 0.34
13 1.02 � 9.4 0.17 0.41 0.19
0.90 � 10.1 0.19
14 1.02 � 9.3 0.07 0.51 0.28
1.00 � 9.4 0.12
J. Pulliainen et al. / Remote Sensing of Environment 85 (2003) 397–409 403
is surface scattering and the 6-cm vertical drop in the surface
corresponds to increase in two-way radar signal path length
of about 2� k at the nominal incidence angle of 23j. Takinginto account the size of the sampling window from which the
coherence data are calculated and the probable spatial varia-
tions in snow melt, it is most likely that the low level of
coherence is caused by the inhomogeneous drop of snowpack
thickness.
The behavior of coherence can be also analysed by
examining how it is related to intensity images that
correspond to the complex SAR image pairs used for
determining the individual coherence images. The quanti-
Fig. 1. Examples of forest backscattering model (4) fittings to stand-wise rj observations for summer, autumn, and winter conditions (image pairs 2, 4, and 10,
respectively). The average observed rj values for six stem volume classes are also depicted. The 70% prediction band of modeling is depicted for each case.
Refer to Table 3 for estimated model parameters (model fitting separately for each image).
J. Pulliainen et al. / Remote Sensing of Environment 85 (2003) 397–409404
tative characteristic used here is the correlation coefficient
between the intensity images of each image pair. It is
calculated from stand-wise averaged intensity data (rjvalues). Fig. 3 depicts how this characteristic is related to
the dynamic behavior of coherence, i.e. the contrast of
coherence between the open areas and very dense forests.
The coherence contrast is determined by estimating c1,kaccording to the optimization procedure (Eq. (10)). It
defines the drop of coherence between open areas and
opaque forests. In general, the coherence shows low values
if the correlation between the two intensity images is low.
According to Fig. 3, the only exception is again the image
Fig. 2. Fitting of empirical backscattering–coherence models (4) and (5) into stand-wise rj and AcA observations according to procedures (6)– (8) for 14
INSAR image pairs.
J. Pulliainen et al. / Remote Sensing of Environment 85 (2003) 397–409 405
pair no. 11 (6–7 April 1996). This also suggests that the
inhomogeneous melt of snowpack causes the decorrelation
(random shifts in signal phase). A noticeable point is also
that the intensity images of the image pair no. 11 are also
highly correlated with the forest stem volume. This is
depicted in Fig. 4 by showing the response of rj to
increase in stem volume for the SAR intensity images
(both stand-wise observations and model fittings according
to Eq. (8) are depicted). Time series of snow thickness and
air temperature observations for 6 and 7 April are also
presented for comparison.
4.3. Stem volume estimation results
The stem volume estimation was tested for the Tuusula
test area by using 50% of the data (INSAR observations
from 67 forest stands) for training the algorithm and the rest
of the data for independent testing of the stem volume
retrieval performance. A large number of random combina-
tions of training and testing data sets were employed in
order to evaluate the retrieval performance in a statistically
reliable way. In addition to the stem volume estimation
(Eqs. (6)–(12)), standard multiple linear regression was
tested simultaneously with the same training and testing
data sets for comparison. The equation for estimating V for
stand j by multiple linear regression is given by
Vj ¼ a0 þXmk¼1
akAcAobserved;k;j ð16Þ
where a0 and ai,. . .,m are the regression coefficients deter-
mined from the training data.
Fig. 5 shows the overall quantitative accuracy character-
istics of stand-wise stem volume retrieval results as a
function of the number of employed (optimal) images.
The results are determined using the developed inversion
approach with and without the regulating term, using Eqs.
(14) and (11), respectively. Additionally, the multiple linear
regression algorithm (Eq. (16)) is applied. The depicted
results are the average performance characteristics obtained
with 100 random combinations of 50% training and testing
data. The images used for 14 different cases were selected
using a forward selection rule. First, the best individual
image was selected based on the highest correlation between
Table 4
Correlation coefficient (a) between the stand-wise forest stem volume and
stand-wise averaged observed coherence value (b) between the modeled
coherence value according to Eq. (5) and observed coherence value, and (c)
between the modeled coherence value according to Eq. (7) and observed
coherence value
Image
pair no.
(a) Correlation
coefficient (r)
(b) Correlation
coefficient (r)
obtained for Eq. (5)
(c) Correlation
coefficient (r)
obtained for Eq. (7)
1 � 0.40 0.46 0.48
2 � 0.64 0.68 0.67
3 � 0.49 0.55 0.56
4 � 0.56 0.61 0.57
5 � 0.71 0.73 0.57
6 � 0.52 0.56 0.56
7 � 0.74 0.77 0.75
8 � 0.87 0.87 0.83
9 � 0.84 0.86 0.82
10 � 0.79 0.82 0.80
11 � 0.05 0.07 � 0.41
12 � 0.70 0.74 0.74
13 � 0.63 0.67 0.66
14 � 0.69 0.72 0.55
Fig. 3. Effect of weather and seasonal conditions on the level of coherence and on the image pair-wise correlation of intensity images. On x-axis is the
correlation between the stand-wise averaged rj values of each intensity image pair (k= 1. . .14). On y-axis is the contrast between the level of coherence at open
areas and that of very dense forests, i.e. � c1,k determined by Eq. (8).
J. Pulliainen et al. / Remote Sensing of Environment 85 (2003) 397–409406
Fig. 4. Behavior of observed stand-wise backscattering intensity (rj) as a function of forest stem volume for the SAR images from 6 and 7 April 1996 (10.35
UTC), and the corresponding model fittings according to Eq. (6) with 70% prediction bands (dotted lines). Time series of snow-depth and near-surface air
temperature observations are also shown for the image acquisition period.
Fig. 5. Average performance characteristics of stand-wise stem volume retrieval. The results obtained with Eq. (12) using the bias-correction are shown by open
circles and results by Eq. (9) without the bias correction by diamonds. Solid circles depict the results obtained using multiple linear regression. The percentage
RMSE is defined as 100�RMSE/mean true stem volume in testing data set. The standard deviation of obtained correlation coefficients is f0.02 for all the
cases. The standard deviation of RMSE values is f6% for linear regression, f5% for inversion results with and f9% without the bias correction,
respectively. The out-of-scale mean value of percentage RMSE for inversion results without the bias correction using a single image is 72%.
J. Pulliainen et al. / Remote Sensing of Environment 85 (2003) 397–409 407
the predicted and ground truth stem volume values. Then,
the image yielding the highest performance, together with
the first image, was chosen for the second image. This was
repeated until all 14 images were included. The image
selection was carried out using all the data. This was
necessary in order to make the retrieval results representing
a certain number of images comparable with each other. As
the accuracy of stand-wise data was not exactly known, the
sampling errors of the ground truth were not subtracted from
the calculated MSE values, in contrast to what was carried
out, e.g. in Fransson et al. (2001), Santoro et al. (2002).
The results of Fig. 5 indicate that the highest perform-
ance is obtained with two optimal images. With higher
number of images, the performance of stem volume estima-
tion gradually decreases, probably due to fact that the
coherence of the worst interferometric images is not sig-
nificantly correlated to the stem volume. A noticeable point
is that the performance of the developed inversion technique
is better than that of multiple linear regression when the
number of images is smaller than eight, as the bias correc-
tion (the regulating sum term) is applied according to Eq.
(14). According to results, the performance of the inversion
procedure (Eqs. (8)–(14)) decreases if images with the
lowest correlation between the coherence and stem volume
are included. An evident reason is that for those images, the
inversion procedure cannot perfectly compensate for the
random fluctuations between the coherence model predic-
tions and observations.
It turned out that winter images with snow-covered
terrain are superior to images obtained under summer
conditions. This confirms the results of earlier investiga-
tions, see, e.g. Fransson et al. (2001), Koskinen et al.
(2001), Santoro et al. (2002). The two image pairs yielding
the highest stem volume retrieval performance were
obtained in mid- and spring–winter conditions (12 and 13
February, and 2 and 3 March 1996). The highest correlation
coefficient between the estimated stem volume and the
ground truth stem volume showed values as high as
r = 0.89 (R2 = 0.79) and a percentage RMSE level of 48%.
This performance can be regarded as comparable to that of
optical satellite images (with about the same spatial reso-
lution). According to an investigation of a single test site by
Hyyppa et al. (2000), Landsat TM data show an unbiased
RMSE of 56% and R2 = 0.31 at stand level, and ERS
coherence images have a RMSE level of 58% (R2 = 0.24),
respectively. Fransson et al. (2001) reported RMSE ranging
from 24% to 38% for stand-wise stem volume estimates
based on SPOT XS data, whereas the corresponding figure
by Hyyppa et al. (2000) is RMSE = 50%. However, the
quantitative retrieval performance is highly dependent on
the forest site under investigation and on the employed
reference forestry data. For example, Santoro et al. (1999)
tested their stem volume estimation method for the Tuusula
test site, but only applying 18 stands larger than 2 ha for the
algorithm testing (mean stand area around 7 ha). Using that
material for large forest stands, they obtained a retrieval
performance as high as R2 = 0.84 (RMSE = 86 m3/ha) with
two optimal wintertime images.
4.4. Suggested approach for operative stem volume
estimation
Based on the stem volume retrieval experiment, a prac-
tical approach for forest stem volume mapping from INSAR
data based on the developed inversion technique can be
outlined as follows.
1. Segmentation of study area into quasi-homogeneous
regions using some standard segmentation algorithm for
multi-temporal INSAR data (or other available data
sources).
2. Classification of segmented areas into forested regions
and other land use classes.
3. Fitting of forest backscattering model given by Eqs. (1)–
(3), or Eq. (4) in case of ERS INSAR data, into average
rj values of training regions (ground truth data on forest
stem volume available for training regions).
4. Estimation of the empirical parameters of the coherence
model (5) by fitting the coherence model into coherence
observations of training regions separately for each
available image (applying forest backscattering model
parameters determined in step 3). Possible rejection of
images showing a low correlation between the coherence
observations and stem volumes of training regions.
5. Estimation of forest stem volume for any forested region
by the inversion of the coherence model for multi-image
INSAR data.
5. Conclusions
The presented results show that the seasonal and weather
conditions have a major effect on the feasibility of C-band
repeat-pass INSAR coherence images for stem volume
mapping. Even in the case of one-day-repeat cycle, the
conditions at the target area can significantly change
between SAR image acquisitions causing a drop of inter-
ferometric coherence, and thus, degrading the sensitivity of
coherence to stem volume variations. The demonstrated
weather conditions-related phenomena that degrade INSAR
coherence images include (a) precipitation between image
acquisitions, (b) strong wind, (c) freezing between image
acquisitions, and (d) rapid snow melt (decrease of snowpack
thickness) between the moments of repeat-pass image
acquisitions.
A new analytical model-based technique to estimate forest
stem volume from coherence data appears to perform well,
even for small regions when optimum coherence images or
large multi-temporal image sets are employed. It is also
possible to select optimum images beforehand based on
weather data. Based on the results presented here, winter
J. Pulliainen et al. / Remote Sensing of Environment 85 (2003) 397–409408
images with dry snow cover (temperatures well below the
freezing point) are always applicable for stem volume re-
trieval in boreal forests. In contrast to SAR intensity images,
coherence images obtained under wet snow conditions are, at
least occasionally, totally unusable for stem volume (or bio-
mass) mapping. The obtained stem volume retrieval perform-
ance was close to that of optical satellite images.
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