assessing performance of l- and p-band polarimetric interferometric sar data in estimating boreal...

714 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 50, NO. 3, MARCH 2012

Assessing Performance of L- and P-BandPolarimetric Interferometric SAR Data in Estimating

Boreal Forest Above-Ground BiomassMaxim Neumann, Sassan S. Saatchi, Member, IEEE, Lars M. H. Ulander, Senior Member, IEEE, and

Johan E. S. Fransson, Member, IEEE

Abstract—Biomass estimation performance using polarimetricinterferometric synthetic aperture radar (PolInSAR) data is eval-uated at L- and P-band frequencies over boreal forest. PolInSARdata are decomposed into ground and volume contributions, re-trieving vertical forest structure and polarimetric layer charac-teristics. The sensitivity of biomass to the obtained parametersis analyzed, and a set of these parameters is used for biomassestimation, evaluating one parametric and two non-parametricmethodologies: multiple linear regression, support vector ma-chine, and random forest. The methodology is applied to airborneSAR data over the Krycklan Catchment, a boreal forest test sitein northern Sweden. The average forest biomass is 94 tons/ha andgoes up to 183 tons/ha at forest stand level (317 tons/ha at plotlevel). The results indicate that the intensity at HH–VV is moresensitive to biomass than any other polarization at L-band. AtP-band, polarimetric scattering mechanism type indicators are themost correlated with biomass. The combination of polarimetricindicators and estimated structure information, which consists offorest height and ground–volume ratio, improved the root meansquare error (rmse) of biomass estimation by 17%–25% at L-bandand 5%–27% at P-band, depending on the used parameter set.Together with additional ground and volume polarimetric char-acteristics, the rmse was improved up to 27% at L-band and43% at P-band. The cross-validated biomass rmse was reduced to20 tons/ha in the best case. Non-parametric estimation methodsdid not improve the cross-validated rmse of biomass estimation,but could provide a more realistic distribution of biomass values.

Index Terms—Biomass estimation, boreal forest, interferom-etry, linear regression (LR), polarimetry, random forest (RF),support vector machine (SVM), synthetic aperture radar (SAR).

I. INTRODUCTION

FOREST biomass estimation is an arduous task. To measurebiomass requires that a large number of trees are harvested

Manuscript received November 1, 2010; revised May 1, 2011 andOctober 13, 2011; accepted October 30, 2011. Date of publication January 12,2012; date of current version February 24, 2012. This work was supportedby an appointment to the NASA Postdoctoral Program at the Jet PropulsionLaboratory, administered by Oak Ridge Associated Universities through acontract with the National Aeronautics and Space Administration.

M. Neumann and S. S. Saatchi are with the Jet Propulsion Labora-tory, California Institute of Technology, Pasadena, CA 91109 USA (e-mail:[email protected]; [email protected]).

L. M. H. Ulander is with the Department of Radio and Space Science,Chalmers University of Technology, 41296 Gothenburg, Sweden (e-mail:[email protected]).

J. E. S. Fransson is with the Department of Forest Resource Management,Swedish University of Agricultural Sciences, 90183 Umeå, Sweden (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2011.2176133

and weighed on scales. Since this is not realistic to do for largeareas, biomass is rather estimated from field measurements ofstanding trees. Even field data collection is labor intensive andrequires extensive field inventories due to the spatial variabilityof the forest structure. Nevertheless, forest biomass is of interestin forestry and is an important component in the global carbonbudget, which needs to be quantified for climate change studiesand mitigation treaties. The present estimate by the Intergovern-mental Panel on Climate Change is that deforestation amountsto between 10% and 30% of the total anthropogenic carbondioxide (CO2) flux [1]. The range of uncertainty is largedue to the lack of accurate observational techniques. There-fore, several spaceborne remote sensing missions are proposedto address the need for global monitoring of forest carbonstocks and changes, including NASA’s L-band mission De-formation, Ecosystem Structure and Dynamics of Ice—Radar(DESDynI-R), JAXA’s Advanced Land Observing Satellite-2(ALOS-2) L-band mission, and ESA’s P-band missionBIOMASS.

In radar remote sensing, above-ground biomass (AGB) andclosely related stem volume have been estimated from syntheticaperture radar (SAR) backscatter [2]–[7], interferometric SAR(InSAR) coherence [8], and polarimetric interferometric SAR(PolInSAR) [9], by means of empirical and model-basedapproaches. Methods based on radar backscatter signals arelimited by saturation and loss of sensitivity to biomass for highbiomass levels, depending on the wavelength, polarization, andincidence angle. In addition, the saturation is dependent on theforest type, ground topography, and environmental conditions.Estimation approaches based on interferometry were reportedto go beyond the backscatter saturation levels, but have limi-tations in terms of the perpendicular interferometric baseline,temporal decorrelation, and other noise sources. For smallperpendicular baselines, the vertical structure sensitivity is low,while for large baselines, the problems of height ambiguityarise. The usage of multiple baselines improves interferometricdata processing, compensating temporal decorrelation andpermitting more accurate ground–volume separation andvertical structure retrieval [10], [11]. If a sufficient numberof interferometric baselines are available, tomography can beused to probe the vertical structure of the forest in greater detail[12], [13]. Alternatively, lidar remote sensing is a promisingtechnique to estimate AGB remotely by measuring the verticalstructure profile. However, no remote sensing technique canmeasure biomass directly. The scattered radar and lidar waves

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NEUMANN et al.: ASSESSING PERFORMANCE OF L- AND P-BAND POLINSAR DATA 715

from the forest cannot represent biomass entirely and usuallydo not follow a linear or simple relationship with biomass.Intrinsically, the scattered waves, in dependence of the wave-length, image more the structure of the canopy (leaves, needles,and branches) than the main constituents of biomass, i.e.,tree stems. Depending on the wavelength, polarization, inci-dence angle, and the mode of operation (backscatter or InSAR),radar images the canopy and the stems, but the signal carriesinformation about other components of the surface such assoil and canopy moisture, and ground topography. The remotesensing of forest ecosystems is additionally hindered by thespatial variability, the local tree species composition anddistribution, and the often non-monotonous development of theforests in height, density, and volume.

Modeling and experimental investigations at L- andP-band have demonstrated sensitivity to different parts of foreststructure [2]–[5], [10], [12]–[15]. L-band backscatter is dom-inated by the forest canopy layer and the branch structure.Ground–volume interaction can be as strong as the volumecontribution from the canopy. Over medium biomass levels (upto 200 tons/ha) and in structurally open canopy such as borealforests, L-band data can provide sensitivity to the volume andground layers. The polarimetry can distinguish different branchstructures such as separating more orderly distributed branchesof coniferous trees from the more randomly oriented branchesof deciduous trees [10]. P-band (UHV-band) penetrates deeperinto the canopy, and in boreal forests the backscatter is moredominated by the ground layer contributions. This includes theground–trunk contribution, which is credited for good corre-lation of P-band backscatter with biomass and stem volume,especially on flat topography. For high stem volume ranges, theVHF-band has demonstrated very good estimation results [16].The recently developed concept of PolInSAR has demonstratedthe possibility to estimate forest height [17]–[19]. Furthermore,it is possible to separate the ground and volume contributionsand to estimate vertical structure components, compensating fortemporal and thermal decorrelation, as has been demonstratedat L-band in [10] and [20].

In this paper, we systematically investigate the possi-ble improvement of AGB estimation, using parameters frommodel-based PolInSAR inversion of vertical structure andground/volume polarimetric signatures. One direction is toidentify parameters which are best correlated with biomassand to evaluate different biomass estimation methods, usingseveral sets of derived parameters. The analyzed estimationmethods include multiple linear regression (LR), support vectormachine (SVM) regression, and random forest (RF) regression.The first method is a common parametric regression approachwhich can be solved by least squares. The last two are non-parametric in the sense that no parametric model or distributionis assumed. Both SVM and RF are two promising machinelearning classification techniques, which have been adapted toregression problems, and have been applied, for instance, forforest classification from SAR data [21] using SVM and forestheight estimation from different remote sensing products [22]using RF. The AGB estimation performance is evaluated by ex-amining jackknife-type cross-validations and the distributionsof predicted and mapped biomass.

Fig. 1. Optical image (copyright Google Earth) of the Krycklan Catchmentarea, including the swath of radar data and the location of the forest stands.

In Section II, the test site, Krycklan Catchment in northernSweden [23], is introduced, and ground data are discussedand analyzed. In Section III, PolInSAR principles and theRandom Volume over Ground (RVoG) model are presented,and a brief description of main terms and parameters is given.Furthermore, the approaches employed to estimate biomassfrom the retrieved polarimetric and interferometric parametersare explained. In Section IV, the relationship of radar data tobiomass is evaluated, and results of biomass regression andmapping are presented and discussed. Finally, the summary andconclusion are given in Section V.

II. TEST SITE AND GROUND DATA ANALYSIS

As part of studies for the proposed ESA P-band missionBIOMASS, the BioSAR-II campaign in northern Sweden wascarried out in October 2008 to evaluate the possibilities forbiomass estimation in boreal forests [23], [24]. The test siteis located in the Krycklan Catchment and consists of mainlymanaged forest. Most of the forest stands in the test site aredominated by coniferous trees (Scots pine, Pinus sylvestris, andNorway spruce, Picea abies), with a contribution of broadleaftrees (birch, Betula spp.). There is a significant variation inground elevation, ranging between 100 m and 400 m above sealevel, and surface slopes of up to 20◦.

Within the 30 km2 test site, 31 forest stands were selected forobjective field inventory. However, only 27 forest stands werefully covered by radar data and used in the presented analysis.Fig. 1 shows these stands, with areas between 2.4 and 26.3 ha.

The in situ measurements were conducted in circular plotswith 10 m radius, with about ten plots distributed in a randomlypositioned square grid within each stand. Hence, field data werecollected using an objective and unbiased method. In each plot,the diameter at breast height (DBH; i.e., 1.3 m above groundsurface) and the species type have been noted for all treeswith DBH greater than 4 cm. For a sample of trees, the height


Fig. 2. Histograms of biomass estimated from in situ measurements. (a) Based on 310 circular plots with areas of 0.03 ha. (b) Based on 27 forest stands withareas between 2 and 26 ha.

TABLE ICORRELATION COEFFICIENTS (R) BETWEEN DIFFERENT IN SITU MEASURED AND DERIVED BIOPHYSICAL FOREST PARAMETERS [DBH, AGE, FOREST

HEIGHT (LOREY’S HEIGHT), BASAL AREA, STEM VOLUME, AGB, AND STEM DENSITY (NUMBER OF STEMS)] AT STAND LEVEL

and age were also measured in each plot. The heights for therest of the trees were estimated from DBH using regression.These heights were used to estimate Lorey’s height (tree heightweighed with basal area, i.e., cross section of tree trunks inbreast height). Stem volume and AGB (for trunks, branches,and needles/leaves) were estimated using tree species allomet-ric relations. These measurements and allometric relations mayhave large errors in estimating structural attributes of individualtrees, but provide plot or stand-level estimates of structure withhigh accuracy and precision by assuming no bias in estimations.

The in situ data set is supplemented by aerial optical and lidardata. Optical images are used to automatically discriminatethe tree species composition into the main categories of pine,spruce, and broadleaf species at 10 m resolution. lidar data areprocessed to provide ground topography and vertical structureinformation, in terms of canopy heights relative to the ground,corresponding to ten percentiles of relative heights (rh10,rh20, . . ., rh100) at 10 m spatial resolution.

Fig. 2 shows the histograms of AGB values at the forestplot and stand levels. On the plot level, the forest heights (i.e.,Lorey’s heights) are between 3.2 m and 27.8 m, and the AGBvalues range between 0 tons/ha and 317 tons/ha, respectively.On the forest stand level, these values range between 7.5 m and21.4 m in forest height and between 23 tons/ha and 183 tons/hain AGB, with means of 15.2 m and 94.3 tons/ha, respectively.The averaged standard deviation of plot level heights insideindividual forest stands is 2 m (17%), while for biomass it is30 tons/ha (35%). These are typical variations of forest heightand biomass that are expected if estimating these parameters atsub-stand level.

Table I presents the correlation coefficients between differentbiophysical forest parameters at stand level. As expected, sincethe heights of most trees are computed from DBH, a strongcorrelation between these parameters is observed. Similarly, the

TABLE IICORRELATION COEFFICIENTS (R) BETWEEN AGB AND DIFFERENT

HEIGHT METRICS AT STAND AND PLOT LEVELS

stem volume and AGB are also computed from basal area andheight, which explains the high correlation of these parametersas well. In addition, one can observe significant correlation offorest age with height. The stem density did not correlate withbiomass, but there was a negative correlation with DBH andage, suggesting thinning and reduction of stem density withincreasing biomass and tree sizes in forest management.

For the analysis of remote sensing data, it is important toknow the distribution of forest biomass in its structural compo-nents. Depending on tree species and age, about three fourths ofthe tree biomass is in the stem (from 65% in spruces to 81% inpines and birches, as estimated for the test site). It is thereforemost crucial to identify remote sensing variables sensitive to thestem volume and biomass.

Among different forest structural attributes to estimate AGB,the basal area is the best parameter (excluding stem vol-ume). Vertical structure, particularly the forest height (Lorey’sheight), seems to be the second best predictor of biomass.The correlation coefficients between AGB and different heightmetrics from in situ data and lidar maximum relative height(rh100) are presented in Table II at stand and plot levels. Theforest height has the best correlation with AGB compared tothe average tree and lidar maximum relative heights. However,other parameters such as the wood density of different specieswithin the plots or stands may be used as correcting factorswhen estimating AGB using allometric equations.


III. METHODOLOGY

In this section, we provide a summary of the methodologyused in estimating forest parameters from radar data, includinga brief overview of the PolInSAR RVoG model. For more de-tailed information on RVoG model and the inversion approach,the readers can consult, for example, [10], [14], [20], [25],and [26].

A. Polarimetric Interferometric Principles

Acquiring SAR data at different transmit and receive polar-ization combinations provides four scattering coefficients Shh,Svv, Shv , and Svh, where h/v represents horizontal and verticalreceive/transmit polarizations. Under the reciprocity assump-tion, the cross-polarized coefficients are the same (Shv ≈ Svh).For most natural environments on flat topography, the reflectionsymmetry assumption usually holds, causing the covariancesof co-polar and cross-polar channels to be negligible. Thepolarimetric covariance matrix C can be represented by1

C =

⎡⎣ HH HHHV HHV VHHHV ∗ 2HV HV V VHHV V ∗ HV V V ∗ V V

⎤⎦ (1)

where HH = 〈ShhS∗hh〉, V V = 〈SvvS

∗vv〉, and HV =

〈ShvS∗hv〉 are real valued intensities and HHV V = 〈ShhS

∗vv〉

is the co-polar covariance.These matrix elements are sensitive to the size, dielectric

constant, and orientation of the main scatterers in the medium,like the size or volume of branches and stems, their wood den-sity, and ground topography or the orientation direction of thecanopy. Using Pauli matrix basis provides additional compo-nents, such as HH + V V = 〈|Shh + Svv|2〉 and HH−V V =〈|Shh − Svv|2〉, which are related to the illuminated mediumtype. HH + V V is stronger over surfaces and isotropic objects,while HH−V V is an indicator for double-bounce scattering.Polarization basis transformation can compensate for the topog-raphy and dielectric element orientation angles in the azimuthdirection.

Based on the combinations of covariance matrix elements,certain polarimetric measurements such as HV or ratios (e.g.,HV/(HH + V V ), HV/HH) have been reported to be sensi-tive to particular biophysical parameters, such as forest biomass[2], [27].

Incoherent polarimetric decomposition techniques can pro-vide additional information in the form of the random-ness and scattering mechanism type indicators, such as theEntropy–Alpha [28], Freeman–Durden [29], or Delta–Tau de-compositions [10]. Entropy H and alpha angle α are obtainedfrom the eigen-decomposition of the covariance matrix in thePauli-basis. Freeman’s shape parameter ρ [30], the scatteringmechanism type indicator |δ|, and the degree of orientation ran-domness τ can be directly computed from the covariance matrix[31] under the assumption of identical scattering dielectric el-ements. Additionally, the scattered power from different layers

1Symbols T , †, ∗, and 〈·〉 denote the transpose, Hermitian, conjugatecomplex, and ensemble average operations, respectively.

and contributions, particularly the surface; ground–trunk inter-action; and canopy layers can be approximately retrieved frompolarimetric data, with related physical canopy and groundcharacteristics. The polarimetric Freeman decomposition pro-vides the backscatter intensities related to ground (surfaceand double-bounce) and canopy layer scattering (Pg and Pc,respectively).

In the next section, biomass estimation based on thesepolarimetric parameters will be evaluated. We also includedmulti-baseline (MB) interferometry to enhance the biomassestimation approach in two ways: by providing model-basedvertical structure measurements and by enhancing the sepa-ration of ground and volume contributions. In interferometricterminology, the ground contribution refers to the case wherethe interferometric phase center lies at the ground level, and thisincludes both the surface and double-bounce scattering. Thevolume component represents all scattering contributions fromthe canopy, which are distributed along the vertical directionand superpose to an interferometric phase term above theground.

Given n polarimetric interferometric tracks, acquired fromslightly different positions, an MB PolInSAR covariance matrixcan be constructed

CMB = 〈kk†〉 =

⎡⎢⎢⎣C11 Ω12 . . . Ω1n

Ω†12 C22 . . . Ω2n

......

. . ....

Ω†1n Ω′

2n† . . . Cnn

⎤⎥⎥⎦ , k =

⎡⎢⎢⎣k1

k2...kn

⎤⎥⎥⎦

(2)

where ki ∈ C3 are the scattering mechanism vectors consisting

of scattering coefficients from baseline i, i.e., in lexicographicbasis ki = [Si

hh, Sihv, S

ivv]

T . In (2), every baseline ij (i, j ∈[1, n]) and every cross-covariance matrix Ωij are characterizedby a distinctive vertical wavenumber kzij

kzij = 2k0B⊥ij

R0 sin θ0(3)

where k0, B⊥,ij , R0, and θ0 are the wavenumber, the perpen-dicular baseline between the i and j acquisitions, the slantrange distance, and the incidence angle, respectively. Everybaseline is additionally characterized by time lag between theacquisitions. In this paper, only repeat pass interferometricconfiguration is considered.

If the polarimetric stationarity assumption holds [32], theblock-diagonal polarimetric covariance matrices can be as-sumed to be similar (Cii ≈ Cjj ≈ C = 1/n

∑ni=1 Cii). The

PolInSAR coherence of the interferometric pair ij at polariza-tion ω ∈ C

3 is then given by [25]

γij(ω) =ω†Ωijω

ω†Cω. (4)

The coherence phase is mainly a function of the ground topog-raphy and the vertical structure of the resolution cell impactedby noise, while the coherence magnitude is a product of variousnoise sources, including the decorrelation due to the verticalstructure of the vegetation [33]–[35].


B. RVoG Model

Polarimetric interferometric radar data of forested terraincan be modeled in the simplest case as random volume, andRVoG, which can be traced back to the water cloud model [14],[25], [26], [33], [34], [36], [37]. MB PolInSAR RVoG modelprovides the means to decompose the covariance matrix (2) intothe ground (g) and volume (v) contributions [10]

CMB=CMB/g+CMB/v ⇐⇒{C=Cg +Cv

Ωij = γij/gCg + γij/vCv

(5)

or, equivalently, in the form of Kronecker products [11]

CMB = Rg ⊗Cg +Rv ⊗Cv (6)

where

Rx =

⎡⎢⎢⎢⎣

1 γ12/x . . . γ1n/xγ∗12/x 1 . . . γ2n/x...

.... . .

...γ∗1n/x γ∗

2n/x . . . 1

⎤⎥⎥⎥⎦ , x ∈ {g, v}. (7)

Using the complementary information of both polarimetry andinterferometry makes the separation of C into Cg and Cv

possible. The ground contribution consists of attenuated surfacescattering from the soil, the double-bounce scattering betweenthe soil and the trunk and branches, and the volume scatteringfrom a low layer of understory. The volume layer is dominatedby diffuse volume scattering from the dielectric elements, butas well including multiple scattering effects.

The modeled coherence can be considered as a product ofspatial, temporal, and system decorrelation sources [33]. Afterspectral band filtering, the spatial decorrelation reduces to avertical volume decorrelation term

γz =

∫ρ(z)eikzzdz∫

ρ(z)dz(8)

where ρ(z) represents the effective scattering distribution alongthe vertical direction. In the idealized RVoG model, γz/g of theground component is represented by the Dirac delta function2

at the ground topography level ρg(z) = δ(z0). Assuming auniform distribution of the canopy dielectric elements with aconstant attenuation σx, the vertical distribution of the volumecomponent becomes ρv(z) = exp(−(2σx/ cos θ0)z). An addi-tional structural parameter is the ground–volume ratio μ, whichis defined as

μ =trace(Cg)

trace(Cv). (9)

If the surface scattering or the double-bounce scatteringdominates at the ground level, the polarimetric signal from theground becomes strongly polarized. The last condition appearsin the presence of trees with large trunks and on flat terrain,

2Note that ρ() and δ() are functions describing the vertical distributionof scatterers and are not related to the polarimetric scattering mechanismindicators ρ and δ from the previous section.

while the former condition might overweight in sloped ter-rain. In the presence of double-bounce, the ground componentbecomes an important indicator for the tree trunk character-istics. The polarimetry of the volume component can rangefrom purely randomly oriented collection of scatterers withhigh polarization entropy to a less diffuse form with orderedbranch structure. Especially in the presence of distinctive treemorphologies, such as among coniferous tree species in borealforest, the orientation randomness decreases [10].

C. Biomass Estimation Approaches

The inversion of the MB PolInSAR RVoG model in (5)provides the forest height hv , ground–volume ratio μ, andground and volume polarimetric covariance matrices Cg

and Cv . The forest height estimated from this approach can berelated to forest canopy height or the lidar rh100 height. Thisallows us to evaluate biomass estimation performance basedon the structural parameters hv and μ and the polarimetricindicators derived from the covariance matrices Cg , Cv , andthe entire C.

Three different methods for biomass estimation from theseparameters are evaluated: one parametric method including LRand two non-parametric methods including SVM and RF. Thelast two non-parametric methods are based on machine learningclassification approaches, adapted to regression problems. Afterevaluating all three methods for the combination of radar-derived parameters, we develop spatial predictions of AGB overthe test site and compare the results in magnitude and spatialvariations. In the following, these methods are briefly outlined.

1) LR: For every data set (forest stand) j, given a set ofm independent variables pi,j (i ∈ {1, . . . ,m}) and a biomassvalue Bj estimated from field measurements, multiple LRconsists in estimating the coefficients ai by minimizing thefollowing sum of squares

∑j

(Bj − a0 −

m∑i=1

aipi,j

)2

. (10)

2) SVM: SVM is a framework for non-parametric and non-linear classification and regression. The basic idea consists intransforming the input data into a higher dimensional featurespace, where the problem can be addressed in linearized man-ner. In the end, training a SVM involves solving a quadraticoptimization problem. In this paper, the Gaussian radial basisfunction kernel is used for the transformation. The externallibrary libSVM [38] was used for the implementation of AGBregression, with automatic tuning of the SVM penalty parame-ter CSVM and the kernel parameter γSVM .

3) RF: RF [39] is an ensemble learning method, wheremany decision trees are constructed based on random sub-sampling of the given data set. In addition, each node of everytree is split based on another random subset of parameters. Thistwo-layer randomization provides a certain level of robustnessto outliers and overfitting. The result is usually aggregated bytaking the average of the predictions from all trees. RF relieson two parameters: the number of trees and the number of


Fig. 3. Polarimetric slant range images in Pauli basis (Red = HH − VV, Green = HV, and Blue = HH + VV) with delineated forest stands (white). The imagescover the same area but are acquired from opposite illumination directions. Near range is to the left; flight direction is from bottom to top. (a) L-band ascending.(b) L-band descending. (c) P-band ascending. (d) P-band descending.

parameters to be used at each node split. Both parameters areoptimized in the estimation process to improve performance.

IV. EXPERIMENTAL RESULTS AND DISCUSSION

A series of experiments has been conducted to evaluate thebiomass estimation performance using different parameter sets.At first, the correlation of biomass with the derived polarimetricand PolInSAR radar parameters is studied. Then, the perfor-mance of multiple LR for biomass estimation is evaluated usingdifferent sets of parameters and cross-validation. Finally, theperformance of more complex non-linear estimation methodsis reported. All experiments are performed at stand level.

The radar data consist of several strips with different flightheadings, acquired by the German Aerospace Center’s (DLR)E-SAR sensor at L- and P-band. Simulating ascending anddescending passes, in every direction and for both frequencies,six tracks were flown with nominal spatial baseline spacings of6 m for L-band and 8 m for P-band (Fig. 3). For the experimentspresented in this paper, data from two strips with oppositeheadings are used, which cover 27 forest stands with in situ

measurements. The resolution is about 1.5 m × 0.9 m in slantrange and azimuth directions for L-band and 1.5 m × 1.5 m forP-band. The data are sub-sampled in the azimuth direction bya factor of 2. The radar images were multi-looked to achievepixels with about 50× 50 m2 pixel size.

Since tracks with two opposite flight directions have beenacquired, it is possible to combine the data from opposite tracksof the same frequency as independent samples because differentincidence angles, present ground topography, acquisition geom-etry, and temporal changes result in distinctive polarimetric andinterferometric characteristics. This leads to having 54 sampleforest stands covered by SAR data for further analysis (eventhough only 27 stands are considered as independent regardingthe in situ measurements).

A. Correlation Results

Table III presents the correlation coefficients betweenbiomass and some common PolSAR- and PolInSAR-derivedparameters. For the polarimetric case, the correlation is com-puted with parameters obtained from the total covariance


TABLE IIICORRELATION COEFFICIENTS (R) BETWEEN AGB AND POLARIMETRIC

INDICATORS FROM TOTAL (C), GROUND (Cg), AND VOLUME (Cv)COVARIANCE MATRICES AT STAND LEVEL

matrix and the ground and volume covariance matrices, asestimated from PolInSAR data. Finally, the correlation is cal-culated between AGB and PolInSAR estimated forest heightand ground–volume ratio.

The results show significant differences between L- andP-band frequencies. At L-band, the common lexicographicbackscatter coefficients provide reasonable correlation due tohigh sensitivity to the tree and canopy structure. At P-band,the signal is largely dominated by the contributions from theground in the form of surface and double-bounce scattering.The P-band backscatter correlations are poor, probably due tolow density of forest biomass, resulting in higher dependenceon ground topography and local incidence angle. In both cases,the best total backscatter correlation is found at the secondPauli-basis polarization HH−V V (0.64 for L-band and 0.43for P-band) primarily due to the needle-leaf forest types withlow biomass and low radar attenuation and strong double-bounce between the ground and the trunk and branches. Notethat, in this analysis, we have not corrected the radar backscattermeasurements for topography and incidence angle effects.

At L-band, the estimated forest height correlates best withAGB. At P-band, the forest height estimation was less suc-cessful for two reasons, causing less correlation of the es-timated height with biomass. First, the ground contributionis dominant at P-band, which is expected for boreal forests,causing relatively small contribution from the forest canopyto the PolInSAR signal. Second, the acquired interferometricbaselines were relatively small, which provided reduced heightsensitivity of InSAR coherence. The ground–volume ratio hasa negative correlation with AGB, particularly at P-band, indi-cating the reduction of canopy backscattering with decreasingbiomass levels.

On the other hand, larger trees on flat terrain cause the groundcontribution to be dominated by the ground–trunk interactions,which, at P-band, provides a strong correlation of biomass withthe scattering mechanism indicator parameters α and |δ| (0.75and 0.76, respectively) for the given range of AGB. α is a well-known scattering mechanism indicator that can be obtainedfrom the eigenvectors of the polarimetric covariance matrix C

in the Pauli basis [28]. |δ| provides the strongest correlationwith AGB at P-band and is given by [20]

|δ| =√

〈|Shh − Svv|2〉+ 4 〈|Shv|2〉〈|Shh + Svv|2〉

. (11)

In case of polarimetrically deterministic targets, there is a directrelationship of |δ| to Cloude’s α angle and Freeman’s shapeparameter ρ [28], [30], [31]: |δ| = tanα = 2(1− ρ)/(1 + ρ).

After the separation of ground and volume contributions, onecan observe improved backscatter correlation at L-band for vol-ume and at P-band for ground components. This can probablybe explained by considering the ground–volume separation asan operation to purify the most important scattering layer ata given frequency. At L-band, this is related to the volumecomponent capturing the canopy structure with indirect relationto total biomass, while at P-band, this is due to the groundcomponent relating the importance of ground–trunk interactionrelative to the canopy volume contribution and, hence, thesensitivity to stem biomass as the largest component of the totalbiomass.

However, most of the considered indicators are correlatedwith each other as well since they are derived from a fewobservables. For example, there is usually a high correlationbetween different backscatter values at stand level or betweenthe scattering mechanism indicators and the co-polarizationcorrelation. These correlations are often stronger for L-bandthan P-band in boreal needle-leaf forests as discussed earlier.

B. Linear Regression

In order to evaluate the performance of multiple LR, wedeveloped several sets of radar data ζ with increasing number ofpolarimetric indicators. The data are grouped based on increas-ing number of polarimetric parameters (from ζ = {HV } to ζ ={HH + V V,HH−V V,HV, α}) on one hand and the increas-ing complexity of PolInSAR-derived parameters and covari-ance matrices on the other hand (Table IV). As shown in the firstrow of Table IV, the polarimetric parameters are first estimatedonly for the total covariance matrix. In the second series of tests,the regression parameter set is extended by inverted structureparameters hv and μ. In the final two test series, the polarimetricparameters from the ground and volume covariance matricesare added as well. Given this configuration, the number ofparameters used for AGB regression is between 1 and 14.

Tables IV and V present the root mean square error (rmse)and the correlation coefficient (R) of biomass estimation formultiple LR at L- and P-band. In every cell, there are twovalues: the first value represents the regression evaluation usingthe entire data set, and the second value represents the cross-validated regression evaluation using leave-two-out approach.In the leave-two-out case, for every two samples from the sameforest stand, the regression function is estimated using all othersamples except for these two, which are then used for testing.This provides reasonable accuracy assessments of the overallperformance of the forest AGB estimation.

Using only a single backscatter value (HV ) with cross-validation, the biomass rmse at L- and P-band is 36.2 and


TABLE IVLR: BIOMASS ESTIMATION RMSE IN TONS/HA (USING TRAINING DATA/USING LEAVE-TWO-OUT APPROACH) FOR L- AND P-BAND, BASED ON

DIFFERENT POLARIMETRIC PARAMETER SETS ζ, APPLIED TO TOTAL (C), GROUND (Cg), VOLUME (Cv) COVARIANCE MATRICES,TOGETHER WITH ESTIMATES OF FOREST HEIGHT hv AND GROUND–VOLUME RATIO μ

TABLE VLR: CORRELATION COEFFICIENTS (R) OF BIOMASS REGRESSION (USING TRAINING DATA/USING LEAVE-TWO-OUT APPROACH) FOR L- AND

P-BAND, BASED ON DIFFERENT POLARIMETRIC PARAMETER SETS ζ, APPLIED TO TOTAL (C), GROUND (Cg), VOLUME (Cv) COVARIANCE MATRICES,TOGETHER WITH ESTIMATES OF FOREST HEIGHT hv AND GROUND–VOLUME RATIO μ

Fig. 4. Scatter plots for scattering mechanism indicators (α and |δ|) regression to AGB (from entire covariance matrices C).

40.7 tons/ha, respectively. If using more polarimetric infor-mation from C, the rmse value stays higher than 28 tons/haat both frequencies. With the addition of forest height andground–volume ratio information, one can observe an improve-ment in AGB estimation. At L-band, the rmse improves up to21.3 tons/ha, and at P-band, it improves up to 27.8 tons/ha.With increasing number of parameters, one can observe thetendency to overfit the data, which is responsible for the differ-ence between the rmse and R obtained with and without cross-validation. Including in addition the polarimetric parametersfrom ground and volume covariance matrices Cg and Cv

improves the rmse to 22.7 tons/ha at P-band. For parameter setswith highest cross-validated performance at both frequencies(HH + VV, HH − VV, and HV for C and Cg together withhv and μ at L-band; HH–VV and HV for C, Cg , and Cv

together with hv and μ at P-band), Fig. 4 shows the scatter

plots of SAR estimated versus ground estimated AGB. Theseparameter sets should represent a sample of possible PolSARand PolInSAR parameter combinations. Using other param-eters will modify the biomass estimation accuracy, but thegeneral performance improvement with increasing the numberof polarimetric and model-based PolInSAR parameters will besimilar.

Overall, using multiple LR on the given data set, the in-clusion of structure information in the form of height andground–volume characteristics improved the rmse of AGB esti-mation by 17%–25% at L-band and 5%–27% at P-band. Usingparameters from the estimated ground and volume covariancematrices improved the rmse up to 27% and 43% at L- andP-band, respectively. The improvement of rmse by using morepolarimetric parameters (instead of only HV ) was up to 22%at L-band and 28% at P-band. However, these results may be


TABLE VISVM: BIOMASS ESTIMATION RMSE IN TONS/HA (USING TRAINING DATA/USING LEAVE-TWO-OUT APPROACH) FOR L- AND P-BAND, BASED ON


TABLE VIIRF: BIOMASS ESTIMATION RMSE IN TONS/HA (USING TRAINING DATA/USING LEAVE-TWO-OUT APPROACH) FOR L- AND P-BAND, BASED ON


slightly different if other combination of parameters are used inthe analysis.

C. SVM and RF

In the attempt to improve the AGB estimation with respect toLR, two other non-parametric methods have been considered:SVM and RF. In general, non-parametric methods performbetter when applied to the training data than LR because of thepotential to fit the data better to the model and the errors or vari-ations that may exist in dependent and independent variables.

The results of biomass estimation for the two non-parametricmethods in terms of rmse are presented in Tables VIand VII. As expected, rmse of training data is improved signif-icantly, up to 9.8 tons/ha. Note the difference between trainingrmse and testing rmse, which indicates overfitting of the datain some instances, going up to 44 tons/ha for RF. When usingmore parameters than reported in this paper, this trend has beenobserved to continue to decrease the training data rmse and toincrease the test data rmse. Although none of these methodsperformed better than LR, some of the cross-validated resultscame close to LR results (19.7 and 24.5 tons/ha at L- andP-band, respectively, for SVM and 24.3 tons/ha and23.0 tons/ha at L- and P-band, respectively, for RF).

Using many more samples and reducing the number ofparameters might compensate for the overfitting. However, usu-ally, the number of in situ AGB stands in a local environment islimited, requiring robust and noise-tolerant methods.

D. AGB Prediction and Mapping

Based on the regression of AGB using the different meth-ods, biomass values for the entire test site can be predicted.

As an example, Fig. 6 shows the predicted AGB maps forthe L-band ascending image from Fig. 3 using the parame-ter combination ζ(C), ζ(Cg), hv , and μ with ζ = {HH +V V,HH−V V,HV, α} (ten parameters). For LR, SVM, andRF, the training data rmse of biomass is 17.4, 17.2, and10.3 tons/ha, respectively. The cross-validated rmse is 22, 21.5,and 24.8 tons/ha. In the predicted AGB maps, regions withoutvegetation have been masked out. Visually, the LR predictedAGB map provides more contrast, while the RF AGB map ismore homogeneous over the forested areas.

As can be seen in the histograms of the predicted AGB values(Fig. 7), the distributions of AGB for the different methodsare quite different, despite using the same input data sets, andhaving comparably similar cross-validation rmse with biomass.In particular, LR often predicts negative biomass values dueto linear extrapolation of very low backscatter and heightvalues. This shows that a single LR relation is insufficientto characterize biomass over the entire range and suggests tomodify the biomass estimation methodology to use several LRparameterizations for different biomass ranges.

SVM and RF have more limited ranges of predicted AGB.Although some of the SVM biomass values are still negative,it is only a small portion. However, only LR distribution fol-lows approximately the Gaussian distribution. The other twoapproaches provide more artificial distributions. In particular,the RF histogram is characterized by concentration of predictedAGB at about a few values. These values probably correspondto the output of a few most likely RF decision trees and nodes,which introduces bias in the result. The mean predicted AGBvalues for LR, SVM, and RF are 59.6, 69.3, and 108 tons/ha,respectively. Examining the differences between AGB values atpixel level shows that the means are closest for LR and SVM,while the standard deviation is closest for SVM and RF.


Fig. 5. Scatter plots for multiple LR of AGB for the training and leave-two-out cross-validated data at (a) L-band and (b) P-band. At L-band, the parametercombination consists of HH+VV, HH–VV, and HV computed for C and Cg together with hv and μ. At P-band, only HH–VV and HV are computed for C, Cg ,and Cv together with hv and μ.

Fig. 6. Maps of predicted AGB from L-band data using (a) LR, (b) SVM, and (c) RF. The color is scaled from −50 to 250 tons/ha. Used parameter set for AGBprediction: ζ(C), ζ(Cg), hv , and μ with ζ = {HH + V V,HH−V V,HV, α} (ten parameters).


Fig. 7. Histograms of predicted L-band AGB for (a) LR, (b) SVM, and (c) RF. Used parameter set for AGB prediction: ζ(C), ζ(Cg), hv , and μ with ζ ={HH + V V,HH−V V,HV, α} (ten parameters). Area per sample is 0.25 ha.

The predicted AGB histograms in Fig. 7 can be comparedwith in situ AGB in Fig. 2. It is important to consider theissue of scale. AGB at forest stands is measured at area scalesbetween 2 and 27 ha, and the circular plots have an area of0.03 ha, while the biomass is regressed using 0.25 ha sam-ples. Since forest dynamics change at different scales, it isimportant to use similar scales for the entire AGB estimationprocess: training, testing, and mapping. However, this may notbe possible in all cases. At the small circular plot scale, theestimation from radar data would introduce errors in the ob-servation parameters, related to insufficient averaging of radardata, geolocation error, and geometry projection. These errorsare reduced using larger areas at the cost of resolution.

In conclusion, one can observe that none of the histogramsseems to be able to represent the test site AGB realisticallyeither due to negative biomass values or due to unrealisticdistributions. Again, a larger number of in situ measurementsamples would constrain the estimation better. An alternativeapproach to try would be to apply estimation methods after arough segmentation of the data into topography and biomass-level specific values. For instance, for low biomass levels,it seems reasonable to use a different LR function than thatfor high biomass levels. Lastly, the issue of scale needs to beaddressed in a future study. All of these methods have beentrained on data based on 2–27 ha forest stands but applied to0.25 ha pixels. This was a compromise between reducing thetraining/estimation error and achieving higher resolution.

V. SUMMARY AND CONCLUSION

In this paper, we have assessed the performance of AGBestimation from model-based PolInSAR data at L- and P-band.The estimated vertical structure, encompassing forest heightand ground–volume ratio, and ground and volume polarimetricscattering characteristics have been shown to enhance biomassestimation. We have analyzed the relationship of biomass to thein situ measured forest structure parameters to identify mainbiomass constituents, to individual PolSAR and PolInSARparameters to find the most correlated biomass indicators, andto sets of parameters evaluating different estimation methods.These methods include regression LR, SVM, and RF regres-sion. The estimation principle is to automatically decomposePolInSAR data into ground and volume contributions, estimat-ing the vertical structure, and to use a set of obtained parametersfor biomass estimation.

The methodology and results are specific for the northernboreal forest and the given PolInSAR data set. The test siteconsists of medium-height forest with biomass levels of upto 200 tons/ha (at hectare-level resolution and above). On thestand level, AGB correlates best with the forest height derivedfrom L-band PolInSAR data. At P-band, AGB correlates bestwith the scattering mechanism indicators. P-band polarimetryseems to be promising for biomass estimation since it is moresensitive to tree trunks which contain the largest parts of AGB,and the change of scattering mechanism type is revealing aboutthe presence of trees with higher biomass. The polarimetricsignal at L-band is dominated by the canopy, and the bestcorrelation with AGB (next to estimated forest height) comesfrom backscatter intensities and, in particular, from the sec-ond Pauli component HH–VV, related to ground–trunk andground–branches scattering. Using forest height and groundand volume characteristics in a multiple LR improved AGBestimation as expected, decreasing biomass rmse by 22%–27%at L-band and 11%–43% at P-band. Trying to use more so-phisticated estimation approaches than LR did not succeed inimproving the cross-validated results because these methods(SVM and RF) partly overfitted the data due to the noisy natureof the radar observables and insufficient number of trainingsamples. However, SVM and RF provided biomass predictionsover the entire test site with more reasonable biomass ranges.

The strong ground contribution and the lower height sensi-tivity due to small InSAR baselines at P-band have limited thepotential of PolInSAR ground–volume separation and heightestimation. However, the evaluation of the presented methodol-ogy in forests with higher biomass levels is, therefore, of majorinterest. Furthermore, this methodology needs to be evaluatedin other forest biomass to assess whether the conclusion drawnin this research with regard to polarimetric interferometricindicators can be extended to other forest types.

A strong limiting factor was the incidence angle and topog-raphy dependence of polarimetry and backscatter intensity. It isexpected that developing and implementing robust topographyand incidence angle compensation would enhance biomassestimation. The analysis of mapped AGB distributions suggeststhat using a more adaptive parametric estimation method couldfurther improve biomass estimation.

Overall, the combination of polarimetry with interferometryprovides the potential for significant improvement of biomassestimation. While in the end the performances at L- andP-band were similar, the internal relationships are different.


For the given boreal forest test site, L-band intensities providesensitivity to biomass and good means for height estimationfrom interferometry. At the same biomass levels, P-band dataare more ground dominated, and the best sensitivity to AGBis given through polarimetric scattering mechanism type indi-cators, which indicate the relative amount of double-bouncescattering with respect to volume and surface scattering.

ACKNOWLEDGMENT

The authors would like to thank the Swedish University ofAgricultural Sciences (SLU) and the Swedish Defence Re-search Agency (FOI) for in situ and lidar data acquisition, theGerman Aerospace Agency (DLR) for radar data acquisition,Dr. M. Davidson and the European Space Agency for provid-ing the data, and Dr. C. Lardeux for the initial introductionto SVM. The authors would finally like to thank the reviewersfor their comments.

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Maxim Neumann was born in Dsheskasgan,Kazakhstan. He received the Dipl.Ing. degree (withdistinction) in computer engineering from the BerlinUniversity of Technology, Berlin, Germany, in2004 and the Ph.D. degree from the University ofRennes 1, Rennes, France, in 2009.

From 2002 to 2003, he was with the Mediaand Machines Laboratory, Washington University,St. Louis. From 2009 to 2011, he was a NASAPostdoctoral Fellow at the Jet Propulsion Laboratory(JPL), California Institute of Technology (Caltech),

Pasadena. Since October 2011, he has been a Research Scientist with the RadarScience and Engineering Section, JPL, Caltech.

Sassan S. Saatchi (S’85–M’88) received the B.S.and M.S. degrees in electrical engineering from theUniversity of Illinois, Chicago, in 1981 and 1983,respectively, and the Ph.D. degree from GeorgeWashington University, Washington, DC, in 1988.

His Ph.D. dissertation was on electrophysics andmodeling of wave propagation in natural media.From 1989 to 1991, he was a Postdoctoral Fellowwith the National Research Council and was with theLaboratory for Terrestrial Physics, NASA/GoddardSpace Flight Center, Greenbelt, MD, working on

the hydrological application of active and passive microwave remote sens-ing. Since April 1991, he has been a Scientist with the Radar Science andEngineering Section, Jet Propulsion Laboratory, California Institute of Tech-nology, Pasadena, where he is involved in developing microwave scatteringand emission models for soil and vegetated surfaces and retrieval algorithmsfor estimating biophysical parameters from spaceborne remote sensing instru-ments. He has been a Principal or Coinvestigator in several interdisciplinaryinternational projects such as FIFE, EFEDA, Magellan, Mac-Hydro, Hapex-Sahel, BOREAS, LCLUC, and LBA. He has been involved in developing andteaching courses in the use of remote sensing for environmental problems. Hispresent research activities include biomass and soil surface moisture estimationin different ecosystems, land use and land cover change, forest regenerationmonitoring over tropical rain forests, and ecological modeling of species rangedistribution and biodiversity using remote sensing. His research interests alsoinclude wave propagation in disordered/random media and EM scatteringtheory.

Lars M. H. Ulander (S’86–M’90–SM’04) receivedthe M.Sc. degree in engineering physics and thePh.D. degree in electrical and computer engi-neering from Chalmers University of Technology,Gothenburg, Sweden, in 1985 and 1991, respectively.

Since 1995, he has been with the Swedish DefenceResearch Agency (FOI), Linköping, Sweden, wherehe is the Director of Research in radar signal process-ing. He is also an Adjunct Professor in radar remotesensing with Chalmers University of Technology. Heis the author or coauthor of over 250 professional

publications, of which more than 50 are in peer-reviewed scientific journals.He is the holder of five patents. His research areas are synthetic aperture radar,electromagnetic scattering models, and remote sensing applications.

Dr. Ulander is a member of the Remote Sensing Committee at the SwedishNational Space Board.

Johan E. S. Fransson (M’02) was born inKarlshamn, Sweden, in 1967. He received the M.Sc.degree in forestry and Ph.D. degree in forestry re-mote sensing from the Swedish University of Agri-cultural Sciences (SLU), Umeå, Sweden, in 1992 and1999, respectively.

Since 1993, he has been with the Department ofForest Resource Management, SLU. In 2000 and2002, he was appointed as an Assistant Professor andan Associate Professor in forestry remote sensing,respectively. He became the Head of the Department

in 2008. His main research interest concerns analysis of SAR images forforestry applications.

Dr. Fransson received the International Space University Certificate from theRoyal Institute of Technology, Stockholm, Sweden, in 1995 and the award fromKungliga Skytteanska samfundet to a younger researcher at SLU in 2002.

assessing performance of l- and p-band polarimetric interferometric sar data in estimating boreal...

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