The Impact of Forest Density on Forest Height Inversion ... - MDPI

remote sensing Article

The Impact of Forest Density on Forest Height Inversion Modeling from Polarimetric InSAR Data Changcheng Wang *, Lei Wang, Haiqiang Fu, Qinghua Xie and Jianjun Zhu School of Geosciences and Info-Physics, Central South University, Changsha 410083, China; [email protected] (L.W.); [email protected] (H.F.); [email protected] (Q.X.); [email protected] (J.Z.) * Correspondence: [email protected]; Tel.: +86-731-8883-6931 Academic Editors: Sangram Ganguly, Compton Tucker, Nicolas Baghdadi and Prasad S. Thenkabail Received: 14 December 2015; Accepted: 21 March 2016; Published: 29 March 2016

Abstract: Forest height is of great significance in analyzing the carbon cycle on a global or a local scale and in reconstructing the accurate forest underlying terrain. Major algorithms for estimating forest height, such as the three-stage inversion process, are depending on the random-volume-over-ground (RVoG) model. However, the RVoG model is characterized by a lot of parameters, which influence its applicability in forest height retrieval. Forest density, as an important biophysical parameter, is one of those main influencing factors. However, its influence to the RVoG model has been ignored in relating researches. For this paper, we study the applicability of the RVoG model in forest height retrieval with different forest densities, using the simulated and real Polarimetric Interferometric SAR data. P-band ESAR datasets of the European Space Agency (ESA) BioSAR 2008 campaign were selected for experiments. The test site was located in Krycklan River catchment in Northern Sweden. The experimental results show that the forest density clearly affects the inversion accuracy of forest height and ground phase. For the four selected forest stands, with the density increasing from 633 to 1827 stems/Ha, the RMSEs of inversion decrease from 4.6 m to 3.1 m. The RVoG model is not quite applicable for forest height retrieval especially in sparsely vegetated areas. We conclude that the forest stand density is positively related to the estimation accuracy of the ground phase, but negatively correlates to the ground-to-volume scattering ratio. Keywords: RVoG model; three-stage inversion process; forest stand density; ground phase; ground-to-volume scattering ratio

1. Introduction Forest height, as one part of the vertical structure information, is an important element to the quantitative analysis of the carbon cycle on a global or local scale. It is also helpful to reconstruct the accurate forest underlying terrain from the digital surface model (DSM) [1]. Originated from SAR technology, Polarimetric SAR interferometry (PolInSAR), is an all-time, all-weather, and strongly penetrative means of forest height obtaining. In addition, by combining polarimetric and interference information, PolInSAR is not only sensitive to the height and motion of scatterers, but also to structure, direction, texture, and dielectric constant of scatterers [2–5]. Compared with single channel Interferometric SAR (InSAR), we can separate volume scattering from surface scattering by using information from different coherence channels. This is one of the main advantages of PolInSAR and the key to estimate forest height. To retrieve forest height from the PolInSAR data, it is necessary to establish a scattering model that can combine forest biophysical parameters with the PolInSAR data. In 1996, the random-volume-over-ground (RVoG) model was firstly utilized to relate the forest biophysical parameters to the InSAR data [6–8]. Now it has become a widely used vegetation scattering model to retrieve forest height from PolInSAR data [9–17]. The RVoG model depicts the scattering process of forest scene as a random volume over ground [9]. In the past few years, this model has Remote Sens. 2016, 8, 291; doi:10.3390/rs8040291

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been developed to improve the accuracy of forest height inversion, such as the RVoG + TD model considering temporal decorrelation [18–22], the RVoG+CFF model [23] considering canopy-fill-factor, and the S-RVoG model [24,25] considering the slope of topography. The RVoG model is characterized by having many independent physical parameters including parameters of SAR system and factors of the forest. Any change of these parameters will influence the results of forest height retrieval, which reflect the applicability of the RVoG model in forest height inversion [9]. Forest density, as a biophysical parameter of vegetation, is important to the RVoG model and forest height retrieval. Many researchers point out that the interferometric phase and coherence are sensitive to the vegetation height and density variations, which makes a challenge for forest parameters inversion [3,6,8,9]. Lavalle et al. [26] investigate the correlation of interferometric coherence with forest height, canopy density, and terrain slope. Garestier et al. [14] demonstrated that the performance of a pine forest height inversion with X-band HH and HV data was more dependent on the forest density than that at lower frequencies. However, the influence of forest density to the RVoG model on forest height inversion has not been studied systematically in current research. Here, we studied the impact of the forest density to the forest height inversion with the RVoG model from PolInSAR data. At present, the six-dimension nonlinear iterative algorithm [9] and the three-stage inversion process [27] have been proposed to invert the RVoG model. The six-dimension nonlinear iterative algorithm brings heavy computation burden and difficulty in obtaining the initial parameters of forest height retrieval. Thus, the three-stage inversion process became the main method to retrieve forest height because of its steady result, strong applicability, and short calculation time. 2. The Random-Volume-Over-Ground (RVoG) Model and Three-Stage Height Inversion Method The RVoG model simplifies the vegetation structure to be a two-layer structure including the canopy layer and ground layer. The canopy layer is considered as an isotropic medium, which means the attenuation process of electromagnetic wave can be expressed by the mean wave extinction that is constant. Without temporal de-correlation and signal-to-noise ratio (SNR) de-correlation, the complex interferometric coherence based on the RVoG model can be expressed as: γpωq “ e jφ0

γv ` µpωq 1 ` µpωq

(1)

where the ground-to-volume scattering ratio µpωq is related to ω, a three-component unitary complex vector representing some kind of polarization state, φ0 is the ground phase, and the volume coherence γv based on RV model is a function of forest height hv and extinction σ, defined as hşv

γv “

2σz e cosθ e jkz z dz

0 hşv

2σz cosθ e dz

(2)

0

σ represents the mean wave extinction in the medium, θ is the incidence angle, and k z is the vertical wavenumber of the interferometer [9,27]. In the RVoG model, the vegetation structure function is to obey exponential distribution, defined as Equation (3): 2σz f pzq “ e cosθ

(3)

The three-stage height inversion method contains the following three key steps [27]: Firstly, a total least square line fitting of the complex coherence with different polarizations in a complex plane: The optional complex coherence could be the linear polarizations (HH, HV, VH, and VV) or the Pauli-basis polarizations (HH+VV and HH´VV). In some cases, the coherence sets


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of the linear polarizations gather together. It is difficult to get a good fitted line. Therefore, some optimized coherence channels are good choices for improving the linearity of the coherence sets [28,29]. For example, the phase diversity (PD) coherence optimization can get two coherence values with maximum (PDH) and minimum (PDL) phases [29]. Secondly, the ground phase φ0 estimation: There are two interactions between the fitted line and the unit circle of the complex plane. The ground phase is determined by the one closer to the polarization with more ground contributions, such as HH-VV or PDL. Finally, the forest height estimation: It is determined by the coherence of volume scattering with highest phase center, such as HV or PDH. Then, a lookup table (LUT) is calculated, which contains the values of volume coherence with all possible mean extinction coefficients and forest heights. By minimizing the difference between the LUT and the volume coherence, we can get the solution of the mean extinction coefficient and forest height. The forest height can be calculated by using this solution and the estimated ground phase. 3. The Simulated Datasets and Real P-Band E-SAR Data 3.1. The Simulated Datasets A set of forest stands was simulated with PolSARpro simulator provided by ESA for free [30]. The simulator could provide polarimetric interferometric SAR datasets with a high level of realism. The main parameters of the simulated data are shown in Table 1. In this experiment, the tree number per hectare was considered the forest stand density, which ranged from 100 stems/Ha to 900 stems/Ha. For the different forest stands simulated with PolSARpro, the density is mutative and the rest main parameters were constant. For analyzing the impact of forest density under different height, three groups of datasets with a reference height of 10 m, 14 m, and 18 m were simulated. Table 1. Main parameters of the simulated data of forest with PolSARpro Forest Simulator. Three datasets with reference height of 10 m, 14 m, and 18 m were simulated. Platform Altitude

3000 m

Horizontal Baseline Vertical Baseline Incidence Angle Center Frequency Tree Species Reference Height

10 m 1m 45˝ 1.5 GHz Pine 10 m, 14 m, and 18 m

3.2. The Real P-Band ESAR Data We also selected two real P-band E-SAR data acquired in the framework of the ESA BioSAR 2008 campaign for experiments [31]. The aim of this campaign was to investigate topographic effects on boreal forest biomass retrieval by PolInSAR data [32,33]. The main radar data sources of the BioSAR 2008 campaign were acquired by DLR’s airborne E-SAR system. The test site mapped by E-SAR is located in Krycklan River catchment of the Vindeln municipality in Northern Sweden (see Figure 1), where the elevation changes from 150 m to 400 m. The test site was dominated with mixed coniferous forest, but studded with a small amount of broad-leaved forest. In addition, forest height measured by Light Detection and Ranging (LiDAR) was available at the test site, which could serve as a reference. Many researchers have used these datasets for the study of biomass estimation, forest height inversion, and forest vertical structure retrieval [34–36]. The selected two P-band E-SAR data were acquired on 14 October 2008 with a time interval of about 33 min. The spatial baseline was about 24 m.

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Figure1.1.The Thetest testsite siteselected selectedfrom fromthe theBIOSAR BIOSAR2008 2008campaign campaign(From (FromGoogle GoogleEarth). Earth).The Thestar starin inthe the Figure bordermap mapindicates indicatesthe thelocation locationof ofstudy studyarea. area.The Thered redrectangle rectangleindicates indicatesthe thecovering coveringarea areaof ofthe the border E-SARdata. data. E-SAR

4.4. Experimental Experimental Results Results and and Analysis Analysis 4.1. 4.1.Results Resultsand andAnalysis Analysisofofthe theSimulated SimulatedDatasets Datasets After height inversion method to the simulated datasets, we acquire the Afterapplying applyingthe thethree-stage three-stage height inversion method to the simulated datasets, we acquire root squaresquare error (RMSE) of inversed height for different forest stand density a reference the mean root mean error (RMSE) of inversed height for different forest standwith density with a height of 10 m, 14ofm, 18m, m.and As shown inshown Figurein 2, Figure all the 2, RMSEs the three groups results reference height 10and m, 14 18 m. As all theof RMSEs of the threeof groups of indicate obvious trend with the increasing forest density. forest The decreasing indicates results an indicate andecreasing obvious decreasing trend with the increasing density. RMSE The decreasing the increasing accuracy of forest height inversion. Forheight the sparse forestsFor (e.g., thesparse stand forests density(e.g., smaller RMSE indicates the increasing accuracy of forest inversion. the the than stems/Ha), thethan height errors larger. The mainbecome reason islarger. that the sparse stand400 density smaller 400inversion stems/Ha), the become height inversion errors The main vegetation cannot assumed as a random volume. When as forest stand density increases to a certain reason is that thebesparse vegetation cannot be assumed a random volume. When forest stand densityitincreases to a the certain it is no longer the main the accuracy of there forest degree, is no longer maindegree, factor affecting the accuracy offactor forestaffecting stand height. However, stand there are stillerrors about because 2 m of underestimated errors because theisphase center of are stillheight. about 2However, m of underestimated the phase center of HV channel located in the HV channel located in top the canopy rather than at the top of the forest [14]. canopy ratheristhan at the of the forest [14].

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Figure 2.2. The The RMSE RMSE of of inversed inversed height height for for different different forest forest stand stand density density from from the the simulated simulated data data Figure Figure 2. The RMSE of inversed height for different forest stand density from the simulated data with withreference referenceheight heightof of10 10m m(line (linewith withplus), plus),14 14m m(line (linewith withcircle), circle),and and18 18m m(line (linewith withasterisk). asterisk). with reference height of 10 m (line with plus), 14 m (line with circle), and 18 m (line with asterisk).

In addition, addition, the the ground-to-volume ground-to-volume scattering scattering ratio ratio isis another another important important factor factor affecting affecting the the In In addition, the ground-to-volume scattering ratio is another important factor affecting the application of the RVoG model, which can be defined as Equation (4): application of the RVoG model, which can be defined as Equation (4): application of the RVoG model, which can be defined as Equation (4):

ωHHTTGroundωω ω Ground μμ((ωω))==ωωHHHTTGround ω ω µpωq “ ω Canopyω T ω H T Canopy ω

(4) (4) (4)

Canopy

where TGround and and TTCanopy are are the the echo echo signal signal intensity intensity of of ground ground and and vegetation vegetation layer, layer, where Ground and TCanopy Canopy where TT are the echo signal intensity of ground and vegetation layer, respectively [27]. Ground respectively [27]. Therefore, we needed to study the relationship between forest density and respectively Therefore, we relationship needed to between study the relationship forest density and Therefore, we[27]. needed to study the forest density andbetween ground-to-volume scattering ground-to-volume scattering ratio. Based on the simulated data, we can estimate the ground-to-volume scatteringdata, ratio. Based on the simulated data, scattering we can ratio estimate ratio. Based on the simulated we can estimate the ground-to-volume of the the HV ground-to-volume scattering ratio of the HV coherence channel for different densities by using the ground-to-volume scattering of theby HV coherence channel fornonlinear differentiterative densitiesalgorithm. by using The the coherence channel for differentratio densities using the six-dimension six-dimension nonlinear iterative algorithm. TheHV HV(1) coherence channel issubstituted substituted intoEquation Equation six-dimension algorithm. The coherence into HV coherence nonlinear channel isiterative substituted into Equation for forestchannel height is retrieval. By comparing the (1) for forest height retrieval. By comparing the average ground-to-volume scattering ratio is for (1) for forest height retrieval. By comparing the average scattering for average ground-to-volume scattering ratio for different forestground-to-volume stand density, we found that ratio there a different forest stand density, we found that there is a negative correlation between forest density different forest standbetween density,forest we found that there is a negative correlation between forest density negative correlation density and ground-to-volume scattering ratio, which is shown in andground-to-volume ground-to-volume scatteringratio, ratio,which whichisisshown shownin inFigure Figure3. 3. and scattering Figure 3.

Figure3. 3.Correlation ground-to-volumescattering scatteringratio fromthe thesimulated simulated Figure 3. Correlation between between the the ground-to-volume ground-to-volume scattering ratio and and density density from from the simulated Figure data with reference height of 10 m. with reference height of 10 m. data with reference height of 10 m.

For sparse sparse vegetation, vegetation, the the electromagnetic electromagnetic wave wave easily easily penetrated penetrated the the vegetation vegetation layer layer and and For sparse vegetation, the electromagnetic wave easily penetrated the vegetation layer and For reached the theground. ground.The Theecho echo signal intensity of ground ground was stronger than that ofvegetation the vegetation vegetation reached signal intensity of of ground waswas stronger thanthan that that of the layer. reached ground. The echo signal intensity stronger of the μ ( ω ) layer. In this case, the corresponding ground-to-volume scattering ratio was larger, although In this case, the corresponding ground-to-volume scattering ratio µpωq was larger, although smaller for layer. In this case, the corresponding ground-to-volume scattering ratio μ (ω ) was larger, although dense vegetation. to simplify theto algorithm thealgorithm traditionalof three-stage inversion process, smaller for dense denseHowever, vegetation. However, to simplifyofthe the algorithm of the traditional traditional three-stage smaller for vegetation. However, simplify the three-stage inversion process, it was assumed that the ground-to-volume scattering ratio is null for the the inversion process, it was assumed that the ground-to-volume scattering ratio is null for


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itintersection was assumed thatinside the ground-to-volume scattering ratio is null for the intersection point (1) inside point the unit circle of interferometric coherence. Thus, Equation canthe be unit circle of simplified as:interferometric coherence. Thus, Equation (1) can be simplified as: jφ0

γ (ω )“=eejφ0 γγvv γpωq

(5) (5)

In fact, fact,to tosatisfy satisfythe theassumption assumptionabove, above,the theminimum minimum ground-to-volume scattering ratio related In ground-to-volume scattering ratio related to to coherence channel should be small—the smaller, the better. Generally, the eligible coherence coherence channel should be small—the smaller, the better. Generally, the eligible coherence channels channels are HV, PDH, etc. Assuming other are the constant, the ground-to-volume are HV, PDH, etc. Assuming other factors arefactors constant, ground-to-volume scattering scattering ratio will ratio will decrease with the increasing forest stand density (see Figure 3), and vice versa. This to is decrease with the increasing forest stand density (see Figure 3), and vice versa. This is beneficial beneficial to forest height estimation. The estimation accuracy of forest height, however, was forest height estimation. The estimation accuracy of forest height, however, was sensitive to the change sensitive to the change of ground-to-volume scatteringground-to-volume ratio, and the minimum ground-to-volume of ground-to-volume scattering ratio, and the minimum scattering ratio needed to scattering to be less than −10 dB to secure the height accuracy of around 10% [27]. be less thanratio ´10needed dB to secure the height accuracy of around 10% [27]. Inshort, short,with with different forest densities, ground-to-volume scattering has aninfluence obvious In different forest densities, ground-to-volume scattering ratio hasratio an obvious influence to the estimation of forest height. vegetation In sparse vegetation areas, the application of to the estimation accuracy ofaccuracy forest height. In sparse areas, the application of the RVoG the RVoG model is limited in forest height retrieval. model is limited in forest height retrieval. 4.2. Results Results of of P-Band P-Band E-SAR E-SAR Datasets Datasets 4.2. Due to to the the good good penetration penetration of of P-band, P-band, the the coherences coherences of of all all the the linear linear polarimetric polarimetric channels channels Due contain a certain degree of the contributions from canopy, trunk, and ground. In consequence, the contain a certain degree of the contributions from canopy, trunk, and ground. In consequence, the coherenceset setisischaracterized characterized high ellipticity, which makes it difficult to measure the ground coherence byby high ellipticity, which makes it difficult to measure the ground phase phase with the total least square (TLS) linear fit [25]. Furthermore, it seems impossible to obtain a with the total least square (TLS) linear fit [25]. Furthermore, it seems impossible to obtain a polarization polarization without ground at contributions at makes P-band, which it the hard to volume estimatecoherence the pure without ground contributions P-band, which it hard to makes estimate pure volume coherence accurately. In order to improve the accuracy of forest height retrieval, phase accurately. In order to improve the accuracy of forest height retrieval, phase diversity (PD) coherence diversity (PD) coherence optimization was introduced in the experiment using real data [29]. The optimization was introduced in the experiment using real data [29]. The result of forest height retrieval result forest height retrieval for the entire 4. test site can be found in Figure 4. for the of entire test site can be found in Figure

Figure Figure 4. 4. Forest Forest height height map map of of the the test test site site and and the the location location of of the the selected selected forest forest stands. stands. The The numbers numbers in in the the red redpolygons polygonsindicate indicatethe thesample sampleforest foreststands standswith withfield fieldinvestigations. investigations.

In the the experiment experiment using using real real data, we also took the tree number per hectare as the In the forest forest density. density. In the thesimulated simulatedexperiment, experiment, type height of different stands were set as constants, In thethe type andand height of different forestforest stands were set as constants, which which ensured thedensity forest density can be calculated accurately tree number per hectare. ensured that thethat forest can be calculated accurately by treeby number per hectare. When When using using realhowever, data, however, different forest stands have different heights, and a single may real data, different forest stands have different heights, and a single forest forest stand stand may have have different forest types. Thus, we could not acquire the forest density by calculating the number different forest types. Thus, we could not acquire the forest density by calculating the number of trees of trees per unit.per unit. In order order to to guarantee guarantee the the reliability reliability of of the the experimental experimental results, results, we we selected selected appropriate appropriate forest forest In stands (forest stand numbers 3689, 4115, 18147, and 4115 shown in Figure 4), which were pure stands (forest stand numbers 3689, 4115, 18147, 4115 shown in Figure 4), which were pure coniferousforest, forest,and andwith withthe theheights heightsranging rangingfrom from Comparing height estimated coniferous 1717 mm to to 2121 m.m. Comparing thethe height estimated in in the experiment with result from LiDAR, could obtain accuracy of forest stand height by the experiment with thethe result from LiDAR, we we could obtain the the accuracy of forest stand height by the the three-stage inversion method. Table 2 lists the result. three-stage inversion method. Table 2 lists the result.


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Table 2. Assessment of forest stand height inversion errors from the three-stage inversion method.

Comparison of the height of all four forest stands (see Table 2) shows their RMSEs ranging from 3.1 Forest m to 4.6 m. Further, the higher densityHeight was, from the smaller theHeight RMSEfrom would Stand Forest Stand Density the Average Average the be. This result RMSE (m) verifies the experimental conclusion from theLiDAR(m) simulated data. Three-Stage Method (m) Number (stems/Ha) 3689

633

20.71

16.39

4.56

Table forest stand height inversion 4115 2. Assessment of925 19.49 errors from the three-stage 17.69 inversion method. 3.87 36169

1498

17.17

15.17

3.76

Forest18147 Stand Forest Stand Average15.77 Height from the 1827Density Average Height 17.63 from 3.13RMSE Number (stems/Ha) LiDAR(m) Three-Stage Method (m) (m) 3689 633 20.71 16.39 4.56 Comparison of the height of all four forest19.49 stands (see Table 2) shows17.69 their RMSEs ranging3.87 from 4115 925 3.1 m36169 to 4.6 m. Further, the higher the density was, the smaller the RMSE would be. This result verifies 1498 17.17 15.17 3.76 the experimental conclusion data. 18147 1827 from the simulated 17.63 15.77 3.13

4.3. The The Ground Ground Phase Phase for for Different Different Density Density 4.3. Inside the the unit unit circle circle of Inside of the the complex complex coherence coherence plane, plane,the thecoherence coherenceloci locifor forthe theRVoG RVoGmodel modelare area is is the geometric expression forfor thethe RVoG model. TheThe coherence lineline intersects the astraight straightline, line,which which the geometric expression RVoG model. coherence intersects circle at two points. One is the coherence point related to the ground phase, which can be determined the circle at two points. One is the coherence point related to the ground phase, which can be by the certain standard. The other is aThe useless for inversion. In theory, the In coherence determined byjudgment the certain judgment standard. othersolution is a useless solution for inversion. theory, points related to different polarization states should be located on the coherence line in the complex the coherence points related to different polarization states should be located on the coherence line plane. to the error caused and temporal the coherence in the However, complex due plane. However, duebytodata theprocessing error caused by data decorrelation, processing and temporal points are actually not distributed line, but on its Thus, we must decorrelation, the coherence pointson arethe actually notscattered distributed ontwo the sides. line, but scattered on rebuild its two the coherence line by a total least squares line fit. In this way, the fitted coherence line will directly sides. Thus, we must rebuild the coherence line by a total least squares line fit. In this way, the fitted influence the of ground phase. coherence lineestimation will directly influence the estimation of ground phase. Using the the ground ground phase phase of of the the four four selected selected forest forest stands, stands, we we were were able able to to analyze analyze the the impact impact of of Using forest density to the ground phase estimation. For comparison, we converted the LiDAR DEM into the forest density to the ground phase estimation. For comparison, we converted the LiDAR DEM into reference phase using the the baseline parameters of the the reference phase using baseline parameters of platform. the platform. The ground phase estimated by the fitted coherence line and and the the reference reference phase phase obtained obtained by by The ground phase estimated by the fitted coherence line using external LiDAR DEM are shown in Figure 5a,b respectively. We could differentiate the reference using external LiDAR DEM are shown in Figure 5a,b respectively. We could differentiate the phase andphase the ground phase to analyze accuracythe of the ground for different density. reference and the ground phase the to analyze accuracy ofphase the ground phaseforest for different However, there was an error in the area where phase changes suddenly from π to ´π, as shown in forest density. However, there was an error in the area where phase changes suddenly from π to −π, as Figure 5c, greatly affecting the RMSE of the ground phase. Before comparing, therefore, we needed to shown in Figure 5c, greatly affecting the RMSE of the ground phase. Before comparing, therefore, we unwrapto the reference and phase groundand phase, respectively, and the corresponding result is shown in needed unwrap thephase reference ground phase, respectively, and the corresponding result Figure 6. is shown in Figure 6.

Figure Figure 5. Cont. Cont.



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Figure 5. 5. The The ground ground phase phase (a); (a); the the reference reference phase phase (b) (b) generated generated by by LiDAR LiDAR DEM DEM and and the the phase phase Figure profiles (c) of the black dashed lines in (a) and (b). Figure 5. The ground phase (a); the reference phase (b) generated by LiDAR DEM and the phase profiles (c) of the black dashed lines in (a) and (b). profiles (c) of the black dashed lines in (a) and (b).

Figure 6. The ground phase (a); the reference phase (b) generated by LiDAR DEM which are

Figure 6. The ground phase (a); the reference phase (b) generated by LiDAR DEM which are unwrapped; and the contrast of the profiles (c) shown as the black dashed lines in (a) and (b). unwrapped; and the contrast of the profiles (c) shown as the black dashed lines in (a) and (b). Estimation of the ground phase depends on the fitted coherence line. Thanks to the introduction

Figure 6. The ground phase (a); the reference phase (b) generated by LiDAR DEM which are of the PD coherence channels, the error caused by the judgment method has Thanks been greatly eliminated. Estimation of thethe ground phase depends onshown the fitted coherence line. the introduction unwrapped; and contrast of by thethe profiles (c) dashed linesrelated in (a)to and (b). The coherence line is limited distribution rangeasofthe theblack coherence points to polarization

of the PD coherence channels, the error caused by the judgment method has been greatly eliminated. states (the visible length of the coherence line). In the complex plane, the sparser the distribution of The coherence line is limited byphase the distribution of the coherence points to introduction polarization Estimation ofpoints, the ground depends onrange the fitted coherence line. Thanks to the coherence the more reliable the fitted coherence line. If other factors are related consistent, such as states visible length ofradar thethe coherence line). In the the judgment complex plane, thehas sparser the of baseline length, wavelength, and polarization channels, the forest density will distribution be aeliminated. main of the (the PDthe coherence channels, error caused by method been greatly factor influencing the distribution of the coherence points. coherence points, the more reliable the fitted coherence line. If other factors are consistent, such as the The coherence line is limited by the distribution range of the coherence points related to polarization As shown in Table 3, the estimation accuracy of the ground phase increases with thebeincreasing baseline length, radar wavelength, and polarization channels, the forest density will a main factor states (the visible length of the coherence line). In the complex plane, the sparser the distribution of forest stand density. The reason is that, for the low density forest stand, the electromagnetic wave influencing the distribution of the coherence points. coherence points, the more reliable the fitted coherence line. If other factors are consistent, such as easily penetrated the vegetation layer, and the phase centers of coherence channels with high As shown in Table 3, the estimationand accuracy of the ground phase with will the increasing the baseline length, radar wavelength, polarization channels, the increases forestIndensity be a main volume scattering were close to the phase centers with high surface scattering. the complex plane, forest density. The reason is that, for the low density forest stand, the electromagnetic factor stand influencing the distribution of the coherence points. the coherence points related to all five coherence channels are densely distributed within the unit wave easilyAs penetrated vegetation layer, the phase of coherence channels withthe high volume circle (see Figure 7a). In this case, and the accuracy fitted coherence had a bad geometrical structure and low shown inthe Table 3, the estimation ofcenters theline ground phase increases with increasing reliability, so the estimation accuracy of the ground phase was poor. Conversely, for the high density scattering were close The to the phase highdensity surfaceforest scattering. complex plane, the forest stand density. reason is centers that, forwith the low stand, In thethe electromagnetic wave coherence points related to all five layer, coherence arecenters denselyofdistributed the unit easily penetrated the vegetation and channels the phase coherencewithin channels with circle high (see Figure 7a). In this case, thetofitted coherence linewith had ahigh badsurface geometrical structure andcomplex low reliability, volume scattering were close the phase centers scattering. In the plane, so estimation accuracy phase was poor. Conversely, for the highwithin density thethe coherence points relatedoftothe allground five coherence channels are densely distributed theforest unit

circle (see Figure 7a). In this case, the fitted coherence line had a bad geometrical structure and low reliability, so the estimation accuracy of the ground phase was poor. Conversely, for the high density


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forest the electromagnetic wave not penetrate the vegetation layerThe easily. Thecenters phase of stand, thestand, electromagnetic wave could notcould penetrate the vegetation layer easily. phase centers of states polarization states with scattering high volume scattering were in the upper part of the Remote Sens. 2016, 8, 291 9 of 13 polarization with high volume were located in the located upper part of the vegetation layer, vegetation layer, which were far away from the phase centers of polarization states with dominant which were far away from the phase centers of polarization states with dominant surface scattering. forest stand, the electromagnetic wave could not penetrate the vegetation layer easily. The phase surface scattering. Additionally, inthe the complex plane, the coherence points were widely Additionally, complex plane, coherence were scattered widely onscattered both sides centersinofthe polarization states with high volume points scattering were located in the upper part of the of the on both sides of the coherence line, as can be seen in Figure 7b. Therefore, it was good for thethe coherence line, as can bewhich seen were in Figure 7b. from Therefore, it was good for the coherence linedominant fitting and vegetation layer, far away the phase centers of polarization states with coherence line fitting and the estimation of the ground phase. estimation of the groundAdditionally, phase. surface scattering. in the complex plane, the coherence points were scattered widely on both sides of the coherence line, as can be seen in Figure 7b. Therefore, it was good for the Table 3. Assessment ofthe theground ground phase estimation Table Assessment phase estimation errorsfor fordifferent differentdensity. density. coherence line3.fitting and the of estimation of the ground phase. errors

Forest Stand Number 3689 4115 36169 18147 Forest Stand Density (stems/Ha) 633 925 1498 1827 Stand Number 3689 Forest StandForest Density (stems/Ha) 633 925 36169 149818147 1827 RMSE (rad) 0.26 4115 0.22 0.15 0.14

Table 3. Assessment of the ground phase3689 estimation4115 errors for 36169 different density. Forest Stand Number 18147

Forest Stand Density (stems/Ha) 0.26 633 RMSE (rad) RMSE (rad) 0.26

925 0.22 0.22

1498 0.15 1827 0.14 0.15 0.14

Figure 7.Figure The 7. coherence line line fitted by by using squares linear fitting method. (a) Low The coherence fitted usingthe thetotal total least least squares fitting method. (a) Low Figure 7. The coherence line fitted by using the total least squareslinear linear fitting method. (a) Low density; (b) high density. density; (b) high density. density; (b) high density. By using the phase corresponding to the volume coherence and the ground phase, we can

ByBy using the corresponding to volume coherence andthe theground ground phase,wewe can using thephase phase corresponding to the the volume coherence and can approximately estimate the height of forest stand. For example, the height related to HHphase, coherence approximately estimate the height of forest stand. For example, the height related to HH coherence approximately estimate the height of forest stand. example, the height related to HH coherence channel can be estimated by Equation (6): channel estimatedbybyEquation Equation(6): (6): channel cancan bebe estimated arg(γ HH ) − φ0 h= (6) arg( − φφ0 k zq)´ HH argpγγHH 0 h = (6) (6) h“ kkzz forest stands can be obtained by comparing the The relative height of phase centers for different result estimated from Equation (6) with the results obtained by LiDAR (see Figure 8). The relative heightofofphase phasecenters centersfor fordifferent different forest stands thethe The relative height standscan canbe beobtained obtainedbybycomparing comparing result estimated from Equation(6) (6)with withthe theresults resultsobtained obtained by by LiDAR result estimated from Equation LiDAR (see (seeFigure Figure8). 8).

Figure 8. Relative height of phase centers for different density.

Figure8.8.Relative Relativeheight height of of phase phase centers Figure centers for fordifferent differentdensity. density.


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For the four forest stands of real data, we can make a quantitative analysis for the distribution of the coherence points by the method above. As shown in Table 4, the STD of phase centers correlates positively with the forest stand density. Furthermore, relative locations of phase centers related to different polarization states gradually become discrete. Table 4. Discrete degree of phase centers for different forest density. Forest Stand Number

3689

4115

36169

18147

Forest stand density (stems/Ha) STD

633 0.075

925 0.095

1498 0.126

1827 0.143

In [14], the authors made a qualitatively analysis of the forest height inversion performance on the sparse pine forest by using X-band HH and HV polarizations. The obtained phase center height difference between the HH and HV polarizations in the sparse area is larger than that of the dense area, which is beneficial to achieve a more accurate forest height. This is in conflict with the trend in Figure 8. The reason is that, in the case of X-band, the phase center of HV channel is always located in the canopy for both the sparse and dense area, while the phase center of HH channel gradually declines with decreasing density because of increasing ground contribution [14]. However, for the P-band data used in this paper, all polarizations had considerable contributions from the ground due to strong penetration. Moreover, with the increasing density, the phase center of HV or PDH polarizations gradually rose, which caused the phase centers of different channels to separate. Therefore, the distribution of the coherence points gradually increases in the complex plane with increasing forest stand density, which is beneficial to the coherence linear fitting and the estimation of the ground phase. According to the procedures of the traditional three-stage inversion process, we find that ground phase is one of the essential parameters of the RVoG model, and accurate ground phase can make a remarkable contribution to improve the accuracy of forest height inversion. 5. Conclusions The impact of forest density on forest height inversion with the RVoG model has been researched for this paper, which offers a beneficial reference for the study of the applicability of models from Polarimetric Interferometric SAR data and methods of forest height inversion. In this paper, forest stand height for different densities was estimated in the experiments using both simulated and real data. In the simulation experiments, the results of three groups of datasets with reference height of 10 m, 14 m, and 18 m showed that all of the RMSEs decrease with increasing forest density. For the extremely sparse forests, the vegetation layer could not be assumed as a random volume. In this case, the height inversion accuracy of the classical three-stage method was poor. Furthermore, we found a positive correlation between the forest density and the estimation accuracy of the forest stand height. According to the results of real data experiments, the applicability of the RVoG model for different forest density was specifically analyzed in two aspects, ground phase and ground-to-volume scattering ratio. The main factor affecting the estimation accuracy of ground phase is the visible length of the coherence line, which is sensitive to the change in forest stand density. In addition, the relationship between density and ground-to-volume scattering ratio is also an important factor that influences the applicability of the RVoG model. For the traditional three-stage inversion process, the ground-to-volume scattering ratio needs to be less than ´10 dB to secure a height accuracy of around 10% [27]. However, in this paper, we found a negative correlation between forest density and ground-to-volume scattering ratio; moreover, in the sparse vegetation areas, ground-to-volume scattering ratio no longer met the assumption of less than ´10 dB. In addition, it was difficult to obtain the accurate volume-only coherence in such a situation. Therefore, it is necessary to consider the ground-to-volume scattering ratio when we estimate forest height in the sparse vegetation areas. For the six-dimension nonlinear iterative algorithm, although


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the ground-to-volume scattering ratio is parameterized for all the polarizations in the forest height inversion, the ill-conditioned problem is usually caused by the small differences of ground-to-volume scattering ratio under different polarizations. In this case, it was difficult for us to obtain robust results. Therefore, the ground-to-volume scattering ratio is an essential factor for influencing the accuracy of forest height inversion. We conclude that, with the increase of forest stand density, the estimation accuracy of the ground phase increases, and the ground-to-volume scattering ratio decreases, which is helpful for the retrieval of forest stand height. At the same time, the applicability of the RVoG model is limited in sparse vegetation areas because of the influence of forest density to the ground-to-volume scattering ratio. However, in real data experiments, we only find a qualitative relationship and not a definitively quantitative relationship. The reason is that, for real forest scenes, the forest density used in this paper could not well reflect the density of the trunk, which is related to the attenuation of the electromagnetic wave, as described in [37]. More prior knowledge about forest geometrical structures is needed to study the relationship between forest density and the density of the trunks. Furthermore, the ground scattering contribution (e.g., odd scattering and double bounce scattering) is affected by the terrain slope [38]. As a result, the ground-to-volume scattering ratio is also affected by the terrain slope. Therefore, terrain slope should also be considered when we study the relationship between ground-to-volume ratio and forest density in future work. Nonetheless, this paper helps us to better understand the performance of the RVoG model over forests with different densities and provides an opportunity for us to modify the RVoG model by integrating the forest density. Acknowledgments: The work was supported by the National Natural Science Foundation of China (No. 41531068, 41371335). Additionally, this paper is supported by PA-SB ESA EO Project Campaign of “Development of methods for Forest Biophysical Parameters Inversion Using POLInSAR Data (ID. 14655).” The authors would also like to thank ESA for providing free PolSARproSim tools. Author Contributions: Changcheng Wang conceived the idear, designed the experiments, and revised the paper; Lei Wang performed the experiments and wrote the paper; Haiqiang Fu provided and analyzed the data; Qinghua Xie and Jianjun Zhu analyzed the experimental results. Conflicts of Interest: The authors declare no conflict of interest.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Fu, H.; Wang, C.; Zhu, J.; Xie, Q.; Zhao, R. Inversion of vegetation height from PolInSAR using complex least squares adjustment method. Sci. China Earth Sci. 2015, 58, 1018–1031. [CrossRef] Wu, Y.; Hong, W.; Wang, Y. Research status and edification for polarimetric SAR interferometry. J. Electron. Inf. Technol. 2007, 9, 1258–1263. Askne, J.; Dammert, P.; Ulander, L.; Smith, G. C-band repeat-pass interferometric SAR observations of the forest. IEEE Trans. Geosci. Remote Sens. 1997, 35, 25–35. [CrossRef] Askne, J.; Santoro, M.; Smith, G.; Fransson, J.E. Multitemporal repeat-pass SAR interferometry of boreal forests. IEEE Trans. Geosci. Remote Sens. 2003, 41, 1540–1550. [CrossRef] Askne, J.; Santoro, M. Multitemporal repeat pass SAR interferometry of boreal forests. IEEE Trans. Geosci. Remote Sens. 2005, 43, 1219–1228. [CrossRef] Treuhaft, R.N.; Madsen, S.N.; Moghaddam, M.; Zyl, J.J. Vegetation characteristics and underlying topography from interferometric radar. Radio Sci. 1996, 31, 1449–1485. [CrossRef] Treuhaft, R.N.; Cloude, S.R. The structure of oriented vegetation from polarimetric interferometry. IEEE Trans. Geosci. Remote Sens. 1999, 37, 2620–2624. [CrossRef] Treuhaft, R.N.; Siqueira, P.R. Vertical structure of vegetated land surfaces from interferometric and polarimetric radar. Radio Sci. 2000, 35, 141–177. [CrossRef] Papathanassiou, K.P.; Cloude, S.R. Single-baseline polarimetric SAR interferometry. IEEE Trans. Geosci. Remote Senci. 2001, 39, 2352–2362. [CrossRef] Mette, T.; Kugler, F.; Papathanassiou, K.; Hajnsek, I. Forest and the random volume over ground-nature and effect of 3 possible error types. In Proceedings of the EUSAR 2006—6th European Conference on Synthetic Aperture Radar, Dresden, Germany, 16–18 May 2006.


11. 12. 13. 14. 15. 16.

17. 18.

19.

20. 21. 22.

23.

24. 25. 26.

27. 28. 29.

30.

12 of 13

Lavalle, M.; Solimini, D.; Pottier, E.; Desnos, Y.-L. The Dependence of the PolinSAR degree of coherence on forest parameters. In Proceedings of the PolInSAR Workshop 2009, Frascati, Italy, 26–30 January 2009. Zhou, Y.; Hong, W.; Cao, F. Investigation on volume scattering for vegetation parameter estimation of polarimetric SAR interferometry. PIERS Online 2009, 5, 1–5. [CrossRef] Ballester-Berman, J.D.; Vicente-Guijalba, F.; Lopez-Sanchez, J.M. A simple RVoG test for PolInSAR data. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 2015, 8, 1028–1040. [CrossRef] Garestier, F.; Dubois-Fernandez, P.C.; Papathanassiou, K.P. Pine forest height inversion using single-pass X-band PolInSAR data. IEEE Trans. Geosci. Remote Sens. 2008, 46, 59–68. [CrossRef] Lopez-Martinez, C.; Alonso-Gonzalez, A. Assessment and estimation of the RVoG model in polarimetric SAR interferometry. IEEE Trans. Geosci. Remote Sens. 2014, 52, 3091–3106. [CrossRef] Neumann, M.; Saatchi, S.S.; Ulander, L.M.; Fransson, J.E. Assessing performance of L-and P-band polarimetric interferometric SAR data in estimating boreal forest above-ground biomass. IEEE Trans. Geosci. Remote Sens. 2012, 50, 714–726. [CrossRef] Lei, Y.; Siqueira, P. Estimation of forest height using spaceborne repeat-pass L-Band InSAR correlation magnitude over the US State of maine. Remote Sens. 2014, 6, 10252–10285. [CrossRef] Lavalle, M.; Simard, M.; Pottier, E.; Solimini, D. PolInSAR forestry applications improved by modeling height-dependent temporal decorrelation. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, Honolulu, HI, USA, 25–30 July 2010; pp. 4772–4776. Lavalle, M.; Simard, M.; Solimini, D.; Pottier, E. Height-dependent temporal decorrelation for POLINSAR and TOMOSAR forestry applications. In Proceedings of the 8th European Conference on Synthetic Aperture Radar, Aachen, Germany, 7–10 June 2010; pp. 1–4. Lavalle, M.; Simard, M.; Hensley, S. A temporal decorrelation model for polarimetric radar interferometers. IEEE Trans. Geosci. Remote Sens. 2012, 50, 2880–2889. [CrossRef] Ahmed, R.; Siqueira, P.; Hensley, S.; Chapman, B.; Bergen, K. A survey of temporal decorrelation from spaceborne L-Band repeat-pass InSAR. Remote Sens. Environ. 2011, 115, 2887–2896. [CrossRef] Simard, M.; Hensley, S.; Lavalle, M.; Dubayah, R.; Pinto, N.; Hofton, M. An empirical assessment of temporal decorrelation using the uninhabited aerial vehicle synthetic aperture radar over forested landscapes. Remote Sens. 2012, 4, 975–986. [CrossRef] Neumann, M. Remote Sensing of Vegetation Using Multi-Baseline Polarimetric SAR Interferometry: Theoretical Modeling and Physical Parameter Retrieval. Ph.D. Thesis, University de Rennes 1, Rennes France, 2009. Lu, H.; Suo, Z.; Guo, R.; Bao, Z. S-RVoG model for forest parameters inversion over underlying topography. Electron. Lett. 2013, 49, 618–620. [CrossRef] Xie, Q.; Wang, C.; Zhu, J.; Fu, H. Forest height inversion by combining S-RVOG Model with terrain factor and PD coherence optimization. Acta Geod. Cartogr. Sin. 2015, 44, 686–693. Lavalle, M.; Solimini, D.; Pottier, E.; Desnos, Y.L. PolinSAR for forest biomass retrieval: PALSAR observations and model analysis. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2008, Boston, MA, USA, 7–11 July 2008; Volume 3, pp. 302–305. Cloude, S.R.; Papathanassiou, K.P. Three-stage inversion process for Polarimetric SAR Interferometry. IEEE Proc. Radar Sonar Navig. 2003, 150, 125–134. [CrossRef] Cloude, S.R.; Papathanassiou, K.P. Polarimetric SAR interferometry. IEEE Trans. Geosci. Remote Sens. 1998, 36, 1551–1565. [CrossRef] Tabb, M.; Orrey, J.; Flynn, T.; Carande, R. Phase diversity: A decomposition for vegetation parameter estimation using polarimetric SAR interferometry. In Proceedings of the 4th European Conference on Synthetic Aperture Radar, Cologne, Germany, 4–6 June 2002; pp. 721–724. Pottier, E.; Ferro-Famil, L.; Allain, S.; Cloude, S.; Hajnsek, I.; Papathanassiou, K.P.; Moreira, A.; Williams, M.; Minchella, A.; Lavalle, M.; et al. Overview of the PolSARpro V4. 0 software. The open source toolbox for polarimetric and interferometric polarimetric SAR data processing. In Proceedings of the 2009 IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2009, Cape Town, South Africa, 12–17 July 2009; Volume 4, pp. 936–939.


31.

32.

33. 34.

35.

36.

37. 38.

13 of 13

Ulander, L.M.; Gustavsson, A.; Dubois-Fernandez, P.; Dupuis, X.; Fransson, J.E.; Holmgren, J.; Wallerman, J.; Eriksson, L.; Sandberg, G.; Soja, M. BIOSAR 2010-A SAR campaign in support to the BIOMASS mission. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Vancouver, BC, Canada, 24–29 July 2011; pp. 1528–1531. Ulander, L.M.; Sandberg, G.; Soja, M.J. Biomass retrieval algorithm based on P-band biosar experiments of boreal forest. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Vancouver, BC, Canada, 24–29 July 2011; pp. 4245–4248. Tebaldini, S.; Rocca, F. Multibaseline polarimetric SAR tomography of a boreal forest at P-and L-bands. IEEE Trans. Geosci. Remote Sens. 2012, 50, 232–246. [CrossRef] Santi, E.; Pettinato, S.; Paloscia, S.; Castracane, P.; Di Giammatteo, U. CATARSI—Cap and trade assessment by remote sensing investigation: An algorithm for crop and forest biomass estimate. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Quebec City, QC, Canada, 13–18 July 2014; pp. 733–736. Lee, S.K.; Kugler, F.; Papathanassiou, K.; Hajnsek, I. Polarimetric SAR interferometry for forest application at P-band: Potentials and challenges. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2009, Cape Town, South Africa, 12–17 July 2009; Volume 4, pp. 13–16. Neumann, M.; Saatchi, S.S.; Ulander, L.M.; Fransson, J.E. Parametric and non-parametric forest biomass estimation from PolInSAR data. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Vancouver, BC, Canada, 24–29 July 2011; pp. 420–423. Freeman, A.; Durden, S. A three-component scattering model for polarimetric SAR data. IEEE Trans. Geosci. Remote Sens. 1998, 36, 963–973. [CrossRef] Park, S.E.; Moon, W.M.; Pottier, E. Assessment of scattering mechanism of polarimetric SAR signal from mountainous forest areas. IEEE Trans. Geosci. Remote Sens. 2012, 50, 4711–4719. [CrossRef] © 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).