Evaluating the Impacts of Using Different Digital Surface Models to Estimate Forest Height with TanDEM-X Interferometric Coherence Data

CHEN Hao HILL David A. WHITE Joanne C. CLOUDE Shane R.

CHEN Hao, HILL David A., WHITE Joanne C., et al. Evaluating the impacts of using different digital surface models to estimate forest height with TanDEM-X interferometric coherence data[J]. Journal of Radars, 2020, 9(2): 386–398. DOI:  10.12000/JR20009
引用本文: CHEN Hao, HILL David A., WHITE Joanne C., et al. Evaluating the impacts of using different digital surface models to estimate forest height with TanDEM-X interferometric coherence data[J]. Journal of Radars, 2020, 9(2): 386–398. DOI:  10.12000/JR20009
CHEN Hao, HILL David A., WHITE Joanne C., et al. Evaluating the impacts of using different digital surface models to estimate forest height with TanDEM-X interferometric coherence data[J]. Journal of Radars, 2020, 9(2): 386–398. DOI:  10.12000/JR20009
Citation: CHEN Hao, HILL David A., WHITE Joanne C., et al. Evaluating the impacts of using different digital surface models to estimate forest height with TanDEM-X interferometric coherence data[J]. Journal of Radars, 2020, 9(2): 386–398. DOI:  10.12000/JR20009

Evaluating the Impacts of Using Different Digital Surface Models to Estimate Forest Height with TanDEM-X Interferometric Coherence Data

(English)

doi: 10.12000/JR20009
详细信息
  • 1 https: //asterweb.jpl.nasa.gov/GDEM.ASP2 http://www.eorc.jaxa.jp/ALOS/en/aw3d30/registration.htm3 https://maps.canada.ca/czs/index-en.html4 https://www.intelligence-airbusds.com/worlddem/5 https://geohub.lio.gov.on.ca/
  • 中图分类号: TN959.3

Evaluating the Impacts of Using Different Digital Surface Models to Estimate Forest Height with TanDEM-X Interferometric Coherence Data

(English)

Funds: This work was supported by Natural Resources Canada and the Canadian Space Agency under Multisource Biomass GRIP and by the German Aerospace Centre for provision of TanDEM-X data
More Information
    Author Bio:

    CHEN Hao received the B.Sc. degree in electrical engineering from the University of Beijing Iron and Steel Technology, Beijing, China, in 1983, and the M.Sc. degree in computer science from the University of Victoria, Victoria, BC, Canada, in 2004. He is a senior physical scientist with the Canadian Forest Service (CFS), Natural Resources Canada, working at the Pacific Forestry Centre, Victoria. Since joining the CFS in 2000, his work has focused on radar polarimetry and interferometry for forest applications and he has participated in many national and international radar remote sensing projects as a principal investigator or co-principal investigator. Mr. Chen has more than 20 publications and given presentations to national and international conferences and organizations

    HILL David A. received the B.Sc. degree in Physical Geography from the University of Victoria, Victoria, BC, Canada, in 1983 and a Diploma in Remote Sensing from the College of Geographic Sciences, Lawrencetown, NS, Canada, in 1988. In 1997, he joined the Canadian Forest Service as a Remote Sensing Analyst, where research focused on remote sensing for forest inventory applications using data from Canada’s Radarsat-1/2 satellites, CCRS Convair-580 airborne SAR/INSAR, Germany’s TerraSAR-X/Tandem-X, Japan’s ALOS-1/2, and Landsat 3-8. Mr. Hill currently works on assessment of current and future satellite, airborne, and terrestrial sensors for Canada’s National Forest Inventory Program

    WHITE Joanne C. received the B.Sc. and the M.Sc. degree in geography from the University of Victoria, Victoria, Canada, in 1994 and 1998 respectively, and the D.Sc. degree from the University of Helsinki, Helsinki, Finland, in 2019. She is a research scientist with the Canadian Forest Service, Natural Resources Canada, in Victoria. Her research focuses on the synergistic use of optical time series and 3D remotely sensed data (LiDAR and digital aerial photogrammetry) for large-area forest inventory and monitoring applications. Specializing in the development of novel approaches to characterize forest dynamics with remotely sensed data, she has co-authored more than 150 peer-reviewed scientific publications. For a complete list of publications and access to reprints, please visit the Canadian Forest Service publications site: http://cfs.nrcan.gc.ca/authors/read/19532

    CLOUDE Shane R. received the B.Sc. (Hons.) degree from the University of Dundee, U.K., in 1981, and the Ph.D. degree from the University of Birmingham, U.K., in 1987. He was then a Radar Scientist with the Royal Signals and Radar Establishment, Great Malvern, U.K. Following this, he held teaching and research posts at the University of Dundee, U.K., the University of York, U.K. and the University of Nantes, France, before taking on his present role in 2001. He is now Senior Scientist with AEL Consultants, undertaking research on a range of topics associated with radar and optics. His main research interests are in polarization effects in electromagnetic scattering and their applications in radar and optical remote sensing. He is the author of 2 books, 10 book chapters, 42 journal publications, and over 180 international conference and workshop papers. Dr. Cloude is a Fellow of the Alexander von Humboldt Foundation in Germany, and has held Honorary Professorships and Chairs at the Universities of Dundee and York, UK, the Macaulay Land Use Research Institute in Aberdeen, Scotland, and the University of Adelaide, Australia

    Corresponding author: Hao Chen. E-mail: hao.chen@canada.ca
  • Figure  1.  Study site—the Petawawa Research Forest (red polygon), where forest stand polygons (pink) and field plots (red dots) are situated

    Figure  2.  kz vs. local incidence angle (baseline incidence angle set to 42.6° at scene centre)

    Figure  3.  Height vs. local incidence angle (coherence set to 0.36 for average height of ~21 m)

    Figure  4.  Histograms of the kz values for each candidate DSM and the reference data (2012 ALS DSM)

    Figure  5.  Observed ALS P95 height on x-axis and predicted stand height on y-axis

    Table  1.   kz differences when comparing to kz generated from 2012 ALS DSM

    Diff of kzASTER GDEMALOS GDSMCDSMDRAPE DSMTanDEM-X DSM
    Max0.12520.12960.13560.13890.1433
    Mean0.04350.03320.00970.03600.0204
    下载: 导出CSV

    Table  2.   Height comparisons from 94 forest stands

    BaselineDSM used in Eq. 2Slope mIntercept cAdjusted R2RMSE
    ALS P95ASTER GDEM0.6410.380.7591.69
    ALOS GDSM0.718.930.8491.77
    DRAPE DSM0.758.140.8421.92
    CDSM0.718.880.8411.73
    TanDEM-X DSM0.669.720.8061.70
    ALS CDhtASTER GDEM0.846.900.7962.86
    ALOS GDSM0.925.140.8853.18
    DRAPE DSM0.915.410.8543.18
    CDSM0.925.140.8733.12
    TanDEM-X DSM0.866.120.8462.97
    ALS TophtASTER GDEM1.003.170.7913.20
    ALOS GDSM1.101.000.8833.62
    DRAPE DSM1.091.260.8553.62
    CDSM1.101.040.8693.53
    TanDEM-X DSM1.032.280.8413.35
    下载: 导出CSV
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Evaluating the Impacts of Using Different Digital Surface Models to Estimate Forest Height with TanDEM-X Interferometric Coherence Data

(English)

doi: 10.12000/JR20009
    基金项目:  This work was supported by Natural Resources Canada and the Canadian Space Agency under Multisource Biomass GRIP and by the German Aerospace Centre for provision of TanDEM-X data
    作者简介:

    CHEN Hao received the B.Sc. degree in electrical engineering from the University of Beijing Iron and Steel Technology, Beijing, China, in 1983, and the M.Sc. degree in computer science from the University of Victoria, Victoria, BC, Canada, in 2004. He is a senior physical scientist with the Canadian Forest Service (CFS), Natural Resources Canada, working at the Pacific Forestry Centre, Victoria. Since joining the CFS in 2000, his work has focused on radar polarimetry and interferometry for forest applications and he has participated in many national and international radar remote sensing projects as a principal investigator or co-principal investigator. Mr. Chen has more than 20 publications and given presentations to national and international conferences and organizations

    HILL David A. received the B.Sc. degree in Physical Geography from the University of Victoria, Victoria, BC, Canada, in 1983 and a Diploma in Remote Sensing from the College of Geographic Sciences, Lawrencetown, NS, Canada, in 1988. In 1997, he joined the Canadian Forest Service as a Remote Sensing Analyst, where research focused on remote sensing for forest inventory applications using data from Canada’s Radarsat-1/2 satellites, CCRS Convair-580 airborne SAR/INSAR, Germany’s TerraSAR-X/Tandem-X, Japan’s ALOS-1/2, and Landsat 3-8. Mr. Hill currently works on assessment of current and future satellite, airborne, and terrestrial sensors for Canada’s National Forest Inventory Program

    WHITE Joanne C. received the B.Sc. and the M.Sc. degree in geography from the University of Victoria, Victoria, Canada, in 1994 and 1998 respectively, and the D.Sc. degree from the University of Helsinki, Helsinki, Finland, in 2019. She is a research scientist with the Canadian Forest Service, Natural Resources Canada, in Victoria. Her research focuses on the synergistic use of optical time series and 3D remotely sensed data (LiDAR and digital aerial photogrammetry) for large-area forest inventory and monitoring applications. Specializing in the development of novel approaches to characterize forest dynamics with remotely sensed data, she has co-authored more than 150 peer-reviewed scientific publications. For a complete list of publications and access to reprints, please visit the Canadian Forest Service publications site: http://cfs.nrcan.gc.ca/authors/read/19532

    CLOUDE Shane R. received the B.Sc. (Hons.) degree from the University of Dundee, U.K., in 1981, and the Ph.D. degree from the University of Birmingham, U.K., in 1987. He was then a Radar Scientist with the Royal Signals and Radar Establishment, Great Malvern, U.K. Following this, he held teaching and research posts at the University of Dundee, U.K., the University of York, U.K. and the University of Nantes, France, before taking on his present role in 2001. He is now Senior Scientist with AEL Consultants, undertaking research on a range of topics associated with radar and optics. His main research interests are in polarization effects in electromagnetic scattering and their applications in radar and optical remote sensing. He is the author of 2 books, 10 book chapters, 42 journal publications, and over 180 international conference and workshop papers. Dr. Cloude is a Fellow of the Alexander von Humboldt Foundation in Germany, and has held Honorary Professorships and Chairs at the Universities of Dundee and York, UK, the Macaulay Land Use Research Institute in Aberdeen, Scotland, and the University of Adelaide, Australia

    通讯作者: Hao Chen. E-mail: hao.chen@canada.ca
  • 1 https: //asterweb.jpl.nasa.gov/GDEM.ASP2 http://www.eorc.jaxa.jp/ALOS/en/aw3d30/registration.htm3 https://maps.canada.ca/czs/index-en.html4 https://www.intelligence-airbusds.com/worlddem/5 https://geohub.lio.gov.on.ca/
  • 中图分类号: TN959.3

English Abstract

CHEN Hao, HILL David A., WHITE Joanne C., et al. Evaluating the impacts of using different digital surface models to estimate forest height with TanDEM-X interferometric coherence data[J]. Journal of Radars, 2020, 9(2): 386–398. DOI:  10.12000/JR20009
引用本文: CHEN Hao, HILL David A., WHITE Joanne C., et al. Evaluating the impacts of using different digital surface models to estimate forest height with TanDEM-X interferometric coherence data[J]. Journal of Radars, 2020, 9(2): 386–398. DOI:  10.12000/JR20009
CHEN Hao, HILL David A., WHITE Joanne C., et al. Evaluating the impacts of using different digital surface models to estimate forest height with TanDEM-X interferometric coherence data[J]. Journal of Radars, 2020, 9(2): 386–398. DOI:  10.12000/JR20009
Citation: CHEN Hao, HILL David A., WHITE Joanne C., et al. Evaluating the impacts of using different digital surface models to estimate forest height with TanDEM-X interferometric coherence data[J]. Journal of Radars, 2020, 9(2): 386–398. DOI:  10.12000/JR20009
    • Canada contains more than 347 million hectares of forestlands[1], distributed across vast regions that are largely inaccessible. Spatially-extensive, timely and cost-effective inventory and monitoring tools based on remotely sensed datasets are required to assess current forest status and track the impacts of disturbances across a range of ecosystems. One of the key attributes in forest inventories is forest height, an indicator of the timber production potential of a stand and closely related to forest biomass through allometric relations[2-4].

      Airborne Laser Scanning (ALS) data has been widely used for generating spatially continuous forest height maps with high accuracy and spatial resolution[5,6]. ALS metrics, such as the 95th height percentile, co-dominant and dominant tree height, and top tree height[7-10], are efficient predictors of forest height and effective for stand-level measurements. Although national coverage of ALS data is common in some jurisdictions, ALS acquisitions are typically targeted over limited spatial extents, which does not generally allow for wall-to-wall forest height mapping over extensive areas, such as an area size of Canada’s forested ecosystems[11].

      For large area mapping, forest height can be derived from optical and ancillary datasets through the upscaling of samples of height estimated from the spaceborne Geoscience Laser Altimeter System (GLAS) aboard ICESat[10,12,13], or airborne ALS transects[14]. Alternatively, Beaudoin et al. Ref. [15] mapped a suite of 91 National Forest Inventory (NFI) attributes including forest height from MODIS imagery for years 2001 and 2011. However, such large-area approaches usually come at the cost of decreased accuracy and/or resolution that does not meet forest inventory requirements.

      Previous research has demonstrated that interferometric coherence data from a single-polarization mode of the German TanDEM-X (TX) mission was sensitive to the vertical distribution of radar volume scatterers in forests and found it promising in mapping forest height in various forest environments[16-24]. The application of TX single-polarization interferometric data generally requires inversion of a simplified version of the semi-empirical invertible scattering model, the Random Volume Over Ground (RVOG), to estimate forest height[19]. This simplified model requires TX interferometric coherence amplitude data as input, as well as an external Digital Surface Model (DSM) to account for TX’s local angle of incidence on sloped surface at a pixel level. It does not rely on any true surface topography for height estimation, but estimates the height from an integral over distributed volume scatterers through the coherence amplitude in the vertical direction, which is different from other approaches as reviewed in the literature[25] where complex coherence, such as phase, is generally employed.

      We applied the simplified RVOG model on TX interferometric amplitude data to derive forest height for different forest regions of Canada: the rolling foothills of Alberta (AB)[19], the mountainous terrain of British Columbia (BC)[20], and the relatively flat terrain of the Northwest Territories (NWT)[21]. While the forest height results were relatively consistent for these varying topographic and forest conditions, a different DSM was used in each study. There are currently several medium-resolution (i.e. ~30 m) candidate DSMs available at no cost and with nearly global/continental coverage, such as the Shuttle Radar Topography Mission (SRTM) DEM[26], the ASTER Global Digital Elevation Map (GDEM)[27], the ALOS Global Digital Surface Model (GDSM)[28], the Canadian Digital Surface Model (CDSM)[29], as well as others.

      In this study, our objective is to examine and quantify the impact of using different DSMs as input into the simplified RVOG model for the Coherence Only Amplitude (COA) approach of deriving forest height, using independent reference data (ALS) for our assessment. In doing so, we provide an improved understanding of the impact of different DSMs on the estimation of forest height with the TX COA approach, and the characteristics of the DSM or DSMs that result in the most accurate height estimates. The results of this study can be used to inform the future use of the existing archive of TX single-polarization interferometric data, as well as similar future data sources for large-area forest height mapping.

    • The Petawawa Research Forest (PRF) is located ~160 km Northwest of Ottawa and within the Great Lakes-St. Lawrence Forest Region, centered on 45.98°N and 77.50°W (Fig. 1). Established in 1918, the PRF is over 10,000 hectares in size and contains both boreal and temperate forest species. The landscape is gently rolling with most topographic relief being less than 40 m and with a median slope value ~4°, max ~27°, and 90% of slopes < 9°. The largest slopes appeared around the lakes of western site of the PRF. From east to west the soil composition varies from a sandy outwash plain, to glacial tills, to some localized thin soil over bedrock or bedrock outcrops. Ecological settings range from wetlands and riparian areas to uplands. Stand densities vary from open to dense, with age classes ranging from immature or mature. Forest stands are generally mixed. Many stands have a complex structure of species and age that are multi-storied[30]. Based on 2012 ALS 95th height percentile data, the height in the study area ranges from 2 m to 42 m with a mean/median height of ~21 m. The PRF is home to more than 500 permanent sample plots and more than 2000 research experiments and demonstration plots, some of which have run over decades and designed to enhance forest management[31].

      Figure 1.  Study site—the Petawawa Research Forest (red polygon), where forest stand polygons (pink) and field plots (red dots) are situated

      The PRF has been the site of numerous operational and experimental remotely sensed data acquisitions[32] that have played a critical role in the development of forest inventories. ALS data have been acquired and used with ground plot data to develop an Enhanced Forest Inventory (EFI) for the PRF[33]. The plethora of available data sources at the PRF has results in the establishment of a remote sensing supersite, designed to enable the development, testing, and validation of algorithms and approaches for forest management[31].

    • The TX archive contains continuous and overlapping global coverage of TX Co-registered Single-look Slant-range Complex (CoSSC) data that were used to create a global DSM, also known as WorldDEMTM[34]. A CoSSC image pair, collected over the PRF on April 21, 2011, was provided to us by the German Aerospace Centre (DLR) as part of their science support program for evaluating CoSSC as an interferometric pre-product of the TX processing chain. This CoSSC data product has single polarization (HH) with a ground range resolution of 2.6 m and azimuth resolution of 3.3 m. The incidence angle at the scene centre is 42.6°. The CoSSC image pair was processed and co-registered by the DLR and the resulting interferogram was provided in slant-range geometry with an auxiliary file of range shifts used to co-register the image pair. The Height of Ambiguity (hoa) is nominally |43.9| m, which means the simplified RVOG model would have a useful dynamic range of ~14 m to ~43 m[20] for the PRF because the 2012 ALS 95th height percentile data indicated a maximum height of 42 m and a mean/median height of ~21 m.

    • The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model Version 2 (GDEM V2) was released by the Ministry of Economy, Trade, and Industry (METI) of Japan and the National Aeronautics and Space Administration (NASA) of the United States in October, 2011. ASTER GDEM V2[35] has a spatial resolution of 30 m and a horizontal datum of WGS84 (World Geodetic System 1984) as well as a vertical reference system of EGM96 (Earth Gravitational Model 1996). The coverage of GDEM V2 spans 99% of Earth’s landmass from 83°N to 83°S.

      The Japan Aerospace Exploration Agency (JAXA) released the Advanced Land Observing Satellite (ALOS) Global Digital Surface Model V1.1 in March 2017. The ALOS GDSM, also known as the ALOS World 3D-30 m (AW3D30)[36], has a spatial resolution of 30 m and the same horizontal and vertical datum as ASTER GDEM V2. The GDSM coverage is from 83°N to 83°S. The ALOS GDSM is also open data, available for download from the JAXA Earth Observation Research Center website.

      The Canadian Digital Surface Model (CDSM) is part of Natural Resources Canada (NRCan)’s altimetry system designed to meet users’ needs for Canadian elevation data and products[29]. The 0.75 arc-second CDSM (20 m) consists of derived products from the 1 arc-second (30 m) SRTM DSM and the Canadian Digital Elevation Model (CDEM)[37]. The SRTM data was re-processed by NRCan with gaps filled using the CDEM to offer a complete coverage of the Canadian landmass. The horizontal datum is the North American Datum 1983 (NAD83) and the vertical reference system is the Canadian Geodetic Vertical Datum 1928 (CGVD28). The data were filtered to remove noise and aligned to the 0.75 arc-second grid resolution, and waterbodies re-flattened. The CDSM is open data, available for download from Natural Resources Canada.

      The TX mission offers a global DSM, WorldDEMTM. The commercial WorldDEMTM with spatial resolutions of 12 m and 30 m were made available in 2017, but are not open and must be purchased from AIRBUS. The TX DSM data has a horizontal and vertical datum of WGS84 and EGM2008 respectively. The TX DSM at 30 m used for this study was provided courtesy of the DLR under their science support program for evaluation of TX DSM.

      The DSM from the Digital Raster Acquisition Project for Eastern Ontario imagery (DRAPE) covers Eastern Ontario, Canada, and is freely available through Land Information Ontario. Leica ADS100 Digital Camera systems were used for the digital imagery acquisition, performed at 2,377 m above mean terrain to produce 20 cm orthorectified imagery and related products. The DRAPE DSM was then derived at 2 m from the digital stereo photography using the Leica GeoSystems software, XPro SGM[38]. The horizontal datum is NAD83 with the vertical reference system of CGVD28.

    • In the summer of 2013, Temporary Sample Plots (TSP) were surveyed in the PRF as part of the Advanced Forest Resources Inventory Technology (AFRIT) program[39]. A total of 223 circular plots were established and each had 14.1 m in radius (~625 m2). The plots were stratified based on forest conditions for the purpose of constructing area-based models with ALS data. The PRF Inventory was completed in 2007, using field data and soft-copy interpretation of stereo aerial photography. In total, there were 1193 forest stands delineated, with a suite of attributes interpreted.

      Discrete-return ALS data with a point density of 14 points per m2 were acquired on August 17, 2012, covering ~13,000 hectares including the PRF. LAStools software was used to derive a DSM at 1 m, as well as the 95th height percentile metric (P95) at a 30 m pixel size. Following an area-based approach[33], a linear model, using P95 and the stand height measurements from the AFRIT plots, was developed to estimate two measures of forest height at 30 m: Topht (averaged height of the thickest 100 stems/ha) and CDht (average height of Co-dominant and Dominant trees). The derived height models were then applied wall-to-wall for the PRF at 30 m. The ALS DSM and the resulting 30 m rasters for P95, Topht, and CDht were used as independent reference sources for validating stand-level TX forest height in the PRF. The AFRIT plot data, the PRF inventory data, and the ALS data/products are freely available for download through the National Forest Information System operated by the Canadian Forest Service, Natural Resources Canada.

    • Our height algorithm developed for the single-polarization TanDEM-X interferometric COA data was a simplified version of RVOG model derived from earlier studies in polarimetric interferometry[40,41]. It estimates height locally by using an inverse SINC function as shown in Eq. (1)[42]

      $$ {\hat h_{\rm{v}}} \approx \frac{{2\pi }}{{{k_{\rm{z}}}}}\left[ {1 - \frac{2}{\pi }{{\sin }^{ - 1}}{{\left| {{{\hat \gamma }_{\rm{v}}}} \right|}^{0.8}}} \right] $$ (1)

      where |$ {{{\hat \gamma }_{\rm{v}}}}$| is a volume coherence amplitude of the interferogram (here to be the HH channel). Direct estimation of $ {{{\hat \gamma }_{\rm{v}}}}$ is sensitive to errors for pixels that have low Signal-to-Noise Ratio (SNR), due to either low backscatter or high TX noise floor. We applied two compensation procedures to the initial estimation of $ {{{\hat \gamma }_{\rm{v}}}}$, which were compensation to the loss of coherence due to SNR decorrelation and compensation to residual errors in the processing chain. The detailed estimation and optimization of $ {{{\hat \gamma }_{\rm{v}}}}$ were described in[19].

      kz in Eq. (1) is an interferometric wavenumber, which is a function of a local angle of incidence and the normal baseline component of the interferometer as in Eq. (2)

      $$ {k_{\rm{z}}} = \frac{{2{\rm{\pi sin}}{\theta _0}}}{{{\rm{hoa}}\sin {\theta _i}}} $$ (2)

      where hoa is height of ambiguity and θ0 an incidence angle at scene centre, both of which were in TX metadata. θi is the variability of local incidence angle on sloped terrain and can be estimated from an external DSM at a pixel level. The interferometric wavenumber kz is what we focus on in this study to understand how local slopes derived from different DSMs would affect height estimation with a view to quantify any errors or limitations.

      In general, we could use any available DSM. However, there were three key features to be considered. First was the spatial extent of a DSM used in application and its availability. Global or regional coverage with open access are preferred. Secondly, it was the spatial resolution of a DSM used to calculate the local slopes. We wanted a DSM with a spatial resolution that was commensurate with that of the target resolution of our final TX height product. Third, scale variations in different DSMs could have a potential influence on kz and then the accuracy of TX height estimation. If the terrain was relatively flat, a DSM may not be of great concern in overall model outcome, as Eq. (2) became to Eq. (3)

      $$ {k_{\rm{z}}} \approx \frac{{2{\rm{\pi }}}}{{{\rm{hoa}}}} $$ (3)

      However, if areas contained large slopes facing either towards or away from the radar, DSM resolutions and accuracies would have a definite impact on kz and forest height estimation, as the local slope may be poorly estimated due to the level of residual errors associated with the DSM (Eq. (4))

      $$ {k_{\rm{z}}} = \frac{{2{\rm{\pi sin}}{\theta _0}}}{{{\rm{hoa}}\sin ({\theta _i} + \Delta \theta )}} $$ (4)

      Fig. 2 and Fig. 3 show a plot of kz and a plot of height estimates respectively from Eq. (4). Here we pre-defined a baseline incidence angle as 42.6° (scene centre) in Fig. 2. When the incidence angle increased or decreased about 4° ($\Delta $θ) from its true value θi, $\Delta $kz would be ~|0.018|, leading to the height estimate change ~|1.7| m. The solid line in Fig. 3, representing the average height of ~21 m, had the coherence $ {\hat \gamma _{\rm{v}}}$ set to 0.36. A DSM that would result in large changes in kz when compared to a more accurate baseline ALS DSM should be avoided.

      Figure 2.  kz vs. local incidence angle (baseline incidence angle set to 42.6° at scene centre)

      Figure 3.  Height vs. local incidence angle (coherence set to 0.36 for average height of ~21 m)

      To generate a TX forest height product, we estimated $ {\hat \gamma _{\rm{v}}}$ with a local averaging process using a boxcar filter with a 9×9 spatial window, reducing the variance and bias on coherence estimates, and then performed the aforementioned coherence compensations to the initial $ {\hat \gamma _{\rm{v}}}$[19]. Next we used the ESA Sentinel Toolboxes (SNAP) and a chosen DSM to perform terrain-correction of the resulting slant-range image $ {\hat \gamma _{\rm{v}}}$ in UTM projection (Zone 18) with a 30 m pixel spacing. During the same time, local incidence angles for all pixels were calculated for kz. Finally, a TX height map with a 30 m resolution was generated by applying Eq. (1).

      We validated and compared the TX height maps derived from different DSMs within the PRF. Forest stands were defined by the 2007 forest inventory data, representing all plantation and natural forest stands within the PRF in polygons. Forest stand height was then extracted using the arithmetic mean of all the pixels in that stand. Because the ALS CDht and Topht were derived from both of ALS P95 and stand height measurements from the AFRIT plots, 174 forest stands, containing the aforementioned 223 field plots, were located and considered as the initial pool of candidates for validation.

      As the DSM datasets varied in data collection and release dates from 2000 to 2014, the 174 forest stands were first examined using high-resolution aerial photographs and Landsat images, acquired between 2000 and 2014, to assess if there had been any changes to these stands over the period considered. The forest stands that experienced change during this period were removed as the slope of a DSM would have been affected by any height change due to forest or vegetation removal. Stands less than two hectares in size were also removed because, at a 30 m resolution, the statistics used for assessment would suffer from boundary effects from larger surrounding stands. At the time of this study, DRAPE DSM was not available for the far west edge of the PRF, so the forest stands in that area were excluded. After the filtering, 94 forest stands remained for validation of TX height estimates.

      We used linear regressions (Eq. (5)) to validate and compare TX height estimates, created within the 2012 ALS coverage, against the stand height maps derived from ALS metrics (hALS)

      $$ {h_{{\rm{ALS}}}} = {{m}}{{\hat h}_{\rm{v}}}{{ + c}} $$ (5)

      where m and c are respectively the estimated slope and the intercept of the linear regression.

      $$ {\rm{RMSE}} = \sqrt {\frac{{ \displaystyle\sum \limits_{i = 1}^{{n}} {{\left( {{{\hat h}_{{{\rm{v}}i}}} - {h_i}} \right)}^2}}}{{{{n}} - 1}}} $$ (6)

      Eq. (6) is used to calculate Root Mean Square Error (RMSE), where $ {{{\hat h}_{{\rm{v}}i}}}$ is the TX height estimation at the ith stand, hi the height measurement from the ALS at the same stand location, and n the number of stands used to calculate the RMSE. Adjusted R2 (here after R2), the estimated slope m, and the intercept c, as well as the RMSE, were used to assess the level of impact of using different DSMs on the performance of the simplified RVOG model.

    • Tab. 1 shows the differences of kz values for each of the DSMs when subtracting the kz image derived from the 2012 ALS DSM over all 94 forest stands. The mean difference of the kz values indicated how different the average slopes were compared to the slope of the 2012 ALS DSM. The kz generated from the CDSM had the best match with the kz from the 2012 ALS DSM with a mean difference kz of 0.0097. The worst match was the ASTER GDEM with a mean difference kz of 0.0435.

      Table 1.  kz differences when comparing to kz generated from 2012 ALS DSM

      Diff of kzASTER GDEMALOS GDSMCDSMDRAPE DSMTanDEM-X DSM
      Max0.12520.12960.13560.13890.1433
      Mean0.04350.03320.00970.03600.0204

      To show kz generated from the CDSM had the best match with the kz from the 2012 ALS DSM in all DSM candidates, we also show the histograms of each kz from all 94 forest stands in Fig. 4. All kz start at 0.1 and end with 0.2. The kz histogram from the CDSM has a form that is much closer to the kz from the 2012 ALS DSM. The kz histogram from the ASTER GDEM has the least similarity with a wider shape when compared to the 2012 ALS DSM. In this way we gained much needed insights on the potential influence of different DSMs as input into the simplified RVOG model.

      Figure 4.  Histograms of the kz values for each candidate DSM and the reference data (2012 ALS DSM)

      We further examined each of the 94 forest stands to determine the cause of the maximum difference in kz value varied from that of the 2012 ALS DSM. The largest differences in the kz values were found in two forest stands that were adjacent to a water surface. In the processing of 2012 ALS DSM, water surfaces were masked out and given a value of 0. When it was resampled to the 30 m spatial resolution to produce kz, these 0 values dominated and skewed the statistics of adjacent stand polygons. We also found several other forest stands that contained large differences in kz values. These maximums were mainly caused by boundary effects of flat open surfaces that were adjacent to the forest stand polygons.

      The means of the kz differences and the distributions of the kz values were used to identify which DSM most closely matched the slopes generated from the 2012 ALS DSM. The CDSM had the lowest mean difference in kz value (0.0097) for all 94 forest stands and the most similar distribution of kz values relative to the 2012 ALS DSM. According to Fig. 3, a different kz value ~|0.018| would result in a difference in an estimated local incidence angle ~|4|°, at which the height variation would be ~|1.7| m. To minimize the errors introduced by a DSM in the simplified RVOG model, we should choose the CDSM for the local slope estimation.

      Fig. 5 and Tab. 2 shows the height comparisons from the 94 forest stands. The TX heights estimated using the CDSM, ALOS GDSM, and DRAPE DSM showed the similar statistics in R2 (~84%) and RMSE (~1.8 m) when compared to the 2012 ALS P95 height. The TX height estimates resulted from the CDSM had an R2 of 84.1% and low RMSE of 1.73. When compared to ALS CDht in Tab. 2, the ALOS GDSM had a higher R2 of 88.5% followed by the CDSM with an R2 of 87.3%, but the CDSM had a smaller RMSE (3.12 m) than the ALOS GDSM (3.18 m). For the Topht comparisons in Tab. 2, the results were similar to the CDht comparisons.

      Table 2.  Height comparisons from 94 forest stands

      BaselineDSM used in Eq. 2Slope mIntercept cAdjusted R2RMSE
      ALS P95ASTER GDEM0.6410.380.7591.69
      ALOS GDSM0.718.930.8491.77
      DRAPE DSM0.758.140.8421.92
      CDSM0.718.880.8411.73
      TanDEM-X DSM0.669.720.8061.70
      ALS CDhtASTER GDEM0.846.900.7962.86
      ALOS GDSM0.925.140.8853.18
      DRAPE DSM0.915.410.8543.18
      CDSM0.925.140.8733.12
      TanDEM-X DSM0.866.120.8462.97
      ALS TophtASTER GDEM1.003.170.7913.20
      ALOS GDSM1.101.000.8833.62
      DRAPE DSM1.091.260.8553.62
      CDSM1.101.040.8693.53
      TanDEM-X DSM1.032.280.8413.35

      Figure 5.  Observed ALS P95 height on x-axis and predicted stand height on y-axis

      Here we show that the CDSM, ALOS GDSM, and DRAPE DSM had very similar performance in height estimation with an R2 of ~84% and RMSE < 2 m when compared to the ALS P95 height over the 94 forest stands that were considered relatively unchanged during the time period between 2000 and 2014. The use of a 2 m resolution DRAPE DSM did not have a marked impact on the height estimates compared to the use of a 30 m resolution DSM due to the resampling process for the final TX height product at 30 m. In the kz images, the 30 m DSMs captured similar large-scale topographic features, whereas the kz from the 2 m DRAPE DSM showed more fine topographic characteristics around the lake edges where large slopes were found, which translated into slight local kz variations.

    • These comparisons were made in the PRF area featuring relatively rolling terrain, which dominates most of northern boreal landscapes in Canada. The height validation results were consistent with those obtained over our northern boreal site in the NWT with an R2 of 88% and RMSE of 2.7 m, where the CDEM was used in the model[21], and over highly stocked boreal forests in AB with an R2 of 85% and RMSE 2.9 m, where SRTM applied[19]. For forest height estimation in areas of rigorous topography with tall and dense temperate forests, for example in rugged mountainous forest regions of BC, Chen et al. Ref. [20] used the provincial TRIM DSM[43], similar to the CDSM, in the model to obtain an R2 of 74% and RMSE 5 m and found that slopes were severe enough that small errors in slope estimation may lead to large height estimation errors. To mitigate the effect of slope variability in such challenging topography, a technique of using multiple baselines of TX CoSSC data should be considered[20]. However, even though the PRF has moderate terrain and a DSM choice might not be expected to be as critical as for mountainous areas, our results still show that choosing a proper DSM would make a difference in final TX height estimation.

      There is a confirmed bias in TX height estimates using the simplified RVOG model as revealed by linear regression’s coefficients, i.e. the slope m and intercept c, and the RMSE measures in Tab. 2. We found a consistent overestimation of height from TX (especially at lower tree heights). There were two possible reasons for this overestimation: the lower part of the height dynamic range was overestimated due to the loss of sensitivity in the SINC function (Eq. 1) as discussed in Ref. [20], and/or potential ground scatter in lower height stands was causing surface effects[42]. Fig. 5(a)Fig. 5(e) indicate an overestimation of approximately 3 m for 20 m trees. The bias may vary in different regions. It was also confirmed that forest cover types had an impact on the height estimates[21]. When expanding the COA approach to other forest regions, the bias and possible influences of differing forest types require further investigation. Normally, we use the linear model (Eq. (5)), calibrated from ALS height measurements or other independent height sources (i.e. field plot measurements), to make an adjustment to m (close to 1) and c (close to 0). The coefficients for the baseline of 2012 ALS P95 in Tab. 2 showed a slope ~0.7 and an intercept ~8 m for the CDSM, ALOS GDSM and DRAPE DSM in the PRF. We did not perform the linear correction in this study because our objective was to assess the relative performance of the different input DSMs and determine which DSM would provide the optimal solution for mapping forest height over large areas with TX CoSSC data.

      Please note an external DSM used in Eq. 2 to calculate local angle of incidence θi is one of the essential factors in the COA approach and its conversion to TX height. A key part of the DSM evaluation is the estimation of θi through the calculation of kz to determine the quality of the DSM. Selecting a quality DSM can certainly help with topography compensation and reduce errors in final TX height estimates. Another essential factor causing the RMSE can be the estimation of the interferometric coherence $ {{\hat \gamma }_{\rm{v}}}$ used in Eq. (1), due to pixels with low SNR or high noise floor. This noise is uncorrelated between the image pairs and should be reduced as much as possible because it can cause decorrelation and loss of coherence in the interferogram. We have seen in our previous studies[19-21] that SNR corrections made a major difference in the level of estimated TX interferometric coherence and improved the final height estimation. Thus, proper coherence compensation procedures for $ {{\hat \gamma }_{\rm{v}}}$ should be considered and performed in order to reduce the overall error level in RMSE.

      There is another possible source of error in TX coherence estimation due to baseline decorrelation because of local topography. It follows from the fact that each point on the earth is viewed from slightly different angles at either end of the baseline. Although the transmitted radar spectrum is common to both receiving signals, its projection onto the earth is slightly different, causing a spectral shift that depends on local slope. In principle, this effect can be compensated by applying range spectral filtering[44]. Since TX CoSSC data is by default range-spectral filtered as part of DLR’s basic SAR processor to remove such effect, users don’t have to implement such a scheme in their data process unless obvious inaccuracy found in the CoSSC data due to local slopes.

      The TX COA approach is in contrast to other similar approaches using TX CoSSC data for forest heights, where phase information from complex coherence is utilized[18,24]. The advantage of using phase is to have two parameters per pixel for height estimation, but generally requires auxiliary data for true surface location underneath the forest. For example a Digital Terrain Model (DTM) from ALS is needed in order to use phase for forest height estimation. The TX COA approach is free of such requirement, permitting large area mapping in regions, where such true surface information is unavailable. However, the main concern is the aforementioned bias in height estimates, which requires small ALS patches or ALS transects or ground plot measurements for final height product calibration.

    • In this study, we assessed the relative performance of several different DSM candidates used in the simplified RVOG model to estimate forest height with TX single polarization CoSSC data in the PRF. Candidate DSMs were selected for their spatial extent (i.e. global or regional coverage), open data policy, and spatial resolution. The assessment of the DSMs was conducted by generating the interferometric wavenumber kz using different DSMs, and comparing each against kz derived using the 2012 ALS DSM. The results showed that the CDSM, ALOS GDSM, and DRAPE DSM had similar performance in height estimation with a mean difference of kz, 0.0097, 0.0332 and 0.0360 respectively, sufficient for the simplified RVOG model to produce TX height maps at 30 m with R2 values greater than 84% and RMSE less than 2 m when compared to the 2012 ALS P95 height metric at the forest stand level. The use of the CDSM resulted in the lowest difference of kz at 0.0097 in all 5 DSM candidates, indicating that the mean local incidence angle estimated from the CDSM differed by less than 4° overall, when compared to the 2012 ALS DSM. Slopes are related to the derivative of a DSM and, if all other criteria are met, the priority of selecting a DSM should be given to the one with a better spatial resolution than the coherence data, but as demonstrated herein there is minimal gain in using a DSM with a very high resolution, such as provided by DRAPE (2 m) for example. Since the CDSM covers all of Canada’s terrestrial area, offers open data access, and has higher spatial resolution of 20 m, if TX single polarization CoSSC data or other similar data were to become openly available, there could be great potential for large area mapping of forest height in Canada using the interferometric COA approach.

    • We acknowledge the financial and research support from the Canadian Forest Service of Natural Resources Canada and the Canadian Space Agency under Multisource Biomass GRIP (IMOU 13MOA41003). We further acknowledge the DLR for the provision of TanDEM-X CoSSC data and TanDEM-X DSM under XTI_VEGE6648 and DEM_FOREST0962 respectively.

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