Estimation of Building Heights and DEM Accuracy Assessment Using ICESat-2 Data Products

: The use of remote sensing for urban monitoring is a very reliable and cost-effective method for studying urban expansion in horizontal and vertical dimensions. The advantage of multi-temporal spatial data and high data accuracy is useful in mapping urban vertical aspects like the compactness of urban areas, population expansion, and urban surface geometry. This study makes use of the ‘Ice, cloud, and land elevation satellite-2 (cid:48) (ICESat-2) ATL 03 photon data for building height estimation using a sample of 30 buildings in three experimental sites. A comparison of computed heights with the heights of the respective buildings from google image and google earth pro was done to assess the accuracy and the result of 2.04 m RMSE was obtained. Another popularly used method by planners and policymakers to map the vertical dimension of urban terrain is the Digital Elevation Model (DEM). An assessment of the openly available DEM products—TanDEM-X and Cartosat-1 has been done over Urban and Rural areas. TanDEM-X is a German earth observation satellite that uses InSAR (Synthetic Aperture Radar Interferometry) technique to acquire DEM while Cartosat-1 is an optical stereo acquisition satellite launched by the Indian Space Research Organization (ISRO) that uses photogrammetric techniques for DEM acquisition. Both the DEMs have been compared with ICESat-2 (ATL-08) Elevation data as the reference and the accuracy has been evaluated using Mean error (ME), Mean absolute error (MAE) and Root mean square error (RMSE). In the case of Greater Hyderabad Municipal Corporation (GHMC), RMSE values 5.29 m and 7.48 m were noted for TanDEM-X 90 and CartoDEM V3 R1 respectively. While the second site of Bellampalli Mandal rural area observed 5.15 and 5.48 RMSE values for the same respectively. Therefore, it was concluded that TanDEM-X has better accuracy as compared to the CartoDEM V3 R1.


Introduction
Digital Elevation Model (DEM) is used globally by policymakers for resource management, planning, and maintenance. It can be processed to extract information about the earth's topography and has applications in various fields. DEM can be generated using various remote sensing techniques, using active remote sensing DEMs like TanDEM-X and SRTM missions, and by using optical stereo missions like Cartosat-1, ASTER, and ALOS PRISM which were launched for DEM generation as one of the aims and are openly accessible. Availability of openly accessible DEMs has increased and thus there is a need for analyzing the quality of DEMs with quantitative accuracy assessment techniques for better results. The TanDEM-X mission with its alike satellite TerraSAR-X (TSX) radar satellite is flying in a close orbit and has a major objective to generate high-precision DEM in the bistatic mode. The Cartsosat-1 satellite is equipped with two high-resolution cameras layer, etc. [8,[23][24][25][26][27] horizontal monitoring can be achieved using low, medium, and highresolution satellites images, whereas vertical monitoring requires high-resolution satellite data where several new techniques have been used such as optical stereophotogrammetry, InSAR, and airborne LiDAR, ICESat-2/GLAS, etc. [8,25,[28][29][30][31].
The present study was to estimate the building heights using ICESat-2 ATL 03 data. It further examines the quality of Cartosat-1 and Tandem-X DEMs over Urban and Rural areas. For building height estimation over 3 different sites, 30 samples were collected and compared with google images which were considered for reference height. Two locations one urban and one rural were selected for assessment of the accuracy of these DEMs using highly accurate ICESat-2 altimetry data. The Urban area selected consists of highly dense built-up and the Rural area selected for experimentation has mostly flat terrain with sparse built-up.

Study Area
Samples for building height estimation were collected from three different sites namely Hyderabad, Paris, and Vancouver. The rationale for selecting these sites for assessment is the availability of many suitable ICESat-2 ground tracks over three sites and the availability of google images for those respective buildings which were attached in Appendix A. A total of 30 buildings that were distributed over the three study areas have been collected their Eng. Proc. 2021, 10, 37 3 of 19 respective track id, beam id, date of acquisition, and building position (lat., long.) shown in Table 1. The sample buildings were selected based on the availability of geolocated photons that fall on the bare Earth, which is treated as the local datum and which also has significant geolocated photons falling on the building's roof. For comparison of DEMs (TanDEM-X 90 and CartoDEM V3 R1) over urban and rural areas, two study areas have been chosen one is Greater Hyderabad Municipal Corporation (Urban area) and another Bellampalli Mandal (Rural area) of Telangana state, India as shown in Figure 1.

Greater Hyderabad Municipal Corporation (GHMC)
The study area lies at around 17.3850° N, 78.4867° E, and is the capital city of Telangana State, India, which is spread over an area of 650 km 2 . It is one of the largest municipal corporations with a population of 7.9 million. The city is situated in the Deccan Plateau and has an average height of 536 m above mean sea level. It is the IT hub of Telangana where it attracts lots of migrants from other states for employment purposes leading to the rapid growth of the city, resulting in a densely built, and populous metropolitan area.

Bellampalli Mandal
Bellampalli is a Mandal in Mancherial District of Telangana State, India, which lies at 19.0715° N, 79.4912° E, noted for its coal mines Singareni Collieries Company Limited, spread over an area of 35.06 km 2 . It is a fertile plain with the Godavari River flowing through the district and the majority of the population in the area is agriculture-dependent.

Digital Elevation Model
A Digital Elevation Model (DEM) is a mathematical representation of the terrain or the topographic surface [30][31][32]. The study uses the CartoDEM version 3 release 1 (V3 R1) data which is generated using CartoSat-1 Stereopairs from National Remote Sensing Centre (NRSC) and TanDEM-X 90 dataset from the German Space Agency (DLR).

CARTOSAT-1 Mission
The Cartosat-1 was launched by the Indian Space Research Organization (ISRO), the eleventh of the IRS series, at the Satish Dhawan Space Centre (SDSC) in Sriharikota. The satellite is positioned in the polar Sun Synchronous Orbit at an altitude of 618 km from the Earth [33]. The satellite became the first global stereo-capable satellite to be launched with a spatial resolution of 2.5 m and was unique in its ability to provide high-resolution

Greater Hyderabad Municipal Corporation (GHMC)
The study area lies at around 17.3850 • N, 78.4867 • E, and is the capital city of Telangana State, India, which is spread over an area of 650 km 2 . It is one of the largest municipal corporations with a population of 7.9 million. The city is situated in the Deccan Plateau and has an average height of 536 m above mean sea level. It is the IT hub of Telangana where it attracts lots of migrants from other states for employment purposes leading to the rapid growth of the city, resulting in a densely built, and populous metropolitan area.

Bellampalli Mandal
Bellampalli is a Mandal in Mancherial District of Telangana State, India, which lies at 19.0715 • N, 79.4912 • E, noted for its coal mines Singareni Collieries Company Limited, spread over an area of 35.06 km 2 . It is a fertile plain with the Godavari River flowing through the district and the majority of the population in the area is agriculture-dependent.

Digital Elevation Model
A Digital Elevation Model (DEM) is a mathematical representation of the terrain or the topographic surface [30][31][32]. The study uses the CartoDEM version 3 release 1 (V3 R1) data which is generated using CartoSat-1 Stereopairs from National Remote Sensing Centre (NRSC) and TanDEM-X 90 dataset from the German Space Agency (DLR).

CARTOSAT-1 Mission
The Cartosat-1 was launched by the Indian Space Research Organization (ISRO), the eleventh of the IRS series, at the Satish Dhawan Space Centre (SDSC) in Sriharikota. The satellite is positioned in the polar Sun Synchronous Orbit at an altitude of 618 km from the Earth [33]. The satellite became the first global stereo-capable satellite to be launched with a spatial resolution of 2.5 m and was unique in its ability to provide high-resolution panchromatic stereoscopic images [34]. The Cartsosat-1 satellite is equipped with two high-resolution cameras (PAN-Fore or the frontward-looking camera and PAN-Aft or the afterward-looking camera) capable of providing imagery of 2.5 m spatial resolution with a b/h ratio of 0.62. The cameras are positioned with mount angles of +26 • and −5 • respectively and are engineered using modern technologies to collect along-the-track stereo imagery with swaths of 30 km (Fore) and 27 km (Aft) and a base-to-height ratio of 0.62 [3]. CartoDEM is a national DEM that was primarily designed for the digital representation of topography and the creation of Digital Terrain Models. CartoDEM version 3 release 1 is the latest derived from Cartosar-1 with the spatial resolution of 1 arc-second (30 m) with 16 bits per pixel and WGS84 datum. The major specifications of this satellite mission and the planned products are tabulated in Table 2. Major utilization of the Cartosat-1 imagery is in the production of Digital Elevation Models (DEMs) of the earth's terrain and Cartography.

TanDEM-X DEM
The TanDEM-X mission with its alike satellite TerraSAR-X (TSX) radar satellite (in space since June 2007) is flying in close orbit with a baseline of 250-500 m formation with adjustable scenarios in both cross and along-track directions, it is to achieve the desired interferometric baselines and the major objective is to generate a DEM at a global level which is steady, timely, and with high-precision in the bistatic mode [35][36][37][38]. Thus bistatic interferometry transmits pulses from one of the satellite's antennae and receives the backscattered signals at the same time from two satellites, which reduces the impacts of substantial temporal decorrelation and atmospheric disturbances of the old repeat-pass InSAR on the procurement of highly accurate cross-track interferograms [5]. This project completed the imaging of the earth at least twice, with extra scope over the areas of complex topography, and it also took into account of relocation of the orbits for avoiding radar shadowing in difficult terrains [39]. Freely accessible TanDEM-X 90 DEM (90 m) is used for the present study and the specifications are given in Table 3.

ICESat-2
The Ice, Cloud, and land Elevation Satellite (ICESat-1) was in operation from 2003 to 2009, the first-ever spaceborne laser altimetry mission for Earth science. This mission uses laser altimetry for determining elevation changes of glaciers, ice sheets, and sea ice thickness distribution [35]. From recommendations by the National Research Council for an ICESat consequent mission, the ICESat-2 mission was launched on 15 September 2018 [5]. ICESat-2 has a multi-beam instrument design known as the Advanced topographic laser altimeter system (ATLAS) which hosts a photon-counting technology. ATLAS Splits into 6 beams set as 3 pairs of beams, all these beam pair consists of a strong and weak energy beam (4:1 ratio), the major specifications shown in Table 4 below. Though the ATLAS instrument is enhanced as a global mission to measure changes in polar ice and land ice thickness, ICESat-2 collects elevation data for all surfaces, from pole to pole by the distribution of signal photons, the ATL08 algorithm gives Land Water Vegetation Elevation which consists of elevation heights along with canopy surface. It also includes canopy cover percentage, surface slope, surface roughness, canopy height, and apparent reflectance [23,38]. As it is providing quality and sufficient reference data, it is suitable for accurate analysis of different DEMs. Neuenschwander et al. [37] in their research carried out a quantitative evaluation of the terrain heights of the ICESat-2 ATL-08 products compared with airborne lidar data where the results have shown a Mean absolute error (MAE) of 0.5 m, while Root Mean Square Error (RMSE) was 0.82 m. The various studies done on ICESat-2 ATL 08 data proved that it is reasonably suitable for use as reference data for the accuracy assessment of DEMs [5,39,40].
ICESat-2 ATL 03 acquires the data containing a global geolocated photon representing the surface elevation detected by the ATLAS sensor, accurate latitude, longitude, with elevation data for each photon, organized by the beam in the along-track direction. These photons were classified by signal versus background including the type of surface with all geophysical corrections, segmented into numerous minute granules [36]. The evaluation of vertical accuracy reported by the various researchers through efficient evaluation is in the range of 2 to 50 cm which is acceptable for urban studies for building height estimation [27].

Methodology
Online visualization and downloading facility for various ICESat-2 data products in a.csv format are provided in the web portal called openAltimetry, with an option for 3D visualizing of the data [23,38]. For this study ICESat-2, ATL 03 data has been downloaded for three site areas from the link mentioned [36]. ATL03 data product provides the data of geolocated photons with their heights along with the time of acquisition. ATL03 classifies each photon based on their confidence levels which range from 0-4 and are represented as noise, buffer, low, medium, high, on which one can understand either an unaffected signal photon event or a noise photon event; where 4 indicates an event with a high level of confidence and 0 implying noise in our study were considered photons of high (blue) and medium (green) confidence level photons. The data product ATL03 undertakes several geophysical corrections which are related to atmosphere, tidal and solid Earth deformation and provides corrected heights for all the photon events [27]. The methodology followed in this study is shown in Figure 2.
Mean elevation from the building surface Elev bldg and mean elevation from the adjoining bare ground (datum) Elev re f were computed and the height estimation is done using Equation (1) for ICESat-2 ATL 03 data. For the ground truth data, identified the buildings, where the ICESat-2 track is passing over the building and having adjoining bare ground, and by using google images and google earth pro the building images were collected and no. of floors of every sample building is identified and then calculated with the assumed flood height of 3 m [41] which has been considered as a reference height for the ground truth height of the building and then compared it with the height of the building achieved through Equation (1) and statistical analysis has been carried out to find the accuracy of the results achieved.
For the assessment of DEMs, TanDEM-X 90 and CartoDEM datasets were downloaded from the respective websites for both study areas GHMC (Urban) and Bellampalli (Rural). ATL 08 product of ICESat-2 has been collected in .csv format from NSIDC shown in Table 5, which was utilized for evaluation of the TanDEM-X 90 DEM and CartoDEM V3 R1 over the two experimental sites of Urban and Rural areas. A study on ALT 08 data has revealed that it provides terrain elevation with vertical accuracy ranges between 1 cm to 49 cm [27]. However, outliers causing poor acquisition conditions such as clouds are filtered before using the product, and the point data has been used to generate DEM using ATL 08 elevation data which was used as reference DEM for accuracy assessment of TanDEM-X 90 and CartoDEM. The methodology followed is shown in Figure 3. as noise, buffer, low, medium, high, on which one can understand either an unaffected signal photon event or a noise photon event; where 4 indicates an event with a high level of confidence and 0 implying noise in our study were considered photons of high (blue) and medium (green) confidence level photons. The data product ATL03 undertakes several geophysical corrections which are related to atmosphere, tidal and solid Earth deformation and provides corrected heights for all the photon events [27]. The methodology followed in this study is shown in Figure 2.   The statistical parameters such as Mean Absolute Error (MAE), Standard Deviation (SD), Mean Error (ME), and Root Mean Square Error (RMSE) were calculated for quality assessment of DEMs. MAE is mathematically linear, while the RMSE is quadratic and has a relatively high weight to large errors because the errors are squared before averaging [6,10]. The difference between the value of the respective height from the TanDEM-X 90 m and CartoDEM V3 R1 (Zi (DEM) ) products; and the reference height from ICESat-2 ATL08 (Zi (REF) ) was computed. Accordingly, RMSE is used to measure the vertical accuracy. The ME (Equation (2)), MAE (Equation (3)), and RMSE (Equation (4)) were calculated using respective equations. ICESat-2 tracks distributed over both study areas GHMC (Urban) and Bellampalli (Rural) were shown in the Figure 4.
here, n equals to no. of observations available for validation.   The statistical parameters such as Mean Absolute Error (MAE), Standard Deviation (SD), Mean Error (ME), and Root Mean Square Error (RMSE) were calculated for quality assessment of DEMs. MAE is mathematically linear, while the RMSE is quadratic and has a relatively high weight to large errors because the errors are squared before averaging [6,10]. The difference between the value of the respective height from the TanDEM-X 90 m and CartoDEM V3 R1 ( ( ) ) products; and the reference height from ICESat-2 ATL08 ( ( ) ) was computed. Accordingly, RMSE is used to measure the vertical accuracy. The ME (Equation (2)), MAE (Equation (3)), and RMSE (Equation (4)) were calculated using respective equations. ICESat-2 tracks distributed over both study areas GHMC (Urban) and Bellampalli (Rural) were shown in the Figure 4.
here, n equals to no. of observations available for validation. (a)

Building Height Estimation
The mean elevation of the building surface ( ) and mean elevation from the adjoining bare ground (datum) ( ) can be inferred from the ICESat-2 ATL 03 track passing over the buildings as shown in Figures 5a and 6a. The following graphs 5c and 6c show the photons reflected from the building surface which are at a higher elevation and bare ground which are at a lower elevation, so the difference between them was computed and the height estimation is done using Equation (1). Identified the buildings, where the ICESat-2 track is passing over the building and having adjoining bare ground, and by using google images and google earth pro the building images were collected, as shown in Figures 5b and 6b and no. of floors for each building were identified and multiplied with an assumed average floor height of 3 m [41], which the author considered as reference height of buildings as shown in Figures 5 and 6. RMSE and percentage error were calculated for evaluation of ICESat-2 data which are shown in Table 6. RMSE is not always a good indicator for describing average model performance in specific situations and gives more weight to larger errors [6,10], so percentage error which is the difference between the exact value and the approximate value of a quantity, divided by the exact value and then multiplied by 100 to represent it as a percentage of the exact value [42] is carried out for individual samples since the height of the sampled done using equation buildings varies from 6m to 150 m.

Building Height Estimation
The mean elevation of the building surface Elev bldg and mean elevation from the adjoining bare ground (datum) Elev re f can be inferred from the ICESat-2 ATL 03 track passing over the buildings as shown in Figures 5a and 6a. The following Figures 5c and 6c show the photons reflected from the building surface which are at a higher elevation and bare ground which are at a lower elevation, so the difference between them was computed and the height estimation is done using Equation (1). Identified the buildings, where the ICESat-2 track is passing over the building and having adjoining bare ground, and by using google images and google earth pro the building images were collected, as shown in Figures 5b and 6b and no. of floors for each building were identified and multiplied with an assumed average floor height of 3 m [41], which the author considered as reference height of buildings as shown in Figures 5 and 6. RMSE and percentage error were calculated for evaluation of ICESat-2 data which are shown in Table 6. RMSE is not always a good indicator for describing average model performance in specific situations and gives more weight to larger errors [6,10], so percentage error which is the difference between the exact value and the approximate value of a quantity, divided by the exact value and then multiplied by 100 to represent it as a percentage of the exact value [42] is carried out for individual samples since the height of the sampled done using equation buildings varies from 6 m to 150 m. Table 6 shows the mean elevation calculated from the reflected photons from the building's roof surface and adjacent bare ground as shown in columns 2 and 3. The height computed from ICESat-2 profile, google photographs are shown in columns 4 and 5, whereas the height difference calculated using Equation (1) between these two estimates is shown in column 6 with the percentage error of each sample building in column 7. The difference values for the building height estimation are ranging from 0.01 m to 3.7 m, and the percentage error varies from 0.004% to 28%. It is observed that either overestimation or underestimation of buildings heights exist in computations. Since the heights of the buildings are calculated from the mean elevation of the building's surface and the adjoining mean elevation of the bare ground (datum), the uncertainties from these two can affect the building height estimation. The architectural aspect of the building is also not considered when the assumed floor height is multiplied by the no. of floors identified. The photons of both medium and high confidence levels were considered which also affected the estimation to an extent.

DEM Accuracy Assessment
TanDEM-X 90 and CartoDEM for both study areas GHMC (Urban) and Bellamapalli (Rural) are shown in Figures 7 and 8. Table 7 describes the statistical evaluation of TanDEM-X 90 and CartoDEM V3 R1 with the ICESat-2 ATL 08 elevation data for the study sites of GHMC and Bellampalle Mandal. ME, MAE, and RMSE reveal that the TanDEM-X DEM performs better both in Urban and Rural areas with RMSE as 5.29 m and 3.12 m in comparison to CartoDEM V3 R1 having RMSE of 7.48 m and 3.32 over Urban and Rural areas respectively. However, GHMC, the urban area selected for the study consists of high dense built-up that tends to result in a higher RMSE for the CartoDEM due to the considerations of photogrammetry. On the other hand, both the DEMs exhibited better results for the Bellampalli Mandal rural area of Telangana State as the built-up is sparse and the terrain is mostly flat. As observed in various studies RMSE is not always a good indicator for describing average model performance in specific situations and is influenced by larger errors, and thus the MAE can measure better statistics for average error [6,10]. areas respectively. However, GHMC, the urban area selected for the study consists of high dense built-up that tends to result in a higher RMSE for the CartoDEM due to the considerations of photogrammetry. On the other hand, both the DEMs exhibited better results for the Bellampalli Mandal rural area of Telangana State as the built-up is sparse and the terrain is mostly flat. As observed in various studies RMSE is not always a good indicator for describing average model performance in specific situations and is influenced by larger errors, and thus the MAE can measure better statistics for average error [6,10].    MAE for the study areas GHMC, and Bellampalli are 3.7 m and 1.4 m for TanDEM-X 90 DEMs, whereas its 6.2 m, and 2.1 m for CartoDEMs for Urban and Rural areas respectively depicting higher accuracies in rural areas. LE90 can be calculated directly from RMSE (LE90 = 1.65 × RMSE) [6] for both the test sites. The RMSE was found greater than 5 m as observed for the two DEMs. TanDEM-X for urban area site is relatively symmetric, where CartoDEM V3 R1 showed positively skewed distribution as per the calculated coefficient of Skewness (Skew) in Table 7. The results varied based on the uncertainties such as the confidence level of photon events, computations from the mean value from building surfaces and bare ground, and the reference heights of the building. The presence of water tanks, solar panels, network towers, or any such materials on the buildings can affect the photon signals, and show the higher elevation when compared to the actual height of the building. The accuracy estimations can further be higher when the reference building heights are collected from the ground surveys and by using the photon events of confidence level 4. The openly accessible DEMs are having variability in the quality over different regions (Urban and Rural) in this study and also over different terrains so it is required to understand the purpose of the study or application to decide which DEMs are required and can give better accuracy for the models [10,38,43].

Conclusions
The study showcases the building height estimations successfully in urban and rural areas using ICESat-2 ground tracks and its ATL 03 data. The statistical results are reasonably acceptable for buildings with a higher number of floors, considering all the uncertainties for reference building height. 70% of the sampled buildings have a percentage error below 10%, with 30% of the buildings having above 10% especially for buildings ranging from 2 to 5 floors. ICESat-2 data due to its along-track and discrete nature cannot be a general solution for height estimation of all buildings. The DEMs were evaluated with ICESat-2 ATL 08 Elevation data, concluding that TanDEM-X DEMs had higher accuracies in both the Urban and Rural regions under study. Both the DEMs exhibited better results for the Bellampalli Mandal rural area of Telangana State as the built-up is sparse and the terrain is mostly flat. This result can assist the decision-makers and planners in choosing suitable DEMs for planning and management purposes and the utilization of ICESat-2 ATL 03 data for higher confidence levels and technological advantages. Data Availability Statement: Publicly available datasets were analyzed in this study. This data can be found at: https://bhuvan.nrsc.gov.in/home/index.php (accessed on 13 August 2021) and https://download.geoservice.dlr.de/TDM90/ (accessed on 13 August 2021), and NASA's: https: //openaltimetry.org/data/icesat2/ (accessed on 14 August 2021). Further, the Google Earth platform is used in the study for data visualization.