Creation of ICESat-2 Footprint Level Global Geodetic Control Points Using Crossover Analysis

Abstract

Precise measurements of the Earth’s surface are possible using satellite laser altimetry data, as demonstrated by NASA’s ICEsat-2 mission. Recently, the vertical accuracy of ICESat-2 data has been validated to <3 cm (bias) and <15 cm RMSE, making these data a prime candidate for a global reference system. This research will demonstrate a methodology and results for the creation of a network of global, geodetic reference points based on ICESat-2 altimetry crossover heights. In this study, we explore the feasibility of utilizing ICESat-2 terrain heights at crossover locations and we look to evaluate the results from the different beam combinations (i.e., strong–strong, weak–weak, and weak–strong) as well as the impact of acquisition time, land cover, and presence of snow on the results. Comparisons of high-quality ICESat-2 crossovers against airborne lidar data serving as reference were found to have a mean error of less than 15 cm for each AOR examined and RMSE of less than 35 cm for two of the three sites; a RMSE value of 85 cm was obtained for the third site. Preliminary results indicate ICESat-2 crossovers are possible even in forested regions and these data can be used to vertically constrain terrain heights of other data products such as DEMs.

1. Introduction

Satellite laser altimetry provides precise measurements of Earth’s surface heights and height changes as a means to help scientists monitor and understand processes within the hydrosphere, biosphere, geosphere, and cryosphere. Laser altimetry relies on the principles of ranging (precise timing), pointing (precision attitude determination, PAD), and positioning (precision orbit determination, POD) to determine a geodetic position of each laser footprint on the Earth’s surface. Given the unprecedented vertical accuracy of laser altimetry, the utility of this technology has a broad reach across the realm of Earth science [1]. NASA has launched three space-based laser altimetry missions: The Ice, Cloud, and land Elevation Satellite (ICESat) (2003–2009), ICESat-2 (2018–present)–both free-flying platforms—and the Global Ecosystem Dynamics Investigation (GEDI) on the International Space Station (2018–present) [2,3,4]. Each of these missions has greatly contributed to tracking many of the critical climate indicators in a multi-disciplinary system over the last two decades [5]. For most space-based altimetry missions, the measurements are carefully validated to determine the footprint-level accuracies and calibrated to any known biases [6,7,8]. Ranging biases are often caused by thermal mechanical variations on-orbit, operational configurations, or surface characteristics [9,10]. Vertical biases are often realized via independent surveys or in situ measurements at the local or regional scale but become difficult to identify globally. Crossovers, where measurements from two or more satellite ground tracks intersect, provide a scenario for systematically identifying biases in the data [11]. Crossover analysis has been used for many satellite altimetry applications including refining satellite orbit positions, estimating ranging calibrations, and deriving sea surface heights, among others [12]. Ice sheet heights at orbit crossover locations between ICESat and ICESat-2 were compared to determine elevation and mass change rates between 2008 and 2019 [13,14]. Similarly, crossovers between ICESat and ICESat-2 have been used to determine the seasonal and long-term surface height changes and rates of change for the Patagonian ice fields [15].

Although laser altimetry is unique in its ability to provide three-dimensional (3D) observations with high vertical and horizontal accuracies, other technologies offer options for similar measurements with wider coverage, albeit existing challenges associated with data quality. Regardless, the science community is seeing a proliferation of radar-derived global digital elevation models (DEMs), as well as photogrammetric methodologies from commercial and government imaging systems. The advantage of using measurements from a collective of technologies is obvious in terms of expanding the overarching spatial coverage of Earth’s surface elevations, maintaining absolute vertical accuracy, and extending the temporal resolution on our changing environments. The lack of a common reference frame for radar, SfM (Structure for Motion) or stereo-photogrammetry, however, precludes the data usefulness. For this reason, data from laser altimetry, particularly ICESat-2 crossovers, potentially provide a critical resource for topographic mapping, especially in areas without quality ground control. Over the past decade, ICESat terrain heights have been used to constrain or validate global DEMs including SRTM, NASADEM, and GLO30, among others [16,17,18,19]. The motivation for this research is to present a methodology and demonstrate preliminary results for a network of global, geodetic reference points based on satellite laser altimetry crossover heights. Crossovers provide an internal quality check on the reported terrain heights from different dates/times, thus eliminating any height discrepancies due to atmospheric, calibration, or algorithmic errors. Crossovers are preferred as they do not require external data for validation; they self-validate. Of the current on-orbit missions, ICESat-2 is well-positioned to provide terrain crossover points as a global ground control network given the high quality vertical and horizontal measurement knowledge. Although GEDI presents the same potential, the uncertainties of the ISS orbit result in geolocation uncertainties, which present challenges for creating a systematic contribution to the framework [20,21].

ICESat-2

Since launch in 2018, ICESat-2 has collected ~10 trillion measurements over all of Earth’s surfaces between 88° north and south latitudes. Unique from other space-based laser altimeters, the ICESat-2 on-board instrument, ATLAS (Advanced Topographic Laser Altimetry System), uses a 532 nm (green) laser to actively profile surface elevations [4]. ATLAS uses photon counting detection technology, with sensitivities to single photon reflections, which is a distinction from traditional full-waveform or discrete return systems [4,5]. A benefit of detecting individual photons is that the laser can be operated at a high laser repetition rate (10 kHz) and low transmit energy, allowing for a nearly continuous profile (70 cm resolution) of surface measurements along the satellite ground track. By collecting a nearly continuous profile, the discrimination between ground and vegetation photons in most cases is feasible, even on sloping surfaces [22]. A limitation, however, is that only a handful of photons are detected from each outgoing laser shot over vegetation, thus under-sampling the vertical canopy structure and potentially the ground beneath.

The overall measurement accuracy from space-based laser altimeters is a function of atmospheric conditions, solar elevation, surface reflectance, surface roughness (i.e., occlusion from vegetation and topographic relief), as well as the fidelity of the ground retrieval algorithms [23]. The accuracy of ICESat-2-derived terrain heights is shown to decrease as a function of topographic slope and to a lesser degree canopy cover [24,25]. ICESat-2 terrain accuracy was reported to have the best agreement with airborne lidar (ALS) data when the ALS estimated cover ranged between 40 and 80% canopy cover [26,27]. In a study in South Carolina, the ICESat-2 terrain heights beneath a forest were reported, with a mean error and RMSE of 0.3 m and 0.75 m, respectively [28]. Similar to the observed performance of GEDI terrain heights, the topographic slope was found to have a significant impact on the observed accuracy of ICESat-2-derived terrain heights [23,29]. For a case study in Spain, [30] the authors reported that the accuracy of ICESat-2 terrain heights from the 100 m ATL08 data product were inversely proportional to the topographic slope and saw significant errors at 30 degrees or more in slope.

The true strength of ICESat-2 is the geolocation accuracy of the elevations. The mission requirement for geolocation knowledge is <6.5 m; however, recent validation analyses for release 006 of the data have determined the horizontal positional knowledge to be better than 2.1 m (Luthcke, pers. comm 2023). The vertical accuracy of ICESat-2 data has been validated to <3 cm (bias) and <15 cm RMSE [31,32]. ICESat-2 data have been impactful for Earth science applications, but many of the mission data products are now being used to validate [33,34,35]), constrain [36], or correct [32,37,38] other 3D products. The heights from ICESat-2 are above the WGS84 (ITRF2014) ellipsoid. Release 007 of the ICESat-2 data is planned for Spring 2025 and heights will be reported in WGS84 (ITRF2020: (https://itrf.ign.fr/en/solutions/itrf2020; accessed 1 March 2025)). Maguder et al. (2020) [39] analyzed ICESat-2 data collected over a geolocation validation corner cube array at White Sands Missile Range (WSMR), a technique that also allowed for estimation of the ICESat-2 footprint diameter. Multiple overpasses of WSMR determined a statistical estimate of the diameter to be between 10 and 12 m. Many scientific studies require some knowledge of the surface area illuminated by the ATLAS laser or an associated energy density; this analysis requires an estimate of the crossover coverage area, which will be assumed to be 12 m. A diffractive optical element splits the laser beam into six independent beams arranged as three beam pairs approximately 3.3 km apart (see Figure 1). Each beam pair consists of a weak and strong beam roughly 90 m apart on the surface in the cross-track direction. The detection ratio between the strong and weak beam was designed to be approximately 4:1 based on the relative energy levels, and this detection ratio is observed over land ice [40]; however, [41] found the detection ratio to be approximately 2.5:1 over forested vegetation. A sufficient number of detected and labeled ground photons are critical for calculating a crossover height.

ICESat-2 is in a 92° near-polar orbit and collects 1387 reference orbits every 91 days. Through 16 December 2024, ICESat-2 has completed 25, 91-day cycles. Over the polar regions, the satellite maintains pointing to the reference ground track, which provides seasonal, repeated measurements over those surfaces. In the mid-latitudes, however, ICESat-2 employs an off-nadir pointing scheme to increase the spatial density of measurements. Because the pointing does not repeat in the mid-latitudes, the crossover geometry cannot be easily derived from the orbit ephemeris information. Rather, the intersections must be directly computed for each beam and orbit track. As such, for every and all intersections of a descending and ascending orbit, there are potentially 36 intersecting points: nine strong–strong, nine weak–weak, and eighteen strong–weak combinations (see Figure 2). Utilizing the software package LEOCAT (https://github.com/jsipps26/LEOCAT (accessed on 20 March 2025); version 1) to compute the number of unique crossovers, or for every 91-day individual cycle, there are 239,951 unique crossovers of the reference ground track between 70°S and 75°N yielding 8,638,236 potential crossovers between all six of the beams. Assuming that only one-third of the crossovers occur over land, this results in approximately 2.87 million crossovers every 91 days. Given the off-pointing strategy across the existing 25 orbit cycles, additional crossover locations are available, making the total estimate of potential crossover points over land to be ~1.62 billion. Certainly, not every crossover instance will provide a successful height measurement comparison. ICESat-2 data are considered cloud-covered if no surface photons are recorded and the atmosphere has an optical depth greater than three [42]. Hancock et al. (2021) [43] computed the global cloud cover fraction based on 2007 Calipso cloud–aerosol lidar data and determined a global average of 54.4% daytime and 56.4% night-time over land with varying levels ranging from near 0 to 100%, depending upon the geographic location. Using 55.4% as an average global cloud fraction results in more than 80% of the potential ICESat-2 crossovers that will never be realized due to cloud cover on either the ascending or descending track. This reduction leaves approximately 324 million potentially viable crossover locations at the end of 2024. Of course, as more ICESat-2 data are collected over time, the number of crossovers will continue to increase.

In this study, we explore the feasibility of utilizing ICESat-2 terrain heights at crossover locations as a global fiducial network. In particular, we look to evaluate the results from the different beam combinations (i.e., strong–strong, weak–weak, and weak–strong) as well as the impact of acquisition time, land cover, and presence of snow on the results. The crux of this process relies upon finding consistent terrain heights from crossing ground tracks that may be months or even years apart. The signal response for ICESat-2 was tuned explicitly for bright reflecting surfaces such as land ice in the Antarctic or Greenland [40]. Over vegetation, however, the relatively low number of signal photons from ground and vegetation make the detection and subsequent labeling of those surfaces challenging. Although a few studies have explored the accuracy of the terrain and canopy heights on the ATL08 100 m data product [27,29,44,45,46], few have done so at the photon level. Generally speaking, ATL08 terrain heights are reported to be more accurate with night acquisitions, strong beam, leaf-off conditions, and with slopes under 30 degrees [30,44]. For this study, we utilize the heights from ground-labeled photons within an ICESat-2 footprint to compute the crossover heights, as the ICESat-2 footprint diameter is considerably smaller than the 100 m ATL08 product size. We hypothesize that analyzing ICESat-2 at the footprint level will yield crossovers with high accuracies under a variety of conditions (i.e., vegetation and topography).

2. Materials and Methods

To explore the feasibility of using ICESat-2 as a network of global control points, we aimed to determine how successful terrain height crossovers would be in forested and mountainous areas in addition to open, flat regions where crossovers are likely more accurate and plentiful. For this study, ICESat-2 data from 2019–2023 (release 006) were extracted for three regions: western North Carolina in the Appalachian Mountains, southern Finland, and the San Joaquin Valley, California. These three locations were chosen as they provide topographic diversity (i.e., mountainous, hilly, and flat) as well as different vegetation characteristics (i.e., mixed temperate forest, boreal forest, and agriculture/desert). Another factor for the selection of these specific sites was the availability of temporally coincident ALS data for comparison.

2.1. Reference Data

The San Joaquin Valley ALS data were collected between February and April of 2021 and have an average point density of 10 points/m². The vertical precision of the data is reported to be better than 10 cm. The data were provided in California State Plane horizontal reference frame of NAD83 and vertical reference frame of NAVD88 with Geoid 18 applied. The data were reprojected into a WGS84 horizontal and vertical reference frame, and the geoid anomaly was removed to represent ellipsoid heights. The TerraScan and TerraModeler software were used for automated data classification by the collection vendor. For this analysis, only ALS points identified as terrain were used to estimate a reference height at each crossover position.

The North Carolina ALS data were collected in collaboration between the North Carolina Emergency Management, North Carolina Geodetic Survey, and the NCDOT. Data acquisition took place between February to April of 2021 over 21 of the western most counties within North Carolina, with a reported point density of approximately 45 points/m² and vertical accuracy of 0.08 m RMSE (OCM Partners, 2024: 2017 NCEM NCDOT USGS Lidar, accessed 1 May 2023). These data were also provided in the North Carolina State Plane horizontal reference frame of NAD83 and vertical reference frame of NAVD88 with Geoid 18 applied. We reprojected the data into a WGS84 horizontal and vertical reference frame and removed the geoid anomaly to represent ellipsoid heights. These data were also automatically classified into terrain and vegetation points by the vendor and those points were selected for subsequent analysis.

The Finland ALS data were collected by the National Land Survey of Finland [47] and the Finnish Forest Centre (Suomen Metsäkeskus, SMK) to acquire a wall-to-wall, national lidar coverage. These datasets can be downloaded free of charge from the webpage of National Land Survey of Finland (https://www.maanmittauslaitos.fi/en/maps-and-spatial-data/datasets-and-interfaces/product-descriptions/laser-scanning-data-5-p (accessed on 20 March 2025)). The airborne lidar were acquired between 2008 and 2019 using discrete return, small footprint lidar systems; however, more recent collections have been added to the data repository. The ALS data were provided as the ETRS89/TM35Fin horizontal reference frame and N2000 heights and were reprojected into the WGS84 horizontal and vertical reference frame. For this analysis, the ALS data were classified into terrain and non-terrain points using a software package VIPER (Vector Image Point Elevation Raster toolbox, version 1) developed at the University of Texas Center for Space Research.

2.2. Methodology

A crossover implies there are cloud-free measurements at both contributing time epochs, which may be difficult to achieve in certain locations prone to non-optimal atmospheric conditions. Furthermore, release 006 of the ATL08 data product does have occasional issues related to ground findings that subsequently affect the accuracy of crossover terrain heights. Regarding the proportion to crossover beam composition pairing (i.e., strong–strong, strong–weak, or weak–weak), it is expected that strong–strong and weak–weak combinations, statistically speaking, should account for 50% of the crossovers and strong–weak combinations should account for the other 50% of crossovers. The same expectation for the pairing proportion is suggested based upon the acquisition time (i.e., night–night, night–day, day–day) where night–night and day–day acquisitions should represent 50% of the crossovers and a mixture of day–night acquisitions would represent the other 50% when considering crossovers over a long time-series. Again, the reality of both of these occurring depends largely upon atmospheric conditions and local conditions in a given area (i.e., topography and vegetation). Crossovers were also examined with respect to snow cover and land cover to determine the feasibility of each scenario within the global network.

Since the goal of this research is to determine the crossover heights at the footprint level rather than the ATL08 100 m segment size, we used Earthdata Search (https://search.earthdata.nasa.gov/search, accessed 1 September 2024) to pull ATL03 and ATL08 data for each area of regard (AOR) and subsequently process the data using PhoREAL (https://github.com/icesat-2UT/PhoREAL (accessed on 20 March 2025), version 3.3), a tool developed for the further analysis of ICESat-2 data over land surfaces. An overall workflow diagram to the methodology is shown in Figure 3. An initial estimation of crossovers is found by examining orbit intersections, identifying both the location of the crossover and which granules are intersected. Using PhoREAL, the ATL08 photon classifications are assigned to the individual photons on the ATL03 data product. Next, the ATL03 data are subsampled by a factor of 100 and the latitude and longitude coordinates are extracted from the labeled photons to create a true per-beam ground track (i.e., beam track). A beam track is generated by interpolating the latitude and longitude values between the labeled photons. This method for determining the true beam track is necessary since the satellite undergoes off-nadir pointing as well as opportunistic pointing maneuvers and relying solely on the planned orbits is not recommended. Once the ground tracks are generated for each beam (i.e., six beam tracks), they are checked against the other beam tracks from all other orbits to determine intersection points. The intersection point is defined here as the exact intersection between two beam tracks and does not include a buffer or spatial tolerance. With an intersection point determined between two beam tracks, the full resolution ATL03 data are extracted +/− 6 m (i.e., 12 m diameter footprint assumption based on [39]) from the intersection point along the beam track in each direction. Using only the ground-labeled photons, the median terrain height within the footprint is calculated for both crossing beams (i.e., cross 1 height and cross 2 height). The crossover difference is computed as the difference between the cross 1 height and the cross 2 height. For this research, we are using a crossover height difference threshold of 10 cm as our criteria for keeping a crossover height as a geodetic point. This value, however, could certainly change for other projects or applications that require a different level of accuracy or precision. Other information, such as flags from the nearest ATL08 land segment to each granule, were also recorded for analysis.

Statistical metrics were computed for the crossover height differences, x_i. We define the mean error as follows:

$$MeanError={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{x}_i.$$

The mean absolute error is defined as follows:

$$MAE={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n\left|x_i\right|.$$

The root mean squared error is defined as follows:

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{\left(x_i\right)}^2}.$$

3. Results

3.1. San Joaquin Valley, California

Five years (2019–2023) of ICESat-2 data were examined for crossover statistics in the San Joaquin Valley, California, which falls latitudinally between 36.5°N and 38°N and is shown in Figure 4. Representing an area approximately ~38,000 km² in size, this region is considered an excellent location for utilizing ICESat-2 heights for geodetic control, as the region is predominantly flat terrain with little forest cover. For this five-year time period, 100,512 potential crossovers exist in the area of regard (AOR) based on the cycles’ orbit geometry and off-nadir pointing configurations. Of these predicted crossovers, 23,245 were physical crossovers, which corresponds to a 23.12% usable crossover rate. Subsequently, a 23.12% crossover rate, in turn, indicates a cloud-free equivalency percentage of approximately 48% (0.48 × 0.48 = 0.2304) for each crossing beam track. The 95th percentile error for all 23,245 ICESat-2 crossover height differences in this study area was 2.17 m; 9505 (41.14%) of the crossovers had height differences less than 10 cm and 5193 (22.48%) had a height difference less than 5 cm.

Table 1. Residuals between ICESat-2 crossover heights < 10 cm and airborne lidar for San Joaquin Valley, CA. A value of N/A indicates no reference data were available for comparison.

	MAE (m)	Mean Error (m)	RMSE (m)	Number and Percentage of Crossovers < 10 cm
Strong–Strong	0.103	0.032	0.299	2814 (29.61%)
Strong–Weak	0.105	0.035	0.227	4712 (49.57%)
Weak–Weak	0.113	0.037	0.209	1979 (20.82%)
Night–Night	0.106	0.029	0.259	1311 (13.79%)
Night–Day	0.104	0.032	0.257	4460 (46.92%)
Day–Day	0.109	0.041	0.228	3734 (39.28%)
Snow–Snow	N/A	N/A	N/A	1 (0.01%)
Snow–No Snow	N/A	N/A	N/A	4 (0.04%)
No Snow–No Snow	0.104	0.025	0.243	9500 (99.95%)
Low Veg	0.106	0.040	0.234	8256 (86.86%)
Water	0.144	0.144	0.147	21 (0.22%)
Urban	0.097	0.024	0.311	620 (6.52%)
Closed Forest	0.094	0.028	0.341	301 (3.17%)
Open Forest	0.122	0.055	0.27	307 (3.23%)

reports the number and percentage of ICESat-2 crossovers with height differences < 10 cm stratified by beam strength, acquisition time, and land cover type. Also listed in Table 1 are the residuals between airborne lidar at each crossover footprint and the ICESat-2 crossover height. For this analysis, the ICESat-2 crossover height is represented as the mean of each crossover height. A histogram of the airborne lidar and high quality ICESat-2 crossover residuals is shown in Figure 5.

When considering ICESat-2 crossovers with a height difference less than 10 cm, the strong–strong beam combination accounted for 29.6% of all crossovers, followed by 49.6% for the strong–weak beam combination and 20.8% for the weak–weak beam combination. Although the ~21% weak–weak combination is statistically less than expected, the weak beam does contribute a terrain height measurement for ~70% of the high-quality crossover pairs (i.e., <10 cm). The residuals between the San Joaquin airborne lidar data and the high-quality crossovers were found to have an overall mean error, mean absolute error (MAE), and root mean squared error (RMSE) of 0.025 m, 0.104 m, and 0.243 m respectively. When examining the residual errors for the different beam strength combinations, the errors for the mean error for all combinations were comparable, ranging between 0.032 and 0.037 m, and RMSE values ranging from 0.209 to 0.299 m. Combinations of night–night crossovers had the lowest mean and RMSE values of 0.029 m/0.259 m, followed by 0.032 m/0.257 m and 0.041 m/0.228 m for night–day and day–day crossovers. For the time-of-day crossover pairs, a statistically noticeable trend is the relatively low number of night–night crossovers, 13.8%, when 25% was the expected amount. Within the San Joaquin Valley, a fog known as the Tule fog develops nightly during the months of November to March [47]. The presence of the Tule fog, similar to cloudy conditions, reduces the number of usable opportunities, which is assumed to be the reason for the statistical disparity in night-time acquisitions. The crossover height differences were also stratified by the presence of snow, and for this AOR, snow was found to not be present in over 99% of the crossovers. For the high-quality ICESat-2 crossovers, there were no available airborne lidar data that coincided with the five crossovers with snow. The majority (86.8%) of the identified high-quality crossovers occur over agricultural and flat terrain and the ME and RMSEs were found to be 0.04 m and 0.234 m. The urban class had a lower mean error than low veg at 0.024 m but a slightly higher RMSE at 0.311 m. The water land cover class had the largest mean error at 0.14 m and RMSE of 0.147 m, but these errors are attributed to temporal differences in the water levels of lakes and rivers. The mean residual error and RMSE for open forests were found to be 0.055 m and 0.027 m compared to 0.028 m and 0.341 m for closed forests, for which it would be assumed to be more difficult to retrieve terrain heights compared to open forests.

3.2. Finland

Following a similar approach as implemented for the San Joaquin Valley, five years of ICESat-2 data were extracted from a roughly 42,000 km² region of southern Finland, lying latitudinally between 61.5°N to 63°N and is shown in Figure 6. This AOR has a higher number of potential crossovers (539,460) due to the increased number of ground tracks passing through the region based on the track convergence at higher latitudes. However, Finland’s 60 deg latitude has a high frequency of cloudy conditions due to colliding air masses. As such, at this location, only 34,387 crossovers (6.37%) were realized. A 6.37% crossover rate is equivalent to a cloud-free percentage of approximately 25% (0.25 × 0.25 = 0.063).

Table 2. Residuals between ICESat-2 Crossover Heights < 10 cm and airborne lidar for southern Finland.

	MAE (m)	Mean Error (m)	RMSE (m)	Number and Percentage of Crossovers < 10 cm
Strong–Strong	0.225	0.106	0.349	2473 (32.97%)
Strong–Weak	0.240	0.129	0.372	3603 (48.03%)
Weak–Weak	0.255	0.148	0.385	1425 (19%)
Night–Night	0.228	0.065	0.335	1288 (17.17%)
Night–Day	0.235	0.117	0.350	3603 (48.03%)
Day–Day	0.247	0.169	0.406	2610 (34.80%)
Snow–Snow	0.252	−0.042	0.349	865 (11.53%)
Snow–No Snow	0.226	0.096	0.343	2517 (33.56%)
No Snow–No Snow	0.242	0.181	0.385	4119 (54.91%)
Low Veg	0.196	0.087	0.315	297 (3.96%)
Urban	0.173	0.113	0.403	135 (1.8%)
Water	0.281	0.230	0.376	2369 (31.58%)
Closed Forest	0.221	0.085	0.352	4072 (54.29%)
Open Forest	0.259	0.148	0.447	705 (9.4%)

reports the number and percentage of ICESat-2 crossovers with height differences < 10 cm stratified by beam strength, acquisition time, and land cover type. Also listed in Table 2 are the residuals between the Finland airborne lidar at each crossover footprint and the ICESat-2 crossover height. A histogram of the airborne lidar and high quality ICESat-2 crossover residuals is shown in Figure 7.

The 95th percentile error for all 34,387 ICESat-2 crossovers is 2.23 m; 7501 (21.81%) of the crossovers had a height difference less than 10 cm and 3865 (11.24%) had a height difference less than 5 cm. Of the high-quality crossovers, 81% had either a strong–strong beam or strong–weak configuration, likely indicating the need for the strong beam to penetrate through the vegetation and yield ground photons. Only 19% of the crossovers were a weak–weak combination. The residuals between the Finland airborne lidar data and the high-quality crossovers were found to have an overall mean error, mean absolute error, and root mean squared error (RMSE) of 0.125 m, 0.238 m, and 0.367 m respectively.

The ME and RMSE for the beam combinations were relatively similar for all combinations, with strong–strong having the lowest ME and RMSE values at 0.106 m and 0.349 m and weak–weak having the highest ME and RMSE of 0.148 m and 0.385 m, respectively. Daytime passes were twice as critical than night-time passes in yielding valid terrain heights, with 34.8% for day–day crossovers compared to 17.2% for night–night crossovers, whereas approximately 48% of the crossovers were a combination of day–night passes. The imbalance of night–night passes is attributed to cloud cover during the winter months when less daylight is present. Day–day combinations of crossovers, however, had the highest error of 0.169 m and 0.406 m ME and RMSE. Regarding the impact of snow cover, ~45% of the crossovers had observable snow on at least one of the crossover times. The crossovers with a snow–snow configuration were biased lower than the no snow passes with a ME −0.041 m and RMSE 0.349 m, respectively, compared to no snow–no snow conditions, with an ME of 0.181 m and RMSE of 0.385 m. The majority (63.7%) of the identified high-quality crossovers occur over closed or open forests and the ME and RMSEs were found to be 0.085 m and 0.352 m and 0.148 m and 0.447 m, respectively. The low vegetation class had the lowest errors compared to the airborne lidar data, with ME and RMSE values of 0.087 m and 0.315 m. The urban class had a higher mean error than low veg at 0.113 m and the highest RMSE at 0.403 m. This land cover class, however, only represented 1.8% of the high-quality crossovers. The water land cover class had the largest mean error at 0.230 m and RMSE at 0.376 m, but these errors are attributed to temporal differences in water levels of lakes and rivers.

Vegetation in this region is predominantly boreal forest, with tree heights extending up to approximately 30 m. Figure 8 depicts the histogram of ICESat-2-determined maximum canopy heights for all ICESat-2 crossovers, as well as those with a crossover height difference less than 10 cm, demonstrating the fact that even in the presence of forested vegetation, obtaining an accurate terrain height is feasible.

3.3. Western North Carolina/Eastern Tennessee

The third study area evaluated is a 34,000 km² region of the Appalachian Mountains of western North Carolina and eastern Tennessee, lying latitudinally between 35°N and 36.5°N and is shown in Figure 9. This AOR has a potential of 84,132 ICESat-2 crossovers during the 2019–2023 period; however, only 2464 (2.9% crossover rate) crossovers were physically identified. A 2.9% crossover rate is equivalent to a cloud-free percentage of 17% (0.17 × 0.17 = 0.029). An observation is the significantly lower crossover rate (2.9%) compared to San Joaquin (~23%) and southern Finland (6.3%).

Table 3. Residuals between ICESat-2 crossover heights < 10 cm and airborne lidar for western North Carolina/eastern Tennessee. N/A indicates no reference data were available for direct comparison.

	MAE (m)	Mean Error (m)	RMSE (m)	Number and Percentage of Crossovers < 10 cm
Strong–Strong	0.567	0.193	0.939	221 (46.53%)
Strong–Weak	0.492	0.116	0.767	204 (42.95%)
Weak–Weak	0.496	0.008	0.668	50 (10.53%)
Night–Night	0.519	−0.083	1.057	120 (25.26%)
Night–Day	0.524	0.178	0.789	235 (49.47%)
Day–Day	0.541	0.290	0.680	120 (25.26%)
Snow–Snow	0.04	0.04	N/A	1 (0.2%)
Snow–No Snow	0.231	−0.231	0.287	4 (0.8%)
No Snow–No Snow	0.533	0.146	0.848	467 (98.32)
Low Veg	0.406	−0.009	0.56	141 (29.68%)
Water	N/A	N/A	N/A	8 (1.68%)
Urban	0.204	−0.141	0.286	27 (5.68%)
Closed Forest	0.692	0.245	1.124	146 (30.74%)
Open Forest	0.482	0.168	0.683	153 (32.21%)

reports the number and percentage of ICESat-2 crossovers with a height differences < 10 cm stratified by beam strength, acquisition time, and land cover type. Also listed in Table 3 are the residuals between the North Carolina airborne lidar at each crossover footprint and the ICESat-2 crossover height. A histogram of the airborne lidar and ICESat-2 crossover residuals is shown in Figure 10.

The 95th percentile error for all 2464 crossovers is 18.27 m; 475 (19.28%) of the crossovers had a height difference less than 10 cm and 267 (10.8%) had a height difference less than 5 cm. However, the histogram in Figure 9 also indicates the presence of several significant height difference outliers, even for the ICESat-2 high quality crossovers. Based on the ICESat-2 crossover statistics, this particular AOR has significantly more outliers than the other two study locations. Of the crossovers, 89.5% had either a strong–strong beam or strong–weak configuration, indicating the need for the strong beam to penetrate through the vegetation. Only 10.5% of the crossovers were a weak–weak combination. Interestingly, the weak–weak combination resulted in the lowest mean and RMSEs of 0.008 m and 0.668 m, respectively. The percentage of night–night and day–day passes were found to be close to the expectation of 25% for each and 50% representing a night–day combination. The night–night passes had the lowest mean error of −0.083 m but the largest RMSE of 1.057 m compared to the day–day passes, with a mean error and RMSE of 0.29 m and 0.68 m, respectively. The presence of snow was not a significant factor on the ICESat-2 crossovers in this AOR, with only five crossovers having snow cover in at least one of the crossovers. Regarding land cover, low vegetation comprised 29.7% of the high-quality ICESat-2 crossovers and the ME and RMSE of the residuals were found to be −0.01 m and 0.56 m. The largest RMSE errors of crossovers occur in the open and closed forest land cover classes, at 0.683 m and 1.124 m, respectively. Of all the crossovers for this AOR, approximately 63% occurred over forested lands. This AOR comprises both dense forests and a mountainous topography, which can prove difficult in correctly labeling the ICESat-2 photons.

Vegetation in this region is predominantly temperate mixed forest of both broadleaf and coniferous trees with tree heights extending up to approximately 45 m. Figure 11 depicts the histogram of ICESat-2 estimated canopy heights for all identified crossovers as well as those with a crossover terrain height difference less than 10 cm. Again, based on the statistics presented in Table 3, obtaining an accurate terrain height in the presence of forested vegetation is feasible with ICESat-2.

4. Discussion

Recently, an effort reported in [48] constructed a sample database of global elevation control points derived from the ICESat-2 100 m ATL08 data product, where ATL08 segments were selected based on the land cover type and whether the terrain height difference between ATL08 and an airborne lidar-derived DEM was below a height threshold. For their dataset, the threshold requirement for their data product was 0.5 m, 0.7 m, and 1.5 m for flat, hilly, and mountainous terrain, respectively. The validity of the threshold heights used in the (2024) study by [48] is predicated on the 100 m segment length of ATL08. A limitation of utilizing ATL08 as a geodetic reference point is the 100 m segment length, which precludes the accurate representation of terrain except for extremely flat surfaces. The requirement for establishing a geodetic reference system is vertical accuracy to within a few centimeters. Achieving that level of accuracy, in turn, requires a small footprint so that topographic effects are minimized. By calculating crossover heights to the footprint level, a higher level of accuracy is possible. Furthermore, another benefit of using crossovers to create this data product is that ancillary high resolution lidar DEMs are not required to determine accurate ICESat-2 terrain heights.

The goal of this paper is to illustrate a methodology for computing ICESat-2 crossovers at the footprint level as a means to generate a global network of fiducial points. To that end, based on the accuracy analysis, there might only be a sub-set of ICESat-2 crossovers with height differences that meet a user’s requirement. In this analysis, crossovers whose height difference is less than 10 cm were analyzed and compared against airborne lidar data, which serve as a reference. The ICESat-2 crossovers over the San Joaquin Valley agreed most closely with the reference airborne lidar data, with a mean error of 0.02 m and RMSE of 0.24 m, as this AOR is largely flat and comprised of low vegetation, bare soil, or agriculture. The agreement of crossover heights from southern Finland were also low, with an overall mean error of 0.125 m and a RMSE of 0.367 m. Although these statistics are ~10 cm higher than those found in the San Jaoquin Valley, this area is heavily forested, with 63% of the crossovers occurring in forested regions. The high quality crossover results over the North Carolina AOR were found to have the highest errors, with a mean error of 0.139 m and RMSE of 0.842 m compared to the airborne lidar data. In this location, there were significantly fewer numbers of crossovers compared to the other two location study sites, which could be responsible for the statistical disparity. This location is also heavily forested and part of the Appalachian Mountains, with a significant topography, which, historically, has been a challenging location for space-based lidar topographic mapping. Potential issues associated with ground findings as part of the ATL08 algorithm likely have reduced the number of crossovers meeting the 10 cm selection criteria. With improved ground finding on ATL08 subsequently resulting in a larger pool of potential crossovers within our 10 cm, the residual errors between the ICESat-2 crossovers and airborne lidar could be reduced. Furthermore, the statistics reported in the results section for various land cover categories should be considered with some caution. The land cover reported on the ATL08 data product and used in this analysis are derived from the 2019 Copernicus land cover, which is produced at a 100 m spatial resolution. The ICESat-2 footprint diameter is estimated to 10–12 m; thus, the land cover at the footprint level could be different than what is reported at the 100 m length scale.

Although much of the literature validating ICESat-2 canopy heights over land and vegetation report that daytime acquisitions and weak beam data are less useful than strong beam/night-time data [30,49], it was demonstrated here that these acquisition scenarios did provide terrain heights that are usable for crossovers. Although weak–weak combinations of beams typically resulted in fewer crossovers than strong–strong combinations, particularly in forested areas, the weak beam was critical to finding a significant number of weak–strong combinations. Weak beam and daytime acquisitions should be utilized for a larger set of geodetic control heights and potentially considered for all applications.

The ICESat-2 data used in this study are from release 006 of the ATL08 data product [22]. Although the photon classifications in release 006 are good in many places, there are known issues related to ground findings that result in a mislabeling of the photons, particularly in areas with a varying topography and dense vegetation cover. Because the crossover technique described here relies solely on the correctness of the photon labels, it is anticipated that a similar crossover analysis based on release 007 of the ICESat-2 data will result in a reduction in crossover errors, as significant improvements to the ground finding algorithm have been implemented. Figure 12 illustrates the upcoming improvements to the ATL08 algorithm for ground findings. At time 308.2, the top of a small hill is truncated by approximately 7 m, resulting in ground photons being mislabeled as canopy in release 006, and correctly labeled as ground in release 007. Smaller terrain improvements are apparent by visibly comparing the two images. With these improvements to the labeling of ground photons, it is anticipated that the crossover errors will decrease and potentially more crossovers may fall beneath a user-specified accuracy threshold. The purpose of this exercise, however, is to demonstrate that ICESat-2 crossovers can be computed and used as a 3D fiducial dataset, even in areas with dense vegetation and topography.

The intersection points calculated between each ICESat-2 beam track in reality have horizontal and vertical geolocation errors on each ascending and descending beam. For the purpose of this paper, the geolocation error was assumed to be zero; however, it should be noted that the horizontal geolocation errors are reported to be on average < 2.5 m (Luetcke pers comm for release 006 data) but vary throughout the orbit. ICESat-2 crossovers are utilized as a means to estimate the geolocation error [50]. In addition to potential geolocation errors, a positional ambiguity for each photon is present. That is, all photons reflected from a single footprint are given a geolocation equal to the center, or bounce point of the beam [7]. Future work is planned to calculate the beam energy divergence as a means to reduce the within-footprint positional ambiguity. A question regarding the scalability of this methodology for creating a global network of fiducial points remains. Certainly, this approach is computationally expensive as each intersection point would require calculation from the ATL03/ATL08 photons. With sufficient computing resources and time, however, this network can be created based on methods presented here. A recommended strategy would be to initially leverage this capability for regions of the world that do not have extensive geodetic control or survey data available.

5. Conclusions

This work demonstrated a technique for calculating crossover heights and errors at the ICESat-2 footprint level over terrestrial surfaces such that they can be used as a global 3D fiducial network. We examined three specific geographic locations with diverse environmental conditions to determine crossover statistics associated with feasibility and utility. We found that when utilizing crossovers, all ICESat-2 data can potentially provide terrain heights that are usable as reference data when selecting the crossover height difference as the selection criterion. Comparisons of high-quality ICESat-2 crossovers against airborne lidar data serving as reference were found to have a mean error of less than 15 cm for each AOR examined and RMSE of less than 35 cm for two of the three sites; a RMSE value of 85 cm was obtained for the third site. ICESat-2 data from weak beams as well as those acquired during the daytime were as important as strong beams and night acquisitions for creating a reference database. Furthermore, terrain crossover height differences beneath vegetation better than 10 cm, or any other threshold, are also possible. These ICESat-2 crossover heights can be used here to create a global reference system, which in turn, can be used to vertically constrain terrain heights of other data products such as high resolution DEMs and DTMs.