Since August 2006, an 11 km ground-based kinematic GPS survey has been conducted monthly near Summit Station, Greenland (Fig. 1). The survey has been part of a larger long-term observation program funded through the National Science Foundation (NSF). The survey route was designed to follow an ICESat reference ground track (no. 0412); the survey route intersects the ICESat reference ground track often to enable a large number of data “crossovers” for direct comparison of ground-based and spaceborne elevations. Data from this survey have been used for ICESat surface elevation validation and have provided an assessment of ICESat inter-campaign surface elevation biases (Siegfried et al., 2011).

The monthly Summit Station ground-based GPS survey represents the most temporally long and dense in situ observation of ice-sheet elevation change. The survey is expected to continue through the ICESat-2 mission to provide a nearly 15 year ground-based dataset. The 11 km GPS survey intersected just 6 km of the ICESat reference ground track (Fig. 1). However, the high temporal resolution and long time series of the ground-based GPS data provide a robust means of validating satellite-derived estimates of ice-sheet elevation change. As such, the exact orbit of ICESat-2, and the resultant satellite ground track, was defined in part based on the location of this survey; similar to ICESat, the survey will intersect approximately 6 km of an ICESat-2 reference ground track (Fig. 1).

The kinematic GPS survey is conducted using a dual-frequency Trimble R7 receiver recording at 0.5 or 1 Hz with a Trimble Zephyr antenna (TRM39105); we note that the kinematic surveys have always been conducted using this equipment. Starting in August 2007, the “roving” antenna was mounted on a static metal post on a sled towed behind a snowmobile at ∼ 5 m s-1 (Siegfried et al., 2011; Fig. 2). Current survey protocols call for the survey technician to measure the length of the static antenna post and the depth of the runners of the sled into the snow surface at the beginning and, usually, at the end of each survey (Table 1). These measurements and the appropriate National Geodetic Survey (NGS) antenna model allow for the calculation of the distance from the phase center of the roving antenna to the surface of the snow (Fig. 2). A continuously operating GPS base station has been installed at Summit Station (3 km east of the start of the survey and 6.5 km southeast of the end of the survey; Fig. 1). For the duration of the survey time series, the base station has been a dual-frequency Trimble NetRS receiver recording at 1 Hz with a Trimble Zephyr Geodetic antenna (TRM41249; Siegfried et al., 2011). Periodically, that station is moved and the base station name is altered to reflect this change (e.g., SUMM prior to July 2009, SMM1 between July 2009 and August 2013, and SMM2 from October 2013 to the present, although the station was not renamed until July 2014). Both the base station and the rover logged data solely from the GPS constellation. The Summit base station GPS data are publicly available for download on the University NAVSTAR Consortium (UNAVCO) Data Archive Interface (http://www.unavco.org/data/gps-gnss/data-access-methods/dai2/app/dai2.html).

When it was logistically possible, the timing of the ground-based survey was coordinated with NASA airborne surveys of the region (Table 1). This allowed for the assessment of airborne lidar performance over ice-sheet interiors (e.g., Brunt et al., 2014). When the timing offset between the airborne and GPS surveys is minimized, assessments of lidar performance are made in the absence of environmental factors (e.g., snow, melt, or wind events) that change the surface and potentially compromise the analysis. Six of the airborne campaigns were offset from the ground-based GPS survey by two days or less; however, three of the campaigns were offset by eight days or more, with the maximum offset being 20 days (Table 1).

ATM (Krabill et al., 2002) is one of the two main airborne laser altimetry systems used by NASA's Operation IceBridge. The current ATM configuration generally consists of a dual instrument configuration, with a wide-scan lidar and a narrow-scan lidar integrated simultaneously. The wide-scan lidar has a full scanning angle of 30∘ and is generally used over the ice sheets; the narrow-scan lidar, which was first integrated with IceBridge in 2012, has a full scanning angle of 5∘ and is generally used over sea ice but has also been used for high-altitude land-ice flights. Both ATM lidars are conically scanning, full-waveform systems that transmit 532 nm wavelength 6 ns pulses with a 3 or 5 kHz repetition rate.

ATM has been in operation since 1993. Components of ATM, such as the data system and scanner assembly, have been improved over time. The details of the version of the data system (e.g., “4B”), scanner assembly (e.g., “T2”), and scanning angle (e.g., “30∘”) that were used for each airborne survey are captured in Table 2.

ATM surveys over Summit Station were generally conducted using the NASA P-3, but ATM has also been integrated with the NASA C-130 (2015 Arctic campaign; Table 1) and the National Oceanic and Atmospheric Administration (NOAA) P-3 (2016 Arctic campaign; Table 1). Surveys were conducted at a nominal aircraft speed of ∼ 100 m s-1 and with a nominal altitude of ∼ 450 m above ground level (a.g.l.). At this air speed, altitude, and repetition frequency, the wide-scan ATM lidar generates a 1 m diameter footprint and a scanning swath width of ∼ 250 m and the narrow-scan ATM lidar generates approximately the same footprint with a scanning swath width of ∼ 40 m (Fig. 3). ATM elevation bias and precision, for the dual instrument configuration, has been assessed based on crossover analyses and comparisons with elevations derived from ground-based GPS surveys of airport departure aprons. ATM elevation bias and precision estimates are 0.07 and 0.03 m, respectively (Martin et al., 2012).

We obtained the ATM Level-1B Qfit Elevation and Return Strength data (Krabill, 2013) through the National Snow and Ice Data Center (NSIDC) Operation IceBridge Data Portal (http://nsidc.org/icebridge/portal/) for the six flights over the Summit Station GPS ground-survey area (Table 1; Fig. 1). The data files include position information of the surface reflection (latitude, longitude, and elevation) that is derived from the combination of data from the laser systems with data from on-board GPS (Javad) and inertial systems (either Applanix POS AV 510 or 610 systems). Positioning information is derived using differential GPS (DGPS) post-processing techniques. DGPS solutions require both a roving GPS receiver and a static base station. ATM position solutions were determined relative to data from a base station that was installed at the departure airport and was accomplished in a software package developed by the ATM team at the NASA Goddard Space Flight Center (GSFC) called GITAR (GPS Inferred Trajectories for Aircraft and Rockets; Martin, 1991). GITAR is optimized for the polar environment and long baselines. It incorporates data from GPS and GLONASS (since 2011) satellites, as well as data from multiple ground stations, for improved satellite geometry, especially at high latitudes.

LVIS (Blair et al., 1999) is the second main airborne laser altimeter used by Operation IceBridge. It is a swath-scanning, full-waveform laser altimeter that transmits 1064 nm wavelength 9 ns pulses with a 500 to 1500 Hz repetition rate (Blair et al., 1999) using a scan angle that varies between ±6∘. LVIS surveys over Summit Station (Table 1) were conducted using both the NASA P-3 (2007) and the DC-8 (2010) at a nominal aircraft speed of ∼ 100 m s-1 and an altitude over Summit Station of ∼ 4600 m a.g.l. At this air speed, altitude, and repetition frequency, LVIS generates a ∼ 10 m diameter footprint and a scanning swath width of ∼ 1000 m (Hofton et al., 2008; Fig. 3). LVIS long-term (e.g., GPS-related) elevation biases, assessed along two repeated several hundred-kilometer-long transects over the Greenland Ice Sheet, were found to be better than ±0.05 m with precision estimates at multiple crossover locations that were better than 0.07 m (Hofton et al., 2008).

There were two LVIS flights over the Summit Station GPS ground-survey area (Table 1; Fig. 1): one associated with Operation IceBridge (14 April 2010) and one as part of a demonstration dataset for future spaceborne concepts (20 September 2007). Similar to ATM, we obtained the IceBridge LVIS L2 Geolocated Surface Elevation Product, version 1.1 (Blair and Hofton, 2015), through the NSIDC Operation IceBridge Data Portal (http://nsidc.org/icebridge/portal/). We obtained the Pre-IceBridge LVIS L2 Geolocated Ground Elevation and Return Energy Quartiles, version 1 (Blair and Hofton, 2011), through the NSIDC (http://nsidc.org/data/blvis2). These files include the position information (latitude, longitude, and elevation) of the lowest reflecting surface in the footprint that is obtained from the combination of laser ranges with laser positioning and pointing information (Hofton et al., 2008). Laser positioning and pointing information are derived from an integrated GPS (either Javad, NovAtel, or Ashtech receivers) and inertial system (either Applanix POS AV 510 or 610 systems) and processed using the commercially available GrafNav (GPS) and POSPac (inertial) software. The 2007 data used DGPS post-processing techniques relative to a base station at Kangerlussuaq, Greenland. The 2010 data utilized precise point positioning (PPP) techniques, which do not require a base station but rather rely on more precise satellite orbit and clock information to determine the position of the roving GPS receiver. Position information for the 2007 and 2010 LVIS campaigns incorporated data from the GPS constellation only.

For completeness, we note that a third NASA laser altimeter has flown over the Summit Station GPS ground-survey area. MABEL is a photon-counting laser altimeter that was developed in support of ICESat-2. In April 2012 it surveyed the Greenland Ice Sheet and Arctic sea ice based out of Keflavík, Iceland; data from this campaign, including analysis of data over the Summit Station ground survey, is presented in Brunt et al. (2014). MABEL is distinct from the other two lidars assessed here in that it has as many as 24 beams profiling in a linear array (as opposed to the swath methods of ATM and LVIS) perpendicular to the direction of flight.

MABEL transmits 532 and 1064 nm wavelength ∼ 1.5 ns pulses with a variable repetition rate (5 to 25 kHz; McGill et al., 2013). MABEL surveys were conducted using the NASA ER-2 at a nominal aircraft speed of ∼ 200 m s-1 and with an altitude over Summit Station of ∼ 16 000 m a.g.l. At this air speed, altitude, and a 5 kHz repetition frequency, MABEL generates a 2 m diameter footprint every 0.04 m with a swath width of as much as 2000 m. Based on an error analysis, Brunt et al. (2014) estimated MABEL elevation uncertainty for the Summit Station region to be 0.15 m. MABEL surface–elevation bias and measurement precision has been assessed based on direct comparisons of MABEL surface elevations with digital elevation models derived from ground-based GPS data collected on airport departure aprons. MABEL surface measurement precision assessments are generally 0.11 to 0.14 m but have been as high as 0.24 m (Brunt et al., 2014, 2016; Magruder and Brunt, 2017). MABEL surface–elevation bias is generally on the order of 1 m; while this bias is relatively large, it is within the mission design goals of MABEL (ICESat-2 algorithm development and error analysis), which focus on surface measurement precision. MABEL data files include position information derived from a GPS integrated with a NovAtel HG1700 AG58 inertial system and are available via the NASA ICESat-2 website (http://icesat-2.gsfc.nasa.gov).

Because MABEL is a multibeam profiling (rather than scanning) lidar, there are relatively few intersections between MABEL beams and the ground-based GPS survey, ultimately resulting in poor quality statistics (Fig. 3) based on small sample size and poor spatial distribution. These limited areas of airborne and ground-based data intersection are highly clustered in the few places where the MABEL profile crossed the GPS survey and therefore do not represent a spatially diverse assessment of MABEL instrument performance. Consequently, we exclude MABEL from further discussion, as the dataset is fundamentally different than that of the other scanning lidars considered here.

Ground-based position solutions from three GPS post-processing software packages, using both PPP and DGPS methods, were compared with airborne elevation data. PPP solutions were acquired using Inertial Explorer version 8.60, a commercial GPS post-processing software package developed by NovAtel. One set of ground-based DGPS solutions was acquired using TRACK (Trajectory Calculation with Kalman Filter), the kinematic DGPS component of GAMIT (a GPS utility that was partially developed and supported by the Massachusetts Institute of Technology). Kinematic GPS positions from TRACK version 1.28 software (Chen, 1998) were determined by carrier-phase differential processing relative to the Summit GPS base station. A second set of ground-based DGPS solutions was acquired using ATM's GITAR post-processing software (Martin, 1991). For the DGPS results, the positions of the Summit GPS base station were obtained using GIPSY–OASIS (GNSS-Inferred Positioning System and Orbit Analysis Simulation Software). For the GITAR solutions, the base station positions represent an average of four days of data, centered on the timing of the ground survey. For the TRACK solutions, the base station positions represent an average recorded over the duration of the ground-based survey.

Independent of post-processing method, all of the ground-based GPS solutions are based on final precise orbit and clock information from the Crustal Dynamics Data Information System (CDDIS) hosted at GSFC. Processing using TRACK corrected for errors associated with the ionosphere by incorporating an IGS data product. To mitigate the effect of multipath distortion, all processing methods used a cut-off angle (7.5, 10, and 12∘ for Inertial Explorer, TRACK, and GITAR, respectively). Inertial Explorer and TRACK used a Saastamoinen model to correct for tropospheric delay, while GITAR used a gridded reanalysis data product from the National Centers for Environmental Prediction (NCEP). All processing methods corrected for solid Earth tides based on an International Earth Rotation and Reference System Services (IERS) model.

All of the ground-based GPS data were solved to the phase center of the antenna. TRACK and PPP solutions used the L1 antenna phase center, while GITAR used the LC phase center. The solutions were then referenced to the ellipsoid (WGS84) and datum of the matching airborne data (either ITRF00, ITRF05, or ITRF08, indicated in Tables 1 and 2). The GPS phase-center elevation solutions were then reduced to the snow surface (Fig. 2) using data from the field (Table 1) and the appropriate NGS antenna model phase-center offsets. Specifically, the calculation of the height of the surface of the snow (h) is h=GPSPC-hAntPost-hNGSmodel+hRunnerDepth, where GPSPC is the surveyed position solution to the phase center of the ground-based roving antenna, hAntPost is the height of the antenna post (1.785 or 1.797 m, depending on the survey; Table 1), hNGSmodel is the NGS model distance between the antenna phase center and the antenna base plane (0.056 or 0.061 m for the L1 or LC phase centers, respectively), and hRunnerDepth is the depth of the sled runners in the snow surface (variable, ranging from 0.0125 to 0.02 m; Table 1). We note that the ground-based GPS data were collected at 1 Hz, with the snowmobile operating at ∼ 5 m s-1, giving the GPS data an effective 5 m diameter footprint.

Once the kinematic GPS data were post-processed and reduced to the snow surface, we compared the ground-based GPS surface elevation data directly to the airborne surface elevation data. We used two different approaches: a “nearest-neighbor” analysis and a “zone” analysis.

We note that the footprint sizes of the altimeters are different; for the data used in these analyses, ATM has a ∼ 1 m diameter footprint and LVIS has a ∼ 10 m diameter footprint. When comparing the ground-based GPS data with the lidar data, we chose a search radius around each lidar data point that was equal to the size of the given lidar footprint; this was intended to ensure that the ground elevation data were representative of what the lidar was sampling.

In the nearest-neighbor analysis, we determined the closest single ground-based GPS data point for every lidar data point. Then we limited our analysis to points where the lidar and GPS measurements were within the search radius that was appropriate for the given lidar. We then assessed the difference between the lidar surface elevation and the closest GPS surface elevation for the data that met the search criteria.

In the zone analysis, we identified every ground-based GPS data point within the appropriate search radius around the lidar data coordinates (which represent the center of the lidar footprint); not every lidar data point had GPS data that met this search criteria. Then we determined the mean of the GPS elevations within this zone. Similar to the nearest-neighbor analysis, we then assessed the difference between the lidar surface elevation data point and the mean of the GPS surface elevations within the zone.

For each airborne mission analysis, once the ground-based GPS surface elevation data (GPSelevation) were associated with the lidar surface elevation data (Lidarelevation), the mean elevation difference is the lidar elevation bias (B): B=∑Lidarelevation-GPSelevationN, where N is the total number of either the nearest-neighbor data points or the total number of zones that met the distance criteria. This lidar bias is relative to the ground-based GPS elevation data, which we are taking to be the truth. By assuming that the ground-based GPS data represent truth, for these analyses we assume their errors are zero. In actuality, these errors are not zero and are a function of several terms including (1) formal errors, which vary based on processing methods and include factors such as ephemeris and clock errors; (2) atmospheric errors, associated with both the ionosphere and troposphere; (3) multipath errors; (4) the precision of the base station estimate to which the survey is related (in the case of the DGPS processing methods); and (5) observational errors such as variable penetration of the sled into the snow along the course of the survey. We note that the existing ground-based and airborne elevation data are likely correlated, as they are based on similar GPS measurements and, in the case of GITAR, processing strategies. The standard deviation of the bias (B) in Eq. (2) is the spread of the data about the mean, taken to be the lidar surface measurement precision. Surface measurement precision is defined here as the vertical dispersion of the lidar measurements about the mean surface and takes into account properties of the surface that will affect the measurement (e.g., slope and roughness) and altimeter precision, which is a function of several terms, including (1) geolocation errors (which are a function of all of the GPS terms described above), inertial measurement errors, altitude, and horizontal uncertainty; (2) errors in altimeter timing; (3) the size of the footprint on the surface, which is a function of altitude and beam divergence; and (4) lidar data processing errors. Over the relatively smooth and flat ice found in the Summit Station region, these surface and instrument effects are not easily distinguished from one another in the lidar surface measurement data.