Seasonal meltwater pools on the surface of the Greenland Ice Sheet (GrIS) during late spring and summer in lakes on the surface and transforms the ice sheet's surface into a wet environment in the ablation zone below the equilibrium line. These supraglacial lakes in topographic lows on the ice surface are connected by a dendritic pattern of meandering streams and channels that together form a hydrological system consisting of supra-, en-, and subglacial components. Here, we use lidar data from NASA's Airborne Topographic Mapper (ATM) instrument suite and high-resolution optical imagery collected as part of Operation IceBridge (OIB) in spring 2019 over the GrIS to develop methods for the study of supraglacial hydrological features. While airborne surveys have a limited temporal and spatial coverage compared to imaging spaceborne sensors, their high footprint density and high-resolution imagery reveal a level of detail that is currently not obtainable from spaceborne measurements. The accuracy and resolution of airborne measurements complement spaceborne measurements, can support calibration and validation of spaceborne methods, and provide information necessary for high-resolution process studies of the supraglacial hydrological system on the GrIS that currently cannot be achieved from spaceborne observations alone.
During the summer months, seasonal surface melting on the Greenland Ice Sheet (GrIS) produces meltwater near the margins of the ice sheet that pools in supraglacial lakes in depressions on the ice surface and forms a dendritic pattern of meandering streams and rivers in the ablation zone below the equilibrium line (e.g., Chu, 2014; Nienow et al., 2017; Pitcher and Smith, 2019, and references therein). The lakes appear as sapphire-blue features to the eye and in natural color imagery (Flowers, 2018) (Fig. 1). The supraglacial streams and channels often connect several lakes and form a hydrological network on the surface of the GrIS that is part of a hydrological system consisting of supra-, en-, and subglacial components (e.g., Chu, 2014; Nienow et al., 2017; Pitcher and Smith, 2019, and references therein). The formation, retention, and drainage of meltwater impacts ice sheet mass balance and therefore ice sheet stability. Over the past decades, runoff from seasonal meltwater production has exceeded ice loss from ice discharge and basal melting at the grounding lines and has become the dominant mechanism of mass loss for the GrIS (Enderlin et al., 2014; van den Broeke et al., 2016). More recently, supraglacial lakes and channels have also been catalogued on the West Antarctic Ice Sheet (Corr et al., 2022).
Several approaches have been used in recent years to study the supraglacial
hydrological network of lakes and streams at various spatial and temporal
scales. On an ice-sheet-wide scale, the network of supraglacial hydrological
features and their temporal evolution can be observed with panchromatic,
natural color, and multi-spectral imagery available from multiple satellite
missions at various spatial resolutions (e.g., Box and Ski, 2007; Pope et
al., 2016; Sneed and Hamilton, 2007, 2011; Yang and
Smith, 2016; Yang et al., 2017, and references therein). Pixel-based surface
classification of satellite imagery is a powerful tool for identifying and
mapping networks of supraglacial lakes and streams; however, challenges
remain with precise spatial registration of repeat high-resolution imagery
(e.g., Yang et al., 2017). Estimating water depths from
satellite imagery based on reflectance–depth relationships (i.e., optical
depth) requires either natural color or multi-spectral imagery
(e.g., Pope et al., 2016). Sneed and Hamilton (2011) list several simplifying assumptions necessary for optical
depth-based estimates including a homogenous and smooth lake surface without
any wind-induced waves and a homogenous lake bottom that is roughly parallel
to the lake surface. As shown later in this paper (Fig. 7a) surface waves
are not uncommon, and an oblique aerial photograph of a supraglacial lake
shows that newly formed thin ice and snow-covered lake ice further
complicate depth estimates based on reflectance (Fig. 1). The photograph
also shows a complex lake bottom topography and reflectance that is far from
homogenous. Dark lake bottom sediments in the form of cryoconite, as well as
meltwater channels and bottom crevasses, can be seen complicating the
analysis, although Pope et al. (2016) developed a method that
accounts for the presence of cryoconite. Yang and Smith (2013) emphasize the need to gain a better understanding of
supraglacial streams, which is limited due to supraglacial streams'
relatively narrow width (
Oblique aerial photograph of a supraglacial lake (approximate
location 67
On a local scale, remotely controlled drone boats and zodiacs equipped with spectroradiometers, digital fathometers, and sonars have been used to measure spectral properties of lakes and streams for calibration and validation of depth estimates based on satellite imagery, as well as directly measure water depth (e.g., Box and Ski, 2007; Das et al., 2008; Legleiter et al., 2014; Pope et al., 2016; Smith et al., 2017; Tedesco and Steiner, 2011).
More recently, spaceborne and airborne lidars have been used to estimate lake depths (Datta and Wouters, 2021; Fair et al., 2020). Airborne measurements can map supraglacial hydrological features on the GrIS at a level of detail that can currently not be accomplished by spaceborne instruments. Airborne measurements can also map supraglacial hydrological features at a spatial scale that cannot be achieved by measurements from short-range drones operated out of remote field camps that often require line-of-sight communication. More detailed studies of the supraglacial fluvial system on the GrIS are needed (Smith et al., 2015, p. 1001). Here, we use airborne laser altimetry and high-resolution optical imagery collected as part of Operation IceBridge (OIB) in spring 2019 over the GrIS (MacGregor et al., 2021) to develop methods that allow the study of the bathymetry of supraglacial hydrological features currently not possible from space or on the ground.
OIB campaigns were scheduled to survey the sea ice maximum in March and survey the GrIS at the end of the winter season in early spring when ice temperatures are still cold to optimize penetration and quality of the ice-penetrating radar data (MacGregor et al., 2021). As a result of this data acquisition strategy, some of the campaigns barely captured the early onset of the summer melt in central and southern Greenland but did not capture the peak of the melt season. In addition to the spring campaigns, several “summer campaigns” have been flown at the end of the Arctic summer to capture the extent of the summer melt. Because of the timing of these campaigns, temperatures were often below freezing and most of the supraglacial hydrological features were already frozen over. Figure A1 shows the daily mean surface temperature from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the surface melt indicator for the locations of the lakes and channels shown in Figs. 1 and 7–9 (Hall et al., 2018; Hall and DiGirolamo, 2019). We analyze nine flights from OIB's 2019 Arctic spring campaign between 5 and 16 May 2019. We also analyzed four flights of the Arctic fall campaign between 10 and 14 September 2019 which cover the region where supraglacial hydrological features in the spring campaign are present (Fig. 2). The four flights in September 2019 did not conclusively show the presence of liquid water surfaces, and therefore no examples of those flights are discussed in this paper, which primarily focuses on method development. All airborne data used in this study are freely available at the National Snow and Ice Data Center (NSIDC).
Location map with spring and fall 2019 flight lines. Ice surface elevation is shown in blue with a 250 m elevation contour interval. Topography and ice mask data are from the Greenland Ice Mapping Project (GIMP) digital elevation model (Howat et al., 2014; Morlighem, 2021). Inset map over the Sermeq Kujalleq (Jakobshavn Isbræ) region showing figure locations is a Sentinel-2A false color image (bands 11, 8A, and 4) from 17 May 2019.
The ATM instrument suite contains two conically scanning laser altimeters
(lidars) that independently measure the surface elevation along the path of
the aircraft at 15
We use both the Level 1B geolocated point cloud spot elevation measurements for faster detection of supraglacial hydrological features and the much larger Level 1B waveform data product for bathymetry estimates. Table 1 provides a summary of the data sets used.
Summary of ATM lidar data products used.
ATM's Continuous Airborne Mapping by Optical Translator (CAMBOT) instrument
is a three-channel, natural color, red, green, and blue (RGB) digital camera
with 4896
We use both CAMBOT Level 0 raw data (Studinger and Harbeck, 2020)
for faster detection of supraglacial hydrological features and the much
larger Level 1B geolocated and orthorectified CAMBOT version 2 data product
(Studinger and Harbeck, 2019) for analysis of the lidar data. Raw
images are collected at 2 Hz, and geolocated data products are provided at 1 Hz, giving sufficient overlap between images at the nominal ground speed of
140 m s
A flow diagram summarizing both the image-based processing steps discussed
in this section and the process of deriving geolocated water depth
estimates, discussed in Sect. 4, is provided in Fig. B3 in the Appendix.
We use the normalized difference water index modified for ice (NDWI
CAMBOT images are not radiometrically calibrated. CAMBOT is a passive
instrument that uses sunlight as the source of illumination. During flight,
the camera operator adjusts shutter speed, aperture, and the camera's
sensitivity to light (ISO number) to minimize motion blur and optimize
exposure over the dynamic range of the camera sensor. The NDWI
We use a Sentinel-2 image mosaic from MacGregor et al. (2020) from August 2019 to delineate the maximum melt and lake extent in 2019 by visual inspection (Fig. 6). We form a spatial mask using this extent to bound the search for hydrological features in the airborne data from May 2019. Whereas meltwater also forms upstream in the catchment areas above the equilibrium line, it primarily pools in lakes and streams below the equilibrium line. We use the approximate elevation of the equilibrium line in the August 2019 Sentinel-2 mosaic as a conservative cut-off elevation mask for identifying hydrological features in airborne data from May 2019. We limit the analysis to CAMBOT images within the melt extent mask and inside the grounded ice mask from Howat et al. (2014) to speed up the feature detection.
Using a simple NDWI
The dielectric contrast between the air–water (lake surface) and the water–ice (lake bottom) interfaces causes reflections of laser energy that can be detected as distinct return pulses. The two-way travel time difference between the lake surface and lake bottom can be used to estimate the depth of hydrological features. The ATM tracking algorithm used for the Level 1B data products is optimized to determine consistent and accurate surface elevations. The ATM tracking algorithm uses 15 % of the maximum amplitude above the baseline as a threshold to determine the centroid of a pulse (Fig. 4a). For overlapping lake surface and bottom return pulses the centroid-based tracker returns an averaged slant range between the surface and bottom of the lake (Fig. 4a). To properly track the surface and bottom returns for overlapping pulses, we use dual-peak Gaussian waveform fitting implemented in a nonlinear regression with seven model parameters. We use MATLAB®'s Signal Processing Toolbox to detect local maxima in the waveforms and use these estimates as initial values as input for the nonlinear regression (Appendix B and Fig. 4b).
For hydrological features, there are several cases that need to be considered to estimate water depth. First, it needs to be determined if a laser shot contains a return pulse from both the surface and the bottom. For some cases, the return from the surface is stronger (Fig. 5a), and for other cases the return from the bottom is stronger (Fig. 5b). For very shallow water depths the surface and bottom returns are typically overlapping (Fig. 5c). Our method is capable of accurately resolving surface and bottom returns in overlapping pulses even if the signal amplitudes are very different (Fig. 5c). For some laser shots there is only a single return which could either be from the lake surface or the much brighter lake bottom. Alternatively, a single return pulse could also be an overlapping surface and bottom return that are so close they appear as a single pulse (Fig. 5d). The algorithm also needs to exclude false pulse detections that are instrument artifacts. The pulses in Fig. 5d are caused by characteristics of the photomultiplier detectors and various other system components such as optical delay fibers and are common in waveform data of airborne and spaceborne lasers (Figs. A2 and A3). The occurrence of these pulses from electronic ringing is consistent in both delay time and percentage of maximum amplitude of the main pulse, and therefore they can reliably be excluded.
Example waveforms of lake return waveforms with Gaussian fits. S marks surface return, B marks bottom return, and IA indicates false return pulses that are caused by instrument artifacts (Fig. A2).
We have evaluated the performance of the nonlinear regression and Gaussian tracker to accurately reproduce the two-way travel time difference as a function of signal-to-noise ratio and pulse separation (Appendix B). A sensitivity analysis of the nonlinear regression was performed by using the mean difference between a prescribed water depth and the depth estimates obtained from linear regression results for 250 000 simulated waveforms with varying signal-to-noise ratios. for each prescribed water depth. Above 0.30 m water depth the difference between the prescribed water depth and the water depth estimated from simulated waveform regressions stabilizes, which we interpret as the reliable detection threshold for the minimum water depth that can be resolved with our approach and instrument system configuration (Fig. B2).
The first step in estimating water depth is to determine the elevation and
geolocation of the lake surface return of each laser shot that is consistent
with ATM's centroid-based surface elevation tracker used for the Level 1B
data products. First, the uncalibrated slant range in air is determined from
the two-way travel time difference between the transmit and receive pulse.
Then, an intensity-dependent range walk calibration that is determined
during the ground test needs to be applied to the uncalibrated ranges to
account for the combined effects of delay fibers and other system components
on the range estimates. Following that, a range correction needs to be
applied to the range estimates due to the atmosphere affecting photon
velocity. Scan azimuth and range bias corrections need to be applied as
well. All required corrections are provided in the ATM waveform products.
The ATM processing flow is detailed in Appendix B and documented in the
MATLAB® code published with this paper
(
Once the elevation and geolocation of the lake surface return have been determined the slant range in water and geolocation of the lake bottom returns are estimated while accounting for the refractive index of water in both geolocation and range. This is done by using Snell's law in vector form in geographic coordinates on the reference ellipsoid. The angle of incidence and geodetic azimuth of the lidar footprint on the lake surface, together with the lake surface elevation, the slant range in water, and the refractive index in air and water, determine the location and elevation of the lidar footprint on the lake bottom.
For laser shots that only have a lake bottom return (e.g., Fig. 5d) the propagation in water needs to be properly accounted for. We first fit a plane through surrounding lake surface elevations and use the resulting elevation of the plane as mean lake surface elevation. We then calculate the intersection of the laser beam transmitted from the aircraft with the mean lake surface using the geodetic azimuth of the laser beam transmitted from the aircraft to the surface target, the off-nadir pointing angle, and the location and elevation of the center of the scan mirror front surface (Fig. A3), which is the fiducial reference point for all two-way travel time estimates. Based on the location of the intersection the slant range and hypothetical two-way travel time between the laser sensor and the intersection of the laser beam with the lake surface can be calculated. Using the hypothetical lidar footprint on the lake surface, the proper location and elevation footprints of laser shots with only lake bottom returns can be calculated.
In general, for waveforms with a lake surface and lake bottom return pulse,
the uncertainty of the water depth estimate is primarily a function of the
uncertainty of the range estimate of the Gaussian tracker used. We use the
data from the T6 and T7 ground tests for this campaign (available at
The primary purpose of this paper is algorithm and method development, and therefore we discuss the bathymetry of only a few select hydrological features here. We have, however, applied the hydrological feature detection algorithm to the entire spring 2019 data set in order to select those examples and begin with a discussion of the example selection and selection criteria.
We analyze all CAMBOT Level 0 images from flights between 5 and 16 May 2019 that are below the approximate elevation cutoff for the
equilibrium line and within the ice mask. The locations of images with
NDWI
We have visually analyzed the images identified as having water surfaces and selected several features that we consider suitable for algorithm and method development. These include a variety of features such as lakes and streams, as well as varying conditions with thin lake ice and surface waves. Lidar data spatial coverage and the depth of lakes are additional criteria used for selection of the below examples. The next section will discuss water depth estimates of these select features.
Locations of hydrological features in central west Greenland identified in spring 2019 data (blue circles). Background image is a Sentinel-2 image mosaic from MacGregor et al. (2020) from August 2019. The approximate location of the transition between the ablation zone and the accumulation zone (equilibrium line) in August 2019 is indicated by the black arrow.
The first example, one of the deepest lakes we found, is approximately 140 m
wide and 500 m long with complete lidar coverage and a smaller 140
The return signal strength (Fig. 7b) over the lakes and ponds is much weaker
than over the snow and ice surfaces seen in the natural-color image mosaic
(Fig. 7a) as expected. The return signal strength in Fig. 7b is from the
Level 1B point cloud data products (ILATM1B and ILNSA1B, Table 1) and
includes lake bottom returns. Furthermore, the wide and narrow scanners are
entirely independent lidars, and therefore the absolute return signal
strength differs as a result of instrument characteristics and instrument
settings during data acquisition. Nevertheless, the correlation between
water surfaces visible in the natural-color imagery and relative return
signal strength of the lidar data is pronounced. The lower return signal
strength also correlates well with NDWI
We use the NDWI
Figure 7f shows the water depth of the main lake, the small lake to the east, and some of the smaller supraglacial hydrological features such as ponds and channels. Over the main lake, water depths gradually deepen from the shore towards the interior of the lake and reach the maximum depth of 7 m in narrow bottom crevasses (marked by arrows). The ability to resolve these crevasses through water depth measurements illustrates the level of detail that can be derived from airborne measurements. The gradual deepening from the shore to 7 m over the distance of approximately 70 m suggests that the assumption of a homogenous lake bottom that is roughly parallel to the lake surface used for optical depth-based estimates must be used with caution (Sneed and Hamilton, 2011).
The deeper water depths toward the interior of the main lake correlate with
higher NDWI
The second example (Fig. 8) is a lake with slightly different conditions
than the first one. Between the day of the airborne survey on 15 May 2019
and the first reported occurrence of melt on 29 April 2019, this location
had experienced 11 d with melt and 6 d without melt (Fig. A1c). The
airborne survey was a coordinated ICESat-2 under flight with airborne data
acquired just 3 h before ICESat-2 passed over the lake. The lake
contains several snow-covered patches of lake ice that are obscuring the
view of the lake bottom and prevent enough lidar light to reach the lake
bottom necessary to trigger the recording of a bottom return pulse (Fig. 8a). Thin layers of lake ice impose limitations not only for airborne and
spaceborne lidar-based water depth estimates but also for any optical
depth-based bathymetry estimates. The high-resolution natural color imagery
reveals relevant details that currently cannot be identified with spaceborne
sensors. On the eastern side of the lake, there is a sharp transition in
the visibility of details such as crevasses and other structures on the lake
bottom to a blurred lake bottom north of it (Fig. 8a). While not discernible
in the natural color imagery, it is likely that the blurring of the lake
bottom is caused by a thin layer of clear lake ice. This thin ice cover also
acts as a specular reflector for laser light and likely reflects lidar
energy away from the detector, thereby causing gaps in bottom returns. This
interpretation is supported by the weaker return signal strength over the
area with thin ice cover compared to the ice-free water surface south of it
(Fig. 8b). Figure 8c shows some of the limitations of using a simple
NDWI
The water depth within this lake gradually deepens from its western shore towards the interior of the lake before becoming shallower again. The deepest returns are around 3.5 m, but most of the deepest part of the lake lacks bottom returns. As can be seen in Fig. 8e, the loss of bottom returns is not a simple function of water depth alone. Some of the deepest returns are located within a narrow bottom crevasse (marked by an arrow in Fig. 8e) that has no returns in the shallower part around it. A possible explanation for this is that the slope of the sidewalls of the crevasse or channel is closer to the normal of the lidar beam than in the surrounding areas, and therefore lidar light is reflected to the sensor on the aircraft. Also, concave-shaped surfaces, such as those found in crevasses and channels, can have a focusing effect that increases the intensity of the reflected lidar light and increases the likelihood of exceeding the signal strength necessary to trigger recording of a bottom return pulse.
The third example shows a network of narrow, 5–10 m wide meltwater channels and streams and reflects the most challenging targets for bathymetric imaging found in this study (Fig. 9). Following the first reported melt between 29 April 2019 and the day of the airborne survey, this location had experienced 11 d of melt and 1 d of freezing (Fig. A1d). There are no ICESat-2 footprints within the extent of the data frame shown. In general, we find that channels and streams show a very low number of both surface and bottom returns compared to lakes (Fig. 9). A possible explanation is that these narrow streams flow in topographic channels that provide more protection from surface winds compared to relatively open lakes shown in Figs. 7 and 8. Wind protection hinders generation of surface capillary waves, which are necessary to reflect lidar energy back to the sensor on the aircraft. The presumably flat water surface of these streams acts as a specular reflector directing lidar energy away from the sensor and resulting in very few surface and bottom returns. The deepest returns of around 1.6 m can be seen in a bend of a channel near the northern end of the data frame.
We compared pulse widths of lake surface and lake bottom return pulses of the hydrological features we have discussed, and we found no relationship between pulse width and slant range in water potentially caused by volume scattering in water. In addition to volume scattering in water the slope and roughness of the lake bottom will likely be bigger contributors to pulse widening than volume scattering. The extremely clear water visible in true-color imagery suggests very low turbidity of these water bodies, which in turn should result in very little volume scattering and associated pulse broadening.
ATM's suite of co-located sensors, small laser footprints (64 cm), high shot density, swath coverage, and high-resolution imagery (10 cm) reveals fine-scale hydrological features, such as very narrow meltwater channels and surface waves, that cannot be detected from space. Airborne measurements can also image supraglacial hydrological features at a spatial scale and coverage that cannot be achieved by local measurements from short-range drones, which are often operated out of remote field camps and require line-of-sight communications. The accuracy and resolution from airborne measurements compared to spaceborne sensors provides critical complementary information that can support calibration and validation of spaceborne methods and provide information necessary for high-resolution process studies of the supraglacial hydrological system on the GrIS that currently cannot be achieved from spaceborne observations alone. The minimum water depth that can be resolved with the current algorithm using a 1.3 ns laser pulse sampled at 4 GHz is around 30 cm, and the maximum water depth measured with the ATM optimized for snow and ice elevation measurement was around 7 m. However, this could also reflect the maximum water depth encountered early in the melt season rather than an instrument limitation.
The KT19 is an infrared radiation pyrometer that is used to measure infrared
radiation wavelengths between 960 and 1150 nm that are used to derive skin
temperatures within the field of view of the sensor. At a nominal flight
elevation of 460 m a.g.l., the 2
Surface temperature (black crosses) and surface melt indicator
(red and blue circles) from MODIS (Hall et al., 2018; Hall
and DiGirolamo, 2019) and mean ATM KT19 infrared surface temperatures
(Studinger, 2019) averaged in 60 s windows over the
hydrological features with 1
Averaged, normalized, unsaturated transmit and return waveforms
of the T6
Schematic diagram of ATM's dual color T7 transceiver with co-located green (532 nm) and IR (1064 nm) footprints.
This section describes the processing flow for the ATM lidar data used in
this paper for estimating surface elevations and water depths. The
MATLAB® code is available at
The position of the Global Navigation Satellite System (GNSS) antenna on top of the fuselage of the survey aircraft is determined from NAVSTAR Global Positioning System (GPS) and Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS) carrier phase measurements recorded by receivers on the aircraft. These measurements are combined in post-flight processing with similar measurements from multiple static ground stations to determine a kinematic differential solution (DGPS) of the antenna trajectory. The lever arm from antenna to ATM scan mirror provided in the ATM waveform data products includes corrections for aircraft-specific changes in antenna phase centers that are determined for each campaign. The reference point for all lidar measurements is the scan mirror fiducial point (Fig. A3). To determine the location of the scan mirror fiducial point in both space and time, the DGPS solutions are combined with aircraft attitude measurements from a commercial inertial navigation system (INS) on the survey aircraft, often also referred to as inertial measurement unit (IMU), and measurements of the lever arm between the antenna and scan mirror in an aircraft-fixed cartesian coordinate system with the origin in the phase center of the antenna. The coordinate translations and rotations are done in a geocentric ECEF (Earth-centered, Earth-fixed) coordinate system, which are then converted to geographic coordinates for the position of the laser sensor.
The two-way travel time difference
In a pressurized aircraft, the transmitted laser pulse travels thru the aircraft's optical window close to the scan mirror (Fig. A2). Backscatter from both the scan mirror and the aircraft's optical window in the fuselage is close in time to the transmitted laser pulse and partially overlap with the transmit waveform. To record a “clean” transmit waveform the transmit pulse is sampled from behind a translucent beam splitter and subsequently injected into a multimode fiber-optic cable to provide a fixed optical delay that results in temporal separation between the recorded transmit pulse and contamination from backscattered photons from the scan mirror and the aircraft's optical window (Fig. A3). The optical delay fiber and other system components introduce a laser time-of-flight range bias that needs to be determined from ground calibration measurements.
In addition to measuring the instrument's system delay the second purpose of
the ground calibration is to determine the intensity-varying change in range
that is known as range walk. ATM data are collected from a stationary target
at known range while varying the return intensity from signal extinction to
detector saturation. The waveform tracking method used will result in
apparent changes in range from the stationary target, and these data can be
applied as a range correction. The ground test calibration values combine
the system delay and range walk correction and are subtracted from the
uncalibrated ranges to yield the calibrated range estimates (
Range bias determination (a.k.a. ground test) using a calibration target with a known distance. The range to the calibration target is measured with an electronic distance meter (a.k.a. “total station”) with an accuracy of a few millimeters.
Flow diagram summarizing both the image-based processing steps discussed in this section and the process of deriving geolocated water depth estimates from lidar data discussed in Sect. 4.
Martin et al. (2012) describe the process of estimating the six mounting biases related to range, scan angle, attitude, and position using ramp passes and cross-over analysis. Harpold et al. (2016) describe an alternative approach using the difference between forward and aft scan elevations. These six biases are already applied to the data in the HDF5 waveform files available from NSIDC.
Some campaigns contain scan-azimuth-dependent elevation biases that can
change over the course of a flight or a campaign. The elevation biases are a
function of scan azimuth and are stored in
The propagation speed of light is lower in a denser medium such as the
atmosphere compared to vacuum. In laser altimetry, this effect is referred
to as atmospheric delay. The density of the atmosphere at the time and
position of the aircraft and the footprint on the surface can be calculated
from parameters provided by global numerical weather models. The density is
primarily a function of the temperature of air, the atmospheric pressure,
and the partial pressure of water vapor and can be used to calculate the
refractive index along the propagation path of a laser beam. The range correction applied due to the atmosphere
affecting photon velocity is provided in
The ultimate reference for in-flight data are the ramps, crossings, and
along-track comparisons to produce consistent elevation measurements over
the course of a campaign and between campaigns. Any residual bias thus
determined (typically on the order of a few centimeters) is included in
The lake surface and lake bottom returns are fitted with a dual-peak
Gaussian function
The performance of the nonlinear regression to accurately reproduce the
two-way travel time difference is primarily a function of pulse separation.
For a 20 cm slant range in water the two-way travel time difference between
the surface and bottom return pulses is 1.78 ns (Fig. B2a), which is close
to the average pulse width of 1.63
The MATLAB®
code developed for this paper for tracking lake surface and lake bottom
returns, analyzing waveforms, geolocating ATM lidar footprints, and
calculating water depths is available at
Chad Greene's MATLAB® function for interpolating
GeoTIFF data is available on MATLAB®`s File
Exchange website at
All ATM Operation IceBridge airborne
data used in this study are freely available at the National Snow and Ice
Data Center at
Greenland-wide topography and ice mask data are from the Greenland Ice
Mapping Project (GIMP) digital elevation model (Howat et al.,
2014; Morlighem, 2021) and are available at NSIDC
at
The Sentinel-2 image mosaic from August 2019 from MacGregor et al. (2020) is available through QGreenland
at
The ice surface temperature and ice surface melt indicator from MODIS
(Hall et al., 2018; Hall and DiGirolamo, 2019) are
available at NSIDC at
The Sentinel-2A image used in Fig. 2 is available from the USGS
EarthExplorer website at
MS led the analysis of the laser altimetry, optical imagery, and integration of results and prepared the manuscript. All authors helped interpret the analysis, develop the methods, and comment on the manuscript.
The contact author has declared that none of the authors has any competing interests.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This paper reflects the combined efforts of all ATM team members over many decades of instrument development and field deployments. Jeremy Harbeck and Nathan Kurtz are thanked for developing the ATM CAMBOT L1B Version 2 data product. We thank the Operation IceBridge flight crews that made data collection for this study possible. We thank the editor Louise Sandberg Sørensen and two anonymous reviewers for thoughtful comments that helped improve the manuscript.
This work was funded by NASA’s Internal Scientist Funding Model and the Airborne Science Program.
This paper was edited by Louise Sandberg Sørensen and reviewed by two anonymous referees.