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Abshire, James

Publications and source records attributed to Abshire, James.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Development of a Mars Lidar (MARLI) for Measuring Wind and Aerosol Profiles from Orbit

Our understanding of the Mars atmosphere and the coupled atmospheric processes that drive its seasonal cycles is limited by a lack of observation data, particularly measurements that capture diurnal and seasonal variations on a global scale. As outlined in the 2011 Planetary Science Decadal Survey and the recent Mars Exploration Program Analysis Group(MEPAG) Goals Document, near-polar-orbital measurements of height-resolved aerosol backscatter and wind profiles area high-priority for the scientific community and would be valuable science products as part of a next-generation orbital science package. To address these needs, we have designed and tested a breadboard version of a direct detection atmospheric wind lidar for Mars orbit. It uses a single-frequency, seeded Nd:YAG laser ring oscillator operating at 1064nm (4 kHz repetition rate), with a 30-ns pulse duration amplified to 4 mJ pulse energy. The receiver uses a Fabry-Perotetalon as part of a dual-edge optical discrimination technique to isolate the Doppler-induced frequency shift of the back scattered photons. To detect weak aerosol backscatter profiles, the instrument uses a 4x4 photon-counting HgCdTeAPD detector with a 7 MHz bandwidth and < 0.4 fW/Hz(exp 1/2) noise equivalent power. With the MARLI lidar breadboard instrument, we were able to measure Doppler shifts continuously between 1 and 30 m/s by using a rotating chopper wheel to impart a Doppler shift to incident laser pulses. We then coupled the transmitter and receiver systems to a laser ranging telescope at the Goddard Geophysical and Astronomical Observatory (GGAO) to measure backscatter and Doppler wind profiles in the atmosphere from the ground. We measured a 5.3 ± 0.8 m/s wind speed from clouds in the planetary boundary layer at a range of 4 to 6 km. This measurement was confirmed with a range-over-time measurement to the same clouds as well as compared to EMC meteorological models. Here we describe the lidar approach and the breadboard instrument, and report some early results from ongoing field experiments.

Cremons, Daniel R.↗
NASA NTRS2018

Fiber-Based Laser Transmitter Technology Maturation for Spectroscopic Measurements from Space

NASA's Goddard Space Flight Center has been developing lidar to remotely measure CO2 in the Earth's atmosphere. We have advanced the tunable laser technology to enable high-fidelity measurements from space. In this paper, we will report on the progress of fiber-based, 1.57-micron wavelength, laser transmitter that has demonstrated the optical performance required for a low earth orbiting instrument. The laser transmitter has been packaged and is undergoing environmental testing to demonstrate its technology readiness for space.

Laser and Masers↗
NASA NTRS2018

Single Photon HgCdTe Avalanche Photodiode and Integrated Detector Cooler Assemblies for Space Lidar Applications

A linear mode photon counting HgCdTe avalanche photodiode (APD) focal plane array (FPA) detector was developed for space lidar applications. An integrated detector cooler assembly (IDCA) was manufactured using a miniature Stirling cooler. The HgCdTe APD demonstrated a greater than 60% photon detection efficiency from 0.9 to 4.3 μm wavelength and a dark count rate less than 250,000/s. The IDCA cooled the FPA to 110K from ambient room temperature at a total electrical power of 7 W. The IDCA has passed environmental tests, including vibration, thermal cycling and thermal vacuum tests.

Sun, Xiaoli↗
NASA NTRS2018

Fiber-Based Laser MOPA Transmitter Packaging for Space Environment

NASA’s Goddard Space Flight Center has been developing lidar to remotely measure CO2 and CH4 in the Earth’s atmosphere. The ultimate goal is to make space-based satellite measurements with global coverage. We are working on maturing the technology readiness of a fiber-based, 1.57-micron wavelength laser transmitter designed for use in atmospheric CO2 remote-sensing. To this end, we are building a ruggedized prototype to demonstrate the required power and performance and survive the required environment. We are building a fiber-based master oscillator power amplifier (MOPA) laser transmitter architecture. The laser is a wavelength-locked, single frequency, externally modulated DBR operating at 1.57-micron followed by erbium-doped fiber amplifiers. The last amplifier stage is a polarization-maintaining, very-large-mode-area fiber with ~1000 μm2 effective area pumped by a Raman fiber laser. The optical output is single-frequency, one microsecond pulses with >450 μJ pulse energy, 7.5 KHz repetition rate, single spatial mode, and > 20 dB polarization extinction.

Lasers and Masers↗
NASA NTRS2017

Airborne Demonstration of Atmospheric Oxygen Optical Depth Measurements with an Integrated Path Differential Absorption Lidar

We report on an airborne demonstration of atmospheric oxygen (O2) optical depth measurements with an Integrated Path Differential Absorption (IPDA) lidar using a fiber-based laser transmitter and photon counting detectors. Accurate atmospheric temperature and pressure measurements are needed for NASA's Active Sensing of CO2 Emissions over Nights, Days and Seasons (ASCENDS) mission. Since O2 is uniformly mixed in the atmosphere, its spectrum can be used to estimate the dry mixing ratio of CO2. In its airborne configuration, the IPDA lidar uses an Erbium Doped Fiber amplifier, a frequency doubler and single photon counting detectors to measure O2 absorption at multiple wavelengths near 765 nm. This instrument was deployed in 2013 and 2014 aboard NASA's DC-8 airborne laboratory as part of two campaigns to measure CO2 mixing ratios over a wide range of topography and weather conditions from altitudes ranging between 3 km and 13 km. In this paper we will review a summary of the results from our flights, discuss the errors that limit the precision and accuracy of the measurement and identify possible areas of improvement.

Methane↗
NASA NTRS2015

Linear Mode HgCdTe Avalanche Photodiodes for Photon Counting Applications

An overview of recent improvements in the understanding and maturity of linear mode photon counting with HgCdTe electron-initiated avalanche photodiodes is presented. The first HgCdTe LMPC 2x8 format array fabricated in 2011 with 64 micron pitch was a remarkable success in terms of demonstrating a high single photon signal to noise ratio of 13.7 with an excess noise factor of 1.3-1.4, a 7 ns minimum time between events, and a broad spectral response extending from 0.4 micron to 4.2 micron. The main limitations were a greater than 10x higher false event rate than expected of greater than 1 MHz, a 5-7x lower than expected APD gain, and a photon detection efficiency of only 50% when greater than 60% was expected. This paper discusses the reasons behind these limitations and the implementation of their mitigations with new results.

HgCdTe↗
NASA NTRS2015

Fiber-Based, Trace-Gas, Laser Transmitter Technology Development for Space

NASA’s Goddard Space Flight Center (GSFC) is working on maturing the technology readiness of a laser transmitter designed for use in atmospheric CO2 remote-sensing. GSFC has been developing an airplane-based CO2 lidar instrument over several years to demonstrate the efficacy of the instrumentation and measurement technique and to link the science models to the instrument performance. The ultimate goal is to make space-based satellite measurements with global coverage. In order to accomplish this, we must demonstrate the technology readiness and performance of the components as well as demonstrate the required power-scaling to make the link with the required signal-to-noise-ratio (SNR). To date, all the instrument components have been shown to have the required performance with the exception of the laser transmitter.In this program we are working on a fiber-based master oscillator power amplifier (MOPA) laser transmitter architecture where we will develop a ruggedized package and perform the relevant environmental tests to demonstrate TRL-6. In this paper we will review our transmitter architecture and progress on the performance and packaging of the laser transmitter.

Laser↗
NASA NTRS2014

A Highly Sensitive Multi-Element HgCdTe E-APD Detector for IPDA Lidar Applications

An HgCdTe electron avalanche photodiode (e-APD) detector has been developed for lidar receivers, one application of which is integrated path differential absorption lidar measurements of such atmospheric trace gases as CO2 and CH4. The HgCdTe APD has a wide, visible to mid-wave-infrared, spectral response, high dynamic range, substantially improved sensitivity, and an expected improvement in operational lifetime. A demonstration sensor-chip assembly consisting of a 4.3 lm cutoff HgCdTe 4 9 4 APD detector array with 80 micrometer pitch pixels and a custom complementary metal-oxide-semiconductor readout integrated circuit was developed. For one typical array the APD gain was 654 at 12 V with corresponding gain normalized dark currents ranging from 1.2 fA to 3.2 fA. The 4 9 4 detector system was characterized at 77 K with a 1.55 micrometer wavelength, 1 microsecond wide, laser pulse. The measured unit gain detector photon conversion efficiency was 91.1%. At 11 V bias the mean measured APD gain at 77 K was 307.8 with sigma/mean uniformity of 1.23%. The average, noise-bandwidth normalized, system noise-equivalent power (NEP) was 1.04 fW/Hz(exp 1/2) with a sigma/mean of 3.8%. The measured, electronics-limited, bandwidth of 6.8 MHz was more than adequate for 1 microsecond pulse detection. The system had an NEP (3 MHz) of 0.4 fW/Hz(exp 1/2) at 12 V APD bias and a linear dynamic range close to 1000. A gain-independent quantum-limited SNR of 80% of full theoretical was indicative of a gain-independent excess noise factor very close to 1.0 and the expected APD mode quantum efficiency.

NEP↗
NASA NTRS2012

Ground and Airborne Methane Measurements using Optical Parametric Amplifiers

We report on an initial airborne demonstration of atmospheric methane column measurements at 1.65 micrometers using a widely tunable, seeded optical parametric amplifier (OPA) lidar and a photon counting detector. Methane is an important greenhouse gas and accurate knowledge of its sources and sinks is needed for climate modeling. Our lidar system uses 20 pulses at increasing wavelengths and integrated path differential absorption (IPDA) to map a methane line at 1650.9 nanometers. The wavelengths are generated by using a Nd:YAG pump laser at 1064.5 nanometers and distributed feedback diode laser at 1650.9 nanometers and a periodically-poled lithium niobate (PPLN) crystal. The pulse width was 3 nanoseconds and the pulse repetition rate was 6.28 KHz. The outgoing energy was approximately 13 microJoules/pulse. A commercial 20 nanometer diameter fiber-coupled telescope with a photon counting detector operated in analog mode with a 0.8 nanometer bandpass filter was used as the lidar receiver. The lidar system was integrated on NASA's DC-8 flying laboratory, based at Dryden Airborne operations Facility (DAOF) in Palmdale CA. Three flights were performed in the central valley of California. Each flight lasted about 2.5 hours and it consisted of several flight segments at constant altitudes at approximately 3, 4.5, 6, 7.6, 9.1, 10.6 km (l0, 15, 20, 25, 30, 35 kft). An in-situ cavity ring down spectrometer made by Picarro Inc. was flown along with the lidar instrument provided us with the "truth" i.e. the local CH4, CO2 and H2O concentrations at the constant flight altitude segments. Using the aircraft's altitude, GPS, and meteorological data we calculated the theoretical differential optical depth of the methane absorption at increasing altitudes. Our results showed good agreement between the experimentally derived optical depth measurements from the lidar instrument and theoretical calculations as the flight altitude was increased from 3 to 10.6 kilometers, assuming a constant methane mixing ratio of 1.8 parts per million. The in-situ spectrometer did not show any significant deviations from the ambient concentrations. Further analysis using meteorological data from the Global Modeling and Assimilation Office (http://gmao.gsfc.nasa.gov/) to derive the theoretical optical depth also showed good agreement with the experimentally derived values. The OPA lidar system with slight modifications has also been used to measure CO2, water vapor, and CO in the near and mid-infrared spectral regions on the ground.

Riris, Haris↗
NASA NTRS2012

Ground and Airborne Methane Measurements with an Optical Parametric Amplifier

Here we report on measurements made with an improved CO2 Sounder lidar during the ASCENDS 2014 and 2016 airborne campaigns. The changes made to the 2011 version of the lidar included incorporating a rapidly wavelength-tunable, step-locked seed laser in the transmittter, using a much more sensitive HgCdTe APD detector andusing an analog digitizer with faster readout time in the receiver. We also improved the lidar's calibration approach and the XCO2 retrieval algorithm. The 2014 and 2016 flights were made over several types of topographic surfaces from3 to 12 km aircraft altitudes in the continental US. The results are compared to the XCO2 values computed from an airborne in situ sensor during spiral-down maneuvers. The 2014 results show significantly better performance and include measurement of horizontal gradients in XCO2 made over the Midwestern US that agree with chemistry transport models. The results from the 2016 airborne lidar retrievals show precisions of 0:7 parts per million (ppm) with 1 s averaging over desert surfaces, which is an improvement of about 8 times compared to similar measurements made in 2011. Measurements in 2016 were also made over fresh snow surfaces that have lower surface reflectance at the laser wavelengths. The results from both campaigns showed that the mean values of XCO2 retrieved from the lidar consistently agreed with those based on the in situ sensor to within 1 ppm. The improved precision and accuracy demonstrated in the 2014 and 2016 flights should benefit future airborne science ampaigns and advance the technique's readiness for a spacebased instrument.

Numata, Kenji↗
NASA NTRS2012

Ground Demonstration of Planetary Gas Lidar Based on Optical Parametric Amplifier

We report on the development effort of a nanosecond-pulsed optical parametric amplifier (OPA) for remote trace gas measurements for Mars and Earth. The OPA output has high spectral purity and is widely tunable both at near-infrared and mid-infrared wavelengths, with an optical-optica1 conversion efficiency of up to approx 39 %. Using this laser source, we demonstrated open-path measurements of CH4 (3291 nm and 1651 nm), CO2 (1573 nm), H2O (1652 nm), and CO (4764 nm) on the ground. The simplicity, tunability. and power scalability of the OPA make it a strong candidate for general planetary lidar instruments, which will offer important information on the origins of the planet's geology, atmosphere, and potential for biology,

Numata, Kenji↗
NASA NTRS2011

Development of Optical Parametric Amplifier for Lidar Measurements of Trace Gases on Earth and Mars

Trace gases in planetary atmospheres offer important clues as to the origins of the planet's hydrology, geology. atmosphere. and potential for biology. Wc report on the development effort of a nanosecond-pulsed optical parametric amplifier (OPA) for remote trace gas measurements for Mars and Earth. The OP A output light is single frequency with high spectral purity and is widely tunable both at 1600 nm and 3300 nm with an optical-optical conversion efficiency of approximately 40%. We demonstrated open-path atmospheric measurements ofCH4 (3291 nm and 1651 nm). CO2 (1573 nm), H20 (1652 nm) with this laser source.

Numata, Kenji↗
NASA NTRS2011

Pulsed Lidar for Measurement of C02 Concentrations for the ASCENDS Mission - Update

We have been developing a laser-based sounding technique for the remote measurement of the tropospheric CO2 concentrations from orbit for NASA is ASCENDS mission. The mission's goals are to provide measurements of tropospheric CO2 abundance with global-coverage, a few hundred km spatial and monthly temporal resolution. These are needed to better understand CO2 fluxes and the processes that regulate CO2 storage by the land and oceans. For the lIP, we are developing and demonstrating the lidar techniques and key lidar technology that will permit measurements of the CO2 column abundance in the lower troposphere from aircraft. Our final goal is to demonstrate the key capabilities needed for a space lidar and mission approach for the ASCENDS mission. We use a pulsed lidar technique, which is much less sensitive to errors from cloud and atmospheric scattering and to noise from solar background. It allows continuous measurements of CO2 mixing ratio in the lower troposphere during day and night. Our approach uses the 1570nm CO2 band and a two-wavelength laser absorption spectrometer, which continuously measures at nadir from a circular polar orbit. It directs the narrow co-aligned laser beams from the instrument's lasers toward nadir, and measures the energy of the laser echoes reflected from land and water surfaces. It uses a pair of tunable laser transmitters, which allowing measurement of the extinction from a single selected CO2 absorption line in the 1570 nm band and from a line pair in the Oxygen A-band near 765 nm. These regions have temperature insensitive absorption lines are free from interference from other gases. The lasers pulse at 10KHz, use tunable diode seed lasers followed by laser amplifiers, and have MHz spectral widths. During the measurement the lasers are stepped across the selected lines at a kHz rate. The receiver uses a 1-m class telescope and photon sensitive detectors and measures the background light and energies of the laser echoes from the surface. The extinction and column densities for the CO2 and O2 gases are estimated from the ratio of the on and off line echo pulse energies via the integrated path differential absorption (IPDA) technique. Our technique exploits the atmospheric pressure broadening of the lines to weight the measurement sensitivity to the atmospheric column below 5 km. Pulsed laser signals, time gated receiver are used to isolate the surface laser echo signals and to exclude photons scattered from clouds and aerosols. We have successfully demonstrated many key aspects of the approach and lidar technology in the laboratory. We have demonstrated CO2 column measurements in airborne flights during the summers of 2009 and 2010. These included measurements from 3-l3 km altitudes made over a variety of surfaces and through thin and broken clouds. We demonstrated initial airborne measurements of O2 column density to 10 km altitudes during the summer 2010 flights. More details approach, key technologies, and demonstration measurements will be given in the presentation.

Abshire, James↗
NASA NTRS2010

Pulsed Airborne Lidar Measurements of Atmospheric CO2 Column Absorption and Line Shapes from 3-13 km Altitudes

We have developed a pulsed lidar technique for measuring the tropospheric CO2 concentrations as a candidate for NASA's planned ASCENDS space mission. Our technique uses two pulsed laser transmitters allowing simultaneous measurement of a CO2 absorption line in the 1570 nm band, O2 extinction in the Oxygen A-band and surface height and backscatter. The lidar measures the energy and time of flight of the laser echoes reflected from the atmosphere and surface. The lasers are rapidly and precisely stepped in wavelength across the CO2 line and an O2 line region during the measurement. The direct detection receiver uses a telescope and photon counting detectors, and measures the background light and energies of the laser echoes from the surface along with scattering from any aerosols in the path. The gas extinction and column densities for the CO2 and O2 gases are estimated from the ratio of the on- and off- line signals via the DIAL technique. Time gating is used to isolate the laser echo signals from the surface, and to reject laser photons scattered in the atmosphere. The time of flight of the laser pulses are also used to estimate the height of the scattering surface and to identify cases of mixed cloud and ground scattering. We have developed an airborne lidar to demonstrate the CO2 measurement from the NASA Glenn Lear-25 aircraft. The airborne lidar steps the pulsed laser's wavelength across the selected CO2 line with 20 steps per scan. The line scan rate is 450 Hz, the laser pulse widths are 1 usec, and laser pulse energy is 24 uJ. The time resolved laser backscatter is collected by a 20 cm telescope, detected by a photomultiplier and is recorded by a photon counting system. We made initial airborne measurements on flights during fall 2008. Laser backscatter and absorption measurements were made over a variety of land and water surfaces and through thin clouds. The atmospheric CO2 column measurements using the 1572.33 nm CO2 lines. Two flights were made above the US Department of Energy's (DOE) SGP ARM site at altitudes from 3-8 km. These flights were coordinated with DOE investigators who flew an in-situ CO2 sensor on a Cessna aircraft under the path. The increasing CO2 line absorptions with altitudes were evident and comparison with in-situ measurements showed agreements to 6 ppm. In spring 2009 we improved the aircraft's nadir window and during July and August we made 9 additional 2 hour long flights and measured the atmospheric CO2 absorption and line shapes using the 1572.33 nm CO2 line. Measurements were made at stepped altitudes from 3-13 km over a variety of surface types in Nebraska, Illinois, the SGP ARM site, and near and over the Chesapeake Bay in North Carolina and eastern Virginia. Strong laser signals and clear CO2 line shapes were observed at all altitudes, and some measurements were made through thin clouds. The flights over the ARM site were underflown with in-situ measurements made from the DOE Cessna. Analysis shows that the average signal levels follow predicted values, the altimetry measurements had an uncertainty of about 4 m, and that the average optical line depths follow the number density calculated from in-situ sensor readings. The Oklahoma and east coast flights were coordinated with a LaRC/ITT CO2 lidar on the LaRC UC-12 aircraft, a LaRC in-situ CO2 sensor, and the Oklahoma flights also included a JPL CO2 lidar on a Twin Otter aircraft. More details of the flights, measurements, analysis and scaling to space will be described in the presentation.

Abshire, James↗
NASA NTRS2010

Lidar Measurements of Methane and Applications for Aircraft and Spacecraft

Atmospheric methane levels have remained relatively constant over the last decade around 1.78 parts per million (ppm) but observations since 2007 show that levels may be increasing. This trend may be caused by increased fossil fuel production, rice farming, livestock and landfills, but the underlying causes are quite uncertain. One hypothesis is that reservoirs of carbon trapped in the permafrost regions of northern Canada, Europe, and Siberia thaw as global temperatures rise and are releasing increasing amounts of methane. Another hypothesis points to increased production of methane by microbes as the permafrost warms. Currently most observations of greenhouse gases are limited to in-situ (surface and tower sites) and limited airborne in-situ measurements. Space column density measurements are starting to become available from the GOSAT mission. Although methane survives for a shorter time in the atmosphere than CO2, its impact on climate change per molecule is about 23 times than that of CO2. Accurate global observations of several greenhouse gases, including methane, are urgently needed in order to better understand climate change processes and to reduce the uncertainty in the carbon budget. Differential absorption lidar is a well-established technique to measure atmospheric gases, and methane has optical absorption bands near 1.65,2.2,3.4 and 7.8 micron. The near infrared overtones lines of CH4 near 1650 nm are relatively free of interference from other species. There are absorption lines near 1651 nm which are both temperature insensitive and have line strengths well suited for lidar measurements. We have developed a laser and demonstrated lidar measurements of CH4 using lines in this band. Our laser uses a narrow linewidth 1064 nm laser pulse passing through a nonlinear crystal. We generate the tunable laser signals near 1651 nm by using the optical parametric amplification (OPA) process. Inside the crystal the 1064 nm beam overlaps with an injection seed laser near 1651 nm from a wavelength tunable diode laser. Incident photons from the pump laser pulse are converted into two photons, with one at the wavelength of the injection seeder. The wavelength of the OPA output is tuned via the wavelength of diode laser. Our laser is tunable, operates near 1651 nm and generates approximately 4 uJ/pulse at 6 KHz. We vary the emission wavelengths within this band by tuning the diode laser's wavelength. We have used this OPA transmitter to make measurements of CH4 at various pressures in a gas cell and over open outdoor horizontal paths. We have measured the lineshape of methane in a 6 cm long cell at various energy levels with this transmitter, with excellent agreement with the lineshape calculated by HITRAN. We have also measured the absorption lineshape of atmospheric methane in an open 3 km outdoor path. The agreement between the measurements and HITRAN, for 1746 ppb and 760 Torr was quite good. We have also made pulsed two wavelength lidar measurements of methane line absorption in the column to a tower at 1.5 km range. These used on- and off-line wavelengths of 1650.957 nm, and 1651.072 nm, and a 20 cm diameter receiver telescope with an infrared PMT detector. The absorption of the on-line photons was 30%. The methane column absorption was estimated via HITRAN, and was in good agreement with the expected methane absorption for a concentration of 1750 ppm. Finally we have calculated the measurement performance of an airborne methane lidar using this transmitter, as well as the energy and telescope scaling needed for a lidar for space. These results, and more details of our experiments will be described in the presentation.

Riris, Haris↗
NASA NTRS2005

Fiber lasers and amplifiers for science and exploration at NASA Goddard Space Flight Center

We discuss present and near-term uses for high-power fiber lasers and amplifiers for NASA- specific applications including planetary topography and atmospheric spectroscopy. Fiber lasers and amplifiers offer numerous advantages for both near-term and future deployment of instruments on exploration and science remote sensing orbiting satellites. Ground-based and airborne systems provide an evolutionary path to space and a means for calibration and verification of space-borne systems. We present experimental progress on both the fiber transmitters and instrument prototypes for ongoing development efforts. These near-infrared instruments are laser sounders and lidars for measuring atmospheric carbon dioxide, oxygen, water vapor and methane and a pseudo-noise (PN) code laser ranging system. The associated fiber transmitters include high-power erbium, ytterbium, neodymium and Raman fiber amplifiers. In addition, we will discuss near-term fiber laser and amplifier requirements and programs for NASA free space optical communications, planetary topography and atmospheric spectroscopy.

Krainak, Michael A.↗
NASA NTRS2005

Space-based Swath Imaging Laser Altimeter for Cryospheric Topographic and Surface Property Mapping

Uncertainties in the response of the Greenland and Antarctic polar ice sheets to global climatic change inspired the development of ICESat/GLAS as part of NASA's Earth Observing System. ICESat's primary purpose is the measurement of ice sheet surface elevation profiles with sufficient accuracy, spatial density, and temporal coverage so that elevation changes can be derived with an accuracy of <1.5 cm/year for averages of measurements over the ice sheets with areas of 100 x 100 km. The primary means to achieve this elevation change detection is spatial averaging of elevation differences at cross-overs between ascending and descending profiles in areas of low ice surface slope. Additional information is included in the original extended abstract.

Abshire, James↗