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At least 955 records · Page 53

Ground-Based Lidar Measurements of Aerosols During ACE-2: Instrument Description, Results, and Comparisons with Other Ground-Based and Airborne Measurements

A micro-pulse lidar system (MPL) was used to measure the vertical and horizontal distribution of aerosols during the Aerosol Characterization Experiment 2 (ACE-2) in June and July of 1997. The MPL measurements were made at the Izana observatory (IZO), a weather station located on a mountain ridge (28 deg 18 min N, 16 deg 30 min W, 2367 m asl) near the center of the island of Tenerife, Canary Islands. The MPL was used to acquire aerosol backscatter, extinction, and optical depth profiles for normal background periods and periods influenced by Saharan dust from North Africa. System tests and calibration procedures are discussed, and an analysis of aerosol optical profiles acquired during ACE-2 is presented. MPL data taken during normal IZO conditions (no dust) showed that upslope aerosols appeared during the day and dissipated at night and that the layers were mostly confined to altitudes a few hundred meters above IZO. MPL data taken during a Saharan dust episode on 17 July showed that peak aerosol extinction values were an order of magnitude greater than molecular scattering over IZO, and that the dust layers extended to 5 km asl. The value of the dust backscatter-extinction ratio was determined to be 0.027 +/- 0.007 sr(exp -1). Comparisons of the MPL data with data from other collocated instruments showed good agreement during the dust episode.

Welton, Ellsworth J.↗

Lidar Observations of Tropospheric Aerosols Over Northeastern South Africa During the ARREX and SAFARI-2000 Dry Season Experiments

During the ARREX-1999 and SAFARI-2000 Dry Season experiments a micropulse lidar (523 nm) instrument was operated at the Skukuza Airport in northeastern South Africa. The Mar was collocated with a diverse array of passive radiometric equipment. For SAFARI-2000 the processed Mar data yields a daytime time-series of layer mean/derived aerosol optical properties, including extinction-to-backscatter ratios and vertical extinction cross-section profile. Combined with 523 run aerosol optical depth and spectral Angstrom exponent calculations from available CIMEL sun-photometer data and normalized broadband flux measurements the temporal evolution of the near surface aerosol layer optical properties is analyzed for climatological trends. For the densest smoke/haze events the extinction-to-backscatter ratio is found to be between 60-80/sr, and corresponding Angstrom exponent calculations near and above 1.75. The optical characteristics of an evolving smoke event from SAFARI-2000 are extensively detailed. The advecting smoke was embedded within two distinct stratified thermodynamic layers, causing the particulate mass to advect over the instrument array in an incoherent manner on the afternoon of its occurrence. Surface broadband flux forcing due to the smoke is calculated, as is the evolution in the vertical aerosol extinction profile as measured by the Han Finally, observations of persistent elevated aerosol during ARREX-1999 are presented and discussed. The lack of corroborating observations the following year makes these observation; both unique and noteworthy in the scope of regional aerosol transport over southern Africa.

Campbell, James R.↗

An Investigation of the Ice Cloud Detection Sensitivity of Cloud Radars Using the Raman Lidar at the ARM SGP Site

The ice cloud detection sensitivity of the millimeter cloud radar (MMCR) and the Ka-band Zenith radar (KAZR) is investigated using a collocated Raman lidar (RL) at the Atmospheric Radiation Measurement Program Southern Great Plains site. Only profiles that are transparent to the RL with ice clouds only are considered in this study. The MMCR underestimates the RL ice cloud optical depth (COD) by 20%. The MMCR detects no ice clouds in 37% of the profiles. These profiles where ice cloud goes undetected by the MMCR typically contain very optically thin clouds, with a mean RL ice COD of 0.03. Higher ice cloud detection sensitivity is found for the KAZR, which underestimates the RL ice COD by 15%. The decrease in the ice COD bias for the KAZR compared to the MMCR is largely due to a decrease in the ice COD bias for the situation where the transparent profiles with ice clouds are detected by both the RL and cloud radar. The climatic net ice cloud radiative effects (CREs) from the RL at the top of the atmosphere (TOA) and the surface are 3.2 W m−2 and −0.6 W m−2, respectively. The ice CREs at the TOA and surface are underestimated for the MMCR by 0.7 W m−2 and 0.16 W m−2 (21% and 29%) and underestimated for the KAZR by 0.6 W m−2 and 0.14 W m−2 (17% and 24%). The ice clouds undetected by the cloud radars led to underestimating the climatic net cloud heating rates below 150 hPa by about 0–0.04 K day−1.

54 ENVIRONMENTAL SCIENCES↗

Satellite measurements of physical properties of Saharan dust

The physical properties of Saharan dust obtained from AVHRR and VISSR images are studied. The techniques of Fraser (1976) and Kaufman and Fraser (1985) are used to derive the aerosol optical depth, mass, and single scattering albedo for the region extending from the west coast of Africa to the Barbados Island for the period of June 21-25, 1984. Optical properties measured by satellite are compared to aircraft measurements taken near Barbados Island during the same period. Remote measurement of thermal properties is also discussed.

Lee, Tae Young↗

Multifrequency Models of Black Hole Photon Rings from Low-luminosity Accretion Disks

Images of black holes encode both astrophysical and gravitational properties. Detecting highly lensed features in images can differentiate between these two effects. We present an accretion disk emission model coupled to the Adaptive Analytical Ray Tracing (AART) code that allows a fast parameter space exploration of black hole photon ring images produced from synchrotron emission from 10 to 670 GHz. As an application, we systematically study several disk models and compute their total flux density, average radii, and optical depth. The model parameters are chosen around fiducial values calibrated to general relativistic magnetohydrodynamic (GRMHD) simulations and observations of M87*. For the parameter space studied, we characterize the transition between optically thin and thick regimes and the frequency at which the first photon ring is observable. Our results highlight the need for careful definitions of photon ring radius in the image domain, as in certain models the highly lensed photon ring is dimmer than the direct emission at certain angles. We find that at low frequencies the ring radii are set by the electron temperature, while at higher frequencies the magnetic field strength plays a more significant role, demonstrating how multifrequency analysis can also be used to infer plasma parameters. Lastly, we show how our implementation can qualitatively reproduce multifrequency black hole images from GRMHD simulations when adding time variability to our disk model through Gaussian random fields. This approach provides a new method for simulating observations from the Event Horizon Telescope and the proposed Black Hole Explorer space mission.

79 ASTRONOMY AND ASTROPHYSICS↗

Models of the quasar population. II - The effects of dust obscuration

A model for dust obscuration is proposed to account for the apparent lack of high-redshift quasars which are assumed to be obscured by dust in intervening galaxies. The distribution function for the optical depth as a function of redshift is constructed and used to determine the expected properties of quasars. The apparent magnitude distribution at three points is used to fit the model. Optical results are given for the comoving number density, redshift distribution, and mean color excess. If the theory is correct, evidence for dust may be seen in quasar spectra and a correlation between quasar continuum slopes and strength of metal line absorption systems should be observed.

Heisler, Julia↗

Remote sensing over oceans of optically thin cirrus and its significance

The extinction characteristics of thin ice-crystal clouds over the oceanic convective rain belts in the tropics and midlatitudes, obtained from the infrared interferometer spectrometer flown on Nimbus 4 satellite in 1970 are examined. It is observed that the optical depth of these clouds in the RF window region is less than 3 and their spectral features are consistent with the cloud particle size of about 10 micron. These optically-thin ice-crystal clouds are extensions of the anvil clouds generated by deep convective systems. The existence of such clouds extending from the upper troposphere into the lower stratosphere in the polar regions during winter and early spring is indicated, and the result of a theoretical simulation are analyzed.

Cuddapah, Prabhakara↗

Initial Validation and Results of Geoscience Laser Altimeter System Optical Properties Retrievals

Verification of Geoscience Laser Altimeter System (GLAS) optical retrievals is . problematic in that passage over ground sites is both instantaneous and sparse plus space-borne passive sensors such as MODIS are too frequently out of sync with the GLAS position. In October 2003, the GLAS Validation Experiment was executed from NASA Dryden Research Center, California to greatly increase validation possibilities. The high-altitude NASA ER-2 aircraft and onboard instrumentation of Cloud Physics Lidar (CPL), MODIS Airborne Simulator (MAS), and/or MODIS/ASTER Airborne Simulator (MASTER) under-flew seven orbit tracks of GLAS for cirrus, smoke, and urban pollution optical properties inter-comparisons. These highly calibrated suite of instruments are the best data set yet to validate GLAS atmospheric parameters. In this presentation, we will focus on the inter-comparison with GLAS and CPL and draw preliminary conclusions about the accuracies of the GLAS 532nm retrievals of optical depth, extinction, backscatter cross section, and calculated extinction-to-backscatter ratio. Comparisons to an AERONET/MPL ground-based site at Monterey, California will be attempted. Examples of GLAS operational optical data products will be shown.

Hlavka, Dennis L.↗

Improving the Capabilities and Computational Efficiency of the RTE+RRTMGP Radiation Code (Final Report)

This report details progress on the RTE+RRTMGP radiation codes made during the period of performance. RTE+RRTMGP is a set of codes for computing radiative fluxes in planetary atmospheres. RRTMGP uses a k-distribution to provide an optical description (absorption and possibly Rayleigh optical depth) of the gaseous atmosphere, along with the relevant source functions, on a pre-determined spectral grid given temperatures, pressures, and gas concentration. RTE computes fluxes given spectrally-resolved optical descriptions and source functions. Spectrally-resolved fluxes are summarized (“reduced”) via a user extensible class. The initial release of the code and the design choices are described in Pincus et al. 2019; the codes are available on Github. Although RRTMGP was based on current (at the time) empirical spectroscopic data, RTE and RRTMGP were developed in large part to modernize software practices. The design focused on flexibility broadly interpreted: by separating code from data and allowing data to drive computation; in coupling to the host model (e.g. the coupling of clouds to radiative fluxes is user-controlled); with respect to programming languages (computational tasks are accessed via widely-compatible C interfaces); and with respect to hardware (the codes run on a range of CPU and GPU architectures). The code also puts an emphasis on modularity and clarity. RTE+RRTMGP v1.0 was released in September 20219. This award supported the evolution of the RTE+RRTMGP code base to support greater flexibility, accuracy, and efficiency.

54 ENVIRONMENTAL SCIENCES↗

Performance Simulations for a Spaceborne Methane Lidar Mission

Future spaceborne lidar measurements of key anthropogenic greenhouse gases are expected to close current observational gaps particularly over remote, polar, and aerosol-contaminated regions, where actual in situ and passive remote sensing observation techniques have difficulties. For methane, a "Methane Remote Lidar Mission" was proposed by Deutsches Zentrum fuer Luft- und Raumfahrt and Centre National d'Etudes Spatiales in the frame of a German-French climate monitoring initiative. Simulations assess the performance of this mission with the help of Moderate Resolution Imaging Spectroradiometer and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations of the earth's surface albedo and atmospheric optical depth. These are key environmental parameters for integrated path differential absorption lidar which uses the surface backscatter to measure the total atmospheric methane column. Results showthat a lidar with an average optical power of 0.45W at 1.6 μm wavelength and a telescope diameter of 0.55 m, installed on a low Earth orbit platform(506 km), will measure methane columns at precisions of 1.2%, 1.7%, and 2.1% over land, water, and snow or ice surfaces, respectively, for monthly aggregated measurement samples within areas of 50 × 50 km2. Globally, the mean precision for the simulated year 2007 is 1.6%, with a standard deviation of 0.7%. At high latitudes, a lower reflectance due to snow and ice is compensated by denser measurements, owing to the orbital pattern. Over key methane source regions such as densely populated areas, boreal and tropical wetlands, or permafrost, our simulations show that the measurement precision will be between 1 and 2%.

methane↗

Highlights from 4STAR Sky-Scanning Retrievals of Aerosol Intensive Optical Properties from Multiple Field Campaigns with Detailed Comparisons of SSA Reported During SEAC4RS

The 4STAR (Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research) instrument combines airborne sun tracking capabilities of the Ames Airborne Tracking Sun Photometer (AATS-14) with AERONET (Aerosol Robotic Network)-like sky-scanning capability and adds state-of-the-art fiber-coupled grating spectrometry to yield hyperspectral measurements of direct solar irradiance and angularly resolved sky radiance. The combination of sun-tracking and sky-scanning capability enables retrievals of wavelength-dependent aerosol optical depth (AOD), mode-resolved aerosol size distribution (SD), asphericity, and complex refractive index, and thus also the scattering phase function, asymmetry parameter, single-scattering albedo (SSA), and absorption aerosol optical thickness (AAOT). From 2012 to 2014 4STAR participated in four major field campaigns: the U.S. Dept. of Energy's TCAP (Two-Column Aerosol Project) I & II campaigns, and NASA's SEAC4RS (Studies of Emissions, Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys) and ARISE (Arctic Radiation - IceBridge Sea & Ice Experiment) campaigns. Establishing a strong performance record, 4STAR operated successfully on all flights conducted during each of these campaigns. Sky radiance spectra from scans in either constant azimuth (principal plane) or constant zenith angle (almucantar) were interspersed with direct beam measurements during level legs. During SEAC4RS and ARISE, 4STAR airborne measurements were augmented with flight-level albedo from the collocated Shortwave Spectral Flux Radiometer (SSFR) providing improved specification of below-aircraft radiative conditions for the retrieval. Calibrated radiances and retrieved products will be presented with particular emphasis on detailed comparisons of ambient SSA retrievals and measurements during SEAC4RS from 4STAR, AERONET, HSRL2 (High Spectral Resolution Lidar), and from in situ measurements.

Radiance↗

4STAR Sky-Scanning Retrievals of Aerosol Intensive Optical Properties from Multiple Field Campaigns with Detailed Comparisons of SSA Reported During SEAC4RS

The 4STAR (Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research) instrument combines airborne sun tracking capabilities of the Ames Airborne Tracking Sun Photometer (AATS-14) with AERONET-like sky-scanning capability and adds state-of-the-art fiber-coupled grating spectrometry to yield hyper spectral measurements of direct solar irradiance and angularly resolved sky radiance. The combination of sun-tracking and sky-scanning capability enables retrievals of wavelength-dependent aerosol optical depth (AOD), mode-resolved aerosol size distribution (SD), asphericity, and complex refractive index, and thus also the scattering phase function, asymmetry parameter, single-scattering albedo (SSA), and absorption aerosol optical thickness (AAOT).From 2012 to 2014 4STAR participated in four major field campaigns: the U.S. Dept. of Energy TCAP I II campaigns, and NASAs SEAC4RS and ARISE campaigns. Establishing a strong performance record, 4STAR operated successfully on all flights conducted during each of these campaigns. Sky radiance spectra from scans in either constant azimuth (principal plane) or constant zenith angle (almucantar) were interspersed with direct beam measurements during level legs. During SEAC4RS and ARISE, 4STAR airborne measurements were augmented with flight-level albedo from the collocated Shortwave Spectral Flux Radiometer (SSFR) providing improved specification of below-aircraft radiative conditions for the retrieval. Calibrated radiances and retrieved products will be presented with particular emphasis on detailed comparisons of ambient SSA retrievals and measurements during SEAC4RS from 4STAR, AERONET, HSRL2, and from in situ measurements.

Flynn, Connor↗

Day 640 infrared line and continuum measurements: Dust formation in SN 1987A

We have measured day 640-645 line and continuum spectra of (Ni II) 6.6 micrometer (Ne II) 12.8 micrometer (line emission was not detected), and (Fe II) 17.9 and 26.0 micrometer from SN 1987A. The high velocity feature at v(sub HVF) approximately 3900 km/sec found in both of our day 410 (Fe II) spectra is again detected in the day 640 (Ni II) spectrum, although the signal-to-noise of the day 640 (Fe II) spectra is insufficient to show this feature. The continuum fluxes provide clear evidence for the formation of dust between day 410 and day 640 and are best fitted by a graybody spectrum with a temperature of 342 +/- 17 K at day 640 and a surface area corresponding to a minimum dust velocity v(sub dust) = 1910 +/- 170 km/sec. Optically thin dust emissivity laws proportional to lambda(exp -1) or lambda(exp -2) are inconsistent with the data. Either the dust grains are large (radius a much greater than 4 micrometer and radiate like individual blackbodies, or else they are located in clumps optically thick in the 6-26 micrometer range. The (Ni II) 6.6 micrometer line flux yields a minimum Ni(+) mass of 5.8 +/- 1.6 x 10(exp -4) solar mass and a Ni/Fe abundance ratio of 0.06 +/- 0.02, equal to the solar value. The ratio of the two (Fe II) line profiles implies a gas temperature 2600 +/- 700 K, a drop of 1800 +/- 800 K from our day 410 measurement. The (Fe II) 26.0 micrometer line flux has decreased by a factor of 2 and the day 640 (Ni II) profile is blueshifted by -440 +/- 270 km/sec, relative to observations before day 500. We show that the decrease in the (Fe II) flux and the blueshift are not produced by a decrease in electron scattering optical depth, electron density, or temperature, but rather are probably due to obscuration by the same dust which produces the infrared continuum. This supports the interpretation that the dust spectrum is produced by optically thick clumps. We discuss possible explanations for the discrepancy between the mass of Fe(+) detected and the total iron mass required to power the light curve. The decrease in the (Fe II) fluxes relative to the decrease required to account for the blueshifts of optical lines from non-iron-group elements and the similarity between v(sub dust) and the Ni(+) expansion velocity imply a spatial association between the dust clumps and the iron-group elements. In addition, the larger blueshift observed for the near and far-infrared, heavy metal transitions relative to non-iron-group lines suggests that the iron-group elements are somewhat segregated from lighter elements such as the Mg(sup 0) and O(sup 0) responsible for shorter wavelength lines. We speculate that FeS may be an important constituent of the dust. A comparison of our line profiles with radiative transfer models shows that while power law and exponential density distributions yield reasonable fits to the data, polytrope distributions provided significantly worse agreement. The best fits require a substantial fraction of the iron to be undetectable, and are consistent with maximum expansion velocities of v(sub max) approximately 3000 km/sec.

Colgan, Sean W. J.↗

A Fast Hybrid (3-D/1-D) Model for Thermal Radiative Transfer in Cirrus via Successive Orders of Scattering

We investigate the impact of cirrus cloud heterogeneity on the direct emission by cloud or surface and on the scattering by ice particles in the thermal infrared (TIR). Realistic 3-D cirri are modeled with the 3DCLOUD code, and top-of-atmosphere radiances are simulated by the 3-D Monte Carlo radiative transfer (RT) algorithm 3DMCPOL for two (8.65 micrometers and 12.05 micrometers) channels of the Imaging Infrared Radiometer on CALIPSO. At nadir, comparisons of 1-D and 3-D RT show that 3-D radiances are larger than their 1-D counterparts for direct emission but smaller for scattered radiation. For our cirrus cases, 99% of the 3-D total radiance is computed by the third scattering order, which corresponds to 90% of the total computational effort, but larger optical thicknesses need more scattering orders. To radically accelerate the 3-D RT computations (using only few percent of 3-D RT time with a Monte Carlo code), even in the presence of large optical depths, we develop a hybrid model based on exact 3-D direct emission, the first scattering order from 1-D in each homogenized column, and an empirical adjustment linearly dependent on the optical thickness to account for higher scattering orders. Good agreement is found between the hybrid model and the exact 3-D radiances for two very different cirrus models without changing the empirical parameters. We anticipate that a future deterministic implementation of the hybrid model will be fast enough to process multiangle thermal imagery in a practical tomographic reconstruction of 3-D cirrus fields.

radiative transfer↗

Vacuum ultraviolet absorption in a hydrogen arcjet

Atomic absorption spectroscopy was utilized to measure the ground state atomic hydrogen number density in the plasma produced in a low power hydrogen arcjet. A microwave driven hydrogen plasma was used as the source of radiation resonant with the vacuum ultraviolet Lyman alpha transition. The suitability of this radiation source is discussed. The optical depth of this transition prevented measurements at locations where the ground state atomic hydrogen number density was larger than 3 x 10 exp 19/cu m. These results indicate that other single-photon optical diagnostic techniques are equally ineffective in locations of higher hydrogen number density unless the spectral line shape of the atomic hydrogen absorbers is known.

Manzella, David H.↗

Fast two-stream method for computing diurnal-mean actinic flux in vertically inhomogeneous atmospheres

Based on a derivation of the two-stream daytime-mean equations of radiative flux transfer, a method for computing the daytime-mean actinic fluxes in the absorbing and scattering vertically inhomogeneous atmosphere is suggested. The method applies direct daytime integration of the particular solutions of the two-stream approximations or the source functions. It is valid for any duration of period of averaging. The merit of the method is that the multiple scattering computation is carried out only once for the whole averaging period. It can be implemented with a number of widely used two-stream approximations. The method agrees with the results obtained with 200-point multiple scattering calculations. The method was also tested in runs with a 1-km cloud layer with optical depth of 10, as well as with aerosol background. Comparison of the results obtained for a cloud subdivided into 20 layers with those obtained for a one-layer cloud with the same optical parameters showed that direct integration of particular solutions possesses an 'analytical' accuracy. In the case of the source function interpolation, the actinic fluxes calculated above the one-layer and 20-layer clouds agreed within 1%-1.5%, while below the cloud they may differ up to 5% (in the worst case). The ways of enhancing the accuracy (in a 'two-stream sense') and computational efficiency of the method are discussed.

Filyushkin, V. V.↗

Contributions From Cloud Morphological Changes to the Interannual Shortwave Cloud Feedback Based on MODIS and ISCCP Satellite Observations

The surface temperature-mediated change in cloud properties, referred to as the cloud feedback, continues to dominate the uncertainty in climate projections. A larger number of contemporary global climate models (GCMs) project a higher degree of warming than the previous generation of GCMs. This greater projected warming has been attributed to a less negative cloud feedback in the Southern Ocean. Here, we apply a novel “double decomposition method” that employs the “cloud radiative kernel” and “cloud regime” concepts, to two data sets of satellite observations to decompose the interannual cloud feedback into contributions arising from changes within and shifts between cloud morphologies. Our results show that contributions from the latter to the cloud feedback are large for certain regimes. We then focus on interpreting how both changes within and between cloud morphologies impact the shortwave cloud optical depth feedback over the Southern Ocean in light of additional observations. Results from the former cloud morphological changes reveal the importance of the wind response to warming increases low- and mid-level cloud optical thickness in the same region. Results from the latter cloud morphological changes reveal that a general shift from thick storm-track clouds to thinner oceanic low-level clouds contributes to a positive feedback over the Southern Ocean that is offset by shifts from thinner broken clouds to thicker mid- and low-level clouds. Our novel analysis can be applied to evaluate GCMs and potentially diagnose shortcomings pertaining to their physical parameterizations of particular cloud morphologies.

58 GEOSCIENCES↗

The lunar environment and its effect on optical astronomy

The Moon's geologic environment features: (1) gravity field one-sixth that of Earth; (2) sidereal rotation period of 27.3 days; (3) surface with greater curvature than Earth's surface (a chord along a 10 km baseline would have a bulge of 7.2 m); (4) seismically and tidally stable platform on which to make astronomical observations (most moonquakes have magnitudes of 1 to 2 on the Richter scale, within the earth's seismic noise, resulting in ground motions only 1 nm); (5) tenuous atmosphere (the total mass at night is only 10(exp 4) kg) that has an optical depth of 10(exp -6) and does not cause wind induced stresses and vibrations on structures; (6) large diurnal temperature variation (100 to 385 K in equatorial regions), which telescopes must be designed to withstand; (7) weak magnetic field, ranging from 3 to 330 x 10(exp -9) T, compared to 3 x 10(exp -5) T on Earth at the equator; (8) surface exposed to radiation, the most dangerous of which are high energy (1 to 100 Mev) particles resulting from solar flares; (9) high flux of micrometeorites which are not slowed down from their cosmic velocities because of the lack of air (data indicate that microcraters greater than 10 microns across will form at the rate of 3000/sq m/yr); (10) regolith 2 to 30 m thick which blankets the entire lunar surface (this layer is fine-grained (average grain sizes range from 40 to 268 microns), has a low density (800 to 1000 kg/cu m in the upper few mm, rising to 1500 to 1800 kg/cu m at depths of 10 to 20 cm), is porous (35 to 45 pct), cohesive (0.1 to 1.0 kN/sq m), and has a low thermal diffusivity (0.7 to 1.0 x 110-8 sq m/sec); about 29 pct of the regolith is less than 20 micron in size (this dust could pose a hazard to optical telescopes); (11) rubbly upper several hundred meters in which intact bedrock is uncommon, especially in the lunar highlands; and (12) craters with diameter-to-depth ratios of 5 if fresh and less than km across (larger and eroded craters have diameter-to-depth ratios greater than 5).

Taylor, G. Jeffrey↗