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An analysis of the multibeam altimeter

The design concept and computer simulations of a multibeam altimeter (MA) to provide satellite-based oceanographic-feature data for map construction within relatively short times are presented. The limitations of the pulse-limited radar altimeter used on GEOS-3 and SEASAT-A, in particular the narrow swath of each measurement pass, are characterized. The MA uses interferometry with two 1.2-m dish antennas separated by an 11-m boom to cover a total swath width of 100 km at satellite altitude 800 km, nominal repetition rate 6 kp/sec, and nominal integration time 2.5 sec. Simulation analysis of antenna element pattern, echo shape, tracking algorithms, tracking noise, and measurement accuracy was performed, and the general feasibility of ocean-current mapping with a one-week time delay, using two MA-equipped satellites, was demonstrated.

Bush, G. B.↗

A morphologic study of Venus Ridge belts

Ridge belts, first identified in the Venera 15/16 images are distinguished as linear regions of concentrated, parallel to anastomosing, ridges. They are tens to several hundreds of km wide, hundreds to over one thousand km long, and composed of individual ridges 5 to 20 km wide and up to 200 km long. The ridges appear symmetrical in the radar images and are either directly adjacent to each other or separated by mottled plains. Cross-strike lineaments, visible as dark or bright lines, are common within the ridge belts, and some truncate individual ridges. In places the ridge belt may be offset by these lineaments, but such offset is rarely consistent across the ridge belt. Once the mode of formation of these ridge belts is understood, their distribution and orientation will help to constrain the homogeneity and orientation of the stresses over the period of ridge belt formation. The look direction for the Venera system was to the west, so ridges appear as pairs of bright and dark lineaments, with the bright line to the east of the dark. The term ridge was used in a general sense to refer to a linear rise. The use of this term is restricted to rises which have a sharp transition from bright to dark at the crest, and are 5 to 15 km wide. These ridges are either continuous or discontinuous. The continuous ridges are over 30 km long and form coherent ridge belts, while the discontinuous ridges are less than 30 km long and do not form a coherent ridge belt. The continuous ridges were divided into 3 components: (1) Anastomosing ridges, in which the individual ridges are sinuous and often meet and cross at small angles, are the most common component; (2) The parallel ridge component also consists of well defined ridges, often with plains separating the individual ridges, but the ridges are more linear and rarely intersect one another; and (3) Parallel ridged plains are composed of indistinct ridges, some of which do not have a distinctive bright-dark pattern. The nature of deformation within the ridge belts is complex and not fully understood at present. Some belts show distinct signs of compression, while others have symmetrical patterns expected in extensional environments. Thus the ridge belts may have formed by more than one style of deformation; some may be extensional, while others are compressional. All the ridge belts are being systematically mapped, especially for symmetrical relationships.

Frank, S. L.↗

Evolution of tropical plumes in VAS water vapor imagery

Synoptic scale tropical plumes are analyzed using satellite data and outgoing longwave radiation data. The evolution of plumes is described and their precursor signals are examined. The horizontal moisture patterns of the plumes are compared with nonplume climatology, and the predictability of plumes based solely on satellite imagery is assessed. The results show that a plume evolves as a stationary, tropical, dry or moist dipole, separated by an exceptionally strong cloud or moisture gradient. Tropical plume evolution is accompanied by a systematic drying of the tropical eastern Pacific atmosphere before development, and moistening and increased cloudiness with development.

Mcguirk, James P.↗

A measurement of the medium-scale anisotropy in the cosmic microwave background radiation

Observations from the first flight of the Medium Scale Anisotropy Measurement (MSAM) are analyzed to place limits on Gaussian fluctuations in the cosmic microwave background radiation (CMBR). This instrument chops a 30 min beam in a three-position pattern with a throw of +/- 40 min; the resulting data is analyzed in statistically independent single- and double-difference sets. We observe in four spectral channels at 5.6, 9.0, 16.5, and 22.5/cm, allowing the separation of interstellar dust emission from CMBR fluctuations. The dust component is correlated with the IRAS 100 micron map. The CMBR component has two regions where the signature of an unresolved source is seen. Rejecting these two source regions, we obtain a detection of fluctuations which match CMBR in our spectral bands of 0.6 x 10(exp -5) is less than Delta (T)/T is less than 2.2 x 10(exp -5) (90% CL interval) for total rms Gaussian fluctuations with correlation angle 0.5 deg, using the single-difference demodulation. Fore the double difference demodulation, the result is 1.1 x 10(exp -5) is less than Delta(T)/T is less than 3.1 x 10(exp -5) (90% CL interval) at a correlation angle of 0.3 deg.

Cheng, E. S.↗

Central East Pacific Flight Routing

With the introduction of the Federal Aviation Administration s Advanced Technology and Oceanic Procedures system at the Oakland Oceanic Center, a level of automation now exists in the oceanic environment to potentially begin accommodating increased user preferred routing requests. This paper presents the results of an initial feasibility assessment which examines the potential benefits of transitioning from the fixed Central East Pacific routes to user preferred routes. As a surrogate for the actual user-provided routing requests, a minimum-travel-time, wind-optimal dynamic programming algorithm was developed and utilized in this paper. After first describing the characteristics (e.g., origin airport, destination airport, vertical distribution and temporal distribution) of the westbound flights utilizing the Central East Pacific routes on Dec. 14-16 and 19-20, the results of both a flight-plan-based simulation and a wind-optimal-based simulation are presented. Whereas the lateral and longitudinal distribution of the aircraft trajectories in these two simulations varied dramatically, the number of simulated first-loss-of-separation events remained relatively constant. One area of concern that was uncovered in this initial analysis was a potential workload issue associated with the redistribution of traffic in the oceanic sectors due to thc prevailing wind patterns.

Grabbe, Shon↗

Infrared-Bolometer Arrays with Reflective Backshorts

Integrated circuits that incorporate square arrays of superconducting-transition- edge bolometers with optically reflective backshorts are being developed for use in image sensors in the spectral range from far infrared to millimeter wavelengths. To maximize the optical efficiency (and, thus, sensitivity) of such a sensor at a specific wavelength, resonant optical structures are created by placing the backshorts at a quarter wavelength behind the bolometer plane. The bolometer and backshort arrays are fabricated separately, then integrated to form a single unit denoted a backshort-under-grid (BUG) bolometer array. In a subsequent fabrication step, the BUG bolometer array is connected, by use of single-sided indium bump bonding, to a readout device that comprises mostly a superconducting quantum interference device (SQUID) multiplexer circuit. The resulting sensor unit comprising the BUG bolometer array and the readout device is operated at a temperature below 1 K. The concept of increasing optical efficiency by use of backshorts at a quarter wavelength behind the bolometers is not new. Instead, the novelty of the present development lies mainly in several features of the design of the BUG bolometer array and the fabrication sequence used to implement the design. Prior to joining with the backshort array, the bolometer array comprises, more specifically, a square grid of free-standing molybdenum/gold superconducting-transition-edge bolometer elements on a 1.4- m-thick top layer of silicon that is part of a silicon support frame made from a silicon-on-insulator wafer. The backshort array is fabricated separately as a frame structure that includes support beams and contains a correspond - ing grid of optically reflective patches on a single-crystal silicon substrate. The process used to fabricate the bolometer array includes standard patterning and etching steps that result in the formation of deep notches in the silicon support frame. These notches are designed to interlock with the support beams on the backshort-array structure to provide structural support and precise relative positioning. The backshort-array structure is inserted in the silicon support frame behind the bolometer array, and the notches in the frame serve to receive the support beams of the backshort-array structure and thus determine the distance between the backshort and bolometer planes. The depth of the notches and, thus, the distance between the backshort and bolometer planes, can be tailored to a value between 25 to 300 m adjusting only a few process steps. The backshort array is designed so as not to interfere with the placement of indium bumps for subsequent indium bump-bonding to the multiplexing readout circuitry

Miller, Timothy M.↗

Supersonic burning in separated flow regions

Activities reported include: (1) the construction of a thermocouple with a protective coating or sheath for obtaining reliable temperature measurements of gases in the base region; (2) the construction of a multiposition back step plate for trough tests for step sizes 0.63 cm and 0.25 cm; and (3) flow pattern studies with the 6.35 cm trough to determine the complex flow resulting when a shear layer reattaches in a corner. Reliable ignition and stable burning were achieved at Mach = 2 for the 0.63 cm trough. Photographs of side wall oil streaks for M=2 flow, and some static and pitot pressure results at M = 3 are included.

Zumwalt, G. W.↗

Dynamic phases, clustering, and chain formation for driven disk systems in the presence of quenched disorder

In this paper, we numerically examine the dynamic phases and pattern formation of two-dimensional monodisperse repulsive disks driven over random quenched disorder. We show that there is a series of distinct dynamic regimes as a function of increasing drive, including a clogged or pile-up phase near depinning, a homogeneous disordered flow state, and a dynamically phase separated regime consisting of high-density crystalline regions surrounded by a low density of disordered disks. At the highest drives the disks arrange into one-dimensional moving chains. The phase separated regime has parallels with the phase separation observed in active matter systems, but arises from a distinct mechanism consisting of the combination of nonequilibrium fluctuations with density-dependent mobility. We discuss the pronounced differences between this system and previous studies of driven particles with longer-range repulsive interactions moving over random substrates, such as superconducting vortices or electron crystals, where dynamical phase separation and distinct one-dimensional moving chains are not observed. Finally, our results should be generic to a broad class of systems in which the particle-particle interactions are short ranged, such as sterically interacting colloids or Yukawa particles with strong screening driven over random pinning arrays, superconducting vortices in the limit of small penetration depths, or quasi-two-dimensional granular matter flowing over rough landscapes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Effects of interlayer spacing and applied pressure on the lanthanide transport in MoS 2 -based two-dimensional channels

Rare-earth elements (REEs) are critical to modern industry but difficult to separate due to their subtle and monotonic changes in physicochemical properties. MoS 2 -based two-dimensional (2D) materials offer novel opportunities for enhancing REE separation, exhibiting a distinct volcano-shaped transport performance distribution that peaks at Sm 3+ . However, the specific contributions of thermodynamic and kinetic factors to ion transport within 2D confinement remain unclear. In this study, we conducted a series of non-equilibrium all-atom molecular dynamics (MD) simulations to explore the effects of interlayer spacing and external pressure on the transport of lanthanide ions in Å-scale acetate functionalized 2D MoS 2 (MoS 2 -COOH) channels. We examined ion entry and permeation rates, water flux, dehydration, and binding modes. The simulation results reveal that the transport trends of lanthanide ions are jointly driven by the dehydration degree and the relative-binding strengths of ions to water and to the acetate within the 2D channels. Notably, the dehydration pattern of lanthanide ions during permeation is closely linked to kinetic factors. Overall, this study provides a detailed atomistic understanding of the mechanisms underlying lanthanide ion transport under confinement. These findings point to the significant potential for tuning confinement and chemical functionalization within Å-scale channels for more efficient REE separation.

2D channels↗

Simulations of a hypersonic turbulent boundary layer over wavy surfaces

Here, we conduct large-eddy simulations of a Mach 5.84 cold wall turbulent boundary layer over one-dimensional wavy walls with varying amplitudes and wavelengths. Across all wall topologies, a series of alternating shock and expansion waves is shown to influence the entire boundary layer, and generate repeating wave patterns in the turbulent stresses, dispersive stresses, and turbulent kinetic energy budget. The series of alternating shocks and expansions imposes repeating adverse and favourable pressure gradients across the wavy wall, and at sufficient wall amplitude, triggers flow separation in the trough of the wave. Flow separation is demonstrated to influence the behaviour of wall pressure fluctuations over the wavy wall. In attached flows, the prominent frequencies are consistent with integral-scale boundary layer turbulence, whereas in separated flows, a two-decade frequency range is present, akin to two-dimensional shock–boundary layer interactions. Counter-rotating streamwise-oriented structures are observed on the windward side of the wave, which diminish over the wave crest. A conditional analysis demonstrates that these structures are present in the upstream boundary layer, and are amplified with increasing wall amplitude. An examination of the Görtler number and probability density function (PDF) of the fluctuating lateral wall shear stress demonstrates the strong correlation between a large Görtler number and growth of the PDF tail density, suggesting that the amplification of the counter-rotating streamwise-oriented structures are linked to centrifugal instabilities in regions of streamline concavity.

boundary layers↗

Effects of Climate Change on Capacity Expansion Decisions of an Electricity Generation Fleet in the Southeast U.S.

The electric power sector in the United States faces many challenges related to climate change. On the demand side, climate change could shift demand patterns due to increased air temperatures. On the supply side, climate change could lead to deratings of thermal units due to changes in air temperature, water temperature, and water availability. Past studies have typically analyzed these risks separately. Here, we developed an integrated, multimodel framework to analyze how compounding risks of climate-change impacts on demand and supply affect long-term planning decisions in the power system. In the southeast U.S., we found that compounding climate-change impacts could result in a 35% increase in installed capacity by 2050 relative to the reference case. Participation of renewables, particularly solar, in the fleet increased, driven mostly by the expected increase in summertime peak demand. Such capacity requirements would increase investment costs by approximately 31 billion (USD 2015) over the next 30 years, compared to the reference case. These changes in investment decisions align with carbon emission mitigation strategies, highlighting how adaptation and mitigation strategies can converge.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Reducing uncertainty of polar to midlatitude linkages using DOE’s E3SM in a coordinated model-experiment setting

This project brought DOE’s climate modeling effort with the Energy Exascale Earth System Model into the Polar Amplification Model Intercomparison Project (PAMIP), which is part of the sixth and latest Coupled Model Intercomparison Project, CMIP6. PAMIP examines the causes and consequences of polar amplification, when external forcing results in a larger temperature increase in high latitudes than the global average, in a coordinated set of model experiments with a common modeling protocol. Our teams from UC Irvine and the University of Toronto have designed, carried out, analyzed, and disseminated PAMIP output from the Energy Exascale Earth System Model (E3SM) and the Community Earth System Model (CESM). PAMIP’s ongoing stream of significant new results have advanced progress in the community’s understanding and led to new outstanding research questions that have motivated further work. PAMIP has led to improved consensus on the atmospheric response to sea ice loss. The important finding is that for a similar sea ice anomaly forcing, the simulated atmospheric response in the troposphere is remarkably consistent among the 16 models’ runs analyzed. The zonal-mean tropospheric response consists of a very robust equatorward shift of the westerly flow in mid-latitudes. However, while the multi-model mean response is robust, it has a weak amplitude relative to internal variability. We identified a weakness in the models (including E3SM) in terms of their response to sea-ice forcing that is related to eddy forcing (or nonlinear dynamical effects) at mid- to high latitudes. In fact, E3SM is an outlier in terms of the models participating, and in that sense, it turned out to be a vital participant model. We found that reductions in energy transport due sea-ice loss and involving dry air only are compensated by increases in moist energy transport from warmer sea surface temperature in midlatitudes. This leads to a large spread in energy transport into the Arctic and is a potential source of spread in Arctic amplification. We identified an important role that climate modes, including tropical modes of variability (El Nino and the Southern Oscillation (ENSO); the Quasi-biennial Oscillation (QBO)) play in the response to sea-ice anomalies, including in ocean coupled experiments. Similarly, we identified and quantified the contribution of sea-ice thickness to the atmospheric response compared to the response to sea-ice extent only. We found that it is important to run large ensembles and even with an ensemble size of 100 simulations the response is largely influenced by internal variability. We demonstrated convincingly that Ural blocking, not sea-ice loss, provides the weakening of the stratospheric polar vortex in fall/early winter and a negative phase of the North Atlantic Oscillation that can last for up to two months. However, sea-ice anomalies can influence the background flow so that the response to Ural blocking is more persistent under low sea-ice conditions in the Barents/Kara Sea than high sea ice Atmospheric model hierarchies that progressively add individual processes have a long history in providing dynamical insight for modeling the atmosphere. Similarly, coupled model hierarchies that progressively add individual ocean processes can provide insights into the workings of the coupled climate system, however such hierarchies have not been available except for a non-dynamical slab ocean model. Because of the missing processes, surface flux corrections must be added to produce a target climate. In this project, we managed to overcome this problem and develop a globally coupled ocean model hierarchy in CESM that can turn on and off the processes of mixed-layer entrainment and Ekman flow. We used the hierarchy to study the impact of Arctic sea-ice loss on the climate system. We find that the effect of mixed-layer entrainment on ocean heat uptake influences the atmospheric circulation by shifting the latitudinal positions of the mid-latitude westerly jet and the Intertropical Convergence Zone (ITCZ). In quadrupled CO 2 experiments, we studied how air-sea coupling affects the response of tropical rainfall under global warming. In order to identify the importance of individual ocean processes, we used the hierarchy of ocean models to separate the effects of seasonal mixed-layer entrainment, wind-driven Ekman flows, and frictional flows. We showed that including Ekman and frictional flows allows our simulation to produce the Pacific Ocean's enhanced equatorial warming pattern and equatorward ITCZ contraction noted in previous climate simulations. We also showed that the frictional flow, which has yet to receive much attention, is as important as the Ekman flow in generating equatorial heat convergence.

54 ENVIRONMENTAL SCIENCES↗

Primary instabilities and bicriticality in flow between counter-rotating cylinders

The primary instabilities and bicritical curves for flow between counter-rotating cylinders have been computed numerically from the Navier-Stokes equations assuming axial periodicity. The computations provide values of the Reynolds numbers, wavenumbers, and wave speeds at the primary transition from Couette flow for radius ratios from 0.40-0.98. Particular attention has been focused on the bicritical curves that separate (as the magnitude of counter-rotation is increased) the transitions from Couette flow to flows with different azimuthal wavenumbers m and m + 1. This lays the foundation for further analysis of nonlinear mode interactions and pattern formation occurring along the bicritical curves and serves as a benchmark for experimental studies. Preliminary experimental measurements of transition Reynolds numbers and wave speeds presented here agree well with the computations from the mathematical model.

Langford, W. F.↗

Two-Color Laser Speckle Shift Strain Measurement System

A two color laser speckle shift strain measurement system based on the technique of Yamaguchi was designed. The dual wavelength light output from an Argon Ion laser was coupled into two separate single-mode optical fibers (patchcords). The output of the patchcords is incident on the test specimen (here a structural fiber). Strain on the fiber, in one direction, is produced using an Instron 4502. Shifting interference patterns or speckle patterns will be detected at real-time rates using 2 CCD cameras with image processing performed by a hardware correlator. Strain detected in fibers with diameters from 21 microns to 143 microns is expected to be resolved to 15 mu epsilon. This system was designed to be compact and robust and does not require surface preparation of the structural fibers.

Tuma, Margaret L.↗

Assessment of Postflight Locomotor Performance Utilizing a Test of Functional Mobility: Strategic and Adaptive Responses

Space flight induces adaptive modification in sensorimotor function, allowing crewmembers to operate in the unique microgravity environment. This adaptive state, however, is inappropriate for a terrestrial environment. During a re-adaptation period upon their return to Earth, crewmembers experience alterations in sensorimotor function, causing various disturbances in perception, spatial orientation, posture, gait, and eye-head coordination. Following long duration space flight, sensorimotor dysfunction would prevent or extend the time required to make an emergency egress from the vehicle; compromising crew safety and mission objectives. We are investigating two types of motor learning that may interact with each other and influence a crewmember's ability to re-adapt to Earth's gravity environment. In strategic learning, crewmembers make rapid modifications in their motor control strategy emphasizing error reduction. This type of learning may be critical during the first minutes and hours after landing. In adaptive learning, long-term plastic transformations occur, involving morphological changes and synaptic modification. In recent literature these two behavioral components have been associated with separate brain structures that control the execution of motor strategies: the strategic component was linked to the posterior parietal cortex and the adaptive component was linked to the cerebellum (Pisella, et al. 2004). The goal of this paper was to demonstrate the relative contributions of the strategic and adaptive components to the re-adaptation process in locomotor control after long duration space flight missions on the International Space Station (ISS). The Functional Mobility Test (FMT) was developed to assess crewmember s ability to ambulate postflight from an operational and functional perspective. Sixteen crewmembers were tested preflight (3 sessions) and postflight (days 1, 2, 4, 7, 25) following a long duration space flight (approx 6 months) on the ISS. We have further analyzed the FMT data to characterize strategic and adaptive components during the postflight readaptation period. Crewmembers walked at a preferred pace through an obstacle course set up on a base of 10 cm thick medium density foam (Sunmate Foam, Dynamic Systems, Inc., Leicester, NC). The 6.0m X 4.0m course consisted of several pylons made of foam; a Styrofoam barrier 46.0cm high that crewmembers stepped over; and a portal constructed of two Styrofoam blocks, each 31cm high, with a horizontal bar covered by foam and suspended from the ceiling which was adjusted to the height of the crewmember s shoulder. The portal required crewmembers to bend at the waist and step over a barrier simultaneously. All obstacles were lightweight, soft and easily knocked over. Crewmembers were instructed to walk through the course as quickly and as safely as possible without touching any of the objects on the course. This task was performed three times in the clockwise direction and three times in the counterclockwise direction that was randomly chosen. The dependent measures for each trial were: time to complete the course (seconds) and the number of obstacles touched or knocked down. For each crewmember, the time to complete each FMT trial from postflight days 1, 2, 4, 7 and 25 were further analyzed. A single logarithmic curve using a least squares calculation was fit through these data to produce a single comprehensive curve (macro). This macro curve composed of data spanning 25 days, illustrates the re-adaptive learning function over the longer time scale term. Additionally, logarithmic curves were fit to the 6 data trials within each individual post flight test day to produce 5 separate daily curves. These micro curves, produced from data obtained over the course of minutes, illustrates the strategic learning function exhibited over a relative shorter time scale. The macro curve for all subjects exhibited adaptive motor learning patterns over the 25 day period. Howev, 9/16 crewmembers exhibited significant strategic motor learning patterns in their micro curves, as defined by m > 1 in the equation of the line y=m*LN(x) +b. These data indicate that postflight recovery in locomotor function involves both strategic and adaptive mechanisms. Future countermeasures will be designed to enhance both recovery processes.

Warren, L. E.↗

Amorphous Phases on the Surface of Mars

Both primary (volcanic/impact glasses) and secondary (opal/silica, allophane, hisingerite, npOx, S-bearing) amorphous phases appear to be major components of martian surface materials based on orbital and in-situ measurements. A key observation is that whereas regional/global scale amorphous components include altered glass and npOx, local scale amorphous phases include hydrated silica/opal. This suggests widespread alteration at low water-to-rock ratios, perhaps due to snow/ice melt with variable pH, and localized alteration at high water-to-rock ratios. Orbital and in-situ measurements of the regional/global amorphous component on Mars suggests that it is made up of at least three phases: npOx, amorphous silicate (likely altered glass), and an amorphous S-bearing phase. Fundamental questions regarding the composition and the formation of the regional/global amorphous component(s) still remain: Do the phases form locally or have they been homogenized through aeolian activity and derived from the global dust? Is the parent glass volcanic, impact, or both? Are the phases separate or intimately mixed (e.g., as in palagonite)? When did the amorphous phases form? To address the question of source (local and/or global), we need to look for variations in the different phases within the amorphous component through continued modeling of the chemical composition of the amorphous phases in samples from Gale using CheMin and APXS data. If we find variations (e.g., a lack of or enrichment in amorphous silicate in some samples), this may imply a local source for some phases. Furthermore, the chemical composition of the weathering products may give insight into the formation mechanisms of the parent glass (e.g., impact glasses contain higher Al and lower Si [30], so we might expect allophane as a weathering product of impact glass). To address the question of whether these phases are separate or intimately mixed, we need to do laboratory studies of naturally altered samples made up of mixed phases (e.g., palagonite) and synthetic single phases to determine their short-range order structures and calculate their XRD patterns to use in models of CheMin data. Finally, to address the timing of the alteration, we need to study rocks on the martian surface of different ages that may contain glass (volcanic or impact) with MSL and future rovers to better understand how glass alters on the martian surface, if that alteration mechanism is universal, and if alteration spans across long periods of time or if there is a time past which unaltered glass remains.

Rampe, E. B.↗

The momentum transfer of incompressible turbulent separated flow due to cavities with steps

An experimental study was conducted using a plate test bed having a turbulent boundary layer to determine the momentum transfer to the faces of step/cavity combinations on the plate. Experimental data were obtained from configurations including an isolated configuration and an array of blocks in tile patterns. A momentum transfer correlation model of pressure forces on an isolated step/cavity was developed with experimental results to relate flow and geometry parameters. Results of the experiments reveal that isolated step/cavity excrecences do not have a unique and unifying parameter group due in part to cavity depth effects and in part to width parameter scale effects. Drag predictions for tile patterns by a kinetic pressure empirical method predict experimental results well. Trends were not, however, predicted by a method of variable roughness density phenomenology.

White, R. E.↗