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NASA NTRSDate not supplied

I’ve Looked at Clouds from Both Sides, Now: Viewpoints from Surface and Spaceborne Lidar Systems

Clouds play a critical role in the Earth’s climate system because they are inextricably linked to the hydrological cycle and radiation budget. Information about cloud height, thickness, occurrence, and amount are critical inputs for a host of numerical applications involving climate research. Therefore, it is important to have highly accurate and quantitative data records of cloud properties that span several years and geographic regions. Verification of even the most basic modeling processes demands long term and continuous observations of global cloud occurrence, if there is to be any confidence in their fidelity. For a number of reasons, however, it is impossible to gauge the complexities of clouds from a single source. Fundamentally, an array of remote sensing methods is needed in order to provide a complete picture. Within the Micropulse Lidar Network (MPLNET), we have developed a new algorithm to improve the quality of our cloud products. The largest impact of the changes to the cloud detection algorithm is evident with high clouds (those with cloud base > 5 km). Furthermore, polarized measurements enable us to determine the cloud thermodynamic phase. Naturally, the next step is to investigate how these improvements compare with observations from spaceborne lidars (e.g. CALIOP) which have a better (unobstructed) view of high clouds. Recent advances in remote sensing have revealed that cirrus clouds are the most common cloud genus observed in the atmosphere. Furthermore, cirrus skew highly towards relatively low cloud optical depths, as observed from both surface and spaceborne viewpoints. The radiative impacts of these findings are quite significant, considering the cumulative effect cirrus exhibit when compared to low clouds.

Jasper R Lewis↗
NASA NTRS1988

Variability in surface ECG morphology: signal or noise?

Using data collected from canine models of acute myocardial ischemia, we investigated two issues of major relevance to electrocardiographic signal averaging: ECG epoch alignment, and the spectral characteristics of the beat-to-beat variability in ECG morphology. With initial digitization rates of 1 kHz, an iterative a posteriori matched filtering alignment scheme, and linear interpolation, we demonstrated that there is sufficient information in the body surface ECG to merit alignment to a precision of 0.1 msecs. Applying this technique to align QRS complexes and atrial pacing artifacts independently, we demonstrated that the conduction delay from atrial stimulus to ventricular activation may be so variable as to preclude using atrial pacing as an alignment mechanism, and that this variability in conduction time be modulated at the frequency of respiration and at a much lower frequency (0.02-0.03Hz). Using a multidimensional spectral technique, we investigated the beat-to-beat variability in ECG morphology, demonstrating that the frequency spectrum of ECG morphological variation reveals a readily discernable modulation at the frequency of respiration. In addition, this technique detects a subtle beat-to-beat alternation in surface ECG morphology which accompanies transient coronary artery occlusion. We conclude that physiologically important information may be stored in the variability in the surface electrocardiogram, and that this information is lost by conventional averaging techniques.

NASA Discipline Cardiopulmonary↗
NASA NTRS1993

Mutual Inductance Problem for a System Consisting of a Current Sheet and a Thin Metal Plate

Rapid inspection of aircraft structures for flaws is of vital importance to the commercial and defense aircraft industry. In particular, inspecting thin aluminum structures for flaws is the focus of a large scale R&D effort in the nondestructive evaluation (NDE) community. Traditional eddy current methods used today are effective, but require long inspection times. New electromagnetic techniques which monitor the normal component of the magnetic field above a sample due to a sheet of current as the excitation, seem to be promising. This paper is an attempt to understand and analyze the magnetic field distribution due to a current sheet above an aluminum test sample. A simple theoretical model, coupled with a two dimensional finite element model (FEM) and experimental data will be presented in the next few sections. A current sheet above a conducting sample generates eddy currents in the material, while a sensor above the current sheet or in between the two plates monitors the normal component of the magnetic field. A rivet or a surface flaw near a rivet in an aircraft aluminum skin will disturb the magnetic field, which is imaged by the sensor. Initial results showed a strong dependence of the flaw induced normal magnetic field strength on the thickness and conductivity of the current-sheet that could not be accounted for by skin depth attenuation alone. It was believed that the eddy current imaging method explained the dependence of the thickness and conductivity of the flaw induced normal magnetic field. Further investigation, suggested the complexity associated with the mutual inductance of the system needed to be studied. The next section gives an analytical model to better understand the phenomenon.

Fulton, J. P.↗
NASA NTRS1984

Thermal performance of FRSI/graphite epoxy materials for the Orbiter TPS application

Radiant tests have been conducted to evaluate the performance of the Flexible Reusable Surface Insulation (FRSI) when bonded to Graphite/Epoxy (G/E) honeycomb sandwich structures. The results from this study indicate reasonable agreement with the baseline FRSI properties that existed prior to this test program. An updated Thermal Math Model (TMM) prediction technique was developed, with the use of the well-defined boundary conditions, which appears to be valid in analyzing the complex heat transfer associated with the honeycomb structure. The updated TM analysis of flight data resulted in good agreement of predicted temperatures with flight data for bondline responses of Orbiter FRSI/GE TPS applications.

Norman, I.↗
NASA NTRS1990

CFD validation for aerodynamic flows - Challenge for the '90's

The process of computational fluid dynamics (CFD) validation is described from two perspectives, numerical error validation and physical model validation. Errors associated with time and space discretization, grid refinement, numerical dissipation, and level of solution convergence, are all possible sources of numerical error. The second aspect of CFD code validation is associated with the governing equations and the physical models, e.g., chemistry and turbulence models. This type of validation requires comparisons with carefully conducted experiments and is the primary aspect of the validation process discussed in this paper. Examples of validation are shown for selected Reynolds-averaged Navier-Stokes codes for conditions from transonic through hypersonic. Since code applications are becoming more complex, it no longer suffices to use data from surface or integral quantities alone to provide the required validation. Flow field surveys and experimental boundary condition measurements are emerging as critical data that must be obtained for CFD code validation. Progress in the overall level of validation is shown to be improving. However, future challenges remain, some of which are enumerated.

Marvin, Joseph G.↗
NASA NTRS1997

Solution adaptive Cartesian grid methods for aerodynamic flows with complex geometries

Cartesian methods for computational fluid dynamics are considered to offer an accurate and robust approach for the simulation of aerodynamic flows around geometrically complex bodies. A part of the ongoing research in this domain is reviewed with the aim of providing insight into the fundamental challenges faced by the practitioners of this approach, and a guide to further research. The integration schemes used in Cartesian solvers are similar to those used in other approaches. The emphasis is on the geometric algorithms, surface modeling and boundary conditions required to design a successful Cartesian mesh scheme.

Aftosmis, Michael J.↗
NASA NTRS2002

Improving the Accuracy of Satellite Sea Surface Temperature Measurements by Explicitly Accounting for the Bulk-Skin Temperature Difference

The focus of this research was to determine whether the accuracy of satellite measurements of sea surface temperature (SST) could be improved by explicitly accounting for the complex temperature gradients at the surface of the ocean associated with the cool skin and diurnal warm layers. To achieve this goal, work was performed in two different major areas. The first centered on the development and deployment of low-cost infrared radiometers to enable the direct validation of satellite measurements of skin temperature. The second involved a modeling and data analysis effort whereby modeled near-surface temperature profiles were integrated into the retrieval of bulk SST estimates from existing satellite data. Under the first work area, two different seagoing infrared radiometers were designed and fabricated and the first of these was deployed on research ships during two major experiments. Analyses of these data contributed significantly to the Ph.D. thesis of one graduate student and these results are currently being converted into a journal publication. The results of the second portion of work demonstrated that, with presently available models and heat flux estimates, accuracy improvements in SST retrievals associated with better physical treatment of the near-surface layer were partially balanced by uncertainties in the models and extra required input data. While no significant accuracy improvement was observed in this experiment, the results are very encouraging for future applications where improved models and coincident environmental data will be available. These results are included in a manuscript undergoing final review with the Journal of Atmospheric and Oceanic Technology.

Wick, Gary A.↗
NASA NTRS2016

Analysis of Summer-Time Ozone and Precursor Species in the Southeast United States

Ozone (O3) is a greenhouse gas and toxic pollutant which plays a major role in air quality and atmospheric chemistry. The understanding and ability to model the horizontal and vertical structure of O3 mixing ratios is difficult due to the complex formation/destruction processes and transport pathways that cause large variability of O3. The Environmental Protection Agency has National Ambient Air Quality Standards for O3 set at 75 ppb with future standards proposed to be as low as 65 ppb. These lower values emphasize the need to better understand/simulate the transport processes, emission sources, and chemical processes controlling precursor species (e.g., NOx, VOCs, and CO) which influence O3 mixing ratios. The uncertainty of these controlling variables is particularly large in the southeast United States (US) which is a region impacted by multiple different emission sources of precursor species (anthropogenic and biogenic) and transport processes resulting in complex spatio-temporal O3 patterns. During this work we will evaluate O3 and precursor species in the southeast US applying models, ground-based and airborne in situ data, and lidar observations. In the summer of 2013, the UAH O3 Differential Absorption Lidar (DIAL) (part of the Tropospheric Ozone Lidar Network (TOLNet)) measured vertical O3 profiles from the surface up to approximately 12 km. During this period, the lidar observed numerous periods of dynamic temporal and vertical O3 structures. In order to determine the sources/processes impacting these O3 mixing ratios we will apply the CTM GEOS-Chem (v9-02) at a 0.25 deg x 0.3125 deg resolution. Using in situ ground-based (e.g., SEARCH Network, CASTNET), airborne (e.g., NOAA WP-3D - SENEX 2013, DC-8 - SEAC4RS), and TOLNet lidar data we will first evaluate the model to determine the capability of GEOS-Chem to simulate the spatio-temporal variability of O3 in the southeast US. Secondly, we will perform model sensitivity studies in order to quantify which emission sources (e.g., anthropogenic, biogenic, lighting, wildfire) and transport processes (e.g., stratospheric, long-range, local scale) are contributing to these TOLNet-observed dynamic O3 patterns. Results from the evaluation of the model and the study of sources/processes impacting observed O3 mixing ratios will be presented.

Optical Radar↗
NASA NTRS2018

The Interplay Between Radiation Pressure and the Photoelectric Instability in Optically Thin Disks of Gas and Dust

In optically thin disks, dust grains are photoelectrically stripped of electrons by starlight, heating nearby gas and possibly creating a dust clumping instability-the photoelectric instability (PeI)-that significantly alters global disk structure. In the current work, we use the Pencil Code to perform the first numerical models of the PeI that include stellar radiation pressure on dust grains in order to explore the parameter regime in which the instability operates. In some models with low gas and dust surface densities, we see a variety of dust structures, including sharp concentric rings. In the most gas- and dust-rich models, nonaxisymmetric clumps, arcs, and spiral arms emerge that represent dust surface density enhancements of factors of ∼5-20. In one high gas surface density model, we include a large, low-order gas viscosity and find that it observably smooths the structures that form in the gas and dust, suggesting that resolved images of a given disk may be useful for deriving constraints on the effective viscosity of its gas. Our models show that radiation pressure does not preclude the formation of complex structure from the PeI, but the qualitative manifestation of the PeI depends strongly on the parameters of the system. The PeI may provide an explanation for unusual disk morphologies, such as the moving blobs of the AU Mic disk, the asymmetric dust distribution of the 49Ceti disk, and the rings and arcs found in the HD 141569A disk.

photoelectric instability (PeI)↗
NASA NTRS2020

Evaluating impacts of snow, surface water, soil and vegetation on empirical vegetation and snow indices for the Utqiaġvik tundra ecosystem in Alaska with the LVS3 model

Satellite observations for the Arctic and boreal region may contain information of vegetation, soil, snow, snowmelt, and/or other surface water bodies. We investigated the impacts of vegetation, soil, snow and surface water on empirical vegetation/snow indices on a tundra ecosystem area located around Utqiaġvik (formerly Barrow) of Alaska with the Moderate Resolution Imaging Spectrometer (MODIS) images in 2001–2014. Empirical vegetation indices, such as normalized difference vegetation index (NDVI), enhanced vegetation index (EVI), the index of near infrared of vegetation (NIRv), and modified EVI (EVI2), have been used to monitor vegetation. Normalized difference snow index (NDSI) has been widely applied to monitor snow. The vegetation cover fraction (VGCF), the soil cover fraction (SOILCF), the snow cover fraction (SNOWCF), the surface water body cover fraction (WaterBodyCF), the fractional absorption of photosynthetically active radiation (PAR) by vegetation chlorophyll (fAPARchl), the fractional absorption of PAR by non-chlorophyll components of the vegetation (fAPARnon-chl), and the fractional absorption of PAR by the entire canopy (fAPARcanopy) are retrieved with the MODIS images and a coupled Leaf-Vegetation-Soil-Snow-Surface water body radiative transfer model, LVS3. The vegetation indices (NDVI, EVI, EVI2 and NIRv) differ from VGCF, fAPARchl, fAPARnon-chl, and fAPARcanopy. In addition to vegetation, we find that soil, snow and surface water also have impacts on vegetation indices NDVI, EVI (EVI2), and NIRv. Presence of snow makes lower the observed values of NDVI, EVI2 and NIRv. After snowmelt is gone, the vegetation indices (NDVI, EVI, EVI2 and NIRv) linearly decrease with SOILCF and WaterBodyCF, and WaterBodyCF has stronger impacts on these vegetation indices than SOILCF. The relationship between EVI and snow is complicated. NDSI non-linearly increases with SNOWCF, but linearly increases with sum of SNOWCF and WaterBodyCF (sum = 0.5893 × NDSI +0.4342, R2 = 0.976). NDSI linearly decreases with VGCF, and the relationship between NDSI and SOILCF is complex. Retrievals of VGCF, fAPARchl, fAPARnon-chl and fAPARcanopy with the LVS3 model provide alternatives for vegetation monitoring and ecological modeling.

Qingyuan Zhang↗
NASA NTRS1995

Thermal emission from particulate surfaces: A comparison of scattering models with measured spectra

Emissivity spectra of particulate mineral samples are highly dependent on particle size when that size is comparable to the wavelength of light emitted (5-50 micrometers for the midinfrared). Proper geologic interpretation of data from planetary infrared spectrometers will require that these particle size effects be well understood. To address this issue, samples of quartz powders were produced with narrow, well-characterized particle size distributions. Mean particle diameters in these samples ranged from 15 to 227 micrometers. Emission spectra of these powders allow the first detailed comparison of the complex spectral variations with particle size observed in laboratory data with the predictions of radiative transfer models. Four such models are considered here. Hapke's relectance theory (converted to emissivity via Kirchoff's law) is the first model tested. Hapke's more recently published emission theory is also employed. The third model, the 'Mie/Conel' model, uses Mie single scattering with a two-stream approximation for multiple scattering. This model, like the first, is a converted reflec- tance model. Mie scattering assumes particles are both spherical and well separated, which is not true for the quartz powders, but includes diffraction effects. The fourth model uses the Mie solution for single scattering by spheres and inputs those results into the multiple scattering formalism of Hapke's emission theory. The results of the four models are considered in relation to the values of the optical constants n and k. We have grouped these as class 1 (k large), class 2 (k moderate, n is approximately 2), class 3 (k small, n is approximately 2), and class 4 (k small, n is approximately 1). In general, the Mie/Hapke hybrid model does best at predicting variations with grain size. In particular, it predicts changes of the correct pattern, although incorrect magnitude, for class 1 bands, where large increases in emissivity with decreasing grain size are observed. This model also does an excellent job on moderate (class 2) and very weak and intraband (class 3) regions, and correctly predicts the emission maximum and its invariance with grain size near the Christiansen frequency (class 4). The Mie/Hapke hybrid model also has the fewest free parameters of the four models examined, while maintaining the most physical treatment of the radiative transfer. The Mie/Conel model performs as well as the Mie/Hapke hybrid model in strong bands (class 1) but does not accurately model the behavior of moderate (class 2) and very weak (class 3) bands.

Moersch, J. E.↗
NASA NTRSDate not supplied

TPSAS-NF1676L-33873-DND

NOAA's National Air Quality Forecasting Capability (NAQFC) model provides 48-hour forecast of surface ozone and other atmospheric constituents serving as the nation's key tool actively used by regulatory professionals in assessing air quality events and the issuance of public air quality alerts. NAQFC incorporates input meteorology from North American Mesoscale Model (NAM) at 12 km horizontal resolution that is coupled to the Community Multi-scale Air Quality Model (CMAQ) to predict emissions, tropospheric gas and aerosol chemistry, and related deposition and removal processes. The NAQFC forecast simulations contain 35 steps in altitude, with about one third of these in a typical afternoon daytime boundary layer (0-1.5 km). While several studies have been conducted comparing NAQFC predictions to surface observations, investigations comparing the vertical distribution to observations remain limited. Vertical comparisons are needed in order to fully assess forecast model behavior and atmospheric mixing conditions leading to the formation of ozone at the surface. The Tropospheric Ozone Lidar Network (TOLNet) instruments provide a unique observational capability in this regard, as ozone vertical measurements can be directly compared to models, such as NAQFC, and provide additional insight into atmospheric processes and enhance forecast capabilities. In this study, we utilize multiple TOLNet lidar observations obtained during the Ozone Water Land Environmental Transition Studies (OWLETS-2017 & OWLETS-2018) and the Long Island Sound Tropospheric Ozone Study (LISTOS-2018) to compare with NAQFC vertical predictions of ozone. These campaigns took place at different coastal locations along the US East coast with each campaign having multiple TOLNet lidars present, providing a unique opportunity to examine vertical structure of ozone in regions with complex water-land boundaries. Preliminary comparison results will be presented on ozone temporal and vertical differences between NAQFC and the TOLNet lidars along with example case studies to illustrate insights into boundary layer and surface processes of trace gases.

Timothy Berkoff↗
NASA NTRS1999

Mars Pathfinder Landing Site: Evidence for a Change in Wind Regime and Climate from Lander and Orbiter Data

Surface features related to the wind are observed in data from the Mars Pathfinder lander and from orbit by the Viking Orbiter and Mars Global Surveyor missions. Features seen from the surface include wind tails associated with small rocks, barchanoid duneforms, ripplelike patterns, and ventifact flutes cut into some rocks. Features seen from orbit include wind tails associated with impact craters, ridges inferred to be duneforms, and modified crater rims interpreted to have been eroded and mantled by windblown material. The orientations of these features show two prevailing directions, one inferred to represent winds from the northeast which is consistent with strongest winds predicted by a general circulation model to occur during the Martian northern winter under current conditions, and a second wind pattern oriented approx. 90 degrees to the first. This latter wind could be from the W-NW or from the E-SE and was responsible for cutting the ventifacts and modifying the crater rims. The two wind regimes could reflect a change in climate related to Mars' obliquity or some other, unknown factor. Regardless of the cause, the MPF area has been subjected to a complex pattern of winds and supply of small particles, in which the original surface formed by sedimentary processes from Tiu and Ares Vallis events has been modified by repeated burial and exhumation.

Greeley, R.↗
NASA NTRS1978

Ultraviolet photometry from the orbiting astronomical observatory. XXX - The Orion reflection nebulosity

Surface-brightness measurements are presented that cover the region of Orion in nine intermediate-width bandpasses ranging from 4250 to 1550 A. The existence of an extended ultraviolet reflection nebulosity in this area is confirmed, and the characteristics of its spectrum and spatial distribution are derived. The observations are consistent with a model in which the dense molecular cloud complex in Orion is illuminated by the foreground Orion aggregate of early-type stars. The interpretation is complicated by the fact that foreground dust may contribute to the observed scattered light. The scattering particles in the cloud appear to exhibit a wavelength-dependent albedo similar to that found for interstellar grains in general, with a strong indication that the phase function changes to a less forward-scattering form in the ultraviolet.

Witt, A. N.↗
NASA NTRS1993

A model for the origin of Martian polygonal terrain

Extensive areas of the Martian northern plains in Utopia and Acidalia Planitiae are characterized by 'polygonal terrain.' Polygonal terrain consists of material cut by complex troughs defining a pattern resembling mudcracks, columnar joints, or frost-wedge polygons on the Earth. However, the Martian polygons are orders of magnitude larger than these potential Earth analogs, leading to severe mechanical difficulties for genetic models based on simple analogy arguments. Stratigraphic studies show that the polygonally fractured material in Utopia Planitia was deposited on a land surface with significant topography, including scattered knobs and mesas, fragments of ancient crater rims, and fresh younger craters. Sediments or volcanics deposited over topographically irregular surfaces can experience differential compaction producing drape folds. Bending stresses due to these drape folds would be superposed on the pervasive tensile stresses due to desiccation or cooling, such that the probability of fracturing is enhanced above buried topographic highs and suppressed above buried topographic lows. Thus it was proposed that the scale of the Martian polygons is controlled by the spacing of topographic highs on the buried surface rather than by the physics of the shrinkage process.

Mcgill, G. E.↗
NASA NTRS1997

Meteorites, Microfossils and Exobiology

The discovery of evidence for biogenic activity and possible microfossils in a Martian meteorite may have initiated a paradigm shift regarding the existence of extraterrestrial microbial life. Terrestrial extremophiles that live in deep granite and hydrothermal vents and nanofossils in volcanic tuffs have altered the premise that microbial life and microfossils are inconsistent with volcanic activity and igneous rocks. Evidence for biogenic activity and microfossils in meteorites can no longer be dismissed solely because the meteoritic rock matrix is not sedimentary. Meteorite impact-ejection and comets provide mechanisms for planetary cross-contamination of biogenic chemicals, microfossils, and living microorganisms. Hence, previously dismissed evidence for complex indigenous biochemicals and possible microfossils in carbonaceous chondrites must be re-examined. Many similar, unidentifiable, biological-like microstructures have been found in different carbonaceous chondrites and the prevailing terrestrial contaminant model is considered suspect. This paper reports the discovery of microfossils indigenous to the Murchison meteorite. These forms were found in-situ in freshly broken, interior surfaces of the meteorite. Environmental Scanning Electron Microscope (ESEM) and optical microscopy images indicate that a population of different biological-like forms are represented. Energy Dispersive Spectroscopy reveals these forms have high carbon content overlaying an elemental distribution similar to the matrix. Efforts at identification with terrestrial microfossils and microorganisms were negative. Some forms strongly resemble bodies previously isolated in the Orgueil meteorite and considered microfossils by prior researchers. The Murchison forms are interpreted to represent an indigenous population of the preserved and altered carbonized remains (microfossils) of microorganisms that lived in the parent body of this meteorite at diverse times during the past 4.5 billion years (Gy).

Hoover, Richard B.↗
NASA NTRS2016

Experimental Investigation of Subsonic Turbulent Boundary Layer Flow Over a Wall-Mounted Axisymmetric Hill

An important goal for modern fluid mechanics experiments is to provide datasets which present a challenge for Computational Fluid Dynamics simulations to reproduce. Such "CFD validation experiments" should be well-characterized and well-documented, and should investigate flows which are difficult for CFD to calculate. It is also often convenient for the experiment to be challenging for CFD in some aspects while simple in others. This report is part of the continuing documentation of a series of experiments conducted to characterize the flow around an axisymmetric, modified-cosine-shaped, wall-mounted hill named "FAITH" (Fundamental Aero Investigates The Hill). Computation of this flow is easy in some ways - subsonic flow over a simple shape - while being complex in others - separated flow and boundary layer interactions. The primary set of experiments were performed on a 15.2 cm high, 45.7 cm base diameter machined aluminum model that was tested at mean speeds of 50 m/s (Reynolds Number based on height = 500,000). The ratio of model height to boundary later height was approximately 3. The flow was characterized using surface oil flow visualization, Cobra probe to determine point-wise steady and unsteady 3D velocities, Particle Image Velocimetry (PIV) to determine 3D velocities and turbulence statistics along specified planes, Pressure Sensitive Paint (PSP) to determine mean surface pressures, and Fringe Imaging Skin Friction (FISF) to determine surface skin friction magnitude and direction. A set of pathfinder experiments were also performed in a water channel on a smaller scale (5.1 cm high, 15.2 cm base diameter) sintered nylon model. The water channel test was conducted at a mean test section speed of 3 cm/s (Reynolds Number of 1500), but at the same ratio of model height to boundary layer thickness. Dye injection from both the model and an upstream rake was used to visualize the flow. This report summarizes the experimental set-up, techniques used, and data acquired. It also describes some details of the dataset that is being constructed for use by other researchers, especially the CFD community.

fluid machanics cfd validation wind tunnel↗
NASA NTRS1982

The digital step edge

The facet model was used to accomplish step edge detection. The essence of the facet model is that any analysis made on the basis of the pixel values in some neighborhood has its final authoritative interpretation relative to the underlying grey tone intensity surface of which the neighborhood pixel values are observed noisy samples. Pixels which are part of regions have simple grey tone intensity surfaces over their areas. Pixels which have an edge in them have complex grey tone intensity surfaces over their areas. Specially, an edge moves through a pixel only if there is some point in the pixel's area having a zero crossing of the second directional derivative taken in the direction of a non-zero gradient at the pixel's center. To determine whether or not a pixel should be marked as a step edge pixel, its underlying grey tone intensity surface was estimated on the basis of the pixels in its neighborhood.

Haralick, R. M.↗