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NASA NTRS2015

A New Lunar Digital Elevation Model from the Lunar Orbiter Laser Altimeter and SELENE Terrain Camera

We present an improved lunar digital elevation model (DEM) covering latitudes within +/-60 deg, at a horizontal resolution of 512 pixels per degree ( approx.60 m at the equator) and a typical vertical accuracy approx.3 to 4 m. This DEM is constructed from approx.4.5 ×10(exp 9) geodetically-accurate topographic heights from the Lunar Orbiter Laser Altimeter (LOLA) onboard the Lunar Reconnaissance Orbiter, to which we co-registered 43,200 stereo-derived DEMs (each 1 deg×1 deg) from the SELENE Terrain Camera (TC) ( approx.10(exp 10) pixels total). After co-registration, approximately 90% of the TC DEMs show root-mean-square vertical residuals with the LOLA data of < 5 m compared to approx.50% prior to co-registration. We use the co-registered TC data to estimate and correct orbital and pointing geolocation errors from the LOLA altimetric profiles (typically amounting to < 10 m horizontally and < 1 m vertically). By combining both co-registered datasets, we obtain a near-global DEM with high geodetic accuracy, and without the need for surface interpolation. We evaluate the resulting LOLA + TC merged DEM (designated as "SLDEM2015") with particular attention to quantifying seams and crossover errors.

Barker, M. K.↗

DOE OSTI2024

Development and Experimental Optimization of High-Temperature Modeling Tools and Methods for Concentrated Solar Power Particle - Systems

A novel, open-source radiative modeling toolset was developed to extend the functionality of particle-based modeling software (e.g. discrete element method (DEM)) to environmental conditions relevant to concentrated solar power applications. This toolset was optimized for deployment on desktop workstations instead of high-performance computing systems, to render such tools more accessible to the research community. Both particle-based modeling and radiative exchange modeling are computationally expensive and often require specialized programming expertise, making these methods cumbersome to use. Recent developments in DEM software by DCS Computing have greatly reduced these challenges, providing a graphical-user-interface based platform and modeling optimization for desktop workstations, HPCs, and cloud computing. The University of Dayton leveraged the experience of DCS Computing in developing a user-friendly, open-source radiative heat transfer expansion for DEM modeling. The University of Dayton DEM+ radiative modeling toolset was developed using a combination of fundamental experimental measurements, modeling, and simplified flow experiments over a range of temperatures and flow conditions. The toolset provides researchers with access to multiple radiative models including an accelerated Monte-Carlo Ray Tracing (application agnostic, highly computationally expensive), an expanded database of distance-based approximations (application limited, computationally light), and a weighted blending of the two methods capable of achieving over 90% reduction in computation time with equivalent accuracy compared to Monte-Carlo Ray Tracing. Through a graphical user interface, users can customize the radiative models to match their desired accuracy and available computational resources, improving access to particle based modeling for the research community. Ceramic sintered bauxite proppants were used in modeling and experimentally as a baseline. Both the radiative heat transfer and flow properties for particulate systems were investigated at elevated temperatures up to 800 °C. The major accomplishments for this work include a verified, open-source radiative modeling toolset to be distributed amongst the research community and the fabrication of three small-scale test facilities to investigate particle behavior and tune DEM flow properties for operation up to 800 °C. The findings have been shared with the research community via conference modeling workshops, deployment of the tools in DCS Computing Aspherix®, and open-source access to the developed radiative modeling tool. The development of next-generation CSP facilities and thermal energy storage systems based on ceramic particles requires providing access to computationally efficient and accurate modeling tools. Particles will experience a wide range of environments (20-800 °C) and handling conditions (dilute curtains or dense packing), requiring specially designed and optimized equipment. Optimizing solid particle physics models and establishing best-practices for particle modeling in CSP environments will assist researchers with designing optimized equipment, accelerating the deployment of more economically-competitive CSP facilities.

14 SOLAR ENERGY↗

DOE OSTI2020

A Review of Computational Models for the Flow of Milled Biomass Part I: Discrete-Particle Models

Biomass is a renewable and sustainable energy resource. Current design of biomass handling and feeding equipment leverage both experiments and numerical modeling. This paper reviews the state-of-the-art discrete element methods (DEM) for the flow of milled biomass (Part I), accompanied by a comprehensive review on continuum-based computational models (Part II). The present review on DEM is primarily focused on the features and suitability of various particle shape models for different types of milled biomass because particle shape is the predominant attribute controlling the flow behavior of complex-shaped granular material. The general strengths and weaknesses in the applicability of those models for the milled biomass modeling are summarized. In particular, comments are provided to balance the numerical model capabilities and the computational cost for the development of DEM models. To our best knowledge, this is the first-of-its-kind review on DEM specifically for biomass. Our study indicates that the current DEM models require further development, calibration, and validation based on a deep understanding of biomass particle contact mechanics and experimental data support before they can be reliably used for predictive simulations in handling and feeding systems.

42 ENGINEERING↗

DOE OSTI2025

X-ray spectroscopy of multi-temperature plasmas using the differential emission measure formalism

We present a theoretical construct that nominally underlies spectroscopic data analysis of multi-temperature plasmas, known as the differential emission measure (DEM). From a data analytic perspective, the DEM formalism is used to derive temperature distributions from line spectra that are formed in the presence of temperature gradients and by time integrations of evolving plasmas. From a modeling perspective, DEMs are convenient intermediaries between radiation hydrodynamics simulations and spectroscopic measurements acquired in the laboratory. The DEM concept and its associated methodologies were originally developed by spectroscopists working with astrophysical data. We borrow from these earlier investigations. In this manuscript, intended primarily as a tutorial, we discuss the basic concepts, but also augment various aspects of the theory by the way of extension and example, including a detailed treatment of various weighting and averaging schemes, intended to mitigate ambiguities that often arise when reporting temperature information. We focus on high-temperature plasmas that are not in local thermodynamic equilibrium and the x-ray spectra that they produce, although the core ideas presented here are applicable to spectroscopy in other energy bands. A few examples involving the derivation and manipulation of model DEMs in simple geometries are provided.

Liedahl, Duane A. [Lawrence Livermore National Lab↗

NASA NTRS1990

A positional estimation technique for an autonomous land vehicle in an unstructured environment

This paper presents a solution to the positional estimation problem of an autonomous land vehicle navigating in an unstructured mountainous terrain. A Digital Elevation Map (DEM) of the area in which the robot is to navigate is assumed to be given. It is also assumed that the robot is equipped with a camera that can be panned and tilted, and a device to measure the elevation of the robot above the ground surface. No recognizable landmarks are assumed to be present in the environment in which the robot is to navigate. The solution presented makes use of the DEM information, and structures the problem as a heuristic search in the DEM for the possible robot location. The shape and position of the horizon line in the image plane and the known camera geometry of the perspective projection are used as parameters to search the DEM. Various heuristics drawn from the geometric constraints are used to prune the search space significantly. The algorithm is made robust to errors in the imaging process by accounting for the worst care errors. The approach is tested using DEM data of areas in Colorado and Texas. The method is suitable for use in outdoor mobile robots and planetary rovers.

Talluri, Raj↗

NASA NTRS1993

Topographic mapping using radar interferometry - Processing techniques

In the summer of 1991 the NASA DC-8 airborne synthetic aperture radar (SAR) system acquired data with the radar configured in a C-band across-track interferometer mode. The data were processed to generate rectified topographic maps. A new processing scheme was developed featuring motion compensation, absolute phase retrieval, and three-dimensional 1ocation. The new processor has been tested using data which were acquired with extreme aircraft motion so that performance could be evaluated under adverse conditions. The topographic maps generated by the radar were compared to Digital Elevation Models (DEM's) derived using conventional optical stereo techniques. In one region we measured rms elevation deviations which were less than the specified DEM accuracy, and in the region covered by the more accurate DEM we found errors varying from 2.2 m rms in relatively flat terrain up to 5.0 m in mountainous areas. The rms difference between radar and DEM elevations over the 6.5 km by 22 km area covered by the more accurate DEM was 3.6 m.

Madsen, Soren N.↗

NASA NTRS1993

Performance evaluation of the JPL TOPSAR system: An across-track interferometric SAR system for topographic mapping

An across-track interferometric (XTI) SAR has the capability of determining the three dimensional target location from the recorded radar echos thus providing high spatial resolution both horizontally and vertically. The output of an XTI SAR will typically include both a radar backscatter map and a digital elevation model (DEM). The accuracy of the derived DEM is determined by factors such as data acquisition geometry, signal-to-noise ratio, knowledge of platform position and attitude as well as the accuracy of the processing system. In the summer of 1992 the authors acquired TOPSAR data over the Ft. Irwin area in California, a desert area with significant relief (height standard deviation 150 m). Very accurate DEM's have been derived for this area by the Topographic Engineering Center (TEC) using digital correlation methods on 1:20,000 scale digitized photographs. Corner reflectors were deployed in the area, and their locations were determined to cm accuracies by the Defense Mapping Agency (DMA) using differential GPS techniques. DEM's generated from the acquired radar data have been rotated and translated to overlay the reference DEM's provided by TEC. A detailed description of the errors and their characteristics will be given. The standard deviations of the radar data sets we acquired measured over a 5.6 by 7 km area were 1.9 and 2.3 m. The corresponding numbers for flat areas were 1.1 and 2.0 m and for mountain areas 3.3 and 2.2 m.

Madsen, Soren N.↗

NASA NTRS2003

Characterizing the Siple Coast Ice Stream System using Satellite Images, Improved Topography, and Integrated Aerogeophysical Measurements

A technique for improving elevation maps of the polar ice sheets has been developed using AVHRR images. The technique is based on 'photoclinometry' or 'shape from shading', a technique used in the past for mapping planetary surfaces where little elevation information was available. The fundamental idea behind photoclinometry is using the brightness of imaged areas to infer their surface slope in the sun-illuminated direction. Our version of the method relies on a calibration of the images based on an existing lower-resolution digital elevation model (DEM), and then using the images to improve the input DEM resolution to the scale of the image data. Most current DEMs covering the ice sheets are based on Radar altimetry data, and have an inherent resolution of 10 to 25 km at best - although the grid scale of the DEM is often finer. These DEMs are highly accurate (to less than 1 meter); but they report the mean elevation of a broad area, thus erasing smaller features of glaciological interest. AVHRR image data, when accurately geolocated and calibrated, provides surface slope measurements (based on the pixel brightness under known lighting conditions) every approximately 1.1 km. The limitations of the technique are noisiness in the image data, small variations in the albedo of the snow surface, and the integration technique used to create an elevation field from the image-derived slopes. Our study applied the technique to several ice sheet areas having some elevation data; Greenland, the Amery Ice Shelf, the Institute Ice Stream, and the Siple Coast. For the latter, the input data set was laser-altimetry data collected under NSF's SOAR Facility (Support Office for Aerogeophysical Research) over the onset area of the Siple Coast. Over the course of the grant, the technique was greatly improved and modified, significantly improving accuracy and reducing noise from the images. Several publications resulted from the work, and a follow-on proposal to NASA has been submitted to apply the same method to MODIS data using ICESat and other elevation input information. This follow-on grant will explore two applications that are facilitated by the improved surface morphology characterizations of the ice sheets: accumulation and temperature variations near small undulations in the ice.

Scambos, Ted↗

NASA NTRS2004

Validation and Improvement of SRTM Performance over Rugged Terrain

We have previously reported work related to basic technique development in phase unwrapping and generation of digital elevation models (DEM). In the final year of this work we have applied our technique work to the improvement of DEM's produced by SRTM. In particular, we have developed a rigorous mathematical algorithm and means to fill in missing data over rough terrain from other data sets. We illustrate this method by using a higher resolution, but globally less accurate, DEM produced by the TOPSAR airborne instrument over the Galapagos Islands to augment the SRTM data set in this area, We combine this data set with SRTM to use each set to fill in holes left over by the other imaging system. The infilling is done by first interpolating each data set using a prediction error filter that reproduces the same statistical characterization as exhibited by the entire data set within the interpolated region. After this procedure is implemented on each data set, the two are combined on a point by point basis with weights that reflect the accuracy of each data point in its original image. In areas that are better covered by SRTM, TOPSAR data are weighted down but still retain TOPSAR statistics. The reverse is true for regions better covered by TOPSAR. The resulting DEM passes statistical tests and appears quite feasible to the eye, but as this DEM is the best available for the region we cannot fully veri@ its accuracy. Spot checks with GPS points show that locally the technique results in a more comprehensive and accurate map than either data set alone.

Zebker, Howard A.↗

NASA NTRS2008

Addition of Electrostatic Forces to EDEM with Applications to Triboelectrically Charged Particles

Tribocharging of particles is common in many processes including fine powder handling and mixing, printer toner transport and dust extraction. In a lunar environment with its high vacuum and lack of water, electrostatic forces are an important factor to consider when designing and operating equipment. Dust mitigation and management is critical to safe and predictable performance of people and equipment. The extreme nature of lunar conditions makes it difficult and costly to carryout experiments on earth which are necessary to better understand how particles gather and transfer charge between each other and with equipment surfaces. DEM (Discrete Element Modeling) provides an excellent virtual laboratory for studying tribocharging of particles as well as for design of devices for dust mitigation and for other purposes related to handling and processing of lunar regolith. Theoretical and experimental work has been performed pursuant to incorporating screened Coulombic electrostatic forces into EDEM Tm, a commercial DEM software package. The DEM software is used to model the trajectories of large numbers of particles for industrial particulate handling and processing applications and can be coupled with other solvers and numerical models to calculate particle interaction with surrounding media and force fields. In this paper we will present overview of the theoretical calculations and experimental data and their comparison to the results of the DEM simulations. We will also discuss current plans to revise the DEM software with advanced electrodynamic and mechanical algorithms.

Hogue, Michael D.↗

NASA NTRS2012

Deriving Plasma Densities and Elemental Abundances from SERTS Differential Emission Measure Analysis

We use high-resolution spectral emission line data obtained by the SERTS instrument during three rocket flights to demonstrate a new approach for constraining electron densities of solar active region plasma.We apply differential emission measure (DEM) forward-fitting techniques to characterize the multithermal solar plasma producing the observed EUV spectra, with constraints on the high-temperature plasma from the Yohkoh Soft X-ray Telescope. In this iterative process, we compare line intensities predicted by an input source distribution to observed line intensities for multiple iron ion species, and search a broad range of densities to optimize chi-square simultaneously for the many available density-sensitive lines. This produces a density weighted by the DEM, which appears to be useful for characterizing the bulk of the emitting plasma over a significant range of temperature. This "DEM-weighted density" technique is complementary to the use of density-sensitive line ratios and less affected by uncertainties in atomic data and ionization fraction for any specific line. Once the DEM shape and the DEM-weighted density have been established from the iron lines, the relative elemental abundances can be determined for other lines in the spectrum. We have also identified spectral lines in the SERTS wavelength range that may be problematic

corona↗

NASA NTRSDate not supplied

Particle Interaction Physics Model Formulation for Plume-Surface Interaction Erosion and Cratering

As part of the Game Changing Development (GCD) Program, funded by NASA’s Space Technology Mission Directorate (STMD), the development of simulation capability for the prediction of extra-terrestrial Plume Surface Interaction (PSI) environments has been undertaken by the Fluid Dynamics Branch at NASA/MSFC. The Predictive Simulation Capability (PSC) Element is focused on creating simulation capability for the reliable and accurate prediction of PSI in Martian (~650 Pa) and Lunar (vacuum) ambient environments. In addition to the predictive simulation capability, the GCD Program also contains a companion Ground Testing Element for development of focused datasets for validation of predictive capability as well as a Flight-focused Instrumentation Element. This paper will present the status of implementing and maturing particle-particle interaction constituent physics models essential in simulating the landing surface granular material flow under PSI effects. This gas-particle multi-phase interaction modeling of plume impingement flow on the extra-terrestrial soil material is performed with the Gas-Granular Flow Solver (GGFS) addressed in a companion paper. The response of regolith particle flow induced by lander PSI requires accurate representation of the regolith granular material fluidic behavior and gas-granular interactions. The lunar regolith, as the extreme example, is poorly sorted with broad particle size distributions and large fines content. It has significant cohesion, due to interlocking particle shapes for the very jagged particles. The combination of particle shape and size distribution has been identified as major drivers in the complex particle flow response and resulting crater shape characteristics of extraterrestrial granular material. Constituent models for spherical particles can be formulated directly from particle kinetics theory. Complex particle shapes can be modeled by gluing together elemental spherical shapes into composite particles, requiring a Discrete Element Model (DEM) particle kinetics modeling approach to extract data and formulate constituent models. Mixture constituent models for poly-disperse mixtures (i.e, containing distribution of particle sizes) have recently been developed. The required non-spherical particle mixture granular material response closure models are then obtained through small-scale unit physics DEM simulations for the range of particle shapes, mixtures and packing densities. The granular material response closure models are then implemented in the Eulerian granular flow formulation. This DEM-based constituent model extraction process and formulation of poly-disperse particle mixtures has been successfully developed by small business and academic partners in the development of the Gas-Granular Flow Solver (GGFS) simulation program simulation framework. The currently implemented capabilities have reached the capability level of modeling bi-disperse, non-spherical particle mixtures is being continuously extended towards computational modeling of full range irregular particle mixtures. Under the GCD project, this technology is being further developed, transferred to NASA analysts, and matured towards application readiness. The predictive simulation capability team under the GCD project has acquired the modeling tools and processes of the DEM based constituent model formulation from the GGFS development team and is developing the capability to replicate the existing process. This is the first important step towards the ability of the NASA team to independently perform such model development in a production setting. Further efforts are underway to migrate the DEM based model simulation process performed with the academic based tools to more capable Open Source, highly parallelized simulation tools for efficient operation on NASA HPC assets. Evaluation of the currently implemented (such as mono-disperse and bi-disperse spherical and irregular shape particle constituent model applications) and continuously evolving full-range particle physics models in the GGFS tool is performed by the NASA team to advance application readiness of the simulations. Application testing for complex PSI erosions and cratering scenarios such as the Apollo LM is performed for axi-symmetric and full 3D simulations to aid the tool developers in achieving practical application readiness for NASA projects. Important validation and application testing will further be performed against experimental data generated under the GCD PSI project experimental component.

Peter A Liever↗

NASA NTRSDate not supplied

Particle Interaction Physics Model Formulation for Plume-Surface Interaction Erosion and Cratering

The Predictive Simulation Capability development team of the STMD Game Changing Development sponsored PSI project is implementing computational simulation capability for the efficient and accurate prediction of Plume-Surface Interaction induced surface erosion and cratering in Martian and Lunar environments. The status of the Focus Area 3 of the PSI project in the generation and efficient application of accurate soil particle composition modeling in the Gas-Granular Flow Solver (GGFS) computational framework is presented. The process of constitutive closure model database generation using DEM particle interaction modeling for capturing the effects of irregular particle shape and poly-disperse mixture distribution effects is outlined. This capability has now been ported to NASA supercomputer assets and NASA engineers successfully demonstrated technology and skillset transfer in model generation for spherical and irregularly shaped, mono-disperse and bi-disperse mixture compositions. Assessment of the computational efficiency and practicality of the academic serially executed DEM tools on NASA supercomputers identified the need to migrate to a DEM framework capable of performing parallel simulations in a simultaneous process orchestrated in an automated setup, execution, database extraction, and dataset delivery ready for application simulations. The LIGGGHTS DEM toolset has been selected as the most suitable tool to migrate the DEM simulations. Once the soil model generation process is implemented, models capturing the shape and poly-dispersity effects will be generated to perform much refined validation simulations against the experiments performed under the PSI project. The application readiness of the soil models currently operational in GGFS was presented for the example of a full scale, 3-D simulation of the plume induced erosion and crater formation of the Apollo LM at an elevation of 5m above ground in a low pressure, near vacuum background.

Peter A Liever↗

NASA NTRSDate not supplied

Particle Interaction Physics Model Formulation for Plume-Surface Interaction Erosion and Cratering

Peter A Liever↗

DOE OSTI2019

Hopper flows of mixtures of spherical and rod‐like particles via the multisphere method

Abstract The discharge of granular media from hoppers plays a vital role in many solids handling operations. The dynamic flow of poly‐disperse nonspherical particles differs markedly from mono‐disperse spheres and highlights the need to rigorously account for particle shape effects. The multisphere discrete element method (MS‐DEM) was utilized here to examine the bulk packing fraction, discharge rate, collisional stress tensor, and order parameter of a bi‐disperse sphere‐rod mixture evacuating a hopper. A modified form of the Myers and Sellers correlation with variable shape factor is capable of replicating the MS‐DEM discharge data. The collisional stress tensor is observed to be highly symmetric for mono‐disperse spheres but becomes asymmetric when rod‐like particles are introduced. The order parameter within the hopper increases significantly during discharge and the rod‐like particles undergo shear induced alignment with their long dimensions orthogonal to the outflow plane.

Lattanzi, Aaron M.↗

DOE OSTI2023

Discrete element simulation of Pebble Bed Reactors on graphics processing units

Prediction of pebble positions in a Pebble Bed Reactor (PBR) is necessary for both reactor physics and thermal hydraulics simulations as the arrangement of pebbles has a significant impact on the resulting core power, coolant flow, and fuel temperature. Knowledge of pebble movement as the fuel is cycled through the core is also critical for predicting the fuel residence time and subsequently, the fuel burnup. Simulation with the Discrete Element Method (DEM) can provide knowledge of both the fuel packing and the fuel movement during cycling. Previous works that have performed 3D full-core DEM simulation of PBRs have used simplified models that neglect reflector wall features. This work employs a graphics processing unit (GPU)-enabled DEM code, Project Chrono, to analyze the differences in pebble packing and pebble velocities between a simplified smooth PBR reflector and a more realistic reflector that includes circular wall features. Additionally, a sensitivity study is performed on the depth of the wall features to ensure that crystallization is prevented. Project Chrono is also validated for PBR cycling applications using experimental data. It is found that wall features with a depth of at least 0.5 pebble diameters significantly reduce crystallization in the near-wall region, leading to discrepancies in both packing fraction and pebble velocity in this region compared to the simplified reflector models. These discrepancies are found to lead to roughly a 5–10% difference in the prediction of the near-wall porosity and a 10% difference in the prediction of the velocity of pebbles near the wall. As a result of these discrepancies, it is suggested that future DEM simulations of PBRs include wall features to reduce modeling errors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

An adaptive, data-driven multiscale approach for dense granular flows

The accuracy of coarse-grained continuum models of dense granular flows is limited by the lack of high-fidelity closure models for granular rheology. One approach to addressing this issue, referred to as the hierarchical multiscale method, is to use a high-fidelity fine-grained model to compute the closure terms needed by the coarse-grained model. The difficulty with this approach is that the overall model can become computationally intractable due to the high computational cost of the high-fidelity model. In this work, we describe a multiscale modeling approach for dense granular flows that utilizes neural networks trained using high-fidelity discrete element method (DEM) simulations to approximate the constitutive granular rheology for a continuum incompressible flow model. Our approach leverages an ensemble of neural networks to estimate predictive uncertainty that allows us to determine whether the rheology at a given point is accurately represented by the neural network model. Additional DEM simulations are only performed when needed, minimizing the number of additional DEM simulations required when updating the rheology. This adaptive coupling significantly reduces the overall computational cost of the approach while controlling the error. In addition, the neural networks are customized to learn regularized rheological behavior to ensure well-posedness of the continuum solution. We first validate the approach using two-dimensional steady-state and decelerating inclined flows. We then demonstrate the efficiency of our approach by modeling three-dimensional sub-aerial granular column collapse for varying initial column aspect ratios, where our multiscale method compares well with the computationally expensive computational fluid dynamics (CFD)-DEM simulation.

Dense granular flows↗

DOE OSTI2020

GradeIT (Road Grade Inference Tool)

The National Renewable Energy Laboratory (NREL) has developed the Road Grade Inference Tool, "GradeIT". This tool is a modular Python package the leverages the United States Geological Survey’s (USGS) 1/3 arc-second Digital Elevation Model (DEM), an open and free public dataset. Roadway gradient (slope) has a strong influence on vehicle energy consumption behavior and longitudinal dynamics. Therefore, any tools, models, or analyses that consider vehicle energy consumption or driving profiles is incomplete without accurate elevation and grade information. Despite the acute need for this data, it is rarely collected alongside GPS (latitude and longitude) data, and tools to post-process GPS data to append elevation and grade are difficult to come by. GradeIT satisfies this significant need in the research community. Utilization of the USGS DEM makes the underlying data available to any potential user and ensures continuous data anywhere in the continental United States. The USGS DEM is a great resource; however, in order to be useful for automotive and traffic engineering applications, significant interpolation and filtering is required to achieve an accurate representation of gradient on the roadway. GradeIT employs a two-dimensional interpolation to approximate elevation at a point on the road from the nearest nodes in the DEM. Then, GradeIT applies multiple filtering techniques to smooth the elevation profile to a realistic road topology. Finally, road grade is derived from the elevation profile and returned as the primary output.

Holden, Jacob↗