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NASA NTRS2021

Measurements of Rainfall Rate, Drop Size Distribution, and Variability at Middle and Higher Latitudes: Application to the Combined DPR-GMI Algorithm

The Global Precipitation Measurement mission is a major U.S.–Japan joint mission to understand the physics of the Earth’s global precipitation as a key component of its weather, climate, and hydrological systems. The core satellite carries a dual-precipitation radar and an advanced microwave imager which provide measurements to retrieve the drop size distribution (DSD) and rain rates using a Combined Radar-Radiometer Algorithm (CORRA). Our objective is to validate key assumptions and parameterizations in CORRA and enable improved estimation of precipitation products, especially in the middle-to-higher latitudes in both hemispheres. The DSD parameters and statistical relationships between DSD parameters and radar measurements are a central part of the rainfall retrieval algorithm, which is complicated by regimes where DSD measurements are abysmally sparse (over the open ocean). In view of this, we have assembled optical disdrometer datasets gathered by research vessels, ground stations, and aircrafts to simulate radar observables and validate the scattering lookup tables used in CORRA. The joint use of all DSD datasets spans a large range of drop concentrations and characteristic drop diameters. The scaling normalization of DSDs defines an intercept parameter N(W), which normalizes the concentrations, and a scaling diameter D(m), which compresses or stretches the diameter coordinate axis. A major finding of this study is that a single relationship between N(W) and D(m), on average, unifies all datasets included, from stratocumulus to heavier rainfall regimes. A comparison with the N(W)–D(m) relation used as a constraint in versions 6 and 7 of CORRA highlights the scope for improvement of rainfall retrievals for small drops (D(m) < 1 mm) and large drops (D(m) > 2 mm). The normalized specific attenuation–reflectivity relationships used in the combined algorithm are also found to match well the equivalent relationships derived using DSDs from the three datasets, suggesting that the currently assumed lookup tables are not a major source of uncertainty in the combined algorithm rainfall estimates.

Viswanathan Bringi↗

NASA NTRS2007

The Impact of Atmospheric InfraRed Sounder (AIRS) Profiles on Short-term Weather Forecasts

The Atmospheric Infrared Sounder (AIRS), together with the Advanced Microwave Sounding Unit (AMSU), represents one of the most advanced spacebased atmospheric sounding systems. The combined AlRS/AMSU system provides radiance measurements used to retrieve temperature profiles with an accuracy of 1 K over 1 km layers under both clear and partly cloudy conditions, while the accuracy of the derived humidity profiles is 15% in 2 km layers. Critical to the successful use of AIRS profiles for weather and climate studies is the use of profile quality indicators and error estimates provided with each profile Aside form monitoring changes in Earth's climate, one of the objectives of AIRS is to provide sounding information of sufficient accuracy such that the assimilation of the new observations, especially in data sparse region, will lead to an improvement in weather forecasts. The purpose of this paper is to describe a procedure to optimally assimilate highresolution AIRS profile data in a regional analysis/forecast model. The paper will focus on the impact of AIRS profiles on a rapidly developing east coast storm and will also discuss preliminary results for a 30-day forecast period, simulating a quasi-operation environment. Temperature and moisture profiles were obtained from the prototype version 5.0 EOS science team retrieval algorithm which includes explicit error information for each profile. The error profile information was used to select the highest quality temperature and moisture data for every profile location and pressure level for assimilation into the ARPS Data Analysis System (ADAS). The AIRS-enhanced analyses were used as initial fields for the Weather Research and Forecast (WRF) system used by the SPORT project for regional weather forecast studies. The ADASWRF system will be run on CONUS domain with an emphasis on the east coast. The preliminary assessment of the impact of the AIRS profiles will focus on quality control issues associated with AIRS, intelligent use of the quality indicators, and forecast verification.

Chou, Shih-Hung↗

NASA NTRS2015

Observing System Simulations for Small Satellite Formations Estimating Bidirectional Reflectance

The bidirectional reflectance distribution function (BRDF) gives the reflectance of a target as a function of illumination geometry and viewing geometry, hence carries information about the anisotropy of the surface. BRDF is needed in remote sensing for the correction of view and illumination angle effects (for example in image standardization and mosaicing), for deriving albedo, for land cover classification, for cloud detection, for atmospheric correction, and other applications. However, current spaceborne instruments provide sparse angular sampling of BRDF and airborne instruments are limited in the spatial and temporal coverage. To fill the gaps in angular coverage within spatial, spectral and temporal requirements, we propose a new measurement technique: Use of small satellites in formation flight, each satellite with a VNIR (visible and near infrared) imaging spectrometer, to make multi-spectral, near-simultaneous measurements of every ground spot in the swath at multiple angles. This paper describes an observing system simulation experiment (OSSE) to evaluate the proposed concept and select the optimal formation architecture that minimizes BRDF uncertainties. The variables of the OSSE are identified; number of satellites, measurement spread in the view zenith and relative azimuth with respect to solar plane, solar zenith angle, BRDF models and wavelength of reflection. Analyzing the sensitivity of BRDF estimation errors to the variables allow simplification of the OSSE, to enable its use to rapidly evaluate formation architectures. A 6-satellite formation is shown to produce lower BRDF estimation errors, purely in terms of angular sampling as evaluated by the OSSE, than a single spacecraft with 9 forward-aft sensors. We demonstrate the ability to use OSSEs to design small satellite formations as complements to flagship mission data. The formations can fill angular sampling gaps and enable better BRDF products than currently possible.

small satellite↗

NASA NTRS2007

Using MODIS and GLAS Data to Develop Timber Volume Estimates in Central Siberia

The boreal forest is the Earth's largest terrestrial biome, covering some 12 million km2 and accounting for about one third of this planet's total forest area. Mapping of boreal forest's type, structure parameters and biomass are critical for understanding the boreal forest's significance in the carbon cycle, its response to and impact on global climate change. Ground based forest inventories, have much uncertainty in the inventory data, particularly in remote areas of Siberia where sampling is sparse and/or lacking. In addition, many of the forest inventories that do exist for Siberia are now a decade or more old. Thus, available forest inventories fail to capture the current conditions. Changes in forest structure in a particular forest-type and region can change significantly due to changing environment conditions, and natural and anthropogenic disturbance. Remote sensing methods can potentially overcome these problems. Multispectral sensors can be used to provide vegetation cover maps that show a timely and accurate geographic distribution of vegetation types rather than decade old ground based maps. Lidar sensors can be used to directly obtain measurements that can be used to derive critical forest structure information (e.g., height, density, and volume). These in turn can used to estimate biomass components using allometric equations without having to use out dated forest inventory. Finally, remote sensing data is ideally suited to provide a sampling basis for a rigorous statistical estimate of the variance and error bound on forest structure measures. In this study, new remote sensing methods were applied to develop estimates timber volume using NASA's MODerate resolution Imaging Spectroradiometer (MODIS) and unique waveform data of the geoscience laser altimeter system (GLAS) for a 10 deg x 10 deg area in central Siberia. Using MODIS and GLAS data, maps were produced for cover type and timber volume for 2003, and a realistic variance (error bound) for timber volume was calculated for the study area. In this 'study we used only GLAS footprints that had a slope value of less than 10 deg. This was done to avoid large errors due to the effect of slope on the GLAS models. The method requires the integration of new remote sensing methods with available ground studies of forest timber volume conducted in Russian forests. The results were compared to traditional ground forest inventory methods reported in the literature and to ground truth collected in the study area.

Ranson, K. Jon↗

NASA NTRS1985

Effect of vegetation on soil moisture sensing observed from orbiting microwave radiometers

The microwave radiometric measurements made by the Skylab 1.4 GHz radiometer and by the 6.6 GHz and 10.7 GHz channels of the Nimbus-7 Scanning Multichannel Microwave Radiometer were analyzed to study the large-area soil moisture variations of land surfaces. Two regions in Texas, one with sparse and the other with dense vegetation covers, were selected for the study. The results gave a confirmation of the vegetation effect observed by ground-level microwave radiometers. Based on the statistics of the satellite data, it was possible to estimate surface soil moisture in about five different levels from dry to wet conditions with a 1.4 GHz radiometer, provided that the biomass of the vegetation cover could be independently measured. At frequencies greater than about 6.6 GHz, the radiometric measurements showed little sensitivity to moisture variation for vegetation-covered soils. The effects of polarization in microwave emission were studied also.

Wang, J. R.↗

NASA NTRS2010

An Investigation of Widespread Ozone Damage to the Soybean Crop in the Upper Midwest Determined From Ground-Based and Satellite Measurements

Elevated concentrations of ground-level ozone (O3) are frequently measured over farmland regions in many parts of the world. While numerous experimental studies show that O3 can significantly decrease crop productivity, independent verifications of yield losses at current ambient O3 concentrations in rural locations are sparse. In this study, soybean crop yield data during a 5-year period over the Midwest of the United States were combined with ground and satellite O3 measurements to provide evidence that yield losses on the order of 10% could be estimated through the use of a multiple linear regression model. Yield loss trends based on both conventional ground-based instrumentation and satellite-derived tropospheric O3 measurements were statistically significant and were consistent with results obtained from open-top chamber experiments and an open-air experimental facility (SoyFACE, Soybean Free Air Concentration Enrichment) in central Illinois. Our analysis suggests that such losses are a relatively new phenomenon due to the increase in background tropospheric O3 levels over recent decades. Extrapolation of these findings supports previous studies that estimate the global economic loss to the farming community of more than $10 billion annually.

Fishman, Jack↗

NASA NTRS1989

A New Population Estimate for the Florida Scrub Jay on Merritt Island National Wildlife Refuge

The variable circular plot method was used to sample avifauna within different vegetation types determined from aerial imagery. The Florida Scrub Jay (Aphelocoma coerulescens coerulescens) population was estimated to range between 1,415 and 3,603 birds. Approximately half of the scrub and slash pine habitat appeared to be unused by Florida Scrub Jay, probably because the slash pine cover was too dense or the oak cover was too sparse. Results from the study suggest that the entire state population may be much lower than believed because the size of two of the three largest populations may have been overestimated.

Breininger, David R.↗

NASA NTRS2014

A Synthesis of Light Absorption Properties of the Arctic Ocean: Application to Semi-analytical Estimates of Dissolved Organic Carbon Concentrations from Space

The light absorption coefficients of particulate and dissolved materials are the main factors determining the light propagation of the visible part of the spectrum and are, thus, important for developing ocean color algorithms. While these absorption properties have recently been documented by a few studies for the Arctic Ocean [e.g., Matsuoka et al., 2007, 2011; Ben Mustapha et al., 2012], the datasets used in the literature were sparse and individually insufficient to draw a general view of the basin-wide spatial and temporal variations in absorption. To achieve such a task, we built a large absorption database at the pan-Arctic scale by pooling the majority of published datasets and merging new datasets. Our results showed that the total non-water absorption coefficients measured in the Eastern Arctic Ocean (EAO; Siberian side) are significantly higher 74 than in the Western Arctic Ocean (WAO; North American side). This higher absorption is explained 75 by higher concentration of colored dissolved organic matter (CDOM) in watersheds on the Siberian 76 side, which contains a large amount of dissolved organic carbon (DOC) compared to waters off 77 North America. In contrast, the relationship between the phytoplankton absorption (a()) and chlorophyll a (chl a) concentration in the EAO was not significantly different from that in the WAO. Because our semi-analytical CDOM absorption algorithm is based on chl a-specific a() values [Matsuoka et al., 2013], this result indirectly suggests that CDOM absorption can be appropriately erived not only for the WAO but also for the EAO using ocean color data. Derived CDOM absorption values were reasonable compared to in situ measurements. By combining this algorithm with empirical DOC versus CDOM relationships, a semi-analytical algorithm for estimating DOC concentrations for coastal waters at the Pan-Arctic scale is presented and applied to satellite ocean color data.

Pan-Arctic↗

NASA NTRS1982

Synoptic studies of chromospheric variability in F - K dwarfs with the IUE

Time-sequential series of IUE spectra for ten F, G and K dwarfs were obtained in 1980 and 1981 to study the rotational dependence of chromospheric flux in the ultraviolet. An interactive computational method using unbiased estimators was developed to measure emission line fluxes free of arbitrary judgement concerning the behavior of the underlying spectrum and shapes of the line profiles. Due to the limited number of observational samples per star, we have used special techniques to analyze the sparsely and anharmonically sampled emission line flux data. Two different autocorrelation measures were computed for each emission line as a function of temporal frequency. Examples and results of this analysis now in progress are given for several stars.

Hallam, K. L.↗

NASA NTRS2018

Assessing Version 4 of the SMAP L4_SM Data Product

Version 4 of the SMAP Level 4 Surface and Root Zone Soil Moisture (L4_SM) product benefits from an improved land surface modeling system. Surface soil moisture is typically drier by several volumetric percent in Version 4 compared to Version 3, whereas root zone soil moisture is wetter in Version 4 in some regions and drier in others. Results from core validation site comparisons show that Version 4 of the L4_SM data product meets the accuracy requirement, which is formulated in terms of the RMSE after removal of the long-term mean difference (ubRMSE). The overall ubRMSE of the 3-hourly L4_SM data at the 9 km scale is 0.039 m3 m-3 for surface soil moisture and 0.029 m3 m-3 for root zone soil moisture, below the 0.04 m3 m-3 requirement. L4_SM surface and root zone soil moisture estimates are more skillful than model-only simulation estimates that are not informed by SMAP brightness temperature observations, with statistically significant improvements at the 5% level for surface soil moisture R and anomaly R values. Results from comparisons of the L4_SM product to in situ measurements from more than 400 sparse network sites corroborate the core validation site results.

Reichle, R.↗

NASA NTRS1979

Thickness of western mare basalts

An isopach map of the basalt thickness in the western mare basins is constructed from measurements of the exposed external rim height of partially buried craters. The data, although numerically sparse, is sufficiently distributed to yield gross thickness variations. The average basalt thickness in Oceanus Procellarum and adjacent regions is 400 m with local lenses in excess of 1500 m in the circular maria. The total volume of basalt in the western maria is estimated to be in the range of 1.5 x 10 to the 6th power cu km. The chief distinction between the eastern and western maria appears to be one of basalt volumes erupted to the surface. Maximum volumes of basalt are deposited west of the central highlands and flood subjacent terrain to a greater extent than on the east. The surface structures of the western maria reflect the probability of a greater degree of isostatic response to a larger surface loading by the greater accumulation of mare basalt.

Dehon, R. A.↗

NASA NTRSDate not supplied

Advances to a Global Agroclimatology Solar Insolation and Meteorological Parameter Data Base: Improved Solar Irradiance up to Hourly Temporal Resolution

A primary objective of NASA’s Prediction of Worldwide Energy Resource (POWER) project is to facilitate the use of NASA Earth Science data holdings within the energy, agricultural, and architectural industries. To this end daily averaged solar data from several NASA projects and metrological data from a NASA assimilation model have long been reformatted and via a user friendly web based data portal (https://power.larc.nasa.gov) at the native resolution of each data products. Potential users can access solar and metrological data in a column formatted DSSAT ASCII format by entering single site specific coordinates or from an area by entering the appropriate area coordinates. Upgrades to the POWER data portal have been implemented that result in a complete upgrade of the base solar insolation data products. From the years 1984 through 2000, a new version of the NASA/GEWEX Surface Radiation Budget (SRB) and Clouds is utilized that reduces the RMS relative to surface measurements. Additionally, Clouds and the Earth’s Radiant Energy System (CERES) SYNoptic 1x1 Degree (SYN1Deg) data products are utilized starting from January 1, 2001 through 3 months of real-time. The CERES Fast Longwave and SHortwave radiative Fluxes (FLASHFlux) is still used to provided daily data spanning from the end of SYN1Deg to within 7 days of real-time. Meteorological parameters now are taken from the NASA Modern Era Retrospective-analysis for Research and Applications (MERRA-2) data set which provides higher resolution data products (hourly and 0.5 x 625 degree) covering the entire globe. Besides updating the solar and meteorological data products, this new version features new data products such as photosynthetically active radiation (PAR), more cloud information, estimates of soil temperatures and improved options for long-term climatological data requests. More than 36+ years daily time slices are included in the combined solar and meteorological data sets. However, perhaps the most important innovation of the POWER GIS-enabled Web Services is the provision of hourly solar and meteorological data products beginning in Jan 1, 2001. The hourly values will enable more detailed modeling and crop analysis that incorporates the diurnal variability of these parameters. The new capability is made possible by utilizing both the CERES SYN1Deg and MERRA-2 data products that include parameters at these resolutions. An assessment of both the meteorological and the solar irradiance data are based upon comparisons with globally distributed surface observations. The meteorological observations from the National Center for Environmental Information’s “Integrated Surface Database” as well as the “Global Summary of the Day” (GSOD) data files. The estimates of solar insolation are compared to the Baseline Solar Radiation Network (BSRN) and other high quality surface measurement networks. Results from the uncertainty assessments demonstrates that the NASA’s meteorological and solar irradiance data can represent a viable alternative to surface observations, particularly in data sparse regions of the world.

solar irradiance↗

NASA NTRS2021

FLUXNET-CH4: a global, multi-ecosystem dataset and analysis of methane seasonality from freshwater wetlands

Methane (CH4) emissions from natural landscapes constitute roughly half of global CH4 contributions to the atmosphere, yet large uncertainties remain in the absolute magnitude and the seasonality of emission quantities and drivers. Eddy covariance (EC) measurements of CH4 flux are ideal for constraining ecosystem-scale CH4 emissions due to quasi-continuous and high-temporal-resolution CH4 flux measurements, coincident carbon dioxide, water, and energy flux measurements, lack of ecosystem disturbance, and increased availability of datasets over the last decade. Here, we (1) describe the newly published dataset, FLUXNET-CH4 Version 1.0, the first open-source global dataset of CH4 EC measurements (available at https://fluxnet.org/data/fluxnet-ch4-community-product/, last access: 7 April 2021). FLUXNET-CH4 includes half-hourly and daily gap-filled and non-gap-filled aggregated CH4 fluxes and meteorological data from 79 sites globally: 42 freshwater wetlands, 6 brackish and saline wetlands, 7 formerly drained ecosystems, 7 rice paddy sites, 2 lakes, and 15 uplands. Then, we (2) evaluate FLUXNET-CH4 representativeness for freshwater wetland coverage globally because the majority of sites in FLUXNET-CH4 Version 1.0 are freshwater wetlands which are a substantial source of total atmospheric CH4 emissions; and (3) we provide the first global estimates of the seasonal variability and seasonality predictors of freshwater wetland CH4 fluxes. Our representativeness analysis suggests that the freshwater wetland sites in the dataset cover global wetland bioclimatic attributes (encompassing energy, moisture, and vegetation-related parameters) in arctic, boreal, and temperate regions but only sparsely cover humid tropical regions. Seasonality metrics of wetland CH4 emissions vary considerably across latitudinal bands. In freshwater wetlands (except those between 20°S to 20°N) the spring onset of elevated CH4 emissions starts 3 d earlier, and the CH4 emission season lasts 4 d longer, for each degree Celsius increase in mean annual air temperature. On average, the spring onset of increasing CH4 emissions lags behind soil warming by 1 month, with very few sites experiencing increased CH4 emissions prior to the onset of soil warming. In contrast, roughly half of these sites experience the spring onset of rising CH4 emissions prior to the spring increase in gross primary productivity (GPP). The timing of peak summer CH4 emissions does not correlate with the timing for either peak summer temperature or peak GPP. Our results provide seasonality parameters for CH4 modeling and highlight seasonality metrics that cannot be predicted by temperature or GPP (i.e., seasonality of CH4 peak). FLUXNET-CH4 is a powerful new resource for diagnosing and understanding the role of terrestrial ecosystems and climate drivers in the global CH4 cycle, and future additions of sites in tropical ecosystems and site years of data collection will provide added value to this database. All seasonality parameters are available at https://doi.org/10.5281/zenodo.4672601 (Delwiche et al., 2021). Additionally, raw FLUXNET-CH4 data used to extract seasonality parameters can be downloaded from https://fluxnet.org/data/fluxnet-ch4-community-product/ (last access: 7 April 2021), and a complete list of the 79 individual site data DOIs is provided in Table 2 of this paper.

FLUXNET-CH4↗

NASA NTRS1990

Space station contamination study: Assessment of contaminant spectral brightness

The results presented show that spectral emissions which arise as a result of vehicle-ambient atmospheric interactions are significant and can become competitive with the natural zodiacal background up to altitudes as high as 400 km for the Vacuun Ultraviolet (VUV) and Visible Infrared Spectra (VIS) for the worst case conditions used. The empirical database on the induced environment of space vehicles is very sparse, and these results are based on a number of assumptions and cannot be regarded as definitive at the present time. Since the technique for doing calculations of this kind was developed in its preliminary form for the purpose of this study, a list of greatly improved estimates are provided of the contamination irradiances. Tasks which are considered most important in order to achieve a higher confidence level for the preliminary conclusions drawn are provided.

Torr, D. G.↗

NASA NTRS1992

Multivariable frequency domain identification via 2-norm minimization

The author develops a computational approach to multivariable frequency domain identification, based on 2-norm minimization. In particular, a Gauss-Newton (GN) iteration is developed to minimize the 2-norm of the error between frequency domain data and a matrix fraction transfer function estimate. To improve the global performance of the optimization algorithm, the GN iteration is initialized using the solution to a particular sequentially reweighted least squares problem, denoted as the SK iteration. The least squares problems which arise from both the SK and GN iterations are shown to involve sparse matrices with identical block structure. A sparse matrix QR factorization method is developed to exploit the special block structure, and to efficiently compute the least squares solution. A numerical example involving the identification of a multiple-input multiple-output (MIMO) plant having 286 unknown parameters is given to illustrate the effectiveness of the algorithm.

Bayard, David S.↗

NASA NTRS1979

Detection and mapping of hydrothermally altered rocks in the vicinity of the comstock lode, Virginia Range, Nevada, using enhanced LANDSAT images

The author has identified the following significant results. LANDSAT images enhanced by the band-ratioing method can be used for reconnaissance alteration mapping in moderately heavily vegetated semiarid terrain as well as in sparsely vegetated to semiarid terrain where the technique was originally developed. Significant vegetation cover in a scene, however, requires the use of MSS ratios 4/5, 4/6, and 6/7 rather than 4/5, 5/6, and 6/7, and requires careful interpretation of the results. Supplemental information suitable to vegetation identification and cover estimates, such as standard LANDSAT false-color composites and low altitude aerial photographs of selected areas is desirable.

Ashley, R. P.↗

NASA NTRSDate not supplied

Multiscale Modeling of Reconstructed Tricalcium Silicate using NASA Multiscale Analysis Tool

To study microstructure characteristics of cementitious materials hydrated in space; previously, cement binder formations were processed under microgravity conditions and was further compared against ground-based experiments. For accurate estimation of process-structure-property linkage, particularly on samples hydrated in the microgravity environment, it is desired to have a high-fidelity volumetric representation of the microstructure. However, owing to small sample size and high porosity of the space-returned samples, conventional experimental characterization techniques are not viable. Hence, a deep learning-based reconstruction algorithm was employed to obtain high fidelity 3D volumes from sparse high resolution 2D Scanning Electron Microscopy (SEM) images, as inputs to micromechanics-based modeling. This machine learning-based reconstruction methodology validated against low-order statistical descriptors, captured the microstructural topology of both sample types (ground, 1g and microgravity, μg). Due to the lack of gravity, hydration products of the samples processed in space differed from those processed-on ground. Such AI-generated virtual samples were analyzed in a multiscale recursive micromechanics approach using the NASA Multiscale Analysis Tool (NASMAT). Here, we present a methodology to rapidly integrate and evaluate these AI-generated volumes in NASMAT. The synthesized microstructural volumes are directly employed as Representative Volume Elements (RVEs) to preserve the fidelity (1 pixel = 0.54 m). Invariably, analysis of such largescale problems (5123 voxels) requires huge amount of computational resources. By taking advantage of the NASMAT architecture, we also focused on systematic multiscale integration of these AI-reconstructed virtual volumes to reduce the computational demands. In this work, this methodology is demonstrated on the ground-based, 1g samples. The estimated stiffness value of 15.90 GPa is comparable to experimentally obtained modulus of hydrated tricalcium silicate sample. The workflow presented here paves the way for utilizing the NASMAT tool to perform multiscale analyses of other multi-phase material systems using either 3D virtual datasets synthesized using AI or obtained via micro-CT.

Machine Learning↗

NASA NTRS1992

Clustering methods for removing outliers from vision-based range estimates

The present approach to the automation of helicopter low-altitude flight uses one or more passive imaging sensors to extract environmental obstacle information; this is then processed via computer-vision techniques to yield a time-varying map of range to obstacles in the sensor's field of view along the vehicle's flight path. Attention is given to two related techniques which can eliminate outliers from a sparse range map, clustering sparse range-map information into different spatial classes that rely on a segmented and labeled image to aid in spatial classification within the image plane.

Hussien, B.↗