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At least 1,243 records · Page 69
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Southern Great Plains 1997 hydrology experiment: The spatial and temporal distribution of soil moisture within a quarter section pasture field

Understanding the spatial and temporal distribution of soil moisture near the soil surface is important to relate ground truth data to remotely sensed data using an electronically scanned thinned array radiometer (ESTAR). The research was conducted at the A-ARM EF site in the Little Washita Watershed in Chickasha Oklahoma. Soil moisture was measured on a 100 x 100-m grid on a quarter section (0.8 km by 0.8 km) size field where the DOE A-ARM SWATS is located. This site has several drainage channels and small ponds. The site is under four different land use practices, namely active pastureland, non-grazed pastureland covered with thick grass, forest area covered with trees, and a single residential area. Soil moisture was measured with a Time Domain Reflectometry (TDR) Delta-T 6-cm theta-probe and gravimetric soil moisture (GSM) technique for the top 6 cm of the soil depth. A fourth order polynomial equation was fitted to each probe calibration curve. The correlation between TDR and GSM measurement technique ranges from 0.81 to 0.91. Comparison of the spatial and temporal distribution of soil moisture measured by the TDR and GSM techniques showed very strong similarities. Such TDR probes can be used successfully to replace the GSM techniques to measure soil moisture content rapidly and accurately with site specific calibration.

Tsegaye, T.↗
NASA NTRS2005

Remote Sensing of Particulate Organic Carbon Pools in the High-Latitude Oceans

The general goal of this project was to characterize spatial distributions at basin scales and variability on monthly to interannual timescales of particulate organic carbon (POC) in the high-latitude oceans. The primary objectives were: (1) To collect in situ data in the north polar waters of the Atlantic and in the Southern Ocean, necessary for the derivation of POC ocean color algorithms for these regions. (2) To derive regional POC algorithms and refine existing regional chlorophyll (Chl) algorithms, to develop understanding of processes that control bio-optical relationships underlying ocean color algorithms for POC and Chl, and to explain bio-optical differentiation between the examined polar regions and within the regions. (3) To determine basin-scale spatial patterns and temporal variability on monthly to interannual scales in satellite-derived estimates of POC and Chl pools in the investigated regions for the period of time covered by SeaWiFS and MODIS missions.

Stramski, Dariusz↗
NASA NTRS1979

Applications of remote sensing for water quality and biological measurements in coastal waters

Potential applications of remote sensing technology to the study of coastal marine environments are reviewed, emphasizing water quality and biological measurements. Parameters measurable by airborne or spaceborne remote sensors include particulates, measured by visual or multispectral photography, chlorophyll a, measured by the Ocean Color Scanner or Coastal Zone Color Scanner, temperature distributions, by IR or microwave sensors, and salinity, by means of microwave radiometers. Research projects in which wide area synoptic or repetitive remote sensing can make a major contribution include the study of estuarine and continental shelf sediment transport dynamics, marine pollutant transport, marine phytoplankton dynamics and ocean fronts.

Johnson, R. W.↗
DOE OSTI2022

Automated Identification of Characteristic Droplet Size Distributions in Stratocumulus Clouds Utilizing a Data Clustering Algorithm

Abstract Droplet-level interactions in clouds are often parameterized by a modified gamma fitted to a “global” droplet size distribution. Do “local” droplet size distributions of relevance to microphysical processes look like these average distributions? This paper describes an algorithm to search and classify characteristic size distributions within a cloud. The approach combines hypothesis testing, specifically, the Kolmogorov–Smirnov (KS) test, and a widely used class of machine learning algorithms for identifying clusters of samples with similar properties: density-based spatial clustering of applications with noise (DBSCAN) is used as the specific example for illustration. The two-sample KS test does not presume any specific distribution, is parameter free, and avoids biases from binning. Importantly, the number of clusters is not an input parameter of the DBSCAN-type algorithms but is independently determined in an unsupervised fashion. As implemented, it works on an abstract space from the KS test results, and hence spatial correlation is not required for a cluster. The method is explored using data obtained from the Holographic Detector for Clouds (HOLODEC) deployed during the Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA) field campaign. The algorithm identifies evidence of the existence of clusters of nearly identical local size distributions. It is found that cloud segments have as few as one and as many as seven characteristic size distributions. To validate the algorithm’s robustness, it is tested on a synthetic dataset and successfully identifies the predefined distributions at plausible noise levels. The algorithm is general and is expected to be useful in other applications, such as remote sensing of cloud and rain properties. Significance Statement A typical cloud can have billions of drops spread over tens or hundreds of kilometers in space. Keeping track of the sizes, positions, and interactions of all of these droplets is impractical, and, as such, information about the relative abundance of large and small drops is typically quantified with a “size distribution.” Droplets in a cloud interact locally, however, so this work is motivated by the question of whether the cloud droplet size distribution is different in different parts of a cloud. A new method, based on hypothesis testing and machine learning, determines how many different size distributions are contained in a given cloud. This is important because the size distribution describes processes such as cloud droplet growth and light transmission through clouds.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2014

Regional Characteristics of the Relationship Between Columnar AOD and Surface PM2.5: Application of Lidar Aerosol Extinction Profiles over Baltimore-Washington Corridor During DISCOVER-AQ

The first field campaign of DISCOVER-AQ (Deriving Information on Surface conditions from COlumn and VERtically resolved observations relevant to Air Quality) took place in July 2011 over Baltimore-Washington Corridor (BWC). A suite of airborne remote sensing and in-situ sensors was deployed along with ground networks for mapping vertical and horizontal distribution of aerosols. Previous researches were based on a single lidar station because of the lack of regional coverage. This study uses the unique airborne HSRL (High Spectral Resolution Lidar) data to baseline PM2.5 (particulate matter of aerodynamic diameter less than 2.5 μm) estimates and applies to regional air quality with satellite AOD (Aerosol Optical Depth) retrievals over BWC (∼6500 sq. km). The linear approximation takes into account aerosols aloft above AML (Aerosol Mixing Layer) by normalizing AOD with haze layer height (i.e., AOD/HLH). The estimated PM2.5 mass concentrations by HSRL AOD/HLH are shown within 2 RMSE (Root Mean Square Error ∼9.6 μg/cu. m) with correlation ∼0.88 with the observed over BWC. Similar statistics are shown when applying HLH data from a single location over the distance of 100 km. In other words, a single lidar is feasible to cover the range of 100 km with expected uncertainties. The employment of MPLNET-AERONET (MicroPulse Lidar NETwork - AErosol RObotic NETwork) measurements at NASA GSFC produces similar statistics of PM2.5 estimates as those derived by HSRL. The synergy of active and passive remote sensing aerosol measurements provides the foundation for satellite application of air quality on a daily basis. For the optimal range of 10 km, the MODIS-estimated PM2.5 values are found satisfactory at 27 (out of 36) sunphotometer locations with mean RMSE of 1.6-3.3 μg/cu. m relative to PM2.5 estimated by sunphotometers. The remaining 6 of 8 marginal sites are found in the coastal zone, for which associated large RMSE values ∼4.5-7.8 μg/cu. m are most likely due to overestimated AOD because of water-contaminated pixels.

DISCOVER-AQ↗
DOE OSTI2024

Using automated machine learning for the upscaling of gross primary productivity

Estimating gross primary productivity (GPP) over space and time is fundamental for understanding the response of the terrestrial biosphere to climate change. Eddy covariance flux towers provide in situ estimates of GPP at the ecosystem scale, but their sparse geographical distribution limits larger-scale inference. Machine learning (ML) techniques have been used to address this problem by extrapolating local GPP measurements over space using satellite remote sensing data. However, the accuracy of the regression model can be affected by uncertainties introduced by model selection, parameterization, and choice of explanatory features, among others. Recent advances in automated ML (AutoML) provide a novel automated way to select and synthesize different ML models. In this work, we explore the potential of AutoML by training three major AutoML frameworks on eddy covariance measurements of GPP at 243 globally distributed sites. We compared their ability to predict GPP and its spatial and temporal variability based on different sets of remote sensing explanatory variables. Explanatory variables from only Moderate Resolution Imaging Spectroradiometer (MODIS) surface reflectance data and photosynthetically active radiation explained over 70 % of the monthly variability in GPP, while satellite-derived proxies for canopy structure, photosynthetic activity, environmental stressors, and meteorological variables from reanalysis (ERA5-Land) further improved the frameworks' predictive ability. We found that the AutoML framework Auto-sklearn consistently outperformed other AutoML frameworks as well as a classical random forest regressor in predicting GPP but with small performance differences, reaching an r 2 of up to 0.75. We deployed the best-performing framework to generate global wall-to-wall maps highlighting GPP patterns in good agreement with satellite-derived reference data. This research benchmarks the application of AutoML in GPP estimation and assesses its potential and limitations in quantifying global photosynthetic activity.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2011

Hyperspectral Mapping of the Invasive Species Pepperweed and the Development of a Habitat Suitability Model

Mapping and predicting the spatial distribution of invasive plant species is central to habitat management, however difficult to implement at landscape and regional scales. Remote sensing techniques can reduce the impact field campaigns have on these ecologically sensitive areas and can provide a regional and multi-temporal view of invasive species spread. Invasive perennial pepperweed (Lepidium latifolium) is now widespread in fragmented estuaries of the South San Francisco Bay, and is shown to degrade native vegetation in estuaries and adjacent habitats, thereby reducing forage and shelter for wildlife. The purpose of this study is to map the present distribution of pepperweed in estuarine areas of the South San Francisco Bay Salt Pond Restoration Project (Alviso, CA), and create a habitat suitability model to predict future spread. Pepperweed reflectance data were collected in-situ with a GER 1500 spectroradiometer along with 88 corresponding pepperweed presence and absence points used for building the statistical models. The spectral angle mapper (SAM) classification algorithm was used to distinguish the reflectance spectrum of pepperweed and map its distribution using an image from EO-1 Hyperion. To map pepperweed, we performed a supervised classification on an ASTER image with a resulting classification accuracy of 71.8%. We generated a weighted overlay analysis model within a geographic information system (GIS) framework to predict areas in the study site most susceptible to pepperweed colonization. Variables for the model included propensity for disturbance, status of pond restoration, proximity to water channels, and terrain curvature. A Generalized Additive Model (GAM) was also used to generate a probability map and investigate the statistical probability that each variable contributed to predict pepperweed spread. Results from the GAM revealed distance to channels, distance to ponds and curvature were statistically significant (p < 0.01) in determining the locations of suitable pepperweed habitats.

Pepperweed↗
NASA NTRS2003

A Secondary Ion Mass Analyzer for Remote Surface Composition Analysis of the Galilean Moons

Galileo in-situ dust measurements have shown that the Galilean moons are surrounded by tenuous dust clouds formed by collisional ejecta from their icy surfaces, kicked up by impacts of interplanetary micrometeoroids. The majority of the ejecta dust particles have been sensed at altitudes below five between 0.5 and 1 micron, just above the detector threshold, indicating a size distribution decreasing towards bigger particles. their parent bodies. They carry information about the properties of the surface from which they have been kicked up. In particular, these grains may carry organic compounds and other chemicals of biological relevance if they exist on the icy Galilean moons. In-situ analysis of the grain composition with a sophisticated dust analyzer instrument flying on a Jupiter Icy Moons Orbiter can provide important information about geochemical and geophysical processes during the evolutionary histories of these moons which are not accessible with other techniques from an orbiter spacecraft. Thus, spacecraft-based in-situ dust measurements can be used as a diagnostic tool for the analysis of the surface composition of the moons. This way, the in-situ measurements turn into a remote sensing technique by using the dust instrument like a telescope for surface investigation. An instrument capable of very high resolution composition analysis of dust particles is the Cometary Secondary Ion Mass Analyzer (COSIMA). The instrument was originally developed for the Comet Rendezvous and Asteroid Flyby (CRAF) mission and has now been built for ESA'S comet orbiter Rosetta. Dust particles are collected on a target and are later located by an optical microscope camera. A pulsed primary indium ion gun partially ionizes the dust grains. The generated secondary ions are accelerated in an electric field and travel through a reflectron-type time-of-flight ion mass spectrometer.

Krueger, H.↗
NASA NTRS1985

Lasers in space

Hinkley and Herring (1984) have considered the differences between active (laser) and passive remote sensing from space. The conclusion was reached that spaceborne lasers will eventually complement passive sensors in providing information on the distributions of key atmospheric species and meteorological parameters. Precise information can also be obtained of ice sheet and crustal dynamics for geological and mapping applications. NASA initiated recently an airborne measurement program directed toward some of these objectives. The program employs optical radar (laser radar) systems onboard the NASA advanced ER-2 high-flying aircraft. The results of the experiments are to provide important information with respect to the potential utility of spaceborne laser remote sensing. A study indicated that a spaceborne pulsed carbon dioxide laser could measure tropospheric winds. Attention is also given to measurements of atmospheric gases by spaceborne lasers, solid-state lasers for spaceborne remote sensing, and laser communication in space.

Hinkley, E. D.↗
NASA NTRS2001

The Spatial Distribution of Forest Biomass in the Brazilian Amazon: A Comparison of Estimates

The amount of carbon released to the atmosphere as a result of deforestation is determined, in part, by the amount of carbon held in the biomass of the forests converted to other uses. Uncertainty in forest biomass is responsible for much of the uncertainty in current estimates of the flux of carbon from land-use change. We compared several estimates of forest biomass for the Brazilian Amazon, based on spatial interpolations of direct measurements, relationships to climatic variables, and remote sensing data. We asked three questions. First, do the methods yield similar estimates? Second, do they yield similar spatial patterns of distribution of biomass? And, third, what factors need most attention if we are to predict more accurately the distribution of forest biomass over large areas? Amazonian forests (including dead and below-ground biomass) vary by more than a factor of two, from a low of 39 PgC to a high of 93 PgC. Furthermore, the estimates disagree as to the regions of high and low biomass. The lack of agreement among estimates confirms the need for reliable determination of aboveground biomass over large areas. Potential methods include direct measurement of biomass through forest inventories with improved allometric regression equations, dynamic modeling of forest recovery following observed stand-replacing disturbances (the approach used in this research), and estimation of aboveground biomass from airborne or satellite-based instruments sensitive to the vertical structure plant canopies.

Houghton, R. A.↗
NASA NTRS2015

Regional and Global Atmospheric CO2 Measurements Using 1.57 Micron IM-CW Lidar

Atmospheric CO2 is a critical forcing for the Earth's climate, and knowledge of its distribution and variations influences predictions of the Earth's future climate. Accurate observations of atmospheric CO2 are also crucial to improving our understanding of CO2 sources, sinks and transports. To meet these science needs, NASA is developing technologies for the Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) space mission, which is aimed at global CO2 observations. Meanwhile an airborne investigation of atmospheric CO2 distributions as part of the NASA Suborbital Atmospheric Carbon and Transport â€" America (ACT-America) mission will be conducted with lidar and in situ instrumentation over the central and eastern United States during all four seasons and under a wide range of meteorological conditions. In preparing for the ASCENDS mission, NASA Langley Research Center and Exelis Inc./Harris Corp. have jointly developed and demonstrated the capability of atmospheric CO2 column measurements with an intensity-modulated continuous-wave (IM-CW) lidar. Since 2005, a total of 14 flight campaigns have been conducted. A measurement precision of approx.0.3 ppmv for a 10-s average over desert and vegetated surfaces has been achieved, and the lidar CO2 measurements also agree well with in-situ observations. Significant atmospheric CO2 variations on various spatiotemporal scales have been observed during these campaigns. For example, around 10-ppm CO2 changes were found within free troposphere in a region of about 200A-300 sq km over Iowa during a summer 2014 flight. Results from recent flight campaigns are presented in this paper. The ability to achieve the science objectives of the ASCENDS mission with an IM-CW lidar is also discussed in this paper, along with the plans for the ACT-America aircraft investigation that begins in the winter of 2016.

Lin, Bing↗
NASA NTRS2013

Earth Observation from Space - The Issue of Environmental Sustainability

Remote sensing scientists work under assumptions that should not be taken for granted and should, therefore, be challenged. These assumptions include the following: 1. Space, especially Low Earth Orbit (LEO), will always be available to governmental and commercial space entities that launch Earth remote sensing missions. 2. Space launches are benign with respect to environmental impacts. 3. Minimization of Type 1 error, which provides increased confidence in the experimental outcome, is the best way to assess the significance of environmental change. 4. Large-area remote sensing investigations, i.e. national, continental, global studies, are best done from space. 5. National space missions should trump international, cooperative space missions to ensure national control and distribution of the data products. At best, all of these points are arguable, and in some cases, they're wrong. Development of observational space systems that are compatible with sustainability principles should be a primary concern when Earth remote sensing space systems are envisioned, designed, and launched. The discussion is based on the hypothesis that reducing the environmental impacts of thedata acquisition step,which is at the very beginning of the information streamleading to decision and action, will enhance coherence in the information streamand strengthen the capacity of measurement processes to meet their stated functional goal, i.e. sustainable management of Earth resources. We suggest that unconventional points of view should be adopted and when appropriate, remedial measures considered that could help to reduce the environmental footprint of space remote sensing and of Earth observation and monitoring systems in general. This article discusses these five assumptions inthe contextof sustainablemanagementof Earth's resources. Takingeachassumptioninturn,we find the following: (1) Space debris may limit access to Low Earth Orbit over the next decades. (2) Relatively speaking, given that they're rare event, space launches may be benign, but study is merited on upper stratospheric and exospheric layers given the chemical activity associated with rocket combustion by-products. (3) Minimization of Type II error should be considered in situations where minimization of Type I error greatly hampers or precludes our ability to correct the environmental condition being studied. (4) In certain situations, airborne collects may be less expensive and more environmentally benign, and comparative studies should be done to determine which path is wisest. (5) International cooperation and data sharing will reduce instrument and launch costs and mission redundancy. Given fiscal concerns of most of the major space agencies e e.g. NASA, ESA, CNES e it seems prudent to combine resources.

Earth observation systems↗
DOE OSTI2022

Point Cloud Based Mapping of Understory Shrub Fuel Distribution, Estimation of Fuel Consumption and Relationship to Pyrolysis Gas Emissions on Experimental Prescribed Burns

Forest fires spread via production and combustion of pyrolysis gases in the understory. The goal of the present paper is to understand the spatial location, distribution, and fraction (relative to the overstory) of understory plants, in this case, sparkleberry shrub, namely its degree of understory consumption upon burn, and to search for correlations between the degree of shrub consumption to the composition of emitted pyrolysis gases. Data were collected in situ at seven small experimental prescribed burns at Ft. Jackson, an army base in South Carolina, USA. Using airborne laser scanning (ALS) to map overstory tree crowns and terrestrial laser scanning (TLS) to characterize understory shrub fuel density, both pre- and postburn estimates of sparkleberry coverage were obtained. Sparkleberry clump polygons were manually digitized from a UAV-derived orthoimage of the understory and intersected with the TLS point cloud-derived rasters of pre- and postburn shrub fuel bulk density; these were compared in relation to overstory crown cover as well as to ground truth. Shrub fuel consumption was estimated from the digitized images; sparkleberry clump distributions were generally found to not correlate well to the overstory tree crowns, suggesting it is shade-tolerant. Moreover, no relationship was found between the magnitude of the fuel consumption and the chemical composition of pyrolysis gases, even though mixing ratios of 25 individual gases were measured.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Detecting Coastal Wetland Degradation by Combining Remote Sensing and Hydrologic Modeling

Sea-level rise and climate change stresses pose increasing threats to coastal wetlands that are vital to wildlife habitats, carbon sequestration, water supply, and other ecosystem services with global significance. However, existing studies are limited in individual sites, and large-scale mapping of coastal wetland degradation patterns over a long period is rare. Our study developed a new framework to detect spatial and temporal patterns of coastal wetland degradation by analyzing fine-scale, long-term remotely sensed Normalized Difference Vegetation Index (NDVI) data. Then, this framework was tested to track the degradation of coastal wetlands at the Alligator River National Wildlife Refuge (ARNWR) in North Carolina, United States, during the period from 1995 to 2019. We identified six types of coastal wetland degradation in the study area. Most of the detected degradation was located within 2 km from the shoreline and occurred in the past five years. Further, we used a state-of-the-art coastal hydrologic model, PIHM-Wetland, to investigate key hydrologic processes/variables that control the coastal wetland degradation. The temporal and spatial distributions of simulated coastal flooding and saltwater intrusion confirmed the location and timing of wetland degradation detected by remote sensing. The combined method also quantified the possible critical thresholds of water tables for wetland degradation. The remote sensing–hydrologic model integrated scheme proposed in this study provides a new tool for detecting and understanding coastal wetland degradation mechanisms. Our study approach can also be extended to other coastal wetland regions to understand how climate change and sea-level rise impact wetland transformations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Possibilities of using practical limitations of an eavesdropper in quantum cryptography

An important advantage of quantum cryptography over classical cryptography consists in the fact that the security of the transmitted keys is not related to the assumptions about the eavesdropper capabilities and is guaranteed by the laws of nature. Nevertheless, in some situations it makes sense to consider some reasonable assumptions about the eavesdropper capabilities, which can increase the secret key distribution rate. Methods are proposed for legitimate users to employ some practical limitations, and attacks are constructed that the eavesdropper can apply under the conditions of these limitations. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Predicting Switchgrass Biomass Yields Using a Spectral Vegetation Index Derived from Multispectral Satellite Imagery

Successful scaling of perennial bioenergy crop production requires a landscape design that optimizes the benefits of finite lands for people, communities, and environments. Utilizing marginal areas is the key to sustainable bioenergy crop production (Ssegane et al., 2015, 2016). Marginal areas are often small-sized lands and unevenly distributed across the agricultural landscape (Ssegane et al., 2016); thus, a systematic, semi-automated remote sensing method is needed as an effective means of estimating bioenergy crop yields across landscapes. Argonne National Laboratory (Argonne) is currently developing a tool, Scaling Up Perennial Bioenergy Economics and Ecosystem Services Tool (SUPERBEEST), to identify marginal agricultural lands and quantify environmental and economic effects of perennial bioenergy crop production systems. The tool aims to provide users a path to foster the sustainable and productive integration of bioenergy crops in the Midwestern agricultural landscape. Reliable, cost-effective, and timely estimation of bioenergy crop yields using remote sensing would help calculate and track the success of integrated bioenergy crops in the landscape for those communities. Argonne previously conducted feasibility studies for estimating biomass yields for bioenergy feedstock, corn and perennial grass using spectral vegetation indices (SVIs)1 derived from optical imagery (Hamada et al., 2015, 2021). In both studies, SVIs, more specifically those sensitive to plant chlorophyll or nitrogen contents, showed potential for estimating or predicting biomass yields with a correlation of determination (R2) ranging from 0.54 to 0.96, indicating a value for further investigation as a viable means of quantifying bioenergy feedstock production across large landscapes. Thus, the goal of this study is to evaluate the feasibility of use of SVIs as a means of estimating or predicting switchgrass biomass yields at harvest using publicly available multispectral satellite imagery. The feasibility analysis was performed using four study areas of mature switchgrass located in Virginia. Objectives are to (1) examine the SVIs and establish their relationships with switchgrass biomass yields at harvest, (2) develop a parsimonious image processing model for predicting at-harvest yields by applying the relationships with the most promising spectral index and (3) map switchgrass yields predicted by the image processing model across the study sites. The calibration to field data will rely on switchgrass biomass yields determined by the baling method, representing a potential challenge to the analysis but an important practical aspect for future applications. With this research design, the study aimed to gain insights into enabling remote sensing-based estimation of bioenergy crop yields in a reliable, cost- effective, and timely manner across large, heterogeneous landscapes.

09 BIOMASS FUELS↗
NASA NTRS1973

Upper Kalamazoo watershed land cover inventory

Approximately 1000 square miles of the eastern portion of the watershed were inventoried based on remote sensing imagery. The classification scheme, imagery and interpretation procedures, and a cost analysis are discussed. The distributions of land cover within the area are tabulated.

Richason, B., III↗
NASA NTRS1974

Aerodynamic influence coefficient method using singularity splines

A numerical lifting surface formulation, including computed results for planar wing cases is presented. This formulation, referred to as the vortex spline scheme, combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of loading function methods. The formulation employes a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfied all the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise. Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral. The current formulation uses the elementary horseshoe vortex as the basic singularity and is therefore restricted to linearized potential flow. As part of the study, a non planar development was considered, but the numerical evaluation of the lifting surface concept was restricted to planar configurations. Also, a second order sideslip analysis based on an asymptotic expansion was investigated using the singularity spline formulation.

Mercer, J. E.↗