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At least 559 records · Page 31

Automated navigation assessment for earth survey sensors using island targets

An automated method has been developed for performing navigation assessment on satellite-based Earth sensor data. The method utilizes islands as targets which can be readily located in the sensor data and identified with reference locations. The essential elements are an algorithm for classifying the sensor data according to source, a reference catalog of island locations, and a robust pattern-matching algorithm for island identification. The algorithms were developed and tested for the Sea-viewing Wide Field-of-view Sensor (SeaWiFS), an ocean color sensor. This method will allow navigation error statistics to be automatically generated for large numbers of points, supporting analysis over large spatial and temporal ranges.

Patt, Frederick S.↗

An Automated Method for Navigation Assessment for Earth Survey Sensors Using Island Targets

An automated method has been developed for performing navigation assessment on satellite-based Earth sensor data. The method utilizes islands as targets which can be readily located in the sensor data and identified with reference locations. The essential elements are an algorithm for classifying the sensor data according to source, a reference catalogue of island locations, and a robust pattern-matching algorithm for island identification. The algorithms were developed and tested for the Sea-viewing Wide Field-of-view Sensor (SeaWiFS), an ocean colour sensor. This method will allow navigation error statistics to be automatically generated for large numbers of points, supporting analysis over large spatial and temporal ranges.

Patt, F. S.↗

NASA Tech Briefs, April 2011

Topics covered include: Amperometric Solid Electrolyte Oxygen Microsensors with Easy Batch Fabrication; Two-Axis Direct Fluid Shear Stress Sensor for Aerodynamic Applications; Target Assembly to Check Boresight Alignment of Active Sensors; Virtual Sensor Test Instrumentation; Evaluation of the Reflection Coefficient of Microstrip Elements for Reflectarray Antennas; Miniaturized Ka-Band Dual-Channel Radar; Continuous-Integration Laser Energy Lidar Monitor; Miniaturized Airborne Imaging Central Server System; Radiation-Tolerant, SpaceWire-Compatible Switching Fabric; Small Microprocessor for ASIC or FPGA Implementation; Source-Coupled, N-Channel, JFET-Based Digital Logic Gate Structure Using Resistive Level Shifters; High-Voltage-Input Level Translator Using Standard CMOS; Monitoring Digital Closed-Loop Feedback Systems; MASCOT - MATLAB Stability and Control Toolbox; MIRO Continuum Calibration for Asteroid Mode; GOATS Image Projection Component; Coded Modulation in C and MATLAB; Low-Dead-Volume Inlet for Vacuum Chamber; Thermal Control Method for High-Current Wire Bundles by Injecting a Thermally Conductive Filler; Method for Selective Cleaning of Mold Release from Composite Honeycomb Surfaces; Infrared-Bolometer Arrays with Reflective Backshorts; Commercialization of LARC (trade mark) -SI Polyimide Technology; Novel Low-Density Ablators Containing Hyperbranched Poly(azomethine)s; Carbon Nanotubes on Titanium Substrates for Stray Light Suppression; Monolithic, High-Speed Fiber-Optic Switching Array for Lidar; Grid-Tied Photovoltaic Power System; Spectroelectrochemical Instrument Measures TOC; A Miniaturized Video System for Monitoring Drosophila Behavior; Hydrofocusing Bioreactor Produces Anti-Cancer Alkaloids; Creep Measurement Video Extensometer; Radius of Curvature Measurement of Large Optics Using Interferometry and Laser Tracker n-B-pi-p Superlattice Infrared Detector; Safe Onboard Guidance and Control Under Probabilistic Uncertainty; General Tool for Evaluating High-Contrast Coronagraphic Telescope Performance Error Budgets; Hidden Statistics of Schroedinger Equation; Optimal Padding for the Two-Dimensional Fast Fourier Transform; Spatial Query for Planetary Data; Higher Order Mode Coupling in Feed Waveguide of a Planar Slot Array Antenna; Evolutionary Computational Methods for Identifying Emergent Behavior in Autonomous Systems; Sampling Theorem in Terms of the Bandwidth and Sampling Interval; Meteoroid/Orbital Debris Shield Engineering Development Practice and Procedure; Self-Balancing, Optical-Center-Pivot, Fast-Steering Mirror; Wireless Orbiter Hang-Angle Inclinometer System; and Internal Electrostatic Discharge Monitor - IESDM.

Source record↗

Background Error Covariance Estimation Using Information from a Single Model Trajectory with Application to Ocean Data Assimilation

An attractive property of ensemble data assimilation methods is that they provide flow dependent background error covariance estimates which can be used to update fields of observed variables as well as fields of unobserved model variables. Two methods to estimate background error covariances are introduced which share the above property with ensemble data assimilation methods but do not involve the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The Space Adaptive Forecast error Estimation (SAFE) algorithm estimates error covariances from the spatial distribution of model variables within a single state vector. The Flow Adaptive error Statistics from a Time series (FAST) method constructs an ensemble sampled from a moving window along a model trajectory.SAFE and FAST are applied to the assimilation of Argo temperature profiles into version 4.1 of the Modular Ocean Model (MOM4.1) coupled to the GEOS-5 atmospheric model and to the CICE sea ice model. The results are validated against unassimilated Argo salinity data. They show that SAFE and FAST are competitive with the ensemble optimal interpolation (EnOI) used by the Global Modeling and Assimilation Office (GMAO) to produce its ocean analysis. Because of their reduced cost, SAFE and FAST hold promise for high-resolution data assimilation applications.

Error Covariance↗

Background Error Covariance Estimation using Information from a Single Model Trajectory with Application to Ocean Data Assimilation into the GEOS-5 Coupled Model

An attractive property of ensemble data assimilation methods is that they provide flow dependent background error covariance estimates which can be used to update fields of observed variables as well as fields of unobserved model variables. Two methods to estimate background error covariances are introduced which share the above property with ensemble data assimilation methods but do not involve the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The Space Adaptive Forecast error Estimation (SAFE) algorithm estimates error covariances from the spatial distribution of model variables within a single state vector. The Flow Adaptive error Statistics from a Time series (FAST) method constructs an ensemble sampled from a moving window along a model trajectory. SAFE and FAST are applied to the assimilation of Argo temperature profiles into version 4.1 of the Modular Ocean Model (MOM4.1) coupled to the GEOS-5 atmospheric model and to the CICE sea ice model. The results are validated against unassimilated Argo salinity data. They show that SAFE and FAST are competitive with the ensemble optimal interpolation (EnOI) used by the Global Modeling and Assimilation Office (GMAO) to produce its ocean analysis. Because of their reduced cost, SAFE and FAST hold promise for high-resolution data assimilation applications.

Data Assimilation↗

Global Precipitation Measurement (GPM) Mission Products and Services at the NASA Goddard Earth Sciences Data and Information Services Center (GES DISC)

The NASA Goddard Earth Sciences (GES) Data and Information Services Center (DISC) hosts and distributes GPM data within the NASA Earth Observation System Data Information System (EOSDIS). The GES DISC is also home to the data archive for the GPM predecessor, the Tropical Rainfall Measuring Mission (TRMM). Over the past 17 years, the GES DISC has served the scientific as well as other communities with TRMM data and user-friendly services. During the GPM era, the GES DISC will continue to provide user-friendly data services and customer support to users around the world. GPM products currently and to-be available: -Level-1 GPM Microwave Imager (GMI) and partner radiometer products, DPR products -Level-2 Goddard Profiling Algorithm (GPROF) GMI and partner products, DPR products -Level-3 daily and monthly products, DPR products -Integrated Multi-satellitE Retrievals for GPM (IMERG) products (early, late, and final) A dedicated Web portal (including user guides, etc.) has been developed for GPM data (http://disc.sci.gsfc.nasa.gov/gpm). Data services that are currently and to-be available include Google-like Mirador (http://mirador.gsfc.nasa.gov/) for data search and access; data access through various Web services (e.g., OPeNDAP, GDS, WMS, WCS); conversion into various formats (e.g., netCDF, HDF, KML (for Google Earth), ASCII); exploration, visualization, and statistical online analysis through Giovanni (http://giovanni.gsfc.nasa.gov); generation of value-added products; parameter and spatial subsetting; time aggregation; regridding; data version control and provenance; documentation; science support for proper data usage, FAQ, help desk; monitoring services (e.g. Current Conditions) for applications. The United User Interface (UUI) is the next step in the evolution of the GES DISC web site. It attempts to provide seamless access to data, information and services through a single interface without sending the user to different applications or URLs (e.g., search, access, subset, Giovanni, documents).

precipitation↗

Potential of GPM IMERG Precipitation Estimates to Monitor Natural Disaster Triggers in Urban Areas: the Case of Rio deJaneiro, Brazil

Extreme rainfall can be a catastrophic trigger for natural disaster events at urban scales. However, there remains large uncertainties as to how satellite precipitation can identify these triggers at a city scale. The objective of this study is to evaluate the potential of satellite-based rainfall estimates to monitor natural disaster triggers in urban areas. Rainfall estimates from the Global Precipitation Measurement (GPM) mission are evaluated over the city of Rio de Janeiro, Brazil, where urban floods and landslides occur periodically as a result of extreme rainfall events. Two rainfall products derived from the Integrated Multi-satellite Retrievals for GPM (IMERG), the IMERG Early and IMERG Final products, are integrated into the Noah Multi-Parameterization (Noah-MP) land surface model in order to simulate the spatial and temporal dynamics of two key hydrometeorological disaster triggers across the city over the wet seasons during 2001-2019. Here, total runoff (TR) and rootzone soil moisture (RZSM) are considered as flood and landslide triggers, respectively. Ground-based observations at 33 pluviometric stations are interpolated, and the resulting rainfall fields are used in an in-situ precipitation-based simulation, considered as the reference for evaluating the IMERG-driven simulations. The evaluation is performed during the wet seasons (November-April), when average rainfall over the city is 4.4mm/day. Results show that IMERG products show low spatial variability at the city scale, generally overestimate rainfall rates by 12-35%, and impacts on TR and RZSM vary spatially mostly as a function of land cover and soil types. Results based on statistical and categorical metrics show that IMERG skill in detecting extreme events is moderate, with IMERG Final performing slightly better for most metrics. By analyzing two recent storms, we observe that IMERG detects mostly hourly extreme events, but underestimates rainfall rates, resulting in underestimated TR and RZSM. An evaluation of normalized time series using percentiles shows that both satellite products have significantly improved skill in detecting extreme events when compared to the evaluation using absolute values, indicating that IMERG precipitation could be potentially used as a predictor for natural disasters in urban areas.

IMERG↗

Evaluating CERES TOA Fluxes using ARISE aircraft observations

Uncertainty in observations of top-of-atmosphere (TOA) radiation fluxes are larger in the Arctic than in other regions. The magnitude of these uncertainties limit our understanding of the Arctic surface energy budget and its variability. The significant uncertainties are due to the low sun angles and wide range of highly reflecting, anisotropic, and highly heterogeneous surface conditions. Therefore, quantifying, attributing, and reducing Arctic TOA radiative flux uncertainty enables a better understanding of the rapidly changing Arctic. To advance this goal, we compare the Cloud and Earth’s Radiant Energy System (CERES) TOA radiative fluxes with measurements from the Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) flow in September 2014. A key objective of ARISE was to evaluate and attribute uncertainty in CERES footprint and gridded TOA radiative fluxes. In this study, we first compare the CERES TOA flux with those obtained from the broadband radiometer measurements from the aircraft using instantaneously matched footprint with the flight track and as the hourly gridded fluxes. This comparison indicates an agreement within uncertainty in the longwave (2 Wm-2 ) for all five grid boxes and agreement in the shortwave (10 Wm-2) for four-out-of-five grid boxes. While not a statistically significant results given the small sample size, the hourly, gridded and the instantaneously matched footprint comparison suggest a -10 Wm-2 bias for CERES in the shortwave. To explore whether this is a robust feature or a statistical artifact, we quantify the individual sources of uncertainty in the differences (temporal and spatial sampling differences, scene evolution, accuracy, angular distribution models, and scene id) to see if any of these differences account for the shortwave bias.

CERES↗

Spatial patterns of increases and decreases in the length of the sea ice season in the north polar region, 1979-1986

Recently it was reported that sea ice extents in the Northern Hemisphere showed a very slight but statistically significant decrease over the 8.8-year period of the Nimbus 7 scanning multichannel microwave radiometer (SMMR) data set. In this paper the same SMMR data are used to reveal spatial patterns in increasing and decreasing sea ice coverage. Specifically, the length of the ice season is mapped for each full year of the SMMR data set (1979-1986), and the trends over the 8 years in these ice season lengths are also mapped. These trends show considerable spatial coherence, with a shortening in the sea ice season apparent in much of the eastern hemisphere of the north polar ice cover, particularly in the Sea of Okhotsk, the Barents Sea, and the Kara Sea, and a lengthening of the sea ice season apparent in much of the western hemisphere of the north polar ice cover, particularly in Davis Strait, the Labrador Sea, and the Beaufort Sea.

Parkinson, Claire L.↗

Assimilation of Quality Controlled AIRS Temperature Profiles using the NCEP GFS

We have previously conducted a number of data assimilation experiments using AIRS Version-5 quality controlled temperature profiles as a step toward finding an optimum balance of spatial coverage and sounding accuracy with regard to improving forecast skill. The data assimilation and forecast system we used was the Goddard Earth Observing System Model , Version-5 (GEOS-5) Data Assimilation System (DAS), which represents a combination of the NASA GEOS-5 forecast model with the National Centers for Environmental Prediction (NCEP) operational Grid Point Statistical Interpolation (GSI) global analysis scheme. All analyses and forecasts were run at a 0.5deg x 0.625deg spatial resolution. Data assimilation experiments were conducted in four different seasons, each in a different year. Three different sets of data assimilation experiments were run during each time period: Control; AIRS T(p); and AIRS Radiance. In the "Control" analysis, all the data used operationally by NCEP was assimilated, but no AIRS data was assimilated. Radiances from the Aqua AMSU-A instrument were also assimilated operationally by NCEP and are included in the "Control". The AIRS Radiance assimilation adds AIRS observed radiance observations for a select set of channels to the data set being assimilated, as done operationally by NCEP. In the AIRS T(p) assimilation, all information used in the Control was assimilated as well as Quality Controlled AIRS Version-5 temperature profiles, i.e., AIRS T(p) information was substituted for AIRS radiance information. The AIRS Version-5 temperature profiles were presented to the GSI analysis as rawinsonde profiles, assimilated down to a case-by-case appropriate pressure level p(sub best) determined using the Quality Control procedure. Version-5 also determines case-by-case, level-by-level error estimates of the temperature profiles, which were used as the uncertainty of each temperature measurement. These experiments using GEOS-5 have shown that forecasts resulting from analyses using the AIRS T(p) assimilation system were superior to those from the Radiance assimilation system, both with regard to global 7 day forecast skill and also the ability to predict storm tracks and intensity.

Susskind, Joel↗

A High-resolution Regional Wave Resource Characterization For The U.S. West Coast

Objectives/Scope: Wave resource characterization is a critical step for wave energy converter deployment in the coastal ocean and relies on long-term, high-resolution wave datasets. This study presents a detailed modeling study of the wave resource along the U.S. West Coast (Washington, Oregon, and California), a coastal region that was identified with high wave energy potential in earlier studies. Methods, Procedures, Process: The wave hindcast covers a 32-year period from 1979 to 2010 and is based on a multi-resolution, unstructured-grid SWAN model framework. Model configuration closely follows and meets the requirements recommended by the International Electrotechnical Commission Technical Specification (IEC TS) for wave energy resource assessment and characterization (Class 2 - feasibility study). The model domain covers the entire U.S. Exclusive Economic Zone (EEZ) in the West Coast and has a spatial resolution varying from ~300 m in the nearshore region (20 km from the shoreline) to ~2500 m within the EEZ and ~5000 m at the open boundary, which extends beyond the EEZ. The model was forced by hourly 2-D wave spectra produced by a two-way nested WaveWatch III model, which covers the global ocean domain and the broader U.S. West Coast region domain with spatial resolutions of 0.5 degree and 10 arc-minutes, respectively. Both wave models are forced by hourly, 0.5-degree wind forcing obtained from NCEP’s Climate Forecast System Reanalysis (CFSR) product. Results, Observations, Conclusions: The standard model output for the SWAN model includes 3-hourly output for the six IEC wave resource parameters (e.g., omnidirectional wave power) at each grid point and hourly 2-D spectra at more than 50 NDBC buoys. Extensive model validation was achieved by comparing the six model-predicted IEC parameters with those derived from field observations at representative NDBC buoys. The error statistics indicated the model’s satisfactory performance. Further analyses were conducted to systematically evaluate the temporal and spatial distributions of wave energy potential and wave climate along the U.S. West Coast. Results suggest that Washington and Oregon coasts have similar nearshore wave resource, which is significantly higher than resources in Southern California. Strong seasonal variations are also observed, e.g., high wave energy tends to occur in the winter months. In summary, this study produced the first high-resolution, comprehensive dataset on wave energy distribution along the U.S. West Coast. Novel/Additive Information: The results are being used by the National Renewable Energy Laboratory to update the MHK Atlas, which was originally derived from NOAA’s 4-arc-minute WaveWatch III model output. In addition, the monthly averaged wave energy climatology dataset can be readily shared to support a variety of research and application efforts within the EEZ of the U.S. West Coast.

Wang, Taiping↗

Remote sensing and statistical analysis of the effects of hurricane María on the forests of Puerto Rico

Widely recognized as one of the worst natural disaster in Puerto Rico's history, hurricane María made landfall on September 20, 2017 in southeast Puerto Rico as a high-end category 4 hurricane on the Saffir-Simpson scale causing widespread destruction, fatalities and forest disturbance. This study focused on hurricane María's effect on Puerto Rico's forests as well as the effect of landform and forest characteristics on observed disturbance patterns. In this work, we used Google Earth Engine (GEE) to assess the severity of forest disturbance using a disturbance metric based on Landsat 8 satellite data composites with pre and post-hurricane María. Forest structure, tree phenology characteristics, and landforms were obtained from satellite data products, including digital elevation model and global forest canopy height. Our analyses showed that forest structure, and characteristics such as forest age and forest type affected patterns of forest disturbance. Among forest types, highest disturbance values were found in sierra palm, transitional, and tall cloud forests; seasonal evergreen forests with coconut palm; and mangrove forests. For landforms, greatest disturbance metrics was found at high elevations, steeper slopes, and windward surfaces. As expected, high levels of disturbance were also found close to the hurricane track, with disturbance less severe as hurricane María moved inland. Results demonstrated that forest and landform characteristics accounted for 34% of the variation in spatial forest spectral disturbance patterns. This study demonstrated an informative regional approach, combining remote sensing with statistical analyses to investigate factors that result in variability in hurricane effects on forest ecosystems.

54 ENVIRONMENTAL SCIENCES↗

Current QSO statistics - Implications for the intergalactic medium

The results of numerous QSO surveys have been compiled and analyzed to form a single spatially averaged QSO ionizing function that is independent of evolution mode (number density or luminosity). An intergalactic medium (IGM) that satisfies the observational constraints may now have a density with respect to closure of approximately 0.1, which is substantially less than hitherto modeled. The aggregate of QSO data also indicate that if evolution is due to number density, then, when split into luminosity classes, an exponential in look-back time fits the data better than a power law, and the evolution rates increase roughly with absolute luminosity if analyzed by the exponential.

Sherman, R. D.↗

Training site statistics from Landsat and Seasat satellite imagery registered to a common map base

Landsat and Seasat satellite imagery and training site boundary coordinates were registered to a common Universal Transverse Mercator map base in the Newport Beach area of Orange County, California. The purpose was to establish a spatially-registered, multi-sensor data base which would test the use of Seasat synthetic aperture radar imagery to improve spectral separability of channels used for land use classification of an urban area. Digital image processing techniques originally developed for the digital mosaics of the California Desert and the State of Arizona were adapted to spatially register multispectral and radar data. Techniques included control point selection from imagery and USGS topographic quadrangle maps, control point cataloguing with the Image Based Information System, and spatial and spectral rectifications of the imagery. The radar imagery was pre-processed to reduce its tendency toward uniform data distributions, so that training site statistics for selected Landsat and pre-processed Seasat imagery indicated good spectral separation between channels.

Clark, J.↗

The Area Coverage of Geophysical Fields as a Function of Sensor Field-of View

In many remote sensing studies of geophysical fields such as clouds, land cover, or sea ice characteristics, the fractional area coverage of the field in an image is estimated as the proportion of pixels that have the characteristic of interest (i.e., are part of the field) as determined by some thresholding operation. The effect of sensor field-of-view on this estimate is examined by modeling the unknown distribution of subpixel area fraction with the beta distribution, whose two parameters depend upon the true fractional area coverage, the pixel size, and the spatial structure of the geophysical field. Since it is often not possible to relate digital number, reflectance, or temperature to subpixel area fraction, the statistical models described are used to determine the effect of pixel size and thresholding operations on the estimate of area fraction for hypothetical geophysical fields. Examples are given for simulated cumuliform clouds and linear openings in sea ice, whose spatial structures are described by an exponential autocovariance function. It is shown that the rate and direction of change in total area fraction with changing pixel size depends on the true area fraction, the spatial structure, and the thresholding operation used.

Key, Jeffrey R.↗

Smart quantum statistical imaging beyond the Abbe-Rayleigh criterion

The wave nature of light imposes limits on the resolution of optical imaging systems. For over a century, the Abbe-Rayleigh criterion has been utilized to assess the spatial resolution limits of imaging instruments. Recently, there has been interest in using spatial projective measurements to enhance the resolution of imaging systems. Unfortunately, these schemes require a priori information regarding the coherence properties of “unknown” light beams and impose stringent alignment conditions. Here, we introduce a smart quantum camera for superresolving imaging that exploits the self-learning features of artificial intelligence to identify the statistical fluctuations of unknown mixtures of light sources at each pixel. This is achieved through a universal quantum model that enables the design of artificial neural networks for the identification of photon fluctuations. Our protocol overcomes limitations of existing superresolution schemes based on spatial mode projections, and consequently provides alternative methods for microscopy, remote sensing, and astronomy.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Short-lead seasonal precipitation forecast in northeastern Brazil using an ensemble of artificial neural networks

This study assesses the deterministic and probabilistic forecasting skill of a 1-month-lead ensemble of Artificial Neural Networks (EANN) based on low-frequency climate oscillation indices. The predictand is the February-April (FMA) rainfall in the Brazilian state of Ceará, which is a prominent subject in climate forecasting studies due to its high seasonal predictability. Additionally, the study proposes combining the EANN with dynamical models into a hybrid multi-model ensemble (MME). The forecast verification is carried out through a leave-one-out cross-validation based on 40 years of data. The EANN forecasting skill is compared with traditional statistical models and the dynamical models that compose Ceará’s operational seasonal forecasting system. A spatial comparison showed that the EANN was among the models with the smallest Root Mean Squared Error (RMSE) and Ranked Probability Score (RPS) in most regions. Moreover, the analysis of the area-aggregated reliability showed that the EANN is better calibrated than the individual dynamical models and has better resolution than Multinomial Logistic Regression for above-normal (AN) and below-normal (BN) categories. It is also shown that combining the EANN and dynamical models into a hybrid MME reduces the overconfidence of the extreme categories observed in a dynamically-based MME, improving the reliability of the forecasting system.

54 ENVIRONMENTAL SCIENCES↗

An experimental study of the existence regions and non-linear interactions of drift wave and Kelvin–Helmholtz instabilities in a linear magnetized plasma

Experimental observations of the intrinsic excitation and non-linear interactions of drift wave (DW) and Kelvin–Helmholtz (KH) instabilities in a linear magnetized plasma column are presented. The experiments are carried out in the inverse mirror plasma experimental device (IMPED)—a cylindrical, magnetized, linear plasma machine designed to study low-frequency waves and instabilities in plasma. A novel feature of IMPED is the ability to control plasma profiles, such as the density n(r)⁠, electron temperature T e (r)⁠, and plasma potential V p (r) by varying the ratio Rm of the magnetic field in the main chamber to that in the source chamber. At high values of Rm, higher-density gradient scale length promotes the drift wave (DW) instability while lower Rm value results in a higher radial electric field, inducing a sheared poloidal flow that enhances the dominance of the Kelvin–Helmholtz (KH) mode. The background and fluctuating plasma parameters are characterized using various configurations of multiple in situ electric probes at different spatial locations to quantify the local gradients that excite the low-frequency primary instabilities. Statistical, spectral, and bispectral analysis of the density and potential signals help identify these modes in terms of wave number, frequency, phase, and amplitude and also delineate the nature of their non-linear interactions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗