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All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Using Grid Benchmarks for Dynamic Scheduling of Grid Applications

Navigation or dynamic scheduling of applications on computational grids can be improved through the use of an application-specific characterization of grid resources. Current grid information systems provide a description of the resources, but do not contain any application-specific information. We define a GridScape as dynamic state of the grid resources. We measure the dynamic performance of these resources using the grid benchmarks. Then we use the GridScape for automatic assignment of the tasks of a grid application to grid resources. The scalability of the system is achieved by limiting the navigation overhead to a few percent of the application resource requirements. Our task submission and assignment protocol guarantees that the navigation system does not cause grid congestion. On a synthetic data mining application we demonstrate that Gridscape-based task assignment reduces the application tunaround time.

Frumkin, Michael↗
NASA NTRS2017

Monitoring Land Surface Albedo and Vegetation Dynamics Using High Spatial and Temporal Resolution Synthetic Time Series from Landsat and the MODIS BRDF/NBAR/Albedo Product

Seasonal vegetation phenology can significantly alter surface albedo which in turn affects the global energy balance and the albedo warmingcooling feedbacks that impact climate change. To monitor and quantify the surface dynamics of heterogeneous landscapes, high temporal and spatial resolution synthetic time series of albedo and the enhanced vegetation index (EVI) were generated from the 500-meter Moderate Resolution Imaging Spectroradiometer (MODIS) operational Collection V006 daily BRDF (Bidirectional Reflectance Distribution Function) / NBAR (Nadir BRDF-Adjusted Reflectance) / albedo products and 30-meter Landsat 5 albedo and near-nadir reflectance data through the use of the Spatial and Temporal Adaptive Reflectance Fusion Model (STARFM). The traditional Landsat Albedo (Shuai et al., 2011) makes use of the MODIS BRDFAlbedo products (MCD43) by assigning appropriate BRDFs from coincident MODIS products to each Landsat image to generate a 30-meter Landsat albedo product for that acquisition date. The available cloud free Landsat 5 albedos (due to clouds, generated every 16 days at best) were used in conjunction with the daily MODIS albedos to determine the appropriate 30-meter albedos for the intervening daily time steps in this study. These enhanced daily 30-meter spatial resolution synthetic time series were then used to track albedo and vegetation phenology dynamics over three Ameriflux tower sites (Harvard Forest in 2007, Santa Rita in 2011 and Walker Branch in 2005). These Ameriflux sites were chosen as they are all quite nearby new towers coming on line for the National Ecological Observatory Network (NEON), and thus represent locations which will be served by spatially paired albedo measures in the near future. The availability of data from the NEON towers will greatly expand the sources of tower albedometer data available for evaluation of satellite products. At these three Ameriflux tower sites the synthetic time series of broadband shortwave albedos were evaluated using the tower albedo measurements with a Root Mean Square Error (RMSE) less than 0.013 and a bias within the range of 0.006. These synthetic time series provide much greater spatial detail than the 500 meter gridded MODIS data, especially over more heterogeneous surfaces, which improves the efforts to characterize and monitor the spatial variation across species and communities. The mean of the difference between maximum and minimum synthetic time series of albedo within the MODIS pixels over a subset of satellite data of Harvard Forest (16 kilometers by 14 kilometers) was as high as 0.2 during the snow-covered period and reduced to around 0.1 during the snow-free period. Similarly, we have used STARFM to also couple MODIS Nadir BRDF-Adjusted Reflectances (NBAR) values with Landsat 5 reflectances to generate daily synthetic times series of NBAR and thus Enhanced Vegetation Index (NBAR-EVI) at a 30-meter resolution. While normally STARFM is used with directional reflectances, the use of the view angle corrected daily MODIS NBAR values will provide more consistent time series. These synthetic times series of EVI are shown to capture seasonal vegetation dynamics with finer spatial and temporal details, especially over heterogeneous land surfaces.

Vegetation Index↗
NASA NTRSDate not supplied

Implicit Large-Eddy Simulations of Compressible Mixing Layers

Implicit large-eddy simulations of the self-similar regions of two compressible mixing layers at high Reynolds number and convective Mach numbers of 0.381 and 0.690 were carried out. Experimental data was used as the input into a synthetic eddy method turbulent inflow boundary condition to initiate simulations. Computational grids with nearly isotropic cells were used and the grid counts ranged from 24 to 270 million points. Agreement with experimental velocity and Reynolds stress data was good given the simplifications of the simulation. The decrease in mixing layer growth rate with increasing compressibility compares well with the literature. Budgets for the Reynolds stress transport equation were extracted from the simulations. It was demonstrated that the grids used did not resolve the dissipation term at the experimental Reynolds number. However, low Reynolds number simulations indicate that the numerical dissipation replaces the physical dissipation and the dissipation term in the transport equation can be represented by the summation term that quantifies the imbalance in the budget. The budgets for the high Reynolds number mixing layers agree well with previous low Reynolds number studies; indicating that the primary mechanism for the reduced growth rate and increased anistropy of the Reynolds stress tensor due to compressibility is a reduction in the pressure-strain and production terms. A new scaling based on the magnitude of the Reynolds stress tensor is proposed. This scaling provides better relative comparisons between the data and shows that the decrease in pressure-strain in the shear component is the primary driver in reducing the transverse normal stress.

turbulence↗
NASA NTRS2024

Extending the Utility of Space-Borne Snow Water Equivalent Observations Over Vegetated Areas With Data Assimilation

Snow is a vital component of the earth system, yet no snow-focused satellite remote sensing platform currently exists. In this study, we investigate how synthetic observations of snow water equivalent (SWE) representative of a synthetic aperture radar remote sensing platform could improve spatiotemporal estimates of snowpack. We use a fraternal twin observing system simulation experiment, specifically investigating how much snow simulated using widely used models and forcing data could be improved by assimilating synthetic observations of SWE. We focus this study across a 24° x 37° domain in the western USA and Canada, simulating snow at 250 m resolution and hourly time steps in water year 2019. We perform two data assimilation experiments, including (1) a simulation excluding synthetic observations in forests where canopies obstruct remote sensing retrievals and (2) a simulation inferring snow distribution in forested grid cells using synthetic observations from nearby canopy-free grid cells. Results found that, relative to a nature run, or assumed true simulation of snow evolution, assimilating synthetic SWE observations improved average SWE biases at maximum snowpack timing in shrub, grass, crop, bare-ground, and wetland land cover types from 14 %, to within 1 %. However, forested grid cells contained a disproportionate amount of SWE volume. In forests, SWE mean absolute errors at the time of maximum snow volume were 111 mm and average SWE biases were on the order of 150 %. Here the data assimilation approach that estimated forest SWE using observations from the nearest canopy-free grid cells substantially improved these SWE biases (18 %) and the SWE mean absolute error (27 mm). Simulations employing data assimilation also improved estimates of the temporal evolution of both SWE and runoff, even in spring snowmelt periods when melting snow and high snow liquid water content prevented synthetic SWE retrievals. In fact, in the Upper Colorado River region, melt-season SWE biases were improved from 63 % to within 1 %, and the Nash–Sutcliffe efficiency of runoff improved from −2.59 to 0.22. These results demonstrate the value of data assimilation and a snow-focused globally relevant remote sensing platform for improving the characterization of SWE and associated water availability.

Justin Pflug↗
NASA NTRS2010

Relating Convective and Stratiform Rain to Latent Heating

The relationship among surface rainfall, its intensity, and its associated stratiform amount is established by examining observed precipitation data from the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR). The results show that for moderate-high stratiform fractions, rain probabilities are strongly skewed toward light rain intensities. For convective-type rain, the peak probability of occurrence shifts to higher intensities but is still significantly skewed toward weaker rain rates. The main differences between the distributions for oceanic and continental rain are for heavily convective rain. The peak occurrence, as well as the tail of the distribution containing the extreme events, is shifted to higher intensities for continental rain. For rainy areas sampled at 0.58 horizontal resolution, the occurrence of conditional rain rates over 100 mm/day is significantly higher over land. Distributions of rain intensity versus stratiform fraction for simulated precipitation data obtained from cloud-resolving model (CRM) simulations are quite similar to those from the satellite, providing a basis for mapping simulated cloud quantities to the satellite observations. An improved convective-stratiform heating (CSH) algorithm is developed based on two sources of information: gridded rainfall quantities (i.e., the conditional intensity and the stratiform fraction) observed from the TRMM PR and synthetic cloud process data (i.e., latent heating, eddy heat flux convergence, and radiative heating/cooling) obtained from CRM simulations of convective cloud systems. The new CSH algorithm-derived heating has a noticeably different heating structure over both ocean and land regions compared to the previous CSH algorithm. Major differences between the new and old algorithms include a significant increase in the amount of low- and midlevel heating, a downward emphasis in the level of maximum cloud heating by about 1 km, and a larger variance between land and ocean in the new CSH algorithm.

Tao, Wei-Kuo↗
NASA NTRS2012

Achieving Accuracy Requirements for Forest Biomass Mapping: A Spaceborne Data Fusion Method for Estimating Forest Biomass and Lidar Sampling Error

The synergistic use of active and passive remote sensing (i.e., data fusion) demonstrates the ability of spaceborne light detection and ranging (LiDAR), synthetic aperture radar (SAR) and multispectral imagery for achieving the accuracy requirements of a global forest biomass mapping mission (+/-20 Mg/ha or 20%, the greater of the two, for at least 80% of grid cells). A data fusion approach also provides a means to extend 3D information from discrete spaceborne LiDAR measurements of forest structure across scales much larger than that of the LiDAR footprint. For estimating biomass, these measurements mix a number of errors including those associated with LiDAR footprint sampling over regional-global extents. A general framework for mapping above ground live forest biomass density (AGB) with a data fusion approach is presented and verified using data from NASA field campaigns near Howland, ME, USA, to assess AGB and LiDAR sampling errors across a regionally representative landscape. We combined SAR and Landsat-derived optical (passive optical) image data to identify contiguous areas (>0.5 ha) that are relatively homogenous in remote sensing metrics (forest patches). We used this image-derived data with simulated spaceborne LiDAR derived from orbit and cloud cover simulations and airborne data from NASA's Laser Vegetation Imaging Sensor (LVIS) to compute AGB and estimate LiDAR sampling error for forest patches and 100 m, 250 m, 500 m, and 1 km grid cells. At both the patch and grid scales, we evaluated differences in AGB estimation and sampling error from the combined use of LiDAR with both SAR and passive optical and with either SAR or passive optical alone. First, this data fusion approach demonstrates that incorporating forest patches into the AGB mapping framework can provide sub-grid forest information for coarser grid-level AGB reporting. Second, a data fusion approach for estimating AGB using simulated spaceborne LiDAR with SAR and passive optical image combinations reduced forest AGB sampling errors 12%-38% from those where LiDAR is used with SAR or passive optical alone. In absolute terms, sampling errors were reduced from 14-40 Mg/ha to 11-28 Mg/ha across all grid scales and prediction methods, where minimum sampling errors were 11, 15, 18, and 22 Mg/ha for 1 km, 500 m, 250 m, and 100 m grid scales, respectively. Third, spaceborne global scale accuracy requirements were achieved whereby at least 80% of the grid cells at 100 m, 250 m, 500 m, and 1 km grid levels met AGB accuracy requirements using a combination of passive optical and SAR along with machine learning methods to predict vegetation structure metrics for forested areas without LiDAR samples. Finally, using either passive optical or SAR, accuracy requirements were met at the 500 m and 250 m grid level, respectively..

LiDAR↗
NASA NTRS2013

X-ray Reflected Spectra from Accretion Disk Models. III. A Complete Grid of Ionized Reflection Calculations

We present a new and complete library of synthetic spectra for modeling the component of emission that is reflected from an illuminated accretion disk. The spectra were computed using an updated version of our code xillver that incorporates new routines and a richer atomic data base. We offer in the form of a table model an extensive grid of reflection models that cover a wide range of parameters. Each individual model is characterized by the photon index Gamma of the illuminating radiation, the ionization parameter zeta at the surface of the disk (i.e., the ratio of the X-ray flux to the gas density), and the iron abundance A(sub Fe) relative to the solar value. The ranges of the parameters covered are: 1.2 <= Gamma <= 3.4, 1 <= zeta <= 104, and 0.5 <= A(sub Fe) <= 10. These ranges capture the physical conditions typically inferred from observations of active galactic nuclei, and also stellar-mass black holes in the hard state. This library is intended for use when the thermal disk flux is faint compared to the incident power-law flux. The models are expected to provide an accurate description of the Fe K emission line, which is the crucial spectral feature used to measure black hole spin. A total of 720 reflection spectra are provided in a single FITS file suitable for the analysis of X-ray observations via the atable model in xspec. Detailed comparisons with previous reflection models illustrate the improvements incorporated in this version of xillver.

X-ray↗
NASA NTRS1992

The constitution of the atmospheric layers and the extreme ultraviolet spectrum of hot hydrogen-rich white dwarfs

An analysis is presented of the atmospheric properties of hot, H-rich, DA white dwarfs that is based on optical, UV, and X-ray observations aimed at predicting detailed spectral properties of these stars in the range 80-800 A. The divergences between observations from a sample of 15 hot DA white dwarfs emitting in the EUV/soft X-ray range and pure H synthetic spectra calculated from a grid of model atmospheres characterized by Teff and g are examined. Seven out of 15 DA stars are found to consistently exhibit pure hydrogen atmospheres, the remaining seven stars showing inconsistency between FUV and EUV/soft X-ray data that can be explained by the presence of trace EUV/soft X-ray absorbers. Synthetic data are computed assuming two other possible chemical structures: photospheric traces of radiatively levitated heavy elements and a stratified hydrogen/helium distribution. Predictions about forthcoming medium-resolution observations of the EUV spectrum of selected hot H-rich white dwarfs are made.

Vennes, Stephane↗
NASA NTRS1995

An improved land mask for the SSM/I grid

This paper discusses the development of a new land/ocean/coastline mask for use with Defense Meteorological Satellite Program (DMSP) Special Sensor Microwave/Imager (SSM/I) data, and other types of data which are mapped to the polar stereographic SSM/I grid. Pre-existing land masks were found to disagree, to lack certain land features, and to disagree with land boundaries that are visible in high resolution sensor imagery, such as imagery from the Synthetic Aperture Radar (SAR) on the Earth Resources Satellite (ERS-1). The Digital Chart of the World (DCW) database was initially selected as a source of shoreline data for this effort. Techniques for developing a land mask from these shoreline data are discussed. The resulting land mask, although not perfect, is seen to exhibit significant improvement over previous land mask products.

Martino, Michael G.↗
NASA NTRS1994

Regional and seasonal estimates of fractional storm coverage based on station precipitation observations

Simulated climates using numerical atmospheric general circulation models (GCMs) have been shown to be highly sensitive to the fraction of GCM grid area assumed to be wetted during rain events. The model hydrologic cycle and land-surface water and energy balance are influenced by the parameter bar-kappa, which is the dimensionless fractional wetted area for GCM grids. Hourly precipitation records for over 1700 precipitation stations within the contiguous United States are used to obtain observation-based estimates of fractional wetting that exhibit regional and seasonal variations. The spatial parameter bar-kappa is estimated from the temporal raingauge data using conditional probability relations. Monthly bar-kappa values are estimated for rectangular grid areas over the contiguous United States as defined by the Goddard Institute for Space Studies 4 deg x 5 deg GCM. A bias in the estimates is evident due to the unavoidably sparse raingauge network density, which causes some storms to go undetected by the network. This bias is corrected by deriving the probability of a storm escaping detection by the network. A Monte Carlo simulation study is also conducted that consists of synthetically generated storm arrivals over an artificial grid area. It is used to confirm the bar-kappa estimation procedure and to test the nature of the bias and its correction. These monthly fractional wetting estimates, based on the analysis of station precipitation data, provide an observational basis for assigning the influential parameter bar-kappa in GCM land-surface hydrology parameterizations.

Gong, Gavin↗
NASA NTRS2010

Validation of Supersonic Film Cooling Modeling for Liquid Rocket Engine Applications

Topics include: upper stage engine key requirements and design drivers; Calspan "stage 1" results, He slot injection into hypersonic flow (air); test articles for shock generator diagram, slot injector details, and instrumentation positions; test conditions; modeling approach; 2-d grid used for film cooling simulations of test article; heat flux profiles from 2-d flat plate simulations (run #4); heat flux profiles from 2-d backward facing step simulations (run #43); isometric sketch of single coolant nozzle, and x-z grid of half-nozzle domain; comparison of 2-d and 3-d simulations of coolant nozzles (run #45); flowfield properties along coolant nozzle centerline (run #45); comparison of 3-d CFD nozzle flow calculations with experimental data; nozzle exit plane reduced to linear profile for use in 2-d film-cooling simulations (run #45); synthetic Schlieren image of coolant injection region (run #45); axial velocity profiles from 2-d film-cooling simulation (run #45); coolant mass fraction profiles from 2-d film-cooling simulation (run #45); heat flux profiles from 2-d film cooling simulations (run #45); heat flux profiles from 2-d film cooling simulations (runs #47, #45, and #47); 3-d grid used for film cooling simulations of test article; heat flux contours from 3-d film-cooling simulation (run #45); and heat flux profiles from 3-d and 2-d film cooling simulations (runs #44, #46, and #47).

Morris, Christopher I.↗
NASA NTRS2010

Inlet Flow Control and Prediction Technologies for Embedded Propulsion Systems

Fail-safe inlet flow control may enable high-speed cruise efficiency, low noise signature, and reduced fuel-burn goals for hybrid wing-body aircraft. The objectives of this program are to develop flow control and prediction methodologies for boundary-layer ingesting (BLI) inlets used in these aircraft. This report covers the second of a three year program. The approach integrates experiments and numerical simulations. Both passive and active flow-control devices were tested in a small-scale wind tunnel. Hybrid actuation approaches, combining a passive microvane and active synthetic jet, were tested in various geometric arrangements. Detailed flow measurements were taken to provide insight into the flow physics. Results of the numerical simulations were correlated against experimental data. The sensitivity of results to grid resolution and turbulence models was examined. Aerodynamic benefits from microvanes and microramps were assessed when installed in an offset BLI inlet. Benefits were quantified in terms of recovery and distortion changes. Microvanes were more effective than microramps at improving recovery and distortion.

McMillan, Michelle L.↗
NASA NTRS2014

Release 2 data products from the Ozone Mapping and Profiler Suite (OMPS) Limb Profiler

The OMPS Limb Profiler (LP) was launched on board the NASA Suomi National Polar-orbiting Partnership (SNPP) satellite in October 2011. OMPS-LP is a limb-scattering hyperspectral sensor that provides ozone profiling capability at 1.5 km vertical resolution from cloud top to 60 km altitude. The use of three parallel slits allows global coverage in approximately four days. We have recently completed a full reprocessing of all LP data products, designated as Release 2, that improves the accuracy and quality of these products. Level 1 gridded radiance (L1G) changes include intra-orbit and seasonal correction of variations in wavelength registration, revised static and intra-orbit tangent height adjustments, and simplified pixel selection from multiple images. Ozone profile retrieval changes include removal of the explicit aerosol correction, exclusion of channels contaminated by stratospheric OH emission, a revised instrument noise characterization, improved synthetic solar spectrum, improved pressure and temperature ancillary data, and a revised ozone climatology. Release 2 data products also include aerosol extinction coefficient profiles derived with the prelaunch retrieval algorithm. Our evaluation of OMPS LP Release 2 data quality is good. Zonal average ozone profile comparisons with Aura MLS data typically show good agreement, within 5-10% over the altitude range 20-50 km between 60 deg S and 60 deg N. The aerosol profiles agree well with concurrent satellite measurements such as CALIPSO and OSIRIS, and clearly detect exceptional events such as volcanic eruptions and the Chelyabinsk bolide in February 2013.

Limb scatter↗
NASA NTRS1989

Methods for local gravity field approximation

The most widely known modern method for estimating gravity field values from observed data is least-squares collocation. Its advantages are that it can make estimates at arbitrary locations based on irregularly spaced observations, and that it makes use of statistical information about errors in the input data while providing corresponding information about the quality of the output estimates. Disadvantages of collocation include the necessity of inverting square matrices of dimension equal to the number of data values and the need to assume covariance models for the gravity field and the data errors. Fourier methods are an important alternative to collocation; having the advantage of greater computational efficiency, but requiring data estimates to be on a regular grid and not using or providing statistical accuracy information. The GEOFAST algorithm is an implementation of collocation that achieves high computational efficiency by transforming the estimation equations into the frequency domain where an accurate approximation may be made to reduce the workload. The forward and inverse Fast Fourier Transforms (FFTs) are utilized. The accuracy and computational efficiency of the GEOFAST algorithm is demonstrated using two sets of synthetic gravity data: marine gravity for an ocean trench region including wavelengths longer than 200 km; and local land gravity containing wavelengths as short as 5 km. These results are discussed along with issues such as the advantages of first removing reference field models before carrying out the estimation algorithm.

Sailor, R. V.↗
NASA NTRSDate not supplied

Zemax Modeling of a Self-aligned Focusing Schlieren System with Simulated Compressible Flow

A self-aligned focusing schlieren system is simulated in the ANSYS Zemax OpticStudio software environment. The model uses a custom scatter-defining dynamic link library on the retroreflective background in order to scatter rays in the direction of the incident ray rather than the specular ray. Simulated compressible flow refractive index fields are imported into Zemax by use of the grid gradient object and a workaround to the maximum point limit is introduced. The Ronchi ruling is built as a high resolution bitmap image in MATLAB and set in Zemax as a slide object allowing the bitmap image to either transmit or terminate rays at each line pair. The Zemax simulations are compared to computational numerical schlieren and experimental conventional, path-integrated schlieren results from a hypersonic stagnation point injection flow configuration and an experimental image of a shock wave from a laser-induced breakdown. In the stagnation point injection simulations, the Zemax schlieren images capture complex flow features such as the Mach disk, shear layers, contact surface, and bow shock well, but contains long, curved features (striations) between the model and the bow shock that are not present in the synthetic schlieren image from the CFD or the experimental image. The image from Zemax of the spark-induced shock wave captures the shape and curvature of the shock but appears blurry due to grid discretization in the computational data.

Nicholas A Mejia↗
NASA NTRS2006

Distributed Computing Framework for Synthetic Radar Application

We are developing an extensible software framework, in response to Air Force and NASA needs for distributed computing facilities for a variety of radar applications. The objective of this work is to develop a Python based software framework, that is the framework elements of the middleware that allows developers to control processing flow on a grid in a distributed computing environment. Framework architectures to date allow developers to connect processing functions together as interchangeable objects, thereby allowing a data flow graph to be devised for a specific problem to be solved. The Pyre framework, developed at the California Institute of Technology (Caltech), and now being used as the basis for next-generation radar processing at JPL, is a Python-based software framework. We have extended the Pyre framework to include new facilities to deploy processing components as services, including components that monitor and assess the state of the distributed network for eventual real-time control of grid resources.

synthetic aperture radar (SAR)↗
NASA NTRS2018

Airframe Noise Simulations of a Full-Scale Aircraft

Computational results for a full-scale simulation of a Gulfstream G-III aircraft are presented. In support of a NASA airframe noise flight test campaign, Exa Corporation’s lattice Boltzmann PowerFLOW® solver was used to perform time-accurate simulations of the flow around a highly detailed, full-scale aircraft model. Free-air boundary conditions were used at a Mach number of 0.23 and a Reynolds number of 10.5 × 10(exp 6) based on mean aerodynamic chord. This paper documents the simulation campaign for the baseline aircraft configuration at several flight conditions, including multiple flap deflections and main landing gear deployed or retracted. The high-fidelity, synthetic data were post-processed using a Ffowcs-Williams and Hawkings integral approach to estimate farfield acoustic behavior, with pressures on the model solid surface or a permeable surface enveloping the acoustic near field used as input. The numerical approach, simulation attributes, and the effects of grid resolution, gear deployment, and multiple flap deflections, are discussed as well.

Appelbaum, Jason↗
NASA NTRS1992

Efficient geometric rectification techniques for spectral analysis algorithm

The spectral analysis algorithm is a viable technique for processing synthetic aperture radar (SAR) data in near real time throughput rates by trading the image resolution. One major challenge of the spectral analysis algorithm is that the output image, often referred to as the range-Doppler image, is represented in the iso-range and iso-Doppler lines, a curved grid format. This phenomenon is known to be the fanshape effect. Therefore, resampling is required to convert the range-Doppler image into a rectangular grid format before the individual images can be overlaid together to form seamless multi-look strip imagery. An efficient algorithm for geometric rectification of the range-Doppler image is presented. The proposed algorithm, realized in two one-dimensional resampling steps, takes into consideration the fanshape phenomenon of the range-Doppler image as well as the high squint angle and updates of the cross-track and along-track Doppler parameters. No ground reference points are required.

Chang, C. Y.↗