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Correction of WindScat Scatterometric Measurements by Combining with AMSR Radiometric Data

The Seawinds scatterometer on the advanced Earth observing satellite-2 (ADEOS-2) will determine surface wind vectors by measuring the radar cross section. Multiple measurements will be made at different points in a wind-vector cell. When dense clouds and rain are present, the signal will be attenuated, thereby giving erroneous results for the wind. This report describes algorithms to use with the advanced mechanically scanned radiometer (AMSR) scanning radiometer on ADEOS-2 to correct for the attenuation. One can determine attenuation from a radiometer measurement based on the excess brightness temperature measured. This is the difference between the total measured brightness temperature and the contribution from surface emission. A major problem that the algorithm must address is determining the surface contribution. Two basic approaches were developed for this, one using the scattering coefficient measured along with the brightness temperature, and the other using the brightness temperature alone. For both methods, best results will occur if the wind from the preceding wind-vector cell can be used as an input to the algorithm. In the method based on the scattering coefficient, we need the wind direction from the preceding cell. In the method using brightness temperature alone, we need the wind speed from the preceding cell. If neither is available, the algorithm can work, but the corrections will be less accurate. Both correction methods require iterative solutions. Simulations show that the algorithms make significant improvements in the measured scattering coefficient and thus is the retrieved wind vector. For stratiform rains, the errors without correction can be quite large, so the correction makes a major improvement. For systems of separated convective cells, the initial error is smaller and the correction, although about the same percentage, has a smaller effect.

Song, S.↗

Application of AWE for RCS Frequency Response Calculations Using Method of Moments

An implementation of the Asymptotic Waveform Evaluation (AWE) technique is presented for obtaining the frequency response of the Radar Cross Section (RCS) of arbitrarily shaped, three-dimensional perfect electric conductor (PEC) bodies. An Electric Field Integral Equation (EFIE) is solved using the Method of Moments (MoM) to compute the RCS. The electric current, thus obtained, is expanded in a Taylor series around the frequency of interest. The coefficients of the Taylor series (called 'moments') are obtained using the frequency derivatives of the EFIE. Using the moments, the electric current on the PEC body is obtained over a frequency band. Using the electric current at different frequencies, RCS of the PEC body is obtained over a wide frequency band. Numerical results for a square plate, a cube, and a sphere are presented over a bandwidth. A good agreement between AWE and the exact solution over the bandwidth is observed.

Reddy, C. J.↗

Asymptotic Waveform Evaluation (AWE) Technique for Frequency Domain Electromagnetic Analysis

The Asymptotic Waveform Evaluation (AWE) technique is applied to a generalized frequency domain electromagnetic problem. Most of the frequency domain techniques in computational electromagnetics result in a matrix equation, which is solved at a single frequency. In the AWE technique, the Taylor series expansion around that frequency is applied to the matrix equation. The coefficients of the Taylor's series are obtained in terms of the frequency derivatives of the matrices evaluated at the expansion frequency. The coefficients hence obtained will be used to predict the frequency response of the system over a frequency range. The detailed derivation of the coefficients (called 'moments') is given along with an illustration for electric field integral equation (or Method of Moments) technique. The radar cross section (RCS) frequency response of a square plate is presented using the AWE technique and is compared with the exact solution at various frequencies.

Cockrell, C. R.↗

Exploratory Investigation of Forebody Strakes for Yaw Control of a Generic Fighter with a Symmetric 60 deg Half-Angle Chine Forebody

Forebody strakes were tested in a low-speed wind tunnel to determine their effectiveness producing yaw control on a generic fighter model with a symmetric 60 deg half-angle chine forebody. Previous studies conducted using smooth, conventionally shaped forebodies show that forebody strakes provide increased levels of yaw control at angles of attack where conventional rudders are ineffective. The chine forebody shape was chosen for this study because chine forebodies can be designed with lower radar cross section (RCS) values than smooth forebody shapes. Because the chine edges of the forebody would fix the point of flow separation, it was unknown if any effectiveness achieved could be modulated as was successfully done on the smooth forebody shapes. The results show that use of forebody strakes on a chine forebody produce high levels of yaw control, and when combined with the rudder effectiveness, significant yaw control is available for a large range of angles of attack. The strake effectiveness was very dependent on radial location. Very small strakes placed at the tip of the forebody were nearly as effective as very long strakes. An axial translation scheme provided almost linear increments of control effectiveness.

Ross, Holly M.↗

A Least-Squares Finite Element Method for Electromagnetic Scattering Problems

The least-squares finite element method (LSFEM) is applied to electromagnetic scattering and radar cross section (RCS) calculations. In contrast to most existing numerical approaches, in which divergence-free constraints are omitted, the LSFF-M directly incorporates two divergence equations in the discretization process. The importance of including the divergence equations is demonstrated by showing that otherwise spurious solutions with large divergence occur near the scatterers. The LSFEM is based on unstructured grids and possesses full flexibility in handling complex geometry and local refinement Moreover, the LSFEM does not require any special handling, such as upwinding, staggered grids, artificial dissipation, flux-differencing, etc. Implicit time discretization is used and the scheme is unconditionally stable. By using a matrix-free iterative method, the computational cost and memory requirement for the present scheme is competitive with other approaches. The accuracy of the LSFEM is verified by several benchmark test problems.

Wu, Jie↗

Application of AWE Along with a Combined FEM/MoM Technique to Compute RCS of a Cavity-Backed Aperture in an Infinite Ground Plane Over a Frequency Range

A hybrid Finite Element Method (FEM)/Method of Moments (MoM) technique in conjunction with the Asymptotic Waveform Evaluation (AWE) technique is applied to obtain radar cross section (RCS) of a cavity-backed aperture in an infinite ground plane over a frequency range. The hybrid FEM/MoM technique when applied to the cavity-backed aperture results in an integro-differential equation with electric field as the unknown variable, the electric field obtained from the solution of the integro-differential equation is expanded in Taylor series. The coefficients of the Taylor series are obtained using the frequency derivatives of the integro-differential equation formed by the hybrid FEM/MoM technique. The series is then matched via the Pade approximation to a rational polynomial, which can be used to extrapolate the electric field over a frequency range. The RCS of the cavity-backed aperture is calculated using the electric field at different frequencies. Numerical results for a rectangular cavity, a circular cavity, and a material filled cavity are presented over a frequency range. Good agreement between AWE and the exact solution over the frequency range is obtained.

Reddy, C.J.↗

Application of Model Based Parameter Estimation for RCS Frequency Response Calculations Using Method of Moments

An implementation of the Model Based Parameter Estimation (MBPE) technique is presented for obtaining the frequency response of the Radar Cross Section (RCS) of arbitrarily shaped, three-dimensional perfect electric conductor (PEC) bodies. An Electric Field Integral Equation (EFTE) is solved using the Method of Moments (MoM) to compute the RCS. The electric current is expanded in a rational function and the coefficients of the rational function are obtained using the frequency derivatives of the EFIE. Using the rational function, the electric current on the PEC body is obtained over a frequency band. Using the electric current at different frequencies, RCS of the PEC body is obtained over a wide frequency band. Numerical results for a square plate, a cube, and a sphere are presented over a bandwidth. Good agreement between MBPE and the exact solution over the bandwidth is observed.

Reddy, C. J.↗

Radar Observations of Asteroid 1620 Geographos

Goldstone radar observations of Geographos from August 28 through September 2, 1994 yield over 400 delay-Doppler images whose linear spatial resolutions range from approx. 75 to approx. 151 in, and 138 pairs of dual-polarization (OC, SC) spectra with one-dimensional resolution of 103 m. Each data type provides thorough rotational coverage. The images contain an intrinsic north/south ambiguity, but the equatorial view allows accurate determination of the shape of the radar-facing part of the asteroid's pole-on silhouette at any rotation phase. Sums of co-registered images that cover nearly a full rotation have defined the extremely elongated shape of that silhouette. Here we present individual images and co-registered sums over approx. 30 deg of rotation phase that show the silhouette's structural characteristics in finer detail and also reveal numerous contrast features "inside" the silhouette. Those features include several candidate craters as well as indications of other sorts of large-scale topographic relief, including a prominent central indentation. Protuberances at the asteroid's ends may be related to the pattern of ejecta removal and deposition caused by the asteroid's gravity field. The asteroid's surface is homogeneous and displays only modest roughness at centimeter-to-meter scales. Our estimates of radar cross section and the currently available constraints on the asteroid's dimensions are consistent with a near-surface bulk density between 2 and 3 g/cu cm. The delay-Doppler trajectory of Geographos' center of mass has been determined to about 200 m on August 28 and to about 100 m on August 31, an improvement of two orders of magnitude over pre-observation ephemerides.

Ostro, Steven J.↗

RADARSAT Underflights: Comparison of C-band VV and HH Backscatter-Wind Retrieval

The primary objective of this grant was to validate the modified CMOD4 wind speed algorithm used to invert RADARSAT data. We proposed to do the following: TASK 1: Participate in at least two underflights of RADARSAT (collecting backscatter measurements with the UMASS C-band and Ku-band scatterometers, CSCAT and KUSCAT. TASK 2: Process data gathered with CSCAT and KUSCAT into one kilometer along-track pixels with each pixel consisting of seventy-two five degree azimuth bins - each bin containing normalized radar cross section (NRCS) values for that particular azimuth angle and for each of the four incidence angles viewed by CSCAT and KUSCAT. Derive wind speed and direction estimates from each NRCS along-track pixel using CMOD4 and NSCAT models. TASK 3: Compare collocated CSCAT vertically polarized (VV) and RADARSAT horizontally polarized (HH) NRCS data and wind estimates, and based on the comparison, evaluate the performance of the modified CMOD4 wind speed algorithm to invert RADARSAT NRCS measurements. The first two tasks were completed. The third task is still on-going since the RADARSAT data for the underflights has not been released to the University of Massachusetts. We expect that the RADARSAT data will become available in the next few months, and we will complete the third task in a promptly manner once the data has been received. Below the missions flown and the data collected are summarized. Two missions, based out of the NASA Wallops Flight Facility, were flown. The first flight was on 21 September 1997 and the second on 24 September 1997. The time for each mission was approximately 2 hours. Figure 1 plots the flight tracks and marks the location of the NOAA buoys that were in the vicinity.

Source record↗

Flux of Millimetric Space Debris

In 21.4 hr of zenith radar observations on 4 days at 8510 MHz, we found 831 particles with altitudes between 177 and 1662 km. From the duration of the echoes and the angular size (0.030 deg) of the antenna beam 157 particles were identified as passing through the side lobes and not through the main beam. Our analysis is based on the 674 particles that did not broaden the beam. On the assumptions that these particles went through the main beam, their radar cross sections vary between 0.02 and 260 sq mm , and their radial velocities vary between +/- 700 m/s. If they are conducting spheres, their diameters lie between 2 and 18 mm. If not, they must be larger. The flux of these particles, that is the number per sq km day, was determined in 100 km intervals. The maximum flux, 3.3 particles per sq km day, occurs at 950 km altitude. The small and large particles are not well mixed. The largest particles occur beyond 1000 km and middle-sized particles are missing below 300 km. If the earth's atmosphere caused the smallest particles to lose energy from initial orbits identical to those of the large particles, the orbits would have lower eccentricity at low altitudes. We find a larger eccentricity for the inner particles, and conclude that two or more populations are present.

Goldstein, R. M.↗

Radar Observations of Asteroid 1620 Geographos

Goldstone radar observations of Geographos from August 28 through September 2, 1994 yield over 400 delay-Doppler images whose linear spatial resolutions range from approximately 75 - 151 m, and 138 pairs of dual-polarization (OC, SC) spectra with one-dimensional resolution of 103 m. Each data type provides thorough rotational coverage. The images contain an intrinsic north/south ambiguity, but the equatorial view allows accurate determination of the shape of the radar-facing part of the asteroid's pole-on silhouette at any rotation phase. Sums of co-registered images that cover nearly a full rotation have defined the extremely elongated shape of that silhouette (S. J. Ostro, K. D. Rosema, R. S. Hudson, R. F. Jurgens, J. D. Giorgini, R. Winkler, D. K. Yeomans, D. Choate, R. Rose, M. A. Slade, S. D. Howard, and D. L. Mitchell 1995, Nature 375, 474-477). Here we present individual images and co-registered sums over approximately 30 deg of rotation phase that show the silhouette's structural characteristics in finer detail and also reveal numerous contrast features "inside" the silhouette. Those features include several candidate craters as well as indications of other sorts of large-scale topographic relief, including a prominent central indentation. Protuberances at the asteroid's ends may be related to the pattern of ejecta removal and deposition caused by the asteroid's gravity field. The asteroid's surface is homogeneous and displays only modest roughness at centimeter-to-meter scales. Our estimates of radar cross section and the currently available constraints on the asteroid's dimensions are consistent with a near-surface bulk density between 2 and 3 g/cc. The delay-Doppler trajectory of Geographos' center of mass has been determined to about 200 m on August 28 and to about 100 m on August 31, an improvement of two orders of magnitude over pre-observation ephemerides.

Ostro, Steven J.↗

A Summary of Scatterometer Returns from Water Surfaces Agitated by Rain

In this paper, we summarize our initial findings from K(a)- and K(u)-band scatterometers which include: a scaling law for backscattered power as a function of rain rate; a linear superposition model for light rains and low wind speeds; evidence of the importance of scattering from rain-generated ring-waves; and progress towards development of a scattering model for computing normalized radar cross sections from wind and rain roughened water surfaces.

Bliven, Larry F.↗

Friction Velocity Estimation Using Dual-Frequency Altimeter Data

Global estimation of wind speeds near the sea-surface can be obtained using normalized radar cross sections sigma(o) from satellite-borne single-frequency altimeters. Indeed recent validation studies of Geosat altimeter-derived wind speeds show that several often cited semiempirical algorithms yield linear trends between wind-speeds from altimeter data and wind speeds from (a) ships of opportunity (Etcheto 1992), (b) buoys (Carter 1992), and (c) atmospheric models (Guillaume 1992). Although the linear trends are striking, there is considerable scatter since the range of standard deviations is from 1.5 to 3 m/s. In fact, the scatter of some particular measurements about the regressions is striking because they depart from the 'standard' by as much as +/- 5 m/s, which is large - even for full gale winds of 20 m/s. These anomalies can cause serious problems for gas exchange, heat, and aerosol estimates. They can also induce considerable errors in wind-driven oceanic circulation models and sea-surface wave models. This paper explores the possibility of improving the accuracy of wind speed estimation using dual-frequency altimeters.

Bliven, Larry F.↗

Altimeter Estimation of Sea Surface Wind Stress for Light to Moderate Winds

Aircraft altimeter and in situ measurements are used to examine relationships between altimeter backscatter and the magnitude of near-surface wind and friction velocities. Comparison of altimeter radar cross section with wind speed is made through the modified Chelton-Wentz algorithm. Improved agreement is found after correcting 10-m winds for both surface current and atmospheric stability. An altimeter friction velocity algorithm is derived based on the wind speed model and an open-ocean drag coefficient. Close agreement between altimeter- and in situ-derived friction velocities is found. For this dataset, quality of the altimeter inversion to surface friction velocity is comparable to that for adjusted winds and clearly better than the inversion to true 10-m wind speed.

Vandemark, Douglas↗

Methods of Attenuation Correction for the TRMM Precipitation Radar Data

The surface reference technique (SRT) has been studied extensively both theoretically and experimentally over the last decade. It is only with the launch of the Tropical Rain Measuring Mission (TRMM) Precipitation Radar, however, that we can begin to test directly whether the technique provides a reliable means of attenuation correction for spaceborne weather radars. Preliminary results indicate that the method yields results that are qualitatively reasonable when the rain rate is moderate or high and when the surface provides a stable reference value. The structure of the normalized radar cross section of the surface (NRCS), however, is highly complex in the sense that the statistics change with background type, incidence angle, location, and season. As a consequence of this, the reliability of the path attenuation estimate is not proportional simply to the amount of rain attenuation but to the rain attenuation relative to the inherent variability of the reference target. To illustrate the behavior of the SRT, several overpasses of the Hurricane Bonnie are shown. We also show that the proper choice of reference data set (spatial, temporal and global) can be critical to the success of the method.

Meneghini, Robert↗

Measuring Directional Wave Spectra and Wind Speed with a Scanning Radar Altimeter

The geometry for the NASA Scanning Radar Altimeter (SRA) is shown. It transmits a 8-ns duration pulse at Ka-band (8.3 mm) and measures time of flight as it scans a 1 degree (two-way) beam from left to right across the aircraft ground track. The most recent configuration determines the surface elevation at 64 points spaced at uniform angular intervals of about 0.7 across a swath whose width is about 0.8 times the aircraft altitude. The system generates these raster lines of the surface topography beneath the aircraft at about a 10 Hz rate. In postflight processing the SRA wave topographic data are transformed with a two-dimensional Fast Fourier Transformation (FFT) and Doppler corrected to produce directional wave spectra. The SRA is not absolutely calibrated in power, but by measuring the relative fall-off of backscatter with increasing incidence angle, the SRA can also determine the mean square slope (mss) of the sea surface, a surrogate for wind speed. For the slope-dependent specular point model of radar sea surface scattering, an expression approximated by a geometric optics form, for the relative variation with incidence angle of the normalized backscatter radar cross section would be sigma (sup 0) (sub rel) = sec (exp 4) theta exp (-tan squared theta/mss) where theta is the off-nadir incidence angle.

Walsh, E. J.↗

The Monostatic/Bistatic Approximation

Many Radar Cross Section (RCS) prediction codes are limited to one monostatic return per run. However, such codes can calculate multiple bistatic returns per incident angle for a relatively small amount of additional computer resources. This note describes a method of using bistatic returns to generate multiple monostatic predictions for each incident angle computed. Typical results are presented and show the accuracy is initially good and then degrades as the separation angle between the incident and viewing angles becomes large. Introduction Since 1990, the monostatic/bistatic approximation has been used to reduce the number of runs required by finite-volume time-domain (FVTD) codes for making RCS versus azimuth plots. This approximation was spawned by the observation of a range test where the transmit and receive antennas were separated by a few degrees to prevent cross talk between the antennas. The measurements from this range are presented as monostatic RCS rather than bistatic: RCS. The procedure of reporting experimental bistatic RCS as the monostatic RCS at the angle bisecting the transmit and receive antennas was extended to FVTD codes and produces excellent results.

Schuh, Michael J.↗

Investigation of High-alpha Lateral-directional Control Power Requirements for High-performance Aircraft

Designers of the next-generation fighter and attack airplanes are faced with the requirements of good high-angle-of-attack maneuverability as well as efficient high speed cruise capability with low radar cross section (RCS) characteristics. As a result, they are challenged with the task of making critical design trades to achieve the desired levels of maneuverability and performance. This task has highlighted the need for comprehensive, flight-validated lateral-directional control power design guidelines for high angles of attack. A joint NASA/U.S. Navy study has been initiated to address this need and to investigate the complex flight dynamics characteristics and controls requirements for high-angle-of-attack lateral-directional maneuvering. A multi-year research program is underway which includes ground-based piloted simulation and flight validation. This paper will give a status update of this program that will include a program overview, description of test methodology and preliminary results.

Foster, John V.↗