A laboratory study of friction-velocity estimates from scatterometry: low and high regimes

Measurements from scatterometers pointing at wind-waves in three large wave-tanks are examined to study fetch effects and the correlation with wind friction-velocity u_?,. Time-series measurements were made at 13, 35 and 95 m with a K_a-band scatterometer aimed upwind at 30° incidence angle and vertical polarization. Average normalized radar cross-section σ_o values from all fetches follow a common trend for σ_o as a function of u_? so the fetch dependence is negligible. An empirical power-law model yields a high correlation between σ_? and u_?but because systematic anomalies arise, we re-examine a turbulence approach that delineates low and high regimes with a transition at u_? of approximately 25cms^-1. Using this criteria, the data are well represented by a two-section power-law relationship between σ_o and u_?.     

Cover photograph Image from GOES-E spacecraft

Azimuthally travelling ocean waves are seldom well imaged by microwave real aperture radar (RAR) operating with conventional HH or VV polarizations. Attenuation of image intensity modulation in the azimuthal direction implies that ocean wave spectra derived from such images also will not be accurate. Real aperture radar cross-section modulation by long ocean waves is normally attributed to two principal sources, tilt modulation and hydrodynamic modulation. In ocean radar images both of these modulation sources are significantly attenuated in the azimuthal direction. Therefore, complete two-dimensional k-space wave spectra derived from microwave data often are quite different than physical ocean spectra. This paper uses fully-polarimetric radar measurements of ocean backscatter to identify a new source of backscatter modulation that is strongest in the azimuthal direction. This modulation source has potential for augmenting tilt and hydrodynamic modulation sources in the azimuthal direction where their weakness causes poor wave visibility. The predicted improvement in the measurement of ocean wave spectra using an optimized polarization is investigated by means of a RAR ocean imaging model. Fully-polarimetric, and conventional, radar spectrometers are proposed which are specifically optimized to sense wave-tilts in the azimuthal direction.     

Evaluation of calibration methods for a helicopter-borne microwave scatterometer

The French frequency modulated continuous waves (FMCW) scatterometer ERASME mounted on small helicopter or aircraft has been designed as dualfrequency (C and X bands) and dualpolarization (HH, VV) to investigate simultaneously the vegetation and the soil responses in radar backscattering. It is operated as a forward looking radar with a large elevation beamwidth (± 10° at 3 db) to observe easily the same surface target over a large range of incidence angles during a single flight. By this ability, ERASME is a complementary research tool for intercalibration of airborne and spaceborne imaging Synthetic Aperture Radars like Radarsat and ASAR and has to be well calibrated in every configuration, both absolutely and relatively for comparisons at different incidence angles.

This paper evaluates different calibration methods to be applied to such an instrument. Absolute calibration within 1 dB is easily obtained by external calibration using metallic corner reflectors. But this method remains insufficient to get the antenna elevation aperture which is essential on natural distributed targets for antenna pattern correction, due to the severe constraint of a narrow azimuthal beam and flight parameters (pitch, roll, altitude) varying quickly in time and range.

The external calibration is strongly improved by using a statistical analysis of data obtained over natural targets which analyses the correlation between the processed data and the recorded flight parameters. This method appears promising, but its application on natural targets with random variations need specific statistical properties of the data set. It is operative for high antenna setting (here 38° incidence angle) and mostly over bare soils, with low of σ⁰ variances and σ² correlation length of the order of the correlation length of pitch. It provides the aperture range around the antenna axis and an accuracy of 0.5 dB upon erσ⁰ is achieved providing the antenna pattern correction are done.     

The validity of the composite surface model and its applications to the modulation of radar backscatter

Abstract

The composite surface model is compared with the Kirchoff method and shown to be equivalent for radar backscatter at moderate incidence angles in most commonly occurring sea states. Based on this comparison, limits are determined for the validity of the composite surface model. The model is then utilized to study the modulation of the radar cross-section of the ocean surface by long surface waves and internal waves. It is shown that apart from the well understood tilt modulation and the direct hydrodynamic modulation of the short waves, there is also an additional indirect modulation of the radar cross-section due to the hydrodynamic modulation of the intermediate waves by the long waves. Computer simulations are used to investigae these modulation mechanisms for different sea states, incidence angles and radar frequencies. It is shown that this modulation is strongest at small incidence angles and high radar frequencies. The simulations show that internal waves may be observed by X-band and Ka-band radars due to the indirect modulation through the intermediate waves. It is also shown that, contrary to previous predictions, the indirect modulation process results in modulation of radar backscatter by surface waves that travel normal to the radar look direction.     

Potential of ASAR/ENVISAT for the characterization of soil surface parameters over bare agricultural fields

The objective of this investigation is to analyze the sensitivity of ASAR (Advanced Synthetic Aperture Radar) data to soil surface parameters (surface roughness and soil moisture) over bare fields, at various polarizations (HH, HV, and VV) and incidence angles (20°-43°). The relationships between backscattering coefficients and soil parameters were examined by means of 16 ASAR images and several field campaigns. We have found that HH and HV polarizations are more sensitive than VV polarization to surface roughness. The results also show that the radar signal is more sensitive to surface roughness at high incidence angle (43°). However, the dynamics of the radar signal as a function of soil roughness are weak for root mean square (rms) surface heights between 0.5 cm and 3.56 cm (only 3 dB for HH polarization and 43° incidence angle). The estimation of soil moisture is optimal at low and medium incidence angles (20°-37°). The backscattering coefficient is more sensitive to volumetric soil moisture in HH polarization than in HV polarization. In fact, the results show that the depolarization ratio σ_HH⁰/σ_HV⁰ is weakly dependent on the roughness condition, whatever the radar incidence. On the other hand, we observe a linear relationship between the ratio σ_HH⁰/σ_HV⁰ and the soil moisture. The backscattering coefficient ratio between a low and a high incidence angle decreases with the rms surface height, and minimizes the effect of the soil moisture.     

A new relationship between radar cross-section and ocean surface wind speed using ERS-t scatterometer and buoy measurements

The ERS–I spacecraft scatterometer, C-band VV polarization, acquired radar cross-section measurements over the global oceans during 1992 and 1993. We investigate the cross-section dependence on mean wind speed U using collocated buoys within ±25km of the scatterometer cells. These collocated measurements result in over 75000 matches in two diITerent oceanic regions. The buoys measure hourly mean wind speeds from 0·2–10 mS ¹ and 0·2–18ms ^-1 in the equatorial Pacific Ocean and at mid^-latitudes off the North American coasts, respectively. We present experimental evidence for a new and compact exponential model dependence on wind speed. The previously used power–law form inadequately characterizes the cross-section measurements based on a single index over a large wind speed range. The cross-sectional slope varies from about zero dB/ms^-1 at high wind speeds U=18ms ^-1 and small incidence angles 0=20° to about 1·3dB/ms ^-1 at low wind speeds U=3ms ^-1 and large incidence angles, 0=55°. The CMOD4 model significantly underestimates the radar cross section measurements for U≤3ms ^-1 whereas the exponential model exhibits less bias.     

Development of polarization ratio model for sea surface wind field retrieval from TerraSAR-X HH polarization data

In this article, the polarization ratio (PR) of TerraSAR-X (TS-X) vertical–vertical (VV) and horizontal–horizontal (HH) polarization data acquired over the ocean is investigated. Similar to the PR of C-band synthetic aperture radar (SAR), the PR of X-band SAR data also shows significant dependence on incidence angle. The normalized radar cross-section (NRCS) in VV polarization data is generally larger than that in HH polarization for incidence angles above 23°. Based on the analysis, two PR models proposed for C-band SAR were retuned using TS-X dual-polarization data. A new PR model, called X-PR hereafter, is proposed as well to convert the NRCS of TS-X in HH polarization to that in VV polarization. By using the developed geophysical model functions of XMOD1 and XMOD2 and the tuned PR models, the sea surface field is retrieved from the TS-X data in HH polarization. The comparisons with in situ buoy measurements show that the combination of XMOD2 and X-PR models yields a good retrieval with a root mean square error (RMSE) of 2.03 m s^–1 and scatter index (SI) of 22.4%. A further comparison with a high-resolution analysis wind model in the North Sea is also presented, which shows better agreement with RMSE of 1.76 m s^–1 and SI of 20.3%. We also find that the difference between the fitting of the X-PR model and the PR derived from TS-X dual-polarization data is close to a constant. By adding the constant to the X-PR model, the accuracy of HH polarization sea surface wind speed is further improved with the bias reduced by 0.3 m s^–1. A case acquired at the offshore wind farm in the East China Sea further demonstrates that the improvement tends to be more effective for incidence angles above 40°.     

Sea surface wind speed and sea state retrievals from dual-frequency altimeter and its preliminary application in global view of wind-sea and swell distributions

Altimeter radar backscatter intensity, in terms of the normalized radar cross section (NRCS), is known to be modulated by surface wind forcing and the state of wind-sea development. Based on a data set of collocated altimeters (including Topex/Poseidon, Jason-1 and Jason-2) and in situ measurements, different responses to various wind speeds and wave ages (i.e. the state of wind-sea development) were illustrated for altimeter dual-frequency NRCSs (K_u-band at 13.6 Hz and C band at 5.4 Hz), which can facilitate the retrieval of wind speed and wave age parameters. A statistical parametric algorithm was developed to retrieve the two dynamic parameters from the altimeter dual-frequency NRCSs using the neutral network method. The wind-sea significant wave height (SWH) was estimated from wind speed and wave age parameters, which partitions the swell SWH from the altimeter SWH measurement. All newly derived parameters were well validated by comparison against in situ buoy measurements. A preliminary application of the method in examining the swell or wind-sea contributions to global waves was performed; it was found the swell dominance in an open ocean, and the wind-sea dominance in marginal and semi-enclosed seas. The methods would benefit other applications such as studies of air–sea interactions, validation of wave model, determination of swell decay rate and studies of wave climate.     

Demonstration of an improved calibration scheme for ERS-l SAR imagery using a scatterometer wind model

The importance of an improved calibration scheme for the derivation of the normalized radar cross-section coefficient σ° for distributed targets using ERS-l SAR imagery is assessed. The improved calibration scheme includes corrections relating to the saturation of the on-board Analogue to Digital Convertor (ADC) and to variations in the replica pulse power. The significance and effectiveness of the additional corrections is demonstrated by comparing the range variation of σ° from 10 ERS-l.SAR.PRI images of the English Channel with that predicted by the CMOD4 scatterometer wind model. Close agreement is found at all range positions, provided the additional corrections are applied.     

Monte-Carlo simulation studies of the nonlinear imaging of a two dimensional surface wave field by a synthetic aperture radar

Abstract

The imaging of ocean surface waves by synthetic aperture radar (SAR) is investigated using two-dimensional Monte-Carlo simulations. The properties of the SAR imaging mechanism for windseas and swell in the Bragg scattering regime are discussed as a function of a few governing non-dimensional parameters formed from a combination of SAR and ocean wave parameters. The parameter ranges may be classified into three regimes corresponding to linear and weakly nonlinear, medium nonlinear and strongly nonlinear imaging. The nonlinearities are induced by motion effects (velocity bunching, velocity spread and acceleration smearing), while the real aperture radar (RAR) tilt and hydrodynamic modulation processes are regarded as linear. In the strongly nonlinear imaging regime, the velocity bunching mechanism causes a rotation of the spectral peak towards the range direction and a stretching of the peak wavelength. In addition, the azimuthal resolution is degraded through the Doppler spreading arising from the different facet velocities within a SAR resolution cell. The imaging properties in this regime are largely governed by two non-dimensional parameters, the velocity bunching and velocity smearing parameter. The nonlinear imaging distortions are strongest for broad spectra (windseas) and are significantly weaker for narrow-band swell. In the linear and weakly nonlinear imaging regime, the superposition of the hydrodynamic and tilt cross-section modulation and the velocity bunching transfer function normally produces a rotation of the spectral peak towards the azimuthal direction. The interference characteristics of these different modulation mechanisms depends on the wave propagation direction and can lead to a significant distortion of the image. This is often seen in large differences in the image modulation depths of waves propagating parallel and anti-parallel to the flight direction.     

Radar imaging of Kelvin arms of ship wakes

The wave pattern generated by a moving ship is formed by two dominant features: the turbulent wake and a 'V'-shaped pattern trailing the ship, consisting of the two Kelvin arms. In this paper we investigate the radar imaging mechanism of Kelvin arms, which are formed by the cusp waves. A composite surface model for the radar backscattering at the ocean surface is used. The radar signatures of Kelvin arms can be attributed to tilt and hydrodynamic modulation of Bragg waves by the cusp waves. The proposed model allows the computation of the normalized radar backscattering cross-section (NRCS) as a function of radar frequency, polarization, incidence angle, wind speed and direction, and wavelength, direction, and slope of the cusp waves. By using this imaging model, radar signatures of cusp waves are calculated for several spaceborne Synthetic Aperture Radars (SARs): (1) the SEASAT L-band HH-polarized SAR, (2) the ERS-1/-2 VV-polarized SAR, (3) the RADARSAT C-band HH-polarized SAR, and (4) the X-, C- and L-band multipolarization SARs of the Space Radar Laboratory flown on the space shuttle during the SIRC/X-SAR mission in 1994. The results of the simulations are compared with SEASAT and SIR-C/X-SAR imagery of ship wake patterns. It is shown that the dependence of the observed radar signatures of Kelvin arms on radar look direction is consistent with the proposed imaging theory and that the measured relative mean NRCS values induced by Kelvin arms can be fairly well reproduced by the proposed model. The simulations indicate that ship wake signatures should be more clearly visible on SEASAT L-band SAR than on ERS-1/-2 or RADARSAT C-band SAR images. The radar signatures of Kelvin arms are strongest at low wind speeds and are not very sensitive to wind direction.     

Radar backscattering from breaking wind waves: field observation and modelling

In this article, the results of a field study of the Ka-band (37.5 GHz) radar backscattering from breaking wind waves are presented. Radar and a video camera were simultaneously used to measure the radar cross section (RCS) of the whitecap zone and the characteristics of wave-breaking events. A comparison is made between absolute geometrical lengths, areas and orientations of the whitecaps and the RCS of the whitecaps at moderate (45°) and high (70°) incidence angles. A thin vegetable oil film covering the illuminated area was made to minimize background Bragg backscattering from the surface free of breaking-wave features. At high incidence angles, a linear-like dependence between breaking crest length and RCS and no significant azimuthal dependence are found. At moderate angles of incidence, a prominent azimuthal variation of the whitecap's RCS is shown, while a linear-like relationship between the active breaking area and the whitecap's RCS is obtained in presence of the film on the sea surface. The results are compared to the model of quasi-specular reflection from the breaking waves. It is shown that accounting for backscattering from the droplets produced by the breaking crest improves prediction of the whitecap's RCS given by this model at high incidence angles.     

Application of tilt modulation of the scatter cross-sections to distinguish between different non-Gaussian rough surfaces: unified full wave approach

The tilt modulations of the like- and cross-polarized cross-sections for arbitrarily oriented resolution cells are determined using the unified full-wave approach. A broad family of non-Gaussian rough surfaces characterized by the gamma surface height probability density functions of order K are considered. Furthermore a Pearson-Moskowitz surface height spectral density function is assumed for the sea surface. The surface height autocorrelation function is also assumed to be non-Gaussian. An arbitrarily oriented mean plane associated with the resolution cell is characterized by tilt angles in and perpendicular to a fixed reference plane of incidence. The ‘tilt modulation’ of the scattering cross-sections is determined as functions of the wavelength of the incident field 𝛌₀ and the backscatter angle 0ⁱ ₀. Each resolution cell represents the real (or synthetic) radar footprint. The size of the resolution cell, orientation, and the statistical characteristics of the non-Gaussian surface determine the radar cross-section. Radar remote sensing options are discussed to distinguish between random rough surfaces characterized by different probability density functions.     

Correlation between soil apparent electroconductivity and plant hyperspectral reflectance in a managed wetland

The apparent electrical conductivity (σ_a) of soil is influenced by a complex combination of soil physical and chemical properties. For this reason, σ_a is proposed as an indicator of plant stress and potential community structure changes in an alkaline wetland setting. However, assessing soil σ_a is relatively laborious and difficult to accomplish over large wetland areas. This work examines the feasibility of using the hyperspectral reflectance of the vegetation canopy to characterize the σ_a of the underlying substrate in a study conducted in a Central California managed wetland. σ_a determined by electromagnetic (EM) inductance was tested for correlation with in-situ hyperspectral reflectance measurements, focusing on a key waterfowl forage species, swamp timothy (Crypsis schoenoides). Three typical hyperspectral indices, individual narrow-band reflectance, first-derivative reflectance and a narrow-band normalized difference spectral index (NDSI), were developed and related to soil σ_a using univariate regression models. The coefficient of determination (R ²) was used to determine optimal models for predicting σ_a, with the highest value of R ² at 2206 nm for the individual narrow bands (R ²?=?0.56), 462 nm for the first-derivative reflectance (R ²?=?0.59), and 1549 and 2205 nm for the narrow-band NDSI (R ²?=?0.57). The root mean squared error (RMSE) and relative root mean squared error (RRMSE) were computed using leave-one-out cross-validation (LOOCV) for accuracy assessment. The results demonstrate that the three indices tested are valid for estimating σ_a, with the first-derivative reflectance performing better (RMSE?=?30.3 mS m^?1, RRMSE?=?16.1%) than the individual narrow-band reflectance (RMSE?=?32.3 mS m^?1, RRMSE?=?17.1%) and the narrow-band NDSI (RMSE?=?31.5 mS m^?1, RRMSE?=?16.7%). The results presented in this paper demonstrate the feasibility of linking plant–soil σ_a interactions using hyperspectral indices based on in-situ spectral measurements.     

An analysis of scatterometer returns from a water surface agitated by artificial rain: evidence that ring-waves are the main feature

Abstract

Both wind and rain roughen the sea surface, but whereas wind generates waves, rain generates craters, stalks and ring-waves. Average backscat-tered power for scatterometer returns From water surfaces is closely related to small scale features on the water surface, so we use backscattered power from short wind-waves as a basis to evaluate the importance of ring-waves. Experiments were conducted with a 13-5 GHz scatterometer (30° incidence angle, vertical polarization) in a wind-wave tank that is enhanced by a rain simulator. Rain intensities ranged from 3-30 mm h^?1 and wind friction velocities were between 10 and 50cms^?1. The variance of surface elevation for small scale features ξ² _smi.e., ring-waves and short wind-waves, was computed for each case using data from a capacitance probe. Comparison of the data sets shows that the range of ξ² _sm for the rain cases is comparable to that from light to moderate wind cases—so ring-wave amplitudes are not negligible. Analysis of the radar data provides evidence that ring-waves are the dominant feature contributing to the backscattered power. Thus ring-waves need to be included in scatterometer numerical models that contain rain effects.     

Multi‐frequency scatterometer measurements on water surfaces agitated by artificial and natural rain

Images of rain events over the ocean acquired by a multi‐frequency/multi‐polarization Synthetic Aperture Radar (SAR) show different radar contrasts at different frequencies and polarizations. In order to better understand these effects, field and laboratory experiments were performed at different rain rates and wind speeds with scatterometers working at different radar frequencies, polarizations, and incidence angles. Our results show that the dominant scattering mechanism on a rain‐roughened water surface, observed at VV polarization, at all incidence angles is Bragg scattering from ring waves. At HH polarization the radar backscatter is caused by both ring waves and non‐propagating splash products, with the dominating effect depending on incidence angle. The reduction and enhancement of the surface roughness by ring waves and sub‐surface phenomena, respectively, result in a transition wavenumber between reduction of the radar backscattering and its enhancement of about 100 rad m^?1. We assume that this transition wavenumber depends on the drop‐size distribution of the rain. Taking into consideration the different dependencies of the radar backscatter at different frequencies and polarizations on rain rate, we suggest a method to estimate rain rates by calculating the ratio of the radar cross‐sections at L band, VV polarization and at C band, HV polarization. Provided an availability of SAR data at the respective frequency–polarization combinations, this method allows for investigating the nature of small‐scale (convective) rain events over the ocean.     

Geometric Properties of the Fractured Tibia Stabilized by Unreamed Interlocking Nail: Development of a Three-Dimensional Finite Element Model

Based upon magnetic resonance scans of five human tibiae a three-dimensional finite element model using eight nodal isoparametric elements was developed to analyze the biomechanical properties of fracture fixation by an unreamed interlocking nail. Tension phenomena and bone implant translations occurring in the borderlines of the fracture zone, bone-implant interface, and the fixation site of the interlocking screws were analyzed with the help of link elements. The proximal fracture segment was fixed with a link element so as to produce exclusively translatory shifts corresponding to the vector of the load applied. Under condition of static loadF= 500 N or axial torsionM_T= 15 Nm the biomechanical properties of a nailed horizontal fracture (42-A3), a three fragment lesion (42-B2), and a comminuted midshaft fracture (42-C3) were evaluated. On condition of axial load maximum dislocations of 0.1549 mm are induced in the direction of the x-axis due to the asymmetric geometry of the human tibia which promotes medially directed translations. Independent from the fracture type present a homogenous tension profile was calculated for the whole tibia diaphysis with a σ_EQVranging from 24.18 to 121.14 MPa due to the relative low elastic modulus of the cortical bone compared to material characteristics of the implant. However, application of a torsional momentM_T= 15 Nm induces significantly increased tension maxima in the nail–interlocking screw interface with a σ_EQV= 7,626 MPa. Maximum translatory movementsu_x= 12.59 mm andu_y= 23.53 mm in the x and y plane indicate that these load conditions bear a high risk of an implant failure.     

A new empirical model to retrieve soil moisture and roughness from C-band radar data

A new empirical model for the retrieval, at a field scale, of the bare soil moisture content and the surface roughness characteristics from radar measurements is proposed. The derivation of the algorithm is based on the results of three experimental radar campaigns conducted under natural conditions over agricultural areas. Radar data were acquired by means of several C-band space borne (SIR-C, RADARSAT) or helicopter borne (ERASME) sensors, operating in different configurations of polarization (HH or VV) and incidence angle. Simultaneously to radar acquisitions, a complete ground truth data base was built up with different surface condition measurements of the mean standard deviation (rms) height s, the correlation length l, and the volumetric surface moisture M_v. This algorithm is more specifically developed using the radar cross-section σ⁰ (HH polarization and 39° incidence angle off nadir), namely, σ_0HH,39, and the differential (HH polarization) radar cross-section Δσ₀=σ_0,23°−σ_0,39° in terms of an original roughness parameter, Z_s, namely Z_s=s²/l, and M_v. A good agreement is observed between model outputs and backscattering measurements over different test fields. Eventually, an inversion technique is proposed to retrieve Z_s and M_v from radar measurements.     

Comparison of ERS-2 SAR and Landsat TM imagery for monitoring agricultural crop and soil conditions

Studies over the past 25 years have shown that measurements of surface reflectance and temperature (termed optical remote sensing) are useful for monitoring crop and soil conditions. Far less attention has been given to the use of radar imagery, even though synthetic aperture radar (SAR) systems have the advantages of cloud penetration, all-weather coverage, high spatial resolution, day/night acquisitions, and signal independence of the solar illumination angle. In this study, we obtained coincident optical and SAR images of an agricultural area to investigate the use of SAR imagery for farm management. The optical and SAR data were normalized to indices ranging from 0 to 1 based on the meteorological conditions and sun/sensor geometry for each date to allow temporal analysis. Using optical images to interpret the response of SAR backscatter (σ^o) to soil and plant conditions, we found that SAR σ^o was sensitive to variations in field tillage, surface soil moisture, vegetation density, and plant litter. In an investigation of the relation between SAR σ^o and soil surface roughness, the optical data were used for two purposes: (1) to filter the SAR images to eliminate fields with substantial vegetation cover and/or high surface soil moisture conditions, and (2) to evaluate the results of the investigation. For dry, bare soil fields, there was a significant correlation (r²=.67) between normalized SAR σ^o and near-infrared (NIR) reflectance, due to the sensitivity of both measurements to surface roughness. Recognizing the limitations of optical remote sensing data due to cloud interference and atmospheric attenuation, the findings of this study encourage further studies of SAR imagery for crop and soil assessment.