Root Mean Square Height Research Articles

An evaluation of wave propagation simulations over a barred beach with a Boussinesq-type model

The FUNWAVE model is used for simulating simulation of monochromatic and irregular wave propagation in a channel with a bar-trough profile. FUNWAVE is based upon the extended Boussinesq equations. The study aims to analyze the model's performance when simulating shoaling, wave breaking and nonlinear interactions that are present in nearshore wave propagation. For that, high-order time domain statistics (root mean-square wave height, skewness, asymmetry and the kurtosis) of the model simulations and of the observations were compared along the whole channel. Also, a frequency domain analysis including standard spectral analysis and the bispectrum was carried out in selected points of the flume. The evaluation included the role of the wave breaking internal model parameters. The main conclusion is that, in general, the one-dimensional version of FUNWAVE simulates quite well the nonlinear transformation of a wave over a bottom with a bar-tough profile, for both regular and irregular wave conditions. The model reproduces the transformation of the wave shape, specially the increasing sharper wave crests and flatter troughs and also the lack of vertical symmetry with crests pitching forward, as it propagates along the domain. However, some differences persist after wave breaking, mainly due to the nature of the wave-breaking module. In this module, the energy dissipation is induced by the increase of viscosity, a rather simple mechanism, without the modification of the wave shape. Also, the energy dissipation develops in a smooth way which is appropriated for spilling breaking waves, but not for plunging breaking waves where the dissipation starts more abruptly.

HIGH RESOLUTION RANGE PROFILE IDENTIFYING SIMULATION OF LASER RADAR BASED ON PULSE BEAM SCATTERING CHARACTERISTICS OF TARGETS

This is a presentation of an innovative technique of rigid body estimation for use with laser high-range resolution profile (LHRRP) simulations. The theory of pulse beam scattering from random rough surface is used to build a theoretical model which computes simulations for the laser pulse HRRP of the whole dimension target. As two especial cases, the LHRRP of sphere and cone are simulated in detail. We discuss and analyze some influential factors on laser radar HRRP imaging such as their dimensions, correlation length and height root mean square of the rough surface, refractive index of the material and width pulse. The simulated results suggest that the Corresponding author: M.-J. Wang (wmjxd@yahoo.com.cn).

INVESTIGATION ON THE SCATTERING CHARACTERISTICS OF GAUSSIAN BEAM FROM TWO DIMENSIONAL DIELECTRIC ROUGH SURFACES BASED ON THE KIRCHHOFF APPROXIMATION

The scattering characteristic of paraxial gaussian beam from two dimensional dielectric rough surfaces is studied in this paper. The modification of the Kirchhoff approximation theory for rough surface scattering by an incident gaussian beam instead of a plane wave are developed based on conventional Kirchhoff scattering theory and plane wave spectrum expansion method. The coherent and incoherent scattered intensity and cross section of two dimensional dielectric rough surfaces is derived in detail. As a application, under incidence wave length λ =1 .06 µm, we calculate the coherent and incoherent scattered intensity and cross section of Gaussian beam scattering from plating aluminium dielectric rough surfaces change with the scattering zenith angles in different rough surface correlation length, rough surface height root mean square and other conditions. In the same scattering conditions, we compare the coherent and incoherent scattered section between the gaussian beam and plane wave to prove that our methods and programming cods is correct. The numerical results are shown

Roughness Measurements of Soil Surfaces by Acoustic Backscatter

The measurement of the roughness of soil surfaces on centimeter scales is important to modeling local soil erodibility. An acoustic backscatter technique was examined for its ability to quantify the roughness of porous soil on centimeter scales. Acoustic backscatter offers the possibility of an inexpensive, mobile, and rapid means of estimating statistical properties of soil surfaces. Four soil plots were constructed with varying amounts of roughness. Surface roughness of the four soil plots was measured with the acoustic backscatter technique and a laser microreliefmeter. The roughness power spectra for the surface plots were obtained from surface profiles measured by the laser microreliefmeter and by the acoustic backscatter technique. Statistical values of the RMS (root mean square) height and correlation length of surface roughness for each plot were calculated from the acoustic backscatter power spectra and laser microreliefmeter power spectra and compared. Agreement between the two techniques for estimating roughness statistics was shown to be good (<13% difference) when an adequate amount of data points were used to map out the roughness power spectra. The acoustic backscatter technique appears to be a potential alternative to rapidly and inexpensively quantify the roughness of soil surfaces.

Wavelet-based simulations of electromagnetic scattering from large-scale two-dimensional perfectly conducting random rough surfaces

Simulations of electromagnetic waves scattering from two-dimensional perfectly conducting random rough surfaces are performed using the method of moment (MoM) and the electric field integral equation (EFIE). Using wavelets as basis and testing functions, the resulting moment matrix is generally sparse after applying a threshold truncation. This property makes wavelets particularly useful in simulating large-scale problems, in which reducing memory storage requirement and CPU time are crucial. In this paper, scattering from Gaussian conducting rough surfaces of a few hundred square wavelengths are studied numerically using Haar wavelets. A matrix sparsity less than 10% is achieved for a range of root mean square (RMS) height at eight sampling points per linear wavelength. Parallelization of the code is also performed. Simulation results of the bistatic scattering coefficients are presented for different surface RMS heights up to 1 wavelength. Comparisons with sparse-matrix/canonical-grid approach (SM/CG) and triangular discretized (RWG basis) results are made as well. Depolarization effects are examined for both TE and TM incident waves. The relative merits of the SM/CG method and the present method are discussed.

Application of time delay spectrometry for rough surface characterization

This paper describes the design and performance of an ultrasound measurement system, utilizing a swept frequency excitation signal, for analyzing the backscattered signal from planar rough surfaces. The implementation is in the form of a time delay spectrometry (TDS) system operating in reflection mode whose advantages are improved signal-to-noise ratio even with low peak power relative to conventional pulse-echo methods. Because of simultaneous transmission and reception, the TDS system requires two transducers. The TDS measurement system uses a swept frequency spectrum analyzer as the central analog processing unit. Both planar piston and focused transducers in the low MHz range were used for the measurements. Due to the statistical nature of rough surface backscatter, the mean of several statistically uncorrelated measurements is required to characterize the scattering behavior of a given rough surface. Backscatter data are obtained for a series of planar rough surfaces, in the form of scattering magnitude vs. frequency and vs. incident (=backscattered) angle. Analysis of the results reveals a good correlation between the root-mean-square (RMS) height and mean backscatter magnitude at 0° incident angle, and between the ratio of RMS height to correlation length and the difference in mean backscatter magnitude between 0° and 5°.

Errors in bathymetric retrievals using linear dispersion in 3-D FFT analysis of marine radar ocean wave imagery

The phenomenon of ocean wave-shoaling, and the associated reduction of ocean wave phase speed with decreased water depth, provides useful information for inferring water depth D (bathymetry) in coastal environments. One strategy for relating D to phase speed C and wave-vector K of long wavelength ocean waves involves using the one-dimensional (1-D) linear (gravity wave) dispersion relationship C/sup 2/=g*tanh(KD)/K. In principle, this approach has limitations because the approach is based on a WKB approximation, so it cannot be applied when D varies appreciably over the wavelength of a shoaling wave. Also, the approach is restricted to waves that have small wave height. The author uses a set of marine radar image sequences and applies this linear approximation, using a 3-D FFT analysis of 88 sets of image sequences spaced half an hour apart. The author inverts the dispersion relation to solve for D. Depths between 3.6 and 5.8 m were tested, for root mean square (RMS) wave heights offshore between 8 and 3 m. The author shows that for low to moderate wave heights, the approach does generally retrieve the correct depth in water depths of 5 m and greater for moderate wave RMS heights. However, an increase in the RMS wave height from 1 m to 3.5 m produced a much poorer depth estimate, proving the need for an application of a nonlinear wave model to the problem. The errors also increase with shallower depths as expected, as the error dependence on depth and wave height is determined.

On the characterization of agricultural soil roughness for radar remote sensing studies

The surface roughness parameters commonly used as inputs to electromagnetic surface scattering models (SPM, PO, GO, and IEM) are the root mean square (RMS) height s, and autocorrelation length l. However, soil moisture retrieval studies based on these models have yielded inconsistent results, not so much because of the failure of the models themselves, but because of the complexity of natural surfaces and the difficulty in estimating appropriate input roughness parameters. In this paper, the authors address the issue of soil roughness characterization in the case of agricultural fields having different tillage (roughness) states by making use of an extensive multisite database of surface profiles collected using a novel laser profiler capable of recording profiles up to 25 m long. Using this dataset, the range of RMS height and correlation values associated with each agricultural roughness state is estimated, and the dependence of these estimates on profile length is investigated. The results show that at spatial scales equivalent to those of the SAR resolution cell, agricultural surface roughness characteristics are well described by the superposition of a single scale process related to the tillage state with a multiscale random fractal process related to field topography.

Sommerfeld and Zenneck wave propagation for a finitely conducting one-dimensional rough surface

Starting with Zenneck and Sommerfeld wave propagation over a flat finitely conducting surface has been extensively studied by Wait (see IEEE Antennas Propagat. Mag., vol.40, p.7-24, 1998) and many other authors. We examine propagation over a finitely conducting rough surface, also studied by many people including Feinberg (1944), Bass and Fuks (1979), and Barrick (see Radio Sci., vol.6, p.517-26, and vol.6., p.527-33). This paper extends the multiple scattering theories based on Dyson and Bethe-Salpeter equations and their smoothing approximations. The theory developed here applies to rough surfaces with small root-mean-square (RMS) heights (/spl sigma/<0.1/spl lambda/). We limit ourselves to the one-dimensional (1-D) rough surface with finite conductivity excited by a magnetic line source, which is equivalent to the Sommerfeld dipole problem in two dimensions (x-z plane). With the presence of finite roughness, the total field decomposes into the coherent field and the incoherent field. The coherent (average) field is obtained by using Dyson's equation, a fundamental integral equation based on the modified perturbation method. Once the coherent field has been obtained, we determine the Sommerfeld pole, the effective surface impedance, and the Zenneck wave for rough surfaces of small RMS heights. The coherent field is written in terms of the Fourier transform, which is equivalent to the Sommerfeld integral. Numerical examples of the attenuation function are compared to Monte Carlo simulations and are shown to contrast the flat and rough surface cases. Next, we obtain the general expression for the incoherent mutual coherence functions and scattering cross section for rough conducting surfaces.

Characterisation of surface roughness by laser light scattering: diffusely scattered intensity measurement

This paper aims to describe a method which would allow us to gain some statistical information about a rough random surface, from the measurement of light diffusely scattered at this surface. At first, we give a short description of a theory which quantitatively relates surface roughness to incoherent intensities backscattered at this surface. The scattered light can be expressed as the product of a structure factor by an angular factor. The structure factor, which is the Fourier transform (FT) of the two-point height distribution function, only depends on the surface roughness. The angular factor depends on the dielectric properties of the surface. If the root mean square of height s is small at the scale of the light wavelength λ, the structure factor can be developed in a power series in σ/ λ. The first term of this series is proportional to the FT of the autocorrelation function of surface heights. This quantity is nothing else than the power spectral density of the surface height function considered as a stationary random function. The higher order terms are the FT of non-classical autocorrelation functions. Particularly, the third order one cancels every time both senses of each direction of the surface are statistically equivalent. Using the expression of the diffusely scattered intensity, we develop a method for determining the power spectral density of a rough surface. This method is tested in the case of a steel sample surface presenting a system of grooves oriented along only one direction. The power spectral density is determined for both directions parallel and perpendicular to grooves. In this particular case of surface roughness, we give an evaluation of the autocorrelation function and of the correlation length of the surface, in direction parallel and perpendicular to grooves. We observe that, contrarily to the assumption made in many previous works, the autocorrelation function and the power spectral density are not Gaussian. For instance, in the direction perpendicular to grooves, the power spectral density is rather exponential and then the autocorrelation function is Lorentzian.

C- and Multiangle Ku-Band Synthetic Aperture Radar Data for Bare Soil Moisture Estimation in Agricultural Areas

A sensitivity analysis of C-band (5.3 GHz) and Ku-band (14.85 GHz) synthetic aperture radar (SAR) data to the bare soil moisture content of agricultural fields was conducted in this study. The C-band data were obtained with a 23° incidence angle, whereas the Ku-band data were obtained with 35°, 55°, and 75° incidence angles. The fields presented either a small-scale or an intermediate-scale periodic soil roughness components, associated with level-basin and furrow irrigation systems, respectively. For fields with a small-scale roughness component, the SAR data were sensitive to soil moisture, particularly at the C-band with a 23° incidence angle and Ku-band with a 35° incidence angle. For fields with a intermediate-scale roughness component, both C- and Ku-band data were nearly insensitive to soil moisture. By using a theoretical surface scattering model, this study also analyzed the effects of different soil roughness components [root mean square (RMS) height h, correlation length, and periodic row structure] in the SAR data. For fields with RMS height <0.3 cm, a small variation in h (from 0.1 to 0.3 cm) provoked a significant variation in the SAR data (up to 8 dB).

Measuring soil moisture with imaging radars

An empirical algorithm for the retrieval of soil moisture content and surface root mean square (RMS) height from remotely sensed radar data was developed using scatterometer data. The algorithm is optimized for bare surfaces and requires two copolarized channels at a frequency between 1.5 and 11 GHz. It gives best results for kh/spl les/2.5, /spl mu//sub /spl upsi///spl les/35%, and /spl theta//spl ges/30/spl deg/. Omitting the usually weaker hv-polarized returns makes the algorithm less sensitive to system cross-talk and system noise, simplifies the calibration process and adds robustness to the algorithm in the presence of vegetation. However, inversion results indicate that significant amounts of vegetation (NDVI>0.4) cause the algorithm to underestimate soil moisture and overestimate RMS height. A simple criteria based on the /spl sigma//sub hv//sup 0///spl sigma//sub vv//sup 0/ ratio is developed to select the areas where the inversion is not impaired by the vegetation. The inversion accuracy is assessed on the original scatterometer data sets but also on several SAR data sets by comparing the derived soil moisture values with in-situ measurements collected over a variety of scenes between 1991 and 1994. Both spaceborne (SIR-C) and airborne (AIRSAR) data are used in the test. Over this large sample of conditions, the RMS error in the soil moisture estimate is found to be less than 4.2% soil moisture.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>