Floyd W. Millet

Validity of rough surface backscattering models

Abstract A study of the regions of validity for rough surface scattering models is conducted for surfaces with Gaussian and power law power spectra. Models included in the study are physical optics (PO), geometrical optics, small perturbation method and small slope approximation. The range of validity of the PO model is commonly described by a bound on the radius curvature of the surface relative to the electromagnetic wavelength. We show empirically that for backscattering the region of accuracy is more accurately described by a bound on surface slope. For surfaces with a Gaussian power spectrum, the PO model is accurate to within 2 dB for RMS surface slope values less than 0.59 cos3θ. For surfaces with a power law power spectral density, the PO model is accurate for significant slope values (RMS surface height/wavelength of the dominant spectral peak) less than 0.037 cos3θ. These conditions are valid up to approximately 30°. The regions of validity of other models in the study are also shown to be well approximated by bounds on surface slope.

Physical and geometrical optics for 2-D rough surfaces with power-law height spectra

Random rough surfaces with slowly decaying power spectral density can have infinite slope variance. Such surfaces do not satisfy the classical curvature criterion for validity of the physical optics (PO) approximation, and the infinite frequency geometrical optics limit or specular point scattering model breaks down. We show for two-dimensional surfaces with infinite slope variance that the Gaussian form of the classical geometrical limit generalizes to a stable distribution function. We also show that the PO integral is insensitive to surface components with spatial frequency above a cutoff wavenumber, which explains past observations that PO can be accurate for surfaces with power law spectra. This result leads to a general validity condition for the PO approximation in the backscattering direction for power-law surfaces, which in the case of a k/sup -4/ spectrum requires that the significant slope of the surface be less than 0.03.

Physical optics-based electromagnetic bias theory with surface height-slope cross-correlation and hydrodynamic modulation

An electromagnetic (EM) bias model for microwave frequencies is derived using the physical optics scattering approximation with a sea surface model that includes the effects of hydrodynamic modulation and non-Gaussian long-wave statistics. Correlation of long-wave slopes with displacement and hydrodynamic modulation of short-wave amplitudes are the two major contributors to the EM bias. The fact that the bias is caused by physical processes with different dependencies on frequency and sea state parameters accounts for some of the difficulties encountered with previous bias modeling efforts. The frequency dependence of the bias is weak because the trends of the hydrodynamic and height-slope skewness contributions with respect to frequency are in opposition. The model provides theoretical support for previous empirical observations of weak correlation of relative bias with wind speed and strong correlation with root-mean-square long-wave slope. While the presence of wind-generated small-wave roughness is crucial to the portion of the bias caused by hydrodynamic modulation, the magnitude of the bias thus induced is largely independent of local wind speed. The bias model is validated by comparison to measured data from two tower radar experiments, the Gulf of Mexico experiment (1991-1992) and the Brigham Young University off-nadir experiment (2003). Both quantitative and qualitative agreements between model and measurements are observed.

Validity study of rough surface scattering models

The limits of accuracy for rough surface models is largely uncertain. Previous numerical studies using the method of moments (MoM) have given broad assessments of the reliability of physical and geometrical optics, the small perturbation method, and other models. Improvements in digital computers allow a dense sampling of points from a chosen parameter space to give more accurate results than previously possible. RMS errors are shown for physical optics (PO), geometrical optics (GO), small perturbation method (SPM), iterated physical optics (ITPO), Monte Carlo physical optics (MCPO), and the small slope approximation (SSA) for power law surfaces. The models investigated show a wide range of regions of validity. Among all models, the ITPO method shows the best correlation to the truth values of the MoM calculations. However, stochastic models require significantly less computation time. Among the stochastic models, the third-order SSA models show the best overall agreement with the truth values. Unlike past studies, this study shows that the regions of validity for the PO and SPM are not disjoint. Instead, for the parameter space used, PO is always at least as accurate as SPM.

Refining electromagnetic bias estimation [sea surface height measurement]

Sea surface height measurements using remote sensing instruments have become increasingly accurate as satellite altimetry technology has matured. Early satellite missions had altimetry errors on the order of tens of centimetres. As these errors have been eliminated, the electromagnetic (EM) bias has become increasingly significant. The latest satellite missions, TOPEX/Poseidon and Jason-1, have EM bias error budgets of 4.2 cm and 2.5 cm, respectively. The purpose of our research has been to investigate methods to reduce the EM bias estimation errors to the sub-cm level. Most current EM bias models create estimates from geophysical properties that can be measured remotely. Typically these parameters are wind speed and significant wave height. The current operational model for the TOPEX/Poseidon and Jason-1 satellite missions is of this type. The operational model uses nonparametric methods to improve the accuracy of the estimates. In addition to improving the bias estimates, the latest operational model has shown a stronger agreement between satellite and tower EM bias models. Combining nonparametric techniques with the wind speed and significant wave height has created the most accurate empirical models to date. However, the amount of variance in the bias requires new methods to improve bias estimates. We made a preliminary study based on the angular dependence of the EM bias. Theoretical scattering models indicate that the bias is dependent on incidence angle, which may allow improved operational correction of the bias using a wide-swath altimeter.

Regional differences in electromagnetic bias due to wave slope

Recent experiments have shown fundamental differences in the electromagnetic (EM) bias between different regions of the world. In order to account for these difference, various sea and weather parameters are analyzed. A new parameter called wave slope is derived. Using data from the Gulf of Mexico Experiment (GME) and the Bass Strait, Australia Experiment (BSE) the correlation between EM bias and wave slope is investigated. A high degree of correlation is seen between the wave slope and EM bias in these two experiments. This correlation indicates that wave slope may be highly indicative of the regional differences in the EM bias throughout the world.

An improved model for determining the electromagnetic bias

Recent experiments have shown fundamental differences id the electromagnetic (EM) bias between different regions of the world. In order to account for these difference, various sea and weather parameters are analyzed. A new parameter called wave slope is derived. Using data from the Gulf of Mexico Experiment (GME) and the Bass Strait, Australia Experiment (BSE) the correlation between EM bias and wave slope is investigated. A high degree of correlation is seen between the wave slope and EM bias in these two experiments. This correlation indicates that wave slope my be highly indicative of the regional differences in the EM bias throughout the world.