Richard T. Austin

Special problems in the estimation of power-law spectra as applied to topographical modeling

An increasing number of topographical studies find that natural surfaces possess power-law roughness spectra. Power-law spectra introduce unique difficulties in the spectral estimation process. The authors describe how an improper window choice allows leakage that yields a spectral estimate that is insensitive to the spectral slope. In addition, the commonly used Fourier-based spectral estimates have higher variances than other available estimators. Higher variance is particularly problematic when data records are short, as is often the case in remote sensing studies. The authors show that Capons spectral estimator has less variance than Fourier-based estimators and measures the spectral slope more accurately. The authors also show how estimates of a 2D roughness spectrum can be obtained from estimates of the 1D spectrum for the isotropic power-law case. >

Fluctuation statistics of millimeter-wave scattering from distributed targets

The applicability of the Rayleigh fading model for characterizing radar scattering from terrain is examined at 35 GHz for both backscattering and bistatic scattering. The model is found to be in excellent agreement with experimental observations for single-frequency observations of uniform targets such as asphalt and snow-covered ground. The use of frequency averaging to reduce signal fading variations was examined experimentally by sweeping the radar signal from 34-36 GHz in 401 steps. The results show that the formulation based on the Rayleigh model relating the reduction in signal fluctuation to the bandwidth used provides a reasonable estimate for the improvement provided by frequency averaging. >

Millimeter‐wave radar scattering from snow: 2. Comparison of theory with experimental observations

Using a truck-mounted platform, backscatter measurements were made at 35, 95, and 140 GHz for a variety of snow conditions to evaluate the radar response to incidence angle, surface roughness, and liquid water content. Good agreement was obtained between the experimental observations and theoretical calculations based on the numerical solution of the radiative transfer equation presented in the preceding paper. A notable exception is when the snowpack is in the refreezing phase of the diurnal cycle, during which the snowpack is characterized by a dry surface boundary with wet layers underneath. To accommodate this type of condition, a hybrid first-order numerical solution is proposed. The hybrid approach provides excellent agreement between theory and experiment.

Multi‐scale roughness spectra of Mount St. Helens debris flows

A roughness spectrum allows surface structure to be interpreted as a sum of sinusoidal components with differing wavelengths. Knowledge of the roughness spectrum gives insight into the mechanisms responsible for electromagnetic scattering at a given wavelength. Measured spectra from 10-year-old primary debris flow surfaces at Mount St. Helens conform to a power-law spectral model, suggesting that these surfaces are scaling over the measured range of spatial frequencies. Measured spectra from water-deposited surfaces deviate from this model.

Surface Characterization of Volcanic Debris Flows at Multiple Scales

The topography of several debris flow units near the Mount St. Helens Volcano was measured at lateral scales of millimeters to meters in September 1990. The measurements were conducted in support of studies of electromagnetic scattering by volcanic terrains. We used a laser profiling system and surveying instruments to obtain elevation data for square areas that varied in size from 10 cm to 32 m on a side. These elevation data were converted to estimates of the power spectrum of surface roughness. The conversions were based upon standard periodogram techniques and modified spectral estimation techniques designed to compensate for errors present in the profilometer data.

Remote measurements of snowfalls in Wakasa Bay, Japan with Airborne Millimeter-wave Imaging Radiometer and Cloud Radar

Results of concurrent airborne measurements of snowfalls with the Millimeter-wave Imaging Radiometer (MIR) and the Airborne Cloud Radar (ACR) are reported in this paper. The measurements were obtained during January-February 2003 in a field experiment in Wakasa Bay, Japan. The MIR is an imaging radiometer that measures radiation at seven channels between 89 GHz and 340 GHz. The ACR operates at 94 GHz and provides nadir-viewing radar reflectivity profiles with very good accuracy. Three days of snowfall events were observed during this field deployment. It was found that the MIR brightness temperature depressions at the frequencies of 183.3/spl plusmn/1, 183.3/spl plusmn/3, 183.3/spl plusmn/7, and 340 GHz strongly correlate with the ACR reflectivity profiles during these snow events. Radiometric signatures from the remaining less opaque channels of the MIR (89, 150 and 220 GHz) showed ambiguity in snowfall detection due to variation in surface emissivities. An attempt to retrieve the ice water path and the median mass equivalent sphere diameter of the snowfalls would be described and results discussed.

Radar scattering by volcanic debris flow surface analogues

Measured roughness spectra from 10-year-old primary volcanic debris flows at Mount St. Helens conform to a power-law spectral model. It is difficult to rigorously test rough surface scattering models using in situ measurements of radar backscatter because natural targets are often inhomogeneous or non-stationary, because volume scattering may he significant, and because characterisation of natural rough surfaces is difficult and time-consuming. The authors have manufactured debris flow surface analogues by milling rough surfaces with specified power-law roughness spectra on homogeneous slabs of polyethylene. Measured radar backscatter from these surface analogues provides test data for scattering studies. The surface analogues serve as test surfaces which are homogeneous, well characterized, and free of volume scattering effects.<<ETX>>