William J. Plant

measuring stream discharge by non‐contact methods: A Proof‐of‐Concept Experiment

This report describes an experiment to make a completely non-contact open-channel discharge measurement. A van-mounted, pulsed doppler (10GHz) radar collected surface-velocity data across the 183-m wide Skagit River, Washington at a USGS streamgaging station using Bragg scattering from short waves produced by turbulent boils on the surface of the river. Surface velocities were converted to mean velocities for 25 sub-sections by assuming a normal open-channel velocity profile (surface velocity times 0.85). Channel cross-sectional area was measured using a 100 MHz ground-penetrating radar antenna suspended from a cableway car over the river. Seven acoustic doppler current profiler discharge measurements and a conventional current-meter discharge measurement were also made. Three non-contact discharge measurements completed in about a 1-hour period were within 1% of the gaging station rating curve discharge values. With further refinements, it is thought that open-channel flow can be measured reliably by non-contact methods.

Bragg Scattering of Electromagnetic Waves from the Air/Sea Interface

The advent of radar during World War II had consequences for research in air/sea interactions which were far from obvious in the face of the immediate wartime need to detect enemy aircraft. When the newly-discovered tool was put to use to detect targets on or near the surface of the sea, these targets were often obscured by strong echos from the ocean itself. This “sea echo” constituted a considerable nuisance to those engaged in locating enemy vessels so investigations into the nature of this unwanted return were launched. Early theoretical work concentrated on explaining sea echo in terms of either return from the sea surface itself or from the spray and bubbles above the surface. Methods of modelling electromagnetic scattering which had proved useful to the characterization of many types of targets were adapted for use modelling sea return. Specular reflection seemed to explain the characteristics of sea echo for small incidence angles but not for larger ones. The standard method of carrying out such calculations utilized the “Kirchoff principle,” also known as physical optics or the tangent plane method, which assumes that the surface is smooth in the sense that the radius of curvature is large compared to the electromagnetic wavelength. In addition to yielding disturbingly low return at large incidence angles, the method was unable to account for the observation that vertically polarized return was generally stronger than horizontal at such angles. Since interference between radiation directly incident on bubbles above the surface and radiation incident on the bubbles following reflection from the surface could in principal yield such polarization differences, theories based on Rayleigh scattering by the bubbles were also proposed.

A model for microwave Doppler sea return at high incidence angles: Bragg scattering from bound, tilted waves

We show that if ocean surface waves of the order of a few meters long are frequently steep enough to generate bound centimetric waves, then composite surface scattering theory can account for many anomalous properties of microwave backscatter from the sea at high incidence angles. The model proposed here postulates that these intermediate waves are made sufficiently steep to generate bound centimetric waves because of their modulation by longer, dominant ocean surface waves. The bound centimetric waves have a nonzero mean tilt because they are located on the steep forward face of the intermediate waves, and they move at the speed of the intermediate waves. Applying composite surface scattering theory to this sea surface model, we show that much of the apparently anomalous behavior of microwave sea return measured at incidence angles between 50° and 80° during the Synthetic Aperture Radar and X Band Ocean Nonlinarities-Forschungsplatform Nordsee (SAXON-FPN) experiment can be explained using reasonable parameters to characterize the surface waves. In the SAXON-FPN measurements the mean values of the first moments of microwave Doppler spectra for horizontally polarized backscatter differ from those for vertically polarized backscatter by an amount which varies with the incidence angle and with the azimuthal angle between the radar look direction and the direction of the dominant wave. The modulation of this first moment by surface waves tens of meters in length is the same for the two polarizations at low to moderate incidence angles and can be interpreted in terms of the advection of free centimetric waves by the long waves. At higher incidence angles, however, this modulation is different for the two polarizations and cannot be explained by simple advection of free waves. Finally, microwave cross sections measured at high incidence angles using horizontal polarization are much larger than can be explained by a composite surface theory that includes only freely propagating centimetric waves. Most of these effects can be explained by the composite surface model presented here, which includes Bragg scattering from both free and bound, tilted waves.

Hydrodynamic modulation of short wind‐wave spectra by long waves and its measurement using microwave backscatter

In this paper we use results of microwave backscattering experiments over the past decade to attempt to present a coherent picture of the ocean wave-radar modulation transfer function (MTF) based on composite surface theory, short-wave modulation, and modulated wind stress. A simplified relaxation model is proposed for the modulation of the gravity-capillary wavenumber spectrum by long waves. The model is based on the relaxation rate and the equilibrium gravity-capillary wavenumber spectrum. It differs from previous models by including all airflow modulation effects in the response of the equilibrium spectrum to changes in the airflow. Thus the explicit modulation of individual source functions such as wind input, short-wave dissipation, and nonlinear interactions need not be known in order to calculate the hydrodynainic MTF. By combining this new model of the hydrodynamic MTF with microwave measurements, we attempt to determine wind shear stress modulation caused by the long waves. In order to extract the hydrodynamic MTF from the microwave data, we remove tilt and range change effects from the measured MTFs using the published analytical forms for these effects. Our results show that the inferred hydrodynamic MTF is higher for II polarization scattering than for V polarization. Since this is impossible if we have obtained the true hydrodynamic MTF, these results strongly indicate a problem with composite scattering theory as it has been traditionally applied. One explanation for this result may be the effects of intermediate-scale waves suggested by Romeiser et al. (1993). Since these effects are much stronger for H polarization than for V polarization, they may explain our observed discrepancy and, if so, imply that V polarization return should yield an acceptable upper limit for the true hydrodynamic MTF. Thus we incorporate our V polarization results into the proposed model to estimate an upper limit for the wind shear stress modulation along the long-wave profile. We infer that the primary source of modulation of Bragg resonant waves depends strongly on Bragg wavenumber and windspeed. For low values of these quantities, straining by long-wave orbital velocities dominates the modulation process, while for higher values modulated wind stress becomes increasingly important. Our calculations indicate that wind stress modulation dominates the process for 3 cm Bragg waves at moderate to high wind speeds.

Growth and equilibrium of short gravity waves in a wind-wave tank

Temporal and spatial development of short gravity waves in a linear wind-wave tank has been measured for wind speeds up to 15 m/s using microwave Doppler spectrometry. Surface waves of wavelength 4·1 cm, 9·8 cm, 16·5 cm and 36 cm were observed as a function of fetch, wind speed and wind duration. The waves grew exponentially from inception until they were about 10 dB smaller than their maximum height, and the temporal growth and spectral transport (spatial growth) rates were about equal when the wave amplitude was sufficiently small. The amplitude of a short gravity wave of fixed wavelength was found to decrease substantially at winds, fetches or durations greater than those at which the short gravity wave was approximately the dominant wave; such phenomena are sometimes referred to as overshoot. The dominant short gravity wave was observed to reach a maximum amplitude which depended only on wavelength, showing that wave breaking induced by an augmented wind drift cannot be the primary limitation to the wave height. Waves travelling against the wind were observed for wavelengths of 9·8 cm, 16·5 cm and 36 cm and were shown to be generated by the air flow at low wind speeds. Measured initial growth rates for 16·5 cm and 36 cm waves were greater than expected, suggesting the existence of a growth mechanism in addition to direct transfer from the wind via linear instability of the boundary-layer flow. Initial temporal growth rates and spectral transport rates were compared to yield an experimental determination of the magnitude of the sum of nonlinear interactions and dissipation in short gravity waves. If the steady-state energy input in the neighbourhood of the dominant wave occurs at the measured initial temporal growth rates, then most of the energy input is locally dissipated; relatively little is advected away. Calculated gravitycapillary nonlinear energy transfer rates match those determined from initial growth rates for 9·8 cm waves and the gravity–capillary wave interaction continues to be significant for waves as long as 16·5 cm. For longer waves the gravity–capillary interaction is too small to bring the short gravity wave to a steady state when it is the dominant wave of the wind-wave system.

Studies of backscattered sea return with a CW, dual-frequency, X-band radar

A coherent, CW, dual-frequency, X -band radar was used to study microwave sea return from the Chesapeake Bay. It is shown that the product of the backscattered fields depends strongly on long surface wave properties. In particular, a sharp line is found in the product power spectrum whose frequency is that of the water wave whose wavelength is in resonance with the spatial period of the beat frequency between the two transmitted signals and whose wave vector is parallel to the horizontal line of sight. Thus, gravity wave dispersion relations can be obtained with the system. Furthermore, the degree of modulation of short waves by long ones is given by the intensity of the line. A broad background corresponding to the convolution of the single-frequency Doppler spectra is also seen in the product power spectrum. These results are shown to be interpretable by composite surface scattering theory.

Measurement of river surface currents with coherent microwave systems

River surface currents have been measured using coherent microwave systems from a bridge, a cableway, several riverbanks, a helicopter, and an airplane. In most cases, the microwave measurements have been compared with conventional measurements of near-surface currents and found to be accurate to within about 10 cm/s. In all cases, the basis for the microwave measurement of surface current is the Doppler shift induced in the signal backscattered from the rough water surface. In this paper, we outline the principles of the measurements and the various implementations that have been used to make microwave measurements of surface currents. Continuous-wave (CW) microwave systems have been used from a bridge to make long-term measurements of surface currents; these are compared with current-meter measurements and with time series of stage. A compact CW system has been developed and used on a cableway to measure surface currents at various distances across a river; these measurements have been compared with acoustic ones. Pulsed Doppler radars have been used to measure river surface currents from a riverbank, a helicopter, and an airplane. In the first two cases, comparisons with both current-meter and acoustic measurements have been made. We suggest that the CW system would be preferable to the pulsed Doppler radar to make such measurements from helicopters in the future. Finally, we consider the implications of our experiments for the measurement of surface currents from aircraft or satellites using interferometric synthetic aperture radars (INSARs). We find that a combination along-track, cross-track INSAR is necessary but that significant limitations are inherent in the technique.

The Modulation Transfer Function: Concept and Applications

This paper outlines the concept of the modulation transfer function used to relate fluctuations in power received by an active microwave system viewing the ocean to the dominant surface waves on the ocean which cause the fluctuations. Expressions are given for the purely geometric modulations related to surface tilting and changes in range. The manner in which the modulation transfer function enters into the interpretation of real and synthetic aperture radar images, wave spectrometer outputs, scatterometer wind retrievals, and altimeter measurements is reviewed. Finally, limitations of the concept are discussed.

Microwave sea return at moderate to high incidence angles

Abstract Bragg scattering is widely recognized as the dominant mechanism by which the ocean surface backscatters microwave radiation, but efforts to identify other, non-Bragg sources of this scattering have been pursued for many years. Non-Bragg backscattering from the sea surface is known to occur at incidence angles close to 0° and 90°. In this paper Bragg scattering is shown to explain most features of sea surface backscatter for incidence angles between about 20° and 80°, except when it predicts very small mean cross sections. The often-quoted evidence for non-Bragg scattering in this incidence angle range is that σ o (HH) is occasionally found to be larger than or equal to σ o (VV) for short integration times. We show that because of fading this is not evidence of non-Bragg scattering. For incidence angles up to about 50°, standard Bragg/composite surface scattering theory yields probabilities of finding σ o (HH)>σ o (VV) that are only slightly smaller than those found experimentally. As the incidence angle increases, greater differences between theoretical and experimental probabilities are found. The addition of Bragg scattering from bound, tilted waves brings theory into excellent agreement with experiment at incidence angles near 45° but still cannot account adequately for the probability of σ o (HH)>σ o (VV) or observed σ o (HH) cross sections at higher incidence angles. We show that the addition of a small, non-Bragg cross section that is independent of the incidence angle and polarization, brings simulated cross sections and probability distributions into good agreement with data. A possible source of this small, non-Bragg sea return is sea spray just above the air/sea interface.

The dependence of microwave backscatter from the sea on illuminated area: Correlation times and lengths

During the Synthetic Aperture Radar (SAR) and X band Ocean Nonlinearities-Forschungsplattform Nordsee experiment, we mounted two continuous wave microwave systems on an elevator on the German Research Platform Nordsee for the purpose of investigating the dependence of microwave backscatter from the sea surface on illuminated area. The two systems operated at X and Ka bands (10 and 35 GHz) and collected HH and VV polarized backscattered signals simultaneously. The elevator system allowed us to vary the altitude of the two microwave systems above the sea surface from 7.5 to 27 m, always in the far field of the antennas. Most data were collected at a 45° incidence angle, which implied that the Ka band system illuminated areas from 0.4 to 6.0 m2 while the X band system viewed spots between 2.9 and 41.3 m2. We examined the dependence of the normalized radar cross section (σ0), its variance, and the bandwidth of the Doppler spectrum on illuminated areas. We were unable to detect any dependence of σ0 on area but found a definite decrease in its variance as area increased. At X band the variance divided by the square of σ0, the normalized variance, decreased from values near 12 for small areas to values near 2 for large areas. At Ka band, corresponding values were 40 and 2. The normalized variance was always slightly larger for HH polarization. By fitting the area dependence of the normalized variance to available theory, we deduce that correlation lengths are on the order of 10 times the microwave wavelength at both X and Ka band. Values for the normalized variance of an elementary scattering facet were also inferred and are presented in this paper. From the Doppler bandwidths we obtained radial velocity spreads over the illuminated areas and found that they agreed well at X and Ka band. These velocity spreads, which are inversely proportional to the correlation time of the backscatter, increased rapidly with illuminated area for small areas but tended to level off to values of about 0.5 m s−1 at large areas. This implies a decorrelation time for large illuminated areas of about 10 ms at X band and 3 ms at Ka band but somewhat larger values for small areas. The dependence of the velocity spread was found to be well explained by theory if an intrinsic velocity spread of 0.07 m s−1 was used to represent scatterer lifetime effects.