This second paper of our set on short wind waves on the ocean utilizes the wavenumber-frequency spectrum of short wave heights, F(k,f), derived in our previous paper to investigate kinematic effects on the dependence of the frequency spectrum, F(f), and the wavenumber spectrum, F(k), on long-wave height. We show that the model predicts that neither F(f) nor F(k) are exactly power law functions of their independent variables and that F(f) varies with significant wave height much more than F(k) does. After calibrating the model against wave gauges, we also investigate the dependence of mean-square-slopes (mss), mean-square heights (msh) and root-mean-square orbital velocities (rmsv) of short ocean waves on wind speed and maximum frequency or wavenumber. We use data from the wire wave gauges on University of Miami's Air-Sea Interaction Spar (ASIS) buoy for calibration purposes. Frequency spectra from the wave gauges begin to be affected by noise at about 2.5 Hz. Therefore, above 1 Hz, we utilize F(f) from the modeled F(k,f) to extend the frequency dependence up to 180 Hz. We set modeled spectral densities by matching measured spectra at 1 Hz. Using the calibrated F(f,k), we are able to estimate the average value of the total mss, for long and short waves, and its upwind and crosswind components up to 180 Hz for a variety of wind speeds. The average mss values are in good agreement with the measurements of Cox and Munk [1954], although the upwind and crosswind components agree less well.

Active and passive microwave signatures of the ocean depend on the ocean wave spectrum alone if bound and breaking waves are neglected. History has not been kind to attempts to explain both radiometer brightness temperatures (T_b) and the normalized radar cross section (σ_o) of the sea using the same ocean wave spectrum. This report documents how adding bound and breaking waves to the models of radiometer and scatterometer microwave signatures of the ocean allows a single wave spectrum to explain both T_b and σ_o to reasonable accuracy.

Bound waves are the roughness produced by gently breaking, or crumpling, waves that travel near the speed of the parent wave, which is a short gravity wave. Bound wave modeling is based on earlier work by Plant (1997) but using additional information about the slope probability distributions of bound waves. Breaking wave and foam modeling both build on the function introduced by Phillips (1985), which describes the average length of breaking wave fronts on the ocean per unit area as a function of breaker velocity. We model this function through a Monte Carlo simulation that assumes that breaking occurs when the slope of the sea surface exceeds a threshold value.

The sea surface is modeled by a linear superposition of waves shorter than 0.15 m that is consistent with the wave spectrum. Thus the wave spectrum completely determines the function. We show that the result of including bound and breaking waves in radiometer and radar models of oceanic signatures is a much closer fit to data using a single spectrum.

Dominant surface waves on the ocean exhibit a dispersion relation that confines their energy to a curve in a wavenumber-frequency spectrum. Short wind waves on the ocean, on the other hand, are advected by these dominant waves so that they do not exhibit a well-defined dispersion relation over many realizations of the surface. Here we show that the short-wave analog to the dispersion relation is a distributed spectrum in the wavenumber-frequency plane that collapses to the standard dispersion relation in the absence of long waves. We compute probability distributions of short-wave wavenumber given a (frequency, direction) pair and of short-wave frequency given a (wavenumber, direction) pair. These two probability distributions must yield a single spectrum of surface displacements as a function of wavenumber and frequency, F(k,f). We show that the folded, azimuthally averaged version of this spectrum has a "butterfly" pattern in the wavenumber-frequency plane if significant long waves are present. Integration of this spectrum over frequency yields the well-known k^-3 wavenumber spectrum. When integrated over wavenumber, the spectrum yields an f^-4 form that agrees with measurement. We also show that a cut through the unfolded F(k,f) at constant k produces the well-known form of moderate-incidence-angle Doppler spectra for electromagnetic scattering from the sea. This development points out the dependence of the short-wave spectrum on the amplitude of the long waves.

Results of an experiment to measure vertical spatial coherence from acoustic paths interacting once with the sea surface but at perpendicular azimuth angles are presented. The measurements were part of the Shallow Water 2006 program that took place off the coast of New Jersey in August 2006. An acoustic source, frequency range 6–20 kHz, was deployed at depth 40 m, and signals were recorded on a 1.4-m long vertical line array centered at depth 25 m and positioned at range 200 m. The vertical array consisted of four omni-directional hydrophones and vertical coherences were computed between pairs of these hydrophones. Measurements were made over four source–receiver bearing angles separated by 90°, during which sea surface conditions remained stable and characterized by a root-mean-square wave height of 0.17 m and a mixture of swell and wind waves. Vertical coherences show a statistically significant difference depending on source–receiver bearing when the acoustic frequency is less than about 12 kHz, with results tending to fade at higher frequencies. This paper presents field observations and comparisons of these observations with two modeling approaches, one based on bistatic forward scattering and the other on a rough surface parabolic wave equation utilizing synthetic sea surfaces.

Whitecaps in deep water are located near maximum slopes of the interference pattern of dominant wind waves and the most probable breaking waves are those waves that travel with the speed of the component of the interference pattern in the wind direction. These breaking waves are in the wavelength range 1 to 12 m, much shorter than typical dominant waves. The patterns of large steepness caused by interfering dominant waves move at speeds less than the group speed of the dominant wave unless the wave spectrum is narrow in both wavenumber and azimuth. For spectra with wavenumber and azimuth angle spreads representative of those observed on the ocean, the velocity of propagation of the pattern of steep waves in the wind direction is the same as the speed at the maximum of Phillips function, the speed of the peak of HH Doppler spectra, and the speed measured by acoustic event tracking.

Shadowing and modulation of microwave backscatter by ocean waves are studied using coherent X-band radars. Two types of shadowing are investigated: geometric shadowing (complete blockage of incident rays) and partial shadowing (polarization-dependent diffraction combined with weak scatterers). We point out that the frequency of occurrence of zero signal-to-noise ratio samples cannot depend on the incident power level or the polarization if geometric shadowing occurs but can if partial shadowing exists. We then compare this behavior with observations, and show that the data do not support the hypothesis that geometric shadowing plays a significant role in low-grazing-angle microwave scattering from the ocean surface. Furthermore, our data indicate that partial shadowing only depends significantly on polarization for the steep waves found near shorelines. We also study the modulation of microwave backscatter by ocean waves using these data by looking at the phase differences between received power and scatterer velocity. These phase differences appear to be rather well explained by standard composite surface theory at VV polarization, having values that are positive looking up wave and negative looking down wave. For HH polarization, however, breaking effects come into play and overshadow composite surface effects of free waves. They cause the phase difference to be near zero for up wave looks and near 180° for down-wave looks. A simple model that involves both breaking and freely propagating waves but does not include any shadowing effects is shown to account for observed phase differences at both polarizations to within about 10°.

Wave number-frequency spectra measured with remote sensing systems consist of energy along the ocean wave dispersion relation and additional features that lie above and below this relation. At low frequencies a feature passing through the origin as a straight line is observed while one or more high-frequency features exhibit substantial curvature. Here we utilize images obtained on the open ocean from microwave Doppler shifts, which are directly related to scatterer velocity and allow us to calculate expected wave-wave interaction effects. We show that the strongest features lying off the first-order dispersion relation are not primarily due to second-order interactions, breaking caused by wind turbulence, advection by turbulence, or shadowing. The low-frequency feature can be seen traveling in the opposite direction to swell when looking nearly crosswind. We show that the most probable cause of these features is the interference of long ocean waves, which causes breaking near local maxima of surface slope. Doppler spectra observed by the radars indicate that the maximum speed reached by water particles on the open ocean is less than 6 m/s and usually close to the speed of the low-frequency feature in the wave number-frequency spectrum. Since this is much less than the phase speeds of dominant wind waves and swell, neither of these waves can be the breaking wave. Rather, we hypothesize that the superposition of these waves steepens short gravity waves on the surface, which then break to produce water parcels traveling near their phase speed, the speed observed by the radar.

Estuarine fronts are well known to influence transport of waterborne constituents such as phytoplankton and sediment, yet due to their ephemeral nature, capturing the physical driving mechanisms and their influence on stratification and mixing is difficult. We investigate a repetitive estuarine frontal feature in the Snohomish River Estuary that results from complex bathymetric shoal/channel interactions. In particular, we highlight a trapping mechanism by which mid-density water trapped over intertidal mudflats converges with dense water in the main channel forming a sharp front. The frontal density interface is maintained via convergent transverse circulation driven by the competition of lateral baroclinic and centrifugal forcing. The frontal presence and propagation give rise to spatial and temporal variations in stratification and vertical mixing. Importantly, this front leads to enhanced stratification and suppressed vertical mixing at the end of the large flood tide, in contrast to what is found in many estuarine systems. The observed mechanism fits within the broader context of frontogenesis mechanisms in which varying bathymetry drives lateral convergence and baroclinic forcing. We expect similar trapping-generated fronts may occur in a wide variety of estuaries with shoal/channel morphology and/or braided channels and will similarly influence stratification, mixing, and transport.

Synchronous and colocated optical and microwave signals from waves in the surf zone are presented and analyzed. The field data were collected using a high-resolution video system and a calibrated horizontally polarized marine radar during the decaying phase of a storm. The resulting changes in the received signals from varying environmental conditions were analyzed. The analysis of the optical signal histograms showed functional shapes that were in accordance with the expected imaging mechanisms from the breaking and nonbreaking waves. For the microwave returns, the histogram shape showed a little dependence on the environmental parameters and exhibited an inflexion point at high returned power that is attributed to a change in the scattering mechanism. The high intensity signals were clearly associated with active wave breaking. However, with either sensor, it can be difficult to effectively isolate the wave breaking signature from other sources, such as a remnant foam or the highly steepened nonbreaking waves. A combined method was developed using the joint histograms from both sensors, and it is shown to effectively discriminate between active breaking, remnant foam, and steepened waves. The new separation method allows a further analysis of the microwave scattering from the breaking waves and a better quantification of the length scales of the breaking wave roller and the spatial/temporal distribution of wave breaking and wave dissipation in the surf zone.

A laboratory experiment is reported in which paddle-generated waves a few meters long and with initial slopes interact with centimetric wind-generated waves. The short waves are modified by the orbital velocity gradients of the long waves and by the modulation of the airflow over the long waves. Both of these effects produce a modulation of the short-wave energy density on the phase of the long waves.

The Wavelet Directional Method is used to track the varying energy density of the short waves with long-wave phase. Two sets of trials are run at six wind speeds for five different long waves for a total of 60 trials. The sensitivity of the mean short-wave energy density to wind speed, long-wave slope, and long-wave period is explored in terms of a balance between wind input and dissipation source terms in the evolution of a spectrum of water waves. The magnitude and phase of the modulation of the short-wave energy reveals the relative effects of straining by orbital velocities and modulation of wind input. We show that these effects are very similar to those measured on the ocean.

The normalized radar cross section of the sea for backscatter is investigated for incidence angles between 0 and 89 degrees using data collected over more than two decades. The most recent measurements were made from several ships using a coherent, dual-polarized, X band radar. These measurements show that vertically polarized transmit and receive signals at high incidence angles exhibit wind speed and azimuth angle dependence similar to those at lower incidence angles. They are nearly as large looking downwind as they are looking upwind and minimize near the crosswind direction. Horizontally polarized transmit and receive signals behave differently at high incidence angles. They are largest looking upwind and smallest looking downwind.

Fits of the multiscale model of microwave backscatter from the ocean to these data along with data collected previously at lower incidence angles show that over the whole range of incidence angles from 0 to 89 degrees is explained by the model, while measured values are generally higher than the model predicts at incidence angles above about 45 degrees. Thus scattering phenomena exist on the ocean surface that affect HH backscatter very strongly at the higher incidence angles while impacting VV-polarized backscatter only slightly. This conclusion is strengthened by our observation of high-incidence-angle backscatter from the ocean where mean HH exceeds mean VV by as much as 15 dB. We examine phenomena that might account for this behavior and suggest that multipath dihedral-type features are likely to be important scatterers since they produce large HH/VV owing to Brewster damping of the first VV bounce.

We report measurements of microwave surface signatures of internal waves with dual-polarized, coherent, X band radars mounted on three ships and an airplane. In shipboard measurements in the South China Sea, internal waves generally increased the backscattering cross section near the peaks of the internal waves with little detectable decrease afterward. The peak of the cross-section signature shifted its location relative to the internal wave crest depending on the maximum strain rate of the internal wave. We show that a similar shift is produced in the modulation of short-gravity waves by internal waves. We suggest that this modulation of "intermediate-scale" waves causes small-scale radar scatterers to maximize at this location.

In shipboard measurements off the New Jersey coast, the range resolution of the radar was sufficiently small to allow us to detect significant modulation of gravity waves on the order of 15–30 m long by the internal waves. At the high incidence angles of the shipboard measurements, the cross section for horizontally polarized transmit and receive signals (HH) regularly exceeded that for vertically polarized transmit and receive signals (VV) near the internal wave crest by 5–10 dB. At the more moderate incidence angles observed from the aircraft, maximum values of HH and VV are more nearly equal, with HH often being comparable to VV and only occasionally exceeding it. These observations suggest that roughness due to breaking short-gravity waves plays a significant role in producing microwave signatures of internal waves, even at moderate incidence angles where it competes with the modulation of wind-generated waves. The intensity of modulation of the cross section caused by internal waves observed from the plane depended little on the direction of observation. Internal wave surface signatures from the aircraft became less visible with increasing wind speed, being very difficult to observe at 9 m/s.

In 2005 and 2007, a coherent, X-band radar was deployed in the South China Sea on two different ships. In both cases, the two parabolic antennas of the radar were fixed at grazing angles of approximately 2 deg looking toward the bow of the ship. The radar transmitted and received through a single antenna but alternated between the two antennas approximately every half second. One antenna was horizontally polarized and the other was vertically polarized. The data were analyzed by computing normalized radar cross sections and scatterer velocities as a function of ground range and time. Surface signatures of the internal waves were obvious in both types of image and at both polarizations as regions of enhanced cross sections or scatterer velocities.

The collected imagery showed that at least two different types of internal waves exist in the South China Sea: small, nearly sinusoidal trains of waves and large soliton-like waves. These different types travel at very different speeds and interact with each other. The small nearly sinusoidal waves travelled at phase speeds near 1 m/s that increased as the small wave trains were overtaken by the faster solitons. Combined with other shipboard measurements, the radar measurements yielded the widths, maximum velocities, and strain rates of the solitons as well as the dependence of phase speed on amplitude. When the speeds of both the ship and the solitons were removed, the measurements showed that soliton full-widths at half-maximum ranged from about 0.5 to 4.5 km. These widths showed a dependence on the amplitude of the soliton. The phase speeds of the solitons also depended on their amplitude, reaching 3 m/s in deep water but only about 1.2 m/s in shallow water. CTD profiles were used to estimate an interface depth for a two-layer fluid model of the propagation of the solitons. The phase speeds predicted by this model agreed well with the observed dependence of the soliton phase speed on amplitude in both shallow and deep water.

We show that at low grazing angles, breaking wave effects are very important in HH polarized microwave backscatter from the ocean but less so at VV polarized backscatter. When the ocean surface is disturbed only by wind, breaking wave effects in VV backscatter are much smaller than Bragg scattering, even at low grazing angles. For HH polarization, on the other hand, breaking wave effects are very important at low grazing angles. In the presence of surface current gradients set up by internal waves, HH cross sections can exceed those at VV by as much as 10 dB near internal wave crests, indicating enhanced breaking wave effects that cannot be described as specular. Breaking effects are nearly as strong as Bragg effects in VV backscatter under these conditions. Spectral comparisons confirm these conclusions.

The spectrum of ocean surface roughness is significantly modified by the presence of background long waves not generated by local wind. Active radar scattering and passive microwave emission from the ocean surface are therefore modified by swell conditions. Here we investigate predictions of the normalized radar cross section (NRCS) of the sea by a multiscale radar scattering model using four different spectral functions, one of which accounts for swell effects. Variations in predicted NRCS using the different spectral functions are quantified. As a result, the effect of swell on microwave backscatter can be separated from uncertainty due to the form of the spectrum without swell. The tilting effects of swell are also examined, and their effect on backscatter is calculated using the model. We find that changes in the ocean surface roughness spectrum due to swell reduce the wind speed dependence of the NRCS at low and moderate incidence angles while tilting effects produce changes in both the incidence angle and wind speed behavior of the NRCS. In general C band NRCS measurements are better explained by the multiscale model and less sensitive to choice of roughness spectral model than are Ku band NRCS values.

Images of river surface features that reflect the bathymetry and flow in the river have been obtained using remote sensing at microwave, visible, and infrared frequencies. The experiments were conducted at Jetty Island near the mouth of the Snohomish River at Everett, Washington, where complex tidal flow occurs over a varied bathymetry, which was measured as part of these experiments. An X band (9.36 GHz) Doppler radar was operated from the river bank and produced images of normalized radar cross sections and radial surface velocities every 20 min over many tidal cycles. The visible and infrared instruments were flown in an airplane. All of these techniques showed surface evidence of frontal features, flow over a sill, and flow conditioned by a deep hole. These features were modeled numerically, and the model results correspond well to the remote observations. In situ measurements made near the hole showed that changes in measured velocities correlate well with the occurrence of the features in the images. In addition to tidal phase, the occurrence of these features in the imagery depends on tidal range. The surface roughness observed in the imagery appears to be generated by the bathymetry and flow themselves rather than by the modulation of wind waves.

Many authors assume that the frequency peak and the wavenumber peak of an ocean wave height variance spectrum are related by the ocean wave dispersion relationship. This note shows that this is not true and that the true relationship depends on the shape of the spectrum, thereby introducing an element of randomness into the relationship.

Measurements in a closed, recirculating wind-wave tank using variable wind speeds showed that wind waves in the gravity-capillary range exhibit a threshold in their growth. Surface wave height variance spectral densities in the wave number domain were measured for gravity-capillary waves using both radar backscatter and a wavelet transform technique applied to a laser probe. The measurements showed that when the wind speed was slowly ramped up, a threshold wind speed or friction velocity was required to produce waves. Turning the wind on suddenly showed that the wind stress did not grow as rapidly as the wind since the surface waves supporting the stress grew relatively slowly. Changing water temperature or current in the water caused a pronounced change in the wind speed threshold but not in the friction velocity threshold. Changes in fetch of as much as a factor of 2 had no discernible effect on the thresholds. The results imply that wind speed, being a condition imposed on the air-water interface, causes wave growth, while friction velocity, being a result of air-water interactions, is closely related to surface roughness, hence radar cross section, and changes during wave growth.

A numerical study of the retrieval of sea surface height profiles from low grazing angle radar observations is described. The study is based on a numerical method for electromagnetic scattering from 1-D rough sea profiles, combined with theimproved linear representation of Creamer for simulating weakly nonlinear sea surface hydrodynamics. Numerical computations are performed for frequencies from 2975 to 3025 MHz so that simulated radar pulse returns are achieved. The geometry utilized models a radar with an antenna height of 14 m, observing the sea surface at ranges from 520 to 1720 m. The low grazing angles of this configuration produce significant shadowing of the sea surface, and standard analytical theories of sea scattering are not directly applicable.

Three approaches for retrieving sea height profile information are compared. The first method uses a statistical relationship between the surface height and the computed radar cross sections versus range (an incoherent measurement). A second method uses the phase difference between scattering measurements in two vertically separated antennas (vertical interferometry) in the retrieval. The final technique retrieves height profiles from variations in the apparent Doppler frequency (coherent measurements) versus range and requires that time-stepped simulations be performed. The relative advantages and disadvantages of each of the three approaches are examined and discussed.

Microwave modulation by swell waves and its relation to microbreaking waves were investigated in an ocean experiment. Simultaneous collocated microwave and infrared (IR) measurements of wind waves and swell on the ocean were made. The normalized radar cross section sigma₀ and the skin temperature T_skin were both modulated by the swell, but with differing phases. In general, sigma₀ maxima occurred on the front face, whereas T_skin maxima occurred on the rear face of the swell. Infrared imagery has shown that swell-induced microbreaking occurred at or near the swell crest and that the resulting warm wakes occurred on the rear face of the wave. When tilt and range modulations are taken into account, the location of microbreaking also accounts for the maximum of sigma₀ occurring on the front face of the swell. Thus, microbreaking waves generated near the crest of low-amplitude swell can produce microwave and IR signatures with the observed phase. The relationship between microwave and IR signals was further emphasized by comparing microwave Doppler spectra with simultaneous IR and visible images of the sea surface from the same location. When small and microscale breaking waves were present, Doppler spectra exhibited characteristics that are similar to those from whitecaps, having peaks with large Doppler offsets and polarization ratios near unity. When no microbreakers were present, Doppler offsets and polarization ratios were much smaller in accordance with a composite surface scattering theory.

For several years, the Applied Physics Laboratory of the University of Washington has been working with the US Geological Survey to monitor surface currents in various rivers in western Washington State using coherent, continuous-wave (CW) and pulsed microwave systems. The results have demonstrated the feasibility of monitoring horizontal profiles of surface current velocity for use in making non-contact river discharge measurements. Using an X-band pulsed Doppler radar, called RiverRad, from the river bank, we have demonstrated that discharge can be determined from surface velocity measurements on streams with unchanging beds. These measurements were made with the radar antennas directed nearly perpendicular to the flow. The results compare well with standard USGS discharge measurements and with those made by other more conventional instruments. In addition, two arrays of K-band CW microwave sensors, called Riverscat, have been mounted on bridges over the Cowlitz and Nooksack Rivers in a configuration where the antennas are directed along the flow. Intermittent data have now been collected at these sites for several years. The results of these measurements show that the surface velocity of rivers is a function of the depth of the river both at the site and at downstream controls. We indicate here how time series of surface velocity and stage may be used to infer depths of unstable rivers.

Simultaneous microwave radar and radiometer observations of the ocean were conducted from aircraft during the ShoWEx'99 experiment. Both radar and radiometer wind dependences show similar signal growth with wind speed increase (except for the radiometer at vertical polarization and a near-Brewster angle). Analysis of the low-wind data shows that wind speed is a poor characteristic of the sea surface state in calm conditions because the wind field itself is quite non-uniform in space and time. Under such conditions both radar and radiometer data show strong scatter versus mean wind speed, but they are still well correlated with each other. We conclude that both active and passive instruments respond to the local variations of the sea surface roughness, which are not related to the mean wind speed at low winds. Our comparison shows that the best correlation is between the radar looking at 40-60deg and the near-nadir looking radiometer, which agrees with the theory of scattering/emission from a rough surface.

Simultaneous microwave radar and radiometer observations of the ocean were conducted from aircraft during the ShoWEx'99 experiment. Both radar and radiometer wind dependences show similar signal growth with wind speed increase (except for the radiometer at vertical polarization and a near-Brewster angle). Analysis of the low-wind data shows that wind speed is a poor characteristic of the sea surface state in calm conditions because the wind field itself is quite non-uniform in space and time. Under such conditions both radar and radiometer data show strong scatter versus mean wind speed, but they are still well correlated with each other. We conclude that both active and passive instruments respond to the local variations of the sea surface roughness, which are not related to the mean wind speed at low winds. Our comparison shows that the best correlation is between the radar looking at 40–60° and the near-nadir looking radiometer, which agrees with the theory of scattering/emission from a rough surface.

In 2005 and 2006, we mounted an X-band Doppler radar on ships that operated in the South China Sea and off the coast of New Jersey, respectively. The measurements were made only at W polarization in 2005 but at both HH and W polarization in 2006. On average, VV normalized radar cross sections, sigma₀(VV), behaved at grazing angles between 1 and 2 degrees in much the same manner that they do at higher grazing angles. In particular, they showed the second-harmonic dependence on the angle between the antenna-look direction and the wind direction that is characteristic of scatterometry. sigma₀(HH), on the other hand, showed little evidence of the second harmonic component, maximizing with the antenna looking into the wind and minimizing in the opposite direction. For both polarizations, sigma₀ was generally well above that expected from Bragg scattering and the polarization ratio sigma₀(VV) / sigma₀(HH) was much smaller. Surface signatures of internal waves (IWs) off the New Jersey coast were much weaker when the antennas looked in the direction of internal wave propagation than when they looked opposite this direction. Interestingly, for the nonlinear internal waves found in the South China Sea, the opposite phenomenon occurred: W signatures were stronger looking in the direction of IW propagation than opposite to it.

Observed probability distributions of QuikSCAT scatterometer cross sections are matched to expected distributions calculated using a Geophysical Model Function (GMF) with a wind speed threshold and inherent wind variability on the subfootprint scale and also on grid scales of numerical weather prediction (NWP) models. Two independent approaches are taken: In one, the 3-D sample size is 2° x 2° and 1 day, and the wind speed is assumed to be Rayleigh distributed while directions relative to QuickSCAT antenna directions are assumed to be uniform; in the other, the data are binned by NWP analyzed wind speeds into 1 m/s bins and sample sizes of the grid area of the NWP models. Using the results, the variability on these scales is mapped as a function of wind speed, latitude, and season in an effort to establish a global climatology of wind-speed variability. On the basis of the stable calibration of QuikSCAT, the bias of surface winds produced by the National Center for Environmental Prediction (NCEP) and the European Center for Medium-Range Weather Forecasts (ECMWF) is shown to be substantial and strongly dependent on wind speed, latitude, and season. Changes in wind-speed variability with changes in averaging scale are further explored and estimates of the kinetic energy spectra of the mesoscale to basin-scale winds are determined.

The effect of rain on the ocean surface alters the relationship between the surface wind vector and microwave backscatter, presenting an obstacle to wind retrieval via scatterometry. To address the effect of rain on surface backscatter, we develop a physically based ocean surface wave model modified by rain. Microwave backscatter is then calculated using a multiscale scattering model. Comparisons to observations at Ku band are used to validate and tune our surface model. Simulations give insight into backscattering surface features: ring waves result primarily from the collapse of the splash-created stalk, and the impulse responsible for the generation of ring waves has a radius roughly 5 times the drop's radius. Comparisons also show that backscatter from stationary splash features is necessary to accurately reproduce the effect of rain at Ku band. For Ku band our simulations expand upon prior measurements showing that rain increases backscatter and diminishes azimuthal variations. There is, however, a wind relative azimuthal signature in the backscatter for most rainfall rates. Simulations at Ka band, C band, and L band without the contribution from stationary splash features show that rain-created ring waves often alter backscatter. The effects are greatest at Ka band where they mirror changes to the very high-frequency region of the surface wave spectrum. C band backscatter is increased at moderate and high incidence angles and is sensitive to rain-induced damping. The effect of rain on L band is to decrease backscatter at high rain rate, and it is also dependent on rain-induced damping.

Conventional measurements of river flows are costly, time-consuming, and frequently dangerous. This report evaluates the use of a continuous wave microwave radar, a monostatic UHF Doppler radar, a pulsed Doppler microwave radar, and a ground-penetrating radar to measure river flows continuously over long periods and without touching the water with any instruments. The experiments duplicate the flow records from conventional stream gauging stations on the San Joaquin River in California and the Cowlitz River in Washington. The purpose of the experiments was to directly measure the parameters necessary to compute flow: surface velocity (converted to mean velocity) and cross-sectional area, thereby avoiding the uncertainty, complexity, and cost of maintaining rating curves. River channel cross sections were measured by ground-penetrating radar suspended above the river. River surface water velocity was obtained by Bragg scattering of microwave and UHF Doppler radars, and the surface velocity data were converted to mean velocity on the basis of detailed velocity profiles measured by current meters and hydroacoustic instruments. Experiments using these radars to acquire a continuous record of flow were conducted for 4 weeks on the San Joaquin River and for 16 weeks on the Cowlitz River.

At the San Joaquin River the radar noncontact measurements produced discharges more than 20% higher than the other independent measurements in the early part of the experiment. After the first 3 days, the noncontact radar discharge measurements were within 5% of the rating values. On the Cowlitz River at Castle Rock, correlation coefficients between the USGS stream gauging station rating curve discharge and discharge computed from three different Doppler radar systems and GPR data over the 16 week experiment were 0.883, 0.969, and 0.992. Noncontact radar results were within a few percent of discharge values obtained by gauging station, current meter, and hydroacoustic methods. Time series of surface velocity obtained by different radars in the Cowlitz River experiment also show small-amplitude pulsations not found in stage records that reflect tidal energy at the gauging station. Noncontact discharge measurements made during a flood on 30 January 2004 agreed with the rated discharge to within 5%. Measurement at both field sites confirm that lognormal velocity profiles exist for a wide range of flows in these rivers, and mean velocity is approximately 0.85 times measured surface velocity. Noncontact methods of flow measurement appear to (1) be as accurate as conventional methods, (2) obtain data when standard contact methods are dangerous or cannot be obtained, and (3) provide insight into flow dynamics not available from detailed stage records alone.

Time series of surface velocity and stage have been collected simultaneously. Surface velocity was measured using an array of newly developed continuous-wave microwave sensors. Stage was obtained from the standard U.S. Geological Survey (USGS) measurements. The depth of the river was measured several times during our experiments using sounding weights. The data clearly showed that the point of zero flow was not the bottom at the measurement site, indicating that a downstream control exists. Fathometer measurements confirmed this finding. A model of the surface velocity expected at a site having a downstream control was developed. The model showed that the standard form for the friction velocity does not apply to sites where a downstream control exists. This model fit our measured surface velocity versus stage plots very well with reasonable values of the parameters. Discharges computed using the surface velocities and measured depths matched the USGS rating curve for the site. Values of depth-weighted mean velocities derived from our data did not agree with those expected from Manning's equation due to the downstream control. These results suggest that if real-time surface velocities were available at a gauging station, unstable stream beds could be monitored.

Simple Bragg scattering is often the type of rough surface scattering applicable to rivers. Thus the center frequency of the Doppler spectrum provides information on the velocity of the surface of the river. We have developed a simple continuous wave microwave system called Riverscat to take advantage of this effect to measure river surface currents. Measurements with this velocity sensor show that surface velocity is well related to the depth of the river. Therefore on unstable streams where the bottom changes either at the measurement site or downstream of it, Riverscat offers the potential for improved monitoring of stream discharge.

A coherent, X-band airborne radar has been developed to measure wind speed and direction simultaneously with directional wave spectra on the ocean. The coherent real aperture radar (CORAR) measures received power, mean Doppler shifts, and mean Doppler bandwidths from small-resolution cells on the ocean surface and converts them into measurements of winds and waves. The system operates with two sets of antennas, one rotating and one looking to the side of the airplane. The rotating antennas yield neutral wind vectors at a height of 10 m above the ocean surface using a scatterometer model function to relate measured cross sections to wind speed and direction. The side-looking antennas produce maps of normalized radar cross section and line-of-sight velocity from which directional ocean wave spectra may be obtained. Capabilities of CORAR for wind and wave measurement are illustrated using data taken during the Shoaling Waves Experiment (SHOWEX) sponsored by the Office of Naval Research. Wind vectors measured by CORAR agree well with those measured by nearby buoys. Directional wave spectra obtained by CORAR also agree with buoy measurements and illustrate that offshore winds can produce dominant waves at an angle to the wind vector that are in good agreement with the measurements. The best agreement is produced using the Joint North Sea Wave Project (JONSWAP) parameterizations of the development of wave height and period with fetch.

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.

Microwave and acoustic systems operated in the large wind-wave tank in Luminy, Marseille, France, show that most small-scale waves produced at large angles to the wind are products of breaking events bound to longer waves in the tank. These longer waves propagate at the dominant wave phase speed for fetches near 7 m but travel at speeds corresponding to the phase speed of a wave half as long as the dominant wave at fetches near 26 m. The microwave and acoustic systems operated at both 8 mm and 2 cm wavelengths. They were set to look at the same surface spot simultaneously at the same incidence and azimuth angles. Measurements were made at seven wind speeds, five incidence angles, seven azimuth angles, and two nominal fetches. Two peaks were found in either the microwave or acoustic Doppler spectrum when looking upwind or downwind but never in both. The low-frequency peak is due to Bragg scattering from freely propagating short waves, while the high-frequency peak is a result of Bragg scattering from short waves bound to longer waves. At azimuth angles not aligned with the wind direction the high-frequency peak was found to move lower until it merged with the low-frequency peak at azimuth angles around 60°.

Fitting the first moments of these Doppler spectra along with the backscattering cross sections to a model of free wave/bound wave scattering showed that the intensity of bound and free short waves generally decreased with azimuth angle but that free wave spectral densities decreased more rapidly. Differences in microwave and acoustic cross sections confirmed that the bound waves were tilted by their parent waves. Spectral densities of bound and free waves were estimated individually by fitting the data to the model. The sum of these spectral densities, the total short-wave spectral density, was similar to, but lower than, previous measurements. The nature of millimeter-length bound waves was found to be different at long fetches than at short fetches, a feature not observed in centimeter-length bound waves.

The aerodynamic friction between air and sea is an important part of the momentum balance in the development of tropical cyclones. Measurements of the drag coefficient, relating the tangential stress (frictional drag) between wind and water to the wind speed and air density, have yielded reliable information in wind speeds less than 20 m/s (about 39 knots). In these moderate conditions it is generally accepted that the drag coefficient (or equivalently, the "aerodynamic roughness") increases with the wind speed. Can one merely extrapolate this wind speed tendency to describe the aerodynamic roughness of the ocean in the extreme wind speeds that occur in hurricanes (wind speeds greater than 30 m/s)? This paper attempts to answer this question, guided by laboratory extreme wind experiments, and concludes that the aerodynamic roughness approaches a limiting value in high winds. A fluid mechanical explanation of this phenomenon is given.

Ku-band backscatter from the Cowlitz River in southwestern Washington State was measured for incidence angles from 0° to 80°. The measurements were made for light-wind conditions with and without rain. In rain-free conditions, Bragg scattering was the dominant scattering mechanism for both horizontal (HH) and vertical (VV) polarizations out to 75°, beyond which the SNR dropped very low at HH. When a light rain was falling on the river, the cross section increased substantially at moderate incidence angles. Doppler spectra taken during rain showed that VV polarized backscatter is primarily from Bragg scattering from ring waves, while HH polarization scatters from both ring waves and stationary splash products, depending on the incidence angle. From the VV polarized measurements, surface wave height spectrum for ring waves is inferred for light rains. Finally, a change in spectral properties was observed when rain changed to hail.

For several years, suggestions have been made that sea surface roughness cannot be adequately explained in terms of weakly interacting, wind-generated waves. Rather, ripples that are generated by longer waves, are tilted by them, and are moving at nearly the speed of the longer wave have been postulated to coexist with waves that are directly generated by the wind, that is, with free waves. Effects of these bound waves have been detected in microwave backscatter on the ocean and in wind-wave tanks, and in surface-slope probability density functions (PDFs) in wind-wave tanks. Here we show that Cox and Munk's sea-surface slope PDFs are fully consistent with this bound wave/free wave model. From the fits of these PDFs to the model, we conclude that probabilities of finding bound waves are nearly the same in wind-wave tanks and on the ocean, and both are much higher than the probability of observing whitecaps. Variances of both bound and free waves are larger on the ocean than in tanks.

During the Kwajalein Experiment (KWAJEX) in 1999 the effect of rain on Ku band normalized radar cross sections of the sea, /spl sigma//sub 0/, was measured for a wide range rainfall rates and incidence angles. The primary result was that rain significantly increases the cross section at moderate to high incidence angles, obscuring, if not eliminating backscatter from wind-generated waves. To verify our understanding of the effect of rain on sea surface roughness and to extend it to smaller incidence angles and other microwave frequencies we modeled microwave backscatter from a rain-disturbed ocean surface. To do this, we developed a realistic representation of the ocean surface perturbed by wind and rain which accounts for the damping of surface waves by rain-induced subsurface turbulence and for the enhancement of gravity-capillary and short gravity waves by rain-generated ring-waves. The spectral representation of the ocean surface is used as input to a scattering model. The multiscale scattering model used here separates surface waves into three distinct scales (short, intermediate, and long) and evaluates /spl sigma//sub 0/ for each scale. Since rain significantly alters short gravity waves (i.e. the intermediate scale), the explicit calculation in the model of backscatter from these waves makes it ideal for diagnosing the effects of rain. We will show that values of /spl sigma//sub 0/ computed by the model are in quantitative agreement with KWAJEX data. We will also show modeled rain effects on the cross section at low incidence angles for a variety of microwave frequencies.

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.

Sea-surface slope probability density functions, which are usually fitted to a Gram-Charlier series, can be fit equally well by a bound wave/free wave model in which the distributions of bound and free waves are Gaussian. Bound waves are generated by longer waves on the surface and travel at nearly the phase speed of the long wave while free waves are generated directly by the wind and travel at their intrinsic phase speed. These two types of short surface waves can usually be separated in measurements that yield their velocities. The integrals over the two distributions yield the probabilities of finding bound or free waves on the surface. We show that the probability of finding bound waves on the ocean is comparable to that in a wind-wave tank and much larger than the probability of whitecapping. The mean slopes of the two distributions yield the mean tilts of bound or free waves. We show that the mean tilt of the bound waves is similar to that in a wind-wave tank and close to that necessary to explain Doppler shifts in microwave backscatter from the sea surface at high incidence angles. Finally, the widths of the two distributions yield the variance of sea-surface slopes at the locations of bound and free waves. We show that these are larger at sea than in a wind-wave tank, which explains why bound waves at sea have not been recognized previously in sea-surface slope probability distributions.

During ONR's Shoaling Waves Experiment (SHOWEX) off the coast of North Carolina in November and December 1999, measurements of wind speed and direction as well as air and water temperatures were made using a variety of techniques. This paper shows a comparison of the measurements taken on December 3, 1999.

Since October of 2002, eight CW microwave sensors have been operating on a bridge over the Cowlitz River in western Washington State in the USA. These sensors measure the river surface velocity via Doppler shifts at eight locations across the river; a ninth unit pointing upwards measures scattering from rain drops.

During the Kwajalein Experiment (KWAJEX) in July and August 1999, measurements of the normalized radar cross section of the ocean, σ_o , were made at Ku-band with HH and VV polarizations from the R/V Ronald H. Brown. Data were collected at a variety of incidence angles during periods of rainfall as well as during clear conditions. During the experiment the rainfall rate ranged from 0 to 80 mm hr^-1. Coincident with the backscatter measurements, measurements of rain rate, wind speed, wind direction, and fluxes of heat and momentum were made. Since we were primarily interested in backscatter from the surface, we removed backscatter from the raindrops themselves for the #963;_o measurements reported here. As a secondary result we show that the backscatter from the rain drops is a good indicator of rain rate. Most of the data were collected with the ship stationary and the bow held into the wind. Thus the azimuth angle between the antenna look direction and the direction from which the wind came was predominantly between 0° and 90°. Over this range, rain was found to increase #963;_o at incidence angles of 30° to 75°, to have little effect near 20°, and to decrease #963;_o very slightly between 14° and 16°. At all incidence angles, no discernible dependence of #963;_o on wind speed was found during rainfall for wind speeds below 10 m s^-1; within experimental error the level of #963;_o depended only on rain rate. For the lower incidence angles, this dependence was very small while at the higher incidence angles, #963;_o depended on rain rate to a power that varied between about 0.5 and 1.2, being somewhat higher at large incidence angles and higher for HH polarization. The implication of these results is that rain produces small-scale surface displacements (wavelengths shorter than about 3 cm) that roughen the ocean surface much more than the wind for wind speeds below 10 m s^-1. The results also imply that when rain fills the entire scatterometer footprint on the surface and the wind speeds are low to moderate, scatterometry at Ku band is impossible.

The United States Geological Survey and the University of Washington collaborated on a series of initial experiments on the Lewis, Toutle, and Cowlitz Rivers during September 2000 and a detailed experiment on the Cowlitz River during May 2001 to determine the feasibility of using helicopter-mounted radar to measure river discharge. Surface velocities were measured using a pulsed Doppler radar, and river depth was measured using ground-penetrating radar. Surface velocities were converted to mean velocities, and horizontal registration of both velocity and depth measurements enabled the calculation of river discharge. The magnitude of the uncertainty in velocity and depth indicate that the method error is in the range of 5 percent. The results of this experiment indicate that helicopter-mounted radar can make the rapid, accurate discharge measurements that are needed in remote locations and during regional floods.

The conventional view of microwave backscatter from the ocean is based on composite surface and quasi-specular theories. In this view, backscatter at intermediate incidence angles is due to Bragg scattering from freely propagating short surface waves that are advected and modulated by longer waves. At small incidence angles the scattering process becomes quasi-specular, coming from small facets aligned normal to the incident waves. The transition between these two processes is said to occur at incidence angles of about 10° to 20°.

In this paper we demonstrate that advances in scattering theory and in computing speed make it possible to improve this view. We show that recent scattering theories agree on the form of the backscatter for incidence angles below that where multiple scattering must be considered, i.e., below about 80°. This form involves the Kirchhoff integral multiplied by a coefficient dependent on dielectric constant and incidence angle. We avoid the higher-order calculations necessary in these theories to include the variable local incidence angle caused by surface wave slopes by applying them over restricted regions of the surface. We successively break the surface into regions from which the scatter comes from small-, intermediate-, and large-scale waves. We show that in this picture, scattering from small-scale waves is classic Bragg scattering and is very common while from large-scale waves it is classic quasi-specular scattering and is rarely important. For intermediate-scale waves we evaluate the Kirchhoff integral numerically; this type of scattering becomes increasingly important with increasing wind speed. For all scales but the large one we correct the incidence angle for the slopes of all longer waves as required by composite surface theory. On this picture the transition from Bragg scattering to Kirchhoff scattering occurs gradually in a manner that is dependent on incidence angle, azimuth angle, wind speed, and the surface wave spectrum. The model indicates that Bragg scattering is often viable to surprisingly low incidence angles at low wind speeds. The model is sensitive to the wave height variance spectrum over a wide range of wave numbers. We use two recently published forms of this spectrum to compare the predictions of the model to various data that have been collected over the incidence angles range from 0° to 50°. At 0° this model produces a better fit to Ku band data from the TOPEX altimeter than does quasi-specular theory and does so with no artificial "effective reflection coefficient." As the incidence angle increases, the model continues to show good agreement with data without an artificial division into "quasi-specular" and "Bragg" scattering. The advantage of this formulation over a quasi-specular one is demonstrated by comparing the two models with data on received power taken at 36 GHz for incidence angles between nadir and 30°.

The dependence of the normalized radar cross section of the sea on wind variability within the resolution cell is examined by considering probability distributions of cross sections and wind vectors. If a threshold wind speed exists below which backscatter is negligible for steady winds, variability of the wind over the resolution cell is shown to cause significant backscatter at mean wind speeds below the threshold. In fact, if the variability is sufficiently high, cross sections become essentially constant at very low wind speeds. The viability of this model is tested by comparing its predictions based on the NASA scatterometer 2 (NSCAT2) model function with probability distributions obtained from NSCAT cross sections that are collocated with buoy measurements. Both the overall probability distribution of cross sections and the probability of negative cross sections obtained from the NSCAT data are shown to be in good agreement with the predictions. A means of improving the accuracy of low wind speed scatterometer measurements is suggested when wind variability is not too high.

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.

Measurements of the normalized radar cross section of the sea at K_u band at an incidence angle of 10° were performed from a manned airship off the Oregon coast in September and October of 1993. The cross section at this incidence angle is often assumed to have little dependence on windspeed and direction. Their measurements, however, indicate that at windspeeds below 6–7 m/s, the cross section is in fact dependent on these quantities, and the azimuthal modulation can reach values on the order of 5–8 dB. Comparisons of the measured values with the predictions of the quasispecular scattering model are presented. The theory is shown to be accurate in predicting the azimuthal modulation and the strength of the backscatter if the effects of swell are included or if measured wind directions are ignored and the upwind direction is forced to be near the maximum cross section. Values of mean-square wind-wave slope and effective-reflection coefficient required to obtain these fits are very close to those obtained by previous investigators. In particular, mean-square wind-wave slopes are about 70–80% of those of Cox and Munk (1954) because the radar responds only to facets larger than about 10 cm, with smaller ripples acting to reduce the reflection coefficient. If swell is included, they find that mean-square slopes in the direction of the swell, that are as much as ten times the measured swell slopes, are required to fit the model to the cross-section data at low windspeeds. They suggest that this may be due to high-order effects of the hydrodynamic modulation of short waves by the swell. They believe that this explanation is more likely than assuming that wind directions were incorrectly measured.