R. D. Chapman

On the statistics of the phase of microwave backscatter from the ocean surface

In this paper we describe what we believe is the first study of the distribution of the phase of microwave fields backscattered from the ocean surface. Scatterometry data from the Synthetic Aperture Radar and X band Ocean Nonlinearities experiment conducted on the German North Sea Research Platform, Forschungsplatform Nordsee, in November 1990 have been analyzed to reveal the distribution of phase differences as a function of time lag. A theoretical model for these statistics is presented based on modulated Gaussian fields. This theoretical model is shown to be in good agreement with the measured statistics. From this agreement we conclude that the backscattered fields have a Gaussian distribution on short time scales but are modulated in amplitude and frequency by the long surface waves. These results are of more than purely academic interest, with direct applications to the design and analysis of interferometric synthetic aperture radars, a relatively new class of instruments that may be capable of providing high-resolution maps of ocean surface currents from aircraft or satellites.

Errors in estimating slope spectra from wave images

Slope spectral density resolved in wave number and direction is an important statistical descriptor of water surface waves. Experimentalists have estimated this descriptor from optical wave imagery by assuming that light from the surface is modulated linearly by the component of wave slope aligned with the imaging azimuth. The level of error arising from this assumption of linearity depends on the optical conditions and can be severe. We have numerically explored this error when only reflected radiance is imaged by using a synthesized sea surface and a clear sky model to simulate sea surface imaging. Additionally, we have developed a method for identifying geometries which minimize nonlinearity. This paper describes our analytic models, our numerical techniques, and the character of our results.

Observations of ship-generated internal waves in SAR images from Loch Linnhe, Scotland, and comparison with theory and in situ internal wave measurements

In the 1989 Loch Linnhe experiment, ship-generated internal waves were imaged from airborne synthetic aperture radars (SARs) operating at various frequencies. In this paper, we examine K/sub a/, K/sub u/, X, and C-band images at moderate incidence angles (21-30/spl deg/) where peak-to-peak modulations of 3.3, 1.6, 1.3, and 0.7 dB, respectively, were observed. In situ time-series measurements of the internal-wave induced currents were made from a spar buoy. The SAR and current-meter data sets were compared by using the images to estimate the equivalent image intensity time series at the location of the spar. This was accomplished using linear internal wave theory with the Keller-Munk formulation of the wave-wake kinematics. The validity of this approach is confirmed by the good agreement obtained between predicted and observed wake geometries. Quantitative comparisons were made between measured radar modulations and predictions from wave-current interaction and radar scattering models. These comparisons indicate that the observed phase relationships between the radar modulation and the current are well predicted for each of the four radar frequencies, but that the magnitude of the predicted modulations is too low at the higher frequencies.

Measurements of the internal wave wake of a ship in a highly stratified sea loch

An internal wave experiment was conducted in Loch Linnhe, Scotland, in which three ships were used to generate internal wave wakes. Synthetic aperture radar images of the wakes confirmed the applicability of the kinematic theory of Keller and Munk for the geometry of the wave pattern. The waves were measured in situ using three-axis current meters and other instrumentation. The waves were quite well represented by linear propagation theory, although the dependence of amplitude on depth did not agree precisely. The time-varying frequency of the waves was determined from the data in two different ways, including a Hubert transform method, and agreed well with that predicted by the theory. The subsurface data were used to estimate the surface current and its gradient (the strain rate). Any dependence of wave amplitude on ship speed was weak enough to be obscured by variations due to changes in the stratification. Amplitude estimates of waves from the 1400- and 5300-tonne ships were similar. Those from the 29,000-tonne ship were 2–3 times greater.

The Sinking of Warm-Core Rings

Abstract Intense cooling of a warm-core ring or warming of the fluids surrounding a ring can increase the density of that ring relative to the surrounding fluids. This increase in density can cause the ring to sink under the surrounding fluids. A simple model of this process in a two and one-half layer (two active and one passive layer) ocean consisting of an inviscid Boussinesq fluid on an f-plane is presented. The model assumes that the cooling or heating occurs in such a way as to maintain a uniform density throughout each of the active layers. This special form of the heat flux allows the results for various relative ring densities to be connected through the conservation of potential vorticity. Analytic solutions are constructed and their structure helps to establish the physical processes accompanying the sinking of a ring. Results show that warm-care rings can sink in a matter of weeks when exposed to typical cold-air outbreaks of −1000 W m−2 surface heat flux. The model predicts that when the ring...

Target Motion Ambiguities in Single-Aperture Synthetic Aperture Radar

A simple approach to the detection and estimation of target motion based on phase measurements from a single-aperture synthetic-aperture radar (SAR) is presented. In this analysis the SAR is treated as a pure range-measuring device. Each stationary object in a scene produces a unique range-time history in the radar. Thus, ideal SAR processing is reduced to finding the response to the set of matched filters associated with stationary targets. For this purely geometrical model, it is shown that there exists a class of moving targets that are absolutely indistinguishable from a stationary target. These are targets that move in such a way that the range to the SAR is always identical to the range from the SAR to some stationary target. Moreover it turns out that most moving targets are also indistinguishable from some other moving targets. The idealized SAR is only sensitive to a single velocity component of the target, and thus most solutions are degenerate. Theoretical limits of the detection of motion are established that are dependent on SAR parameters and observation time. Fast-moving (e.g. spaceborne) SARs can detect along-track motions with less ambiguity than a slow-moving SAR. It is shown that most moving targets do produce apparent motion in sequences of multilook SAR imagery. These apparent motions can be used to estimate the measurable component of target velocity.

A novel wave height sensor

Abstract A novel transducer for the measurement of water level is described. This transducer consists of a tantalum wire anodized in a weak citric acid solution. The anodization forms a uniform, thin layer of tantalum oxide on the surface of the wire. When partially submerged through an air-water interface, the capacitance of the wire is directly proportional to the water level. This transducer has been applied in oceanographic research buoys to measure gravity and capillary wave height. In this application, the transducer offers greater sensitivity, linearity, and ruggedness than conventional capacitive wave sensors.

Note on the reduction of the “full‐wave” method for rough surface scattering to the small‐height limit

The form of the equations for the backscattered fields used in the analysis of Thorsos and Winebrenner (Journal of Geophysical Research, 96, 17,107–17,121, 1991) and that of Bahar (Journal of Geophysical Research, 96, 17,123–17,131, 1991) in the limit as surface heights and slopes become small (SP limit) is examined. Both of these analyses start from the expression for the total full-wave scattered field as given by Bahar (IEEE Transactions on Antennas and Propagation, AP-28, 11–21, 1980). In his analysis, Bahar subtracts from this total field a so-called diffraction field that he claims is important only near the specular direction. If this claim were correct, then such a subtraction should have little effect on the computed cross section for scattering directions away from the specular direction. In the SP limit, however, we show that Bahars diffraction field contributes to the backscatter cross section in all directions. The subtraction of the diffraction field exactly cancels the second-order moments responsible for the difference between the limiting cross sections found in the two analyses. It is because of this subtraction that Bahar is able to show agreement with the SP limit. Furthermore, we find that Bahars expression does not yield the correct diffusely scattered field from a tilted planar surface or from a smooth cosine surface with zero mean slope. The failure of Bahars expression for these simple cases indicates to us that even though it does reduce to the proper SP limit, it is not a correct general expression for the diffusely scattered, horizontally polarized field backscattered from a perfectly conducting, one-dimensionally rough surface as is claimed in his article.

LaRA-2002: results of the airborne laser and radar altimeter campaign over Greenland, Svalbard, and Arctic sea ice

The primary objectives of LaRA-2002 were to assemble measurements of land and sea ice with simultaneous observations from a low-altitude aircraft by laser and radar altimeters. Data from the mission was expected to illustrate similarities and differences between these two very different means of measuring surface height. These objectives were met. This paper provides an overview of the project, and includes highlights of the results.

Multiple sea spike definitions: reducing the clutter

Multiple definitions of sea spikes have been developed and presented in the literature. This study shows the characteristics of spike populations where absolute cross section ratios are not critical to the spike definition.