Specular point scattering contribution to the mean Synthetic Aperture Radar image of the ocean surface

n general, the return signal scattered from the ocean surface used to form synthetic aperture radar (SAR) images contains contributions from at least two scattering mechanisms. In addition to resonant Bragg‐type scattering, specular point scattering becomes important as the angle of incidence becomes small ( ≲ 20°). In this paper we include the specular point rough surface scattering mechanism in a model for the mean SAR image of the ocean surface and examine the effects of this scattering mechanism theoretically. We find that the complete mean SAR intensity image consists of a sum of images due to specular point scattering and Bragg‐type resonant scattering. Because surface specular points have a short coherence time and move with considerable velocities, the contribution to the mean image due to these scatterers is of low azimuthal resolution and is displaced from the actual sea surface, typically by several SAR resolution cells. The bandwidth of this image can easily exceed the bandwidth of a typical SAR processor, leading to a loss of mean image intensity. The local backscatter cross‐section modulation is strong and nonlinear in the slope of the longwave field in the SAR range direction. At small incidence angles, this causes the specular point return from wave slopes tipped toward the SAR to become much brighter than the Bragg‐scattering return. Taken together, these effects are capable of producing azimuthally oriented streaks in SAR images, such as have been observed by Seasat. We present numerical estimates of coherence time, azimuthal displacement, cross‐section modulation, etc., computed using the parameters of the Seasat and shuttle imaging radar‐B SARs as well as typical parameters for an airborne X band SA

Out-of-equilibrium actor-based system-dynamic modeling of the economics of climate change

The actor-based system-dynamic approach to macroeconomic modeling is illustrated for a simple model hierarchy consisting of a basic two-dimensional model with several alternative three-dimensional extensions. The hierarchy is based on an out-of-equilibrium approach: market clearing is not assumed, supply is not equal to demand, and there exists a stock of unsold goods. Depending on actor behaviour, the models exhibit stable exponential growth or instabilities leading to oscillations or economic collapse. In most cases, the simplicity and tractability of the models enables analytical solutions. The examples serve as illustration of more realistic models developed within the Multi Actor Dynamic Integrated Model System (MADIAMS) to assess the long-term impacts of climate mitigation policies

Directional wave spectra observed during JONSWAP 1973

Estimates of the directional wave spectrum obtained from the meteorological buoy of the University of Hamburg and a pitch-and-roll buoy of the Institute of Oceanographic Sciences are reported from a series of measurements made within the framework of the Joint North Sea Wave Project during September 1973. Three main aspects were considered. First, the properties and parameterization of the directional spectrum were studied when the waves were generated by steady winds without any significant swell contribution. The results do not support the parameterization proposed by Mitsuyasu et al. (1975) and are in agreement with a parameterization in which the peak frequency is the relevant scale parameter. Second, comparisons are made between two independent methods of fitting the data exactly by means of a maximum likelihood technique (Long and Hasselmann, 1979) and a least-squares technique. The two methods give very similar fits to the observed data. Finally, the response of the directional wave spectrum to veering winds is considered and a simple model is constructed as a first attempt to describe some of the observations