An improved composite surface model for the radar backscattering cross section of the ocean surface: 1. Theory of the model and optimization/validation by scatterometer data

Abstract

Abstract. An improved composite surface model for the calculation of the normalized radar backscattering cross section (NRCS) of the ocean surface at moderate incidence angles is presented. The model is based on Bragg scattering theory. A Taylor expansion of the NRCS in the two-dimensional surface slope yields nonzero second-order terms which represent a first approximation for the effect of the geometric and hydrodynamic modulation of the Bragg scattering facets by all waves that are long compared to these facets. The corresponding expectation value of the NRCS varies with the wave height spectral density of all these waves, and it depends in a well-defined way on frequency, polarization, incidence angle, and azimuthal look direction of the radar. We show that measured NRCS values at frequencies ranging from 1 GHz (L band) through 34 GHz (Ka band) and wind speeds between 2 and 20 m/s can be well reproduced by the proposed model after some reasonable tuning of the input ocean wave spectrum. Also, polarization effects and upwind/downwind differences of the NRCS appear to be relatively well represented. The model can thus be considered as an advanced wind scatterometer model which is based on physical principles rather than on empirical relationships. The most promising field of application, however, will be the calculation of NRCS variations associated with local distortions of the wave spectrum by surface current gradients or wind effects.

Incidence angle normalization of Wide Swath SAR data for oceanographic applications

“…400 km) and all backscatter variations are altered from that sea state. For example, according to Bragg scattering theory, the resonant sea wavelengths (λ) for ENVISAT ASAR WSM images captured in the C-band of the 5.6 cm wavelength and at incidence angles of approximately 15 ∘ -45 ∘ are in the range of 10.8-3.4 cm [18]. Hereafter, a second assumption that the incidence angle of θ ref = 30 ∘ is the most appropriate angle for image normalization is necessary.…”

“…This model is based on physical principles rather than on an empirical relationship and calculates the σ ∘ values based on geometric and hydrodynamic modulation. The Bragg scattering model is widely applied, however, neither the measured σ ∘ values for specific combinations of radar parameters and environmental conditions nor their observed variation can be explained satisfactorily by pure Bragg scattering theory [18]. A more advanced microwave backscatter model is described by [17].…”

“…Backscatter energy over the sea surface is strongly related to the incidence angle and wind speed and presents a broad range of backscatter levels: −40 dB < σ ∘ < +10 dB from far to near range. Ocean backscatter modeling is often described by the Bragg model [15][16][17][18], which is appropriate for intermediate incidence angles (approximately 20 ∘ -60 ∘ ) and describes scattering from short gravity-capillary waves at the C-band wavelength. This model is based on physical principles rather than on an empirical relationship and calculates the σ ∘ values based on geometric and hydrodynamic modulation.…”

Directional wavenumber characteristics of short sea waves

“…The data is stored in 5.12 second blocks, is indexed by board, and is also indexed by time step; the first data point (time tl) for the first 16 channels (board 1) is stored, then the second data point (time t2) for the first 16 channels is stored, and so on until 512 data points for each of the 16 channels has been stored. Each of the remaining three boards (channels 17-32, channels 33-48, and channels [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64] is stored the in the same fashion. Once the first 512 samples of each of the 64 channels have been stored, then the cycle repeats for the second block of 512 samples.…”

“…Finally, Romeiser et al [55], accepted the basis of the Apel form of Donelan's spectrum, but noted that it did not accurately reproduce measured cross-wind/downwind ratios measured with scatterometers from L to Ka-band. The model they propose takes the following…”