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A comprehensive exploration of the transformer and dual-receiver system-based direction-of-arrival (DOA) estimation is presented in the context of sea surface scattering, particularly under varying sea conditions. A bidirectional encoder representation from transformer (BERT) with a physics-based loss function is utilized to process two individual channel radars. The datasets are the radar scattering coefficients of sea surface simulated at C-band for copolarizations and cross-polarizations. Through detailed analysis of simulated datasets and root mean square error (RMSE) evaluations, the model’s performance is investigated across different observation modes, namely, the co-polar (CP), co-azimuth (CA), full-bistatic (FB), and Beaufort wind scale from 3 to 5. Our study demonstrates that the bidirectional encoder representation from transformer model, employing a physics-based loss function, outperforms the baseline long short-term memory (LSTM) model, especially under high noise levels and with larger datasets. Significant correlations between wind conditions and DOA accuracy are observed, highlighting the bidirectional encoder representation from transformer model’s adaptability to dynamic environmental factors, particularly under increased wind scales. The choice of observation mode, with CP and FB consistently outperforming CA, proves pivotal. Precise simulation of speckle variations and optimized observation mode selection are identified as crucial avenues for enhancing the model’s practical utility.

This article employs the modulated correlation function (MCF) model to describe the ocean surface in radar backscattering. Surface correlation functions derived from wind wave spectra: Apel, Elfouhaily, Kudryavtsev, and Hwang models are examined. The spectral properties of the above spectra are also analyzed, including the height, slope, and saturation spectra. The results suggest that the MCF model is applicable in depicting spatial correlation of ocean surface. At the same time, the spectrum of MCF may not be proper in describing the energy cascade of ocean waves. The comparisons of backscatter are made among the MCF model and wind wave spectra, with regard to dependences of radar frequency at L-, C-, X-, and Ku-bands, wind vector, and incidence angle. The results indicate that the MCF model yields the overall minimum errors in radar backscatter against geophysical model functions (GMFs). We validate the model with the airborne and spaceborne radar measurements and show that the MCF model gives good agreement at the C-band but only moderate at the Ku-band. Meanwhile, the backscatters calculated based on different wind wave spectra can significantly deviate from each other, related to the magnitudes of the short-wave spectrum. Besides, the breaking wave effect on radar backscatter is also discussed.

We analyzed the spatiotemporal variations of the imaging swath and region using the lunar-based synthetic aperture radar (LBSAR) for Earth observation. The ground and slant swaths following the Earth-observing geometry and synthetic aperture radar (SAR) configurations were formulated. The bounds of the imaging swath were highlighted for appropriately configuring the LBSAR. The results suggested that the imaging swath is determined by the coupling of orbit elements, near-look angle, antenna beamwidth, and to some extent by the Earth’s ellipsoidal shape and LBSARs site location on the Moon’s surface. The side-looking direction, despite its modest impact on the imaging swath, plays a dominant role in ascertaining LBSARs imaging region. Furthermore, spatiotemporal variations of ground swath in various epochs were analyzed to emphasize the challenge and importance of characterizing Earth observation capability in the LBSAR.

Surface parameters (roughness and soil permittivity) are crucial for characterizing backscattering from bare soil. However, the estimation of roughness parameters (root-mean-square (rms) height and correlation length) depends on the sample surface size. The conversion between dielectric constant and soil moisture is disturbed by the dielectric model. These estimation biases significantly compromise the reliability of backscattering coefficients derived from analytic modeling, numerical simulations, and experimental measurements. In this study, we illustrate the statistical relationship between sample surface size and estimation bias of surface roughness at varied accuracy levels. To quantify the estimation bias of surface roughness with sample surface size and the estimation bias of soil permittivity, we analyze the propagation from the estimation bias of surface parameters to the backscattering coefficient error by the advanced integral equation model (AIEM) model. By comparing it with measurement data, we quantitatively confirm the impact of roughness parameter estimation bias. Ultimately, quantifying the backscattering coefficient error as a function of sample surface size and incident angle allows for selecting the optimal sample surface sizes suitable for L-band synthetic aperture radar (SAR) simulation and soil moisture retrieval, along with their applicability over various incident angles. This study suggests sample surface sizes for estimating roughness parameters and backscattering coefficients at various levels of accuracy.