DOI: 10.14284/446
title: Synthetic data of ATI-SAR images from swell-like ocean surfaces, using the ATI-SAR velocity bunching model of Bao, Bruening and Alpers (1997). ATW scenarios: A construction from 01-Feb-2018 to 31-March-2019

description: Synthetic data of ATI-SAR images from swell-like ocean surfaces, using the ATI-SAR velocity bunching model of (Bao-Bruening-Alpers, 1997). This comprises three netCDF4 files, where each of them defines a particular ATW scenario. Each scenario was constructed to test three techniques that solve an inverse problem in oceanography.
description: The dataset comprises the following three scenarios:* The ATW scenario, which characterises azimuthally travelling waves (ATW). File is ATI_SAR_Data_SwellOceanSurface_ATW.nc.* The ATW_R16 scenario, where the wind direction is 20 degrees from ATW, and the nominal slant range is 16 kilometres. File is ATI_SAR_Data_SwellOceanSurface_ATW_R16.nc.* The ATW_R18 scenario, where the wind direction is 20 degrees from ATW, and the nominal slant range is 18 kilometres. File is ATI_SAR_Data_SwellOceanSurface_ATW_R18.nc. The following information describes any of the above-mentioned scenarios:For a given simulated ocean variance spectrum Z, let z denote its associated scalar field of sea surface elevations, and let ur denote its associated scalar field of radial velocities. Also, let ATI-SAR-VB denote the ATI-SAR velocity bunching model of (Bao-Bruening-Alpers, 1997). For our research purposes, the ATI-SAR-VB model is a forward mapping that takes radial velocities and produces a particular complex-valued radar intensity. In the simulation, each intensity is a numerical integration that employs a Newton-Cotes formula. The set of intensities forms the two-dimensional ATI-SAR image I that is associated with the simulated ocean surface. There are five two-dimensional scalar fields that can be mentioned: * The field z describes the simulated ocean surface in terms of its sea surface elevations. It is a real-valued matrix of size Ny x Nx. * The field ur is regarded as the independent variable from which the ATI-SAR image D is generated. It is a real-valued matrix of size Ny x Nx. * The ATI-SAR image D is a perturbed version of I. In our modelling, such a perturbation consists of additive, complex, Gaussian, zero-mean, random noise. The level of noise is characterised by a small standard deviation, which in turn depends on the scaling parameter eps = 0.05. The ATI-SAR image D is a complex-valued matrix of size Ny x Nx. * The estimated solution ur_star_X of the corresponding Ny inverse problems, via X. Here, X denotes one of three solution strategies: SSNLE, UMF and FDDM. * The image D_star_X of ur_star_X under the ATI-SAR velocity bunching model of (Bao-Bruening-Alpers, 1997). Again, X denotes one of three solution strategies: SSNLE, UMF and FDDM. General specification: * All the samples in frequency domain are given in "DFT order": the zero frequency goes first; then the positive frequencies in ascending order (reaching the frequency sample that is immediately before the discarded positive Nyquist frequency); and finally, the negative frequencies in ascending order, from the most negative one (the negative Nyquist frequency) to the less negative one. This occurs for both one-dimensional and two-dimensional fields in the frequency domain. * The ocean parameters and the radar parameters are known in advance. * The azimuthally look direction phi0 borns at the positive x-direction. For the ATW scenarios, phi0 is always PI/2 [rad]. * For the ATW scenarios, the range direction is parallel to the y-axis (parallel to the columns of each matrix). * For the ATW scenarios, the azimuth direction is parallel to the x-axis (parallel to the rows of each matrix). * The wind direction is an angle that borns at the positive x-direction. It is zero [rad] in the ATW scenario, whereas it is PI/9 [rad] in the scenarios ATW_R16 and ATW_R18. * The simulated ocean variance spectrum comes from a swell spectrum, whose dominant wave has a wavelength of 100 metres. * The field z characterises a velocity bunching scenario. This includes azimuthally travelling waves (ATW scenario), and "almost" azimuthally travelling waves (scenarios ATW_R16 and ATW_R18). * The matrices z, ur, D, ur_star_X and D_star_X are mutually related by its corresponding (s,r)-th entries. * The ATI-SAR image I that takes part in the formation of D is computed by a numerical integration that employs the extended Simpson's rule.