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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
Citable as data publication
Perez, F.; Moreles, M. A.; Morales, H.; Centro de Investigación en Matemáticas A.C. (CIMAT); Departamento de Matemáticas; UAM Iztapalapa; Universidad Autonoma Metropolitana: México; (2021): 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. Marine Data Archive. https://doi.org/10.14284/446

Archived data
Availability: Unrestricted after moratorium period
Data are initially restricted, but the access condition relaxes to academic or unrestricted once a specified period of time after an event (such as collection, publication, completion of QC procedures or project cessation) has elapsed

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. more

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.


Scope
Themes:
Physical > Waves - swell
Keywords:
Marine, ATI-SAR image, ATI-SAR velocity bunching model, Gaussian process, Harmonic random process, Linear wave theory, Monte carlo simulation, Ocean variance spectrum, Ocean wave spectra, Spectral representation model, Stochastic processes, Swell-like ocean surfaces, Velocity bunching theory

Temporal coverage
1 February 2018 - 31 March 2019

Parameters
ar: Field of radial accelerations Methodology , B: Half the distance between the antennas Methodology , D: ATI-SAR image Methodology , D_star_fddm: Ny images of corresp Ny estimated solutions in ur_star_fddm Methodology , D_star_ssnle: Ny images of corresp Ny estimated solutions in ur_star_ssnle Methodology , D_star_umf: Ny images of corresp Ny estimated solutions in ur_star_umf Methodology , eps: Scalar parameter to control the amount of variance in the noise model Methodology , F: Fetch Methodology , f0: Carrier frequency of the radar Methodology , kx: Frequency sampling in the x-direction Methodology , ky: Frequency sampling in the y-direction Methodology , Lx: Space extent in the x-direction Methodology , Ly: Space extent in the y-direction Methodology , NRCS: Normalised radar cross section Methodology , Nx: Number of samples in the x-direction Methodology , Ny: Number of samples in the y-direction Methodology , phi0: Azimuthally look direction Methodology , phiw: Wind direction Methodology , pol: Polarisation Methodology , R: Slant range Methodology , S_1S: One-sided directional variance spectrum (quadrants I and IV) Methodology , S_2S: Two-sided directional variance spectrum (quadrants I, II, III, IV) Methodology , S1: Omnidirectional spectrum Methodology , spec: Omnidirectional spectrum Methodology , spre: Directional spreading function Methodology , SVS: Sampled-variance spectrum Methodology , T0: Target exposure time for each antenna Methodology , theta0: Incidence angle of the radar Methodology , ts: Scene coherence time Methodology , U: Wind speed Methodology , ur: Field of radial velocities Methodology , ur_star_fddm: Ny estimated solutions of corresp Ny inverse problems (FDDM) Methodology , ur_star_ssnle: Ny estimated solutions of corr. Ny inverse problems (SSNLE) Methodology , ur_star_umf: Ny estimated solutions of corresp Ny inverse problems (UMF) Methodology , V: platform speed Methodology , x: Radar sampling in the x-direction Methodology , x0: Ocean-surface sampling in the x-direction Methodology , y: Radar sampling in the y-direction Methodology , y0: Ocean-surface sampling in the y-direction Methodology , Z: Directional ocean variance spectrum Methodology , z: Field of sea surface elevations Methodology
ar: Field of radial accelerations: Metres per squared seconds (two-dimensional real-valued scalar field). The sampling is governed by the Inverse Discrete Fourier Transform (IDFT).
B: Half the distance between the antennas: Metres (positive real-valued scalar). In the ATI-SAR scheme, both antennas are mounted in baseline along the azimuth direction.
D: ATI-SAR image: Dimensionless (two-dimensional complex-valued scalar field). The sampling comes from the space-time scalar fields that take part in the formation of the ATI-SAR image.
D_star_fddm: Ny images of corresp Ny estimated solutions in ur_star_fddm: Dimensionless (two-dimensional complex-valued scalar field). This is a forward mapping whose numerical quadrature is computed by means of the Simpson's rule (a Newton-Cotes formula).
D_star_ssnle: Ny images of corresp Ny estimated solutions in ur_star_ssnle: Dimensionless (two-dimensional complex-valued scalar field). This is a forward mapping whose numerical quadrature is computed by means of the Simpson's rule (a Newton-Cotes formula).
D_star_umf: Ny images of corresp Ny estimated solutions in ur_star_umf: Dimensionless (two-dimensional complex-valued scalar field). This is a forward mapping whose numerical quadrature is computed by means of the Simpson's rule (a Newton-Cotes formula).
eps: Scalar parameter to control the amount of variance in the noise model: Dimensionless (positive real-valued scalar). For each position of the ATI-SAR image D, a specific value of the standard deviation is defined. Such value depends on eps, and then a certain level of noise is defined at that position.
F: Fetch: Metres (positive real-valued scalar). It can be assumed that the simulation of a swell-like ocean surface works under the "infinite-fetch assumption".
f0: Carrier frequency of the radar: Cycles per second (positive real-valued scalar). Although it is assumed that the radar system is already operating with a demodulated baseband signal, the carrier frequency serves to compute the radar wavelength.
kx: Frequency sampling in the x-direction: Radians per metre (one-dimensional real-valued scalar field). The separation value between adjacent frequency samples is constant over entire sampling. Such frequencies are integer multiples of the nonzero fundamental frequency (in the x-direction).
ky: Frequency sampling in the y-direction: Radians per metre (one-dimensional real-valued scalar field). The separation value between adjacent frequency samples is constant over entire sampling. Such frequencies are integer multiples of the nonzero fundamental frequency (in the y-direction).
Lx: Space extent in the x-direction: Metres (positive real-valued scalar). This value is at least one order of magnitude greater than the wavelength of the dominant wave in the ocean surface.
Ly: Space extent in the y-direction: Metres (positive real-valued scalar). This value is at least one order of magnitude greater than the wavelength of the dominant wave in the ocean surface.
NRCS: Normalised radar cross section: Dimensionless (two-dimensional positive real-valued scalar field). This is the first order approximation of the NRCS model of (Romeiser-Alpers-Wismann, 1997). Based on Bragg scattering theory and the two-scale model.
Nx: Number of samples in the x-direction: Samples (positive integer, scalar). An integer greater or equal than four.
Ny: Number of samples in the y-direction: Samples (positive integer, scalar). An integer greater or equal than four.
phi0: Azimuthally look direction: Radians (real-valued scalar). If phi0 and phiw are orthogonal, azimuthally travelling waves (ATW) are obtained. If not, but difference (in absolute value) lies in [PI/3 [rad], (2*PI)/3 [rad]], then "almost" azimuthally travelling waves are obtained.
phiw: Wind direction: Radians (real-valued scalar). The wind blows at an angle that borns at the positive x-direction. The x-direction is parallel to the azimuth direction.
pol: Polarisation: String (set of characters). The kind of polarisation is related to the reflectivity model of the radar.
R: Slant range: Metres (positive real-valued scalar). For a given target at the ocean surface, the slant range is the distance of closest approach from the midpoint between the antennas (at the height of the aircraft) to such target.
S_1S: One-sided directional variance spectrum (quadrants I and IV): Squared metres per squared angular spatial frequency (two-dimensional real-valued scalar field). According to (Mobley, 2016), the complex exponential form of each harmonic wave component is employed.
S_2S: Two-sided directional variance spectrum (quadrants I, II, III, IV): Squared metres per squared angular spatial frequency (2D real-valued scalar field). According to (Mobley, 2016), the complex exponential form of each harmonic wave component is employed. Energy evenly distributed from quadr I and IV to III and II.
S1: Omnidirectional spectrum: Squared metres per angular spatial frequency (1D real-valued scalar field). Swell spectrum from (Bruening-Alpers-Hasselmann, 1990), characterised by large peak enhancement factor. According to (Bao-Bruening-Alpers, 1997) its dominant wave has λ=100m.
spec: Omnidirectional spectrum: String (set of characters). Swell consists of low-frequency long-crested ocean waves that travel at a very long distance from their generation area.
spre: Directional spreading function: String (set of characters). A two-sided cosine-power model is employed.
SVS: Sampled-variance spectrum: Squared metres (two-dimensional real-valued scalar field). This spectrum is the square of the magnitude of the directional ocean variance spectrum. It accounts for the amount of sampled variance of the ocean surface realisation at each wavenumber.
T0: Target exposure time for each antenna: Seconds (posit real-valued scalar). By construction, each physical antenna is rectangular, dimensions aligned with azimuth axis and vertical axis. In conjunction with other 3 radar parameters, T0 depends on size of physical antenna along azimuth axis
theta0: Incidence angle of the radar: Radians (real-valued scalar). It is assumed that a relatively high roughness of the ocean surface exists. This particularly occurs for a swell-like ocean surface.
ts: Scene coherence time: Seconds (positive real-valued scalar). Due to the inherent motion of the ocean surface, the scene coherence time is never fully coherent. However, a relatively high degree of coherence can be established.
U: Wind speed: Metres per second (positive real-valued scalar). This is a small value of wind speed, which is relatively appropriate at swell-like ocean surfaces.
ur: Field of radial velocities: Metres per second (two-dimensional real-valued scalar field). The sampling is governed by the Inverse Discrete Fourier Transform (IDFT).
ur_star_fddm: Ny estimated solutions of corresp Ny inverse problems (FDDM): Metres per second (two-dimensional real-valued scalar field). At each optimisation step, the numerical quadrature of its corresponding integral form is computed by means of the Trapezoidal rule (a Newton-Cotes formula).
ur_star_ssnle: Ny estimated solutions of corr. Ny inverse problems (SSNLE): Metres per second (two-dimensional real-valued scalar field). At each optimisation step, the numerical quadrature of its corresponding integral form is computed by means of the Trapezoidal rule (a Newton-Cotes formula).
ur_star_umf: Ny estimated solutions of corresp Ny inverse problems (UMF): Metres per second (two-dimensional real-valued scalar field). At each optimisation step, the numerical quadrature of its corresponding integral form is computed by means of the Trapezoidal rule (a Newton-Cotes formula).
V: platform speed: Metres per second (positive real-valued scalar). The platform speed is typical of an aircraft. See for example (Cumming & Wong, 2005).
x: Radar sampling in the x-direction: Metres (1-D real-valued scalar field). Number spatial samples = number frequency samples. Separation value between adjacent spatial samples is constant over entire sampling (in x-direct). X almost same as x0, difference is constant spatial shift.
x0: Ocean-surface sampling in the x-direction: Metres (one-dimensional real-valued scalar field). Number of spatial samples equals the number of frequency samples. Separation value between adjacent spatial samples is constant over the entire sampling (in the x-direction).
y: Radar sampling in the y-direction: Metres (1-D real-valued scalar field). Number spatial samples = number frequency samples. Separation value between adjacent spatial samples is constant over entire sampling (in y-direct). y almost same as y0, difference is constant spatial shift.
y0: Ocean-surface sampling in the y-direction: Metres (one-dimensional real-valued scalar field). Number of spatial samples equals the number of frequency samples. Separation value between adjacent spatial samples is constant over the entire sampling (in the y-direction).
Z: Directional ocean variance spectrum: Metres (2D complex-valued scalar field). Spectral representation of a random harmonic process using Monte Carlo simulation. See (Mobley, 2016), (Sun, 2006), (Grigoriu, 1993), (Shinozuka-Deodatis,1991) .This is a randomised instance of S_2S.
z: Field of sea surface elevations: Metres (two-dimensional real-valued scalar field). The sampling is governed by the Inverse Discrete Fourier Transform (IDFT).

Contributors
Centro de Investigación en Matemáticas, A.C. (CIMAT), moredata creator
Universidad Autonoma Metropolitana; UAM Iztapalapa; Departamento de Matemáticas, moredata creator

Publication
Based on this dataset
Perez, F.; Moreles, M.A.; Morales, H. (2020). Ocean surface radial velocity imaging in the AT-INSAR Velocity Bunching Model. A functional approach. arXiv (Archive) 2004.14549v1, more

Dataset status: Completed
Data type: Software/models/scripts
Data origin: Research: lab experiment
Metadatarecord created: 2021-01-22
Information last updated: 2021-01-22
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