2019 IEEE/OES Twelfth Current, Waves and Turbulence Measurement (CWTM), 2019
The effect of sinusoidal platform motion on the first- and second-order high-frequency radar cros... more The effect of sinusoidal platform motion on the first- and second-order high-frequency radar cross-sections per unit area was derived for the monostatic case in the works of Walsh et al. [1]–[2], and more recently for a dual-frequency platform motion model, as well as for a bistatic configuration, in the works of Ma et al. [3]–[4] In all these works, the cross-sections on a floating platform were expressed as a Doppler-domain convolution of the fixed radar cross-section with an infinite weighted sum of Bessel functions of the first kind. Herein, the effect of platform motion is more easily expressed as the product of the time-domain radar cross-section per unit area and a single zeroth-order Bessel function of the first kind for each frequency component of the platform motion. A representative result using this new expression, shows that motion compensation may be performed exactly up to numerical error in the time domain by performing division on the autocorrelation of the received electric field by a known function in the time-domain dependent on the periodic platform motion.
In this paper, the analysis of rain effects on wave height estimation from X-band nautical radar ... more In this paper, the analysis of rain effects on wave height estimation from X-band nautical radar sea surface images is presented. A modified shadowing-analysis-based algorithm is applied to the radar data acquired in a sea trial in the North Atlantic Ocean under both rainy and rain-free conditions. The result shows that rain enhances the image pixel intensity and reduces shadowed areas, leading to the underestimation of wave heights. An increase of about 0.31 m in the bias with respect to in-situ measurements is found in the wave height retrieved from rain contaminated data compared to the results obtained from data without rain.
The Polar Fourier Transform (PFT) can be used to estimate the ocean wave number spectrum. The mai... more The Polar Fourier Transform (PFT) can be used to estimate the ocean wave number spectrum. The main advantage of the PFT over the Cartesian Fourier Transform (CFT) is the ability to be applied on the native radar data without the need for the intermediate stage of scan conversion. However, by definition, the PFT may not be used to detect negative wavenumbers. Therefore, a process of wavenumber mapping is proposed in order to circumvent this problem. In this technique, which is implemented before applying the PFT, the wave number content of the radar signal is compressed by a factor of 1/2 and shifted by pi/2. This mapping migrates all wave numbers to fit into the range of 0 to pi so that the PFT is required to deal with only positive wavenumbers.
Global Oceans 2020: Singapore – U.S. Gulf Coast, 2020
Declining sea ice conditions are often cited as an indicator of climate change, but limited infor... more Declining sea ice conditions are often cited as an indicator of climate change, but limited information is available on sea ice ridges, which comprise up to 50% of ice volume in certain regions. Multi-year (MY) ridges are more hazardous barriers to navigation than first year (FY) ridges and they are more likely to survive the summer melt season, but little effort has been made to identify FY and MY ridges from remote sensing data. This paper describes an analytical method to model electromagnetic scattering from ridges around the VHF range (100–500 MHz) when ridges are modeled as a rough surface over stratified media. Models considering the macroscopic properties of FY and MY ridges relevant to VHF scatter are presented. Simulations show that FY and MY ridges have different scattering characteristics, making it possible to separate the two ice types. Future work will consider how variability in ice ridge characteristics and changes during the ice season affect the separability of FY and MY ridges based on their scattering characteristics.
The extraction of oceanic wave spectrum information from radar data has been a challenging proble... more The extraction of oceanic wave spectrum information from radar data has been a challenging problem that has been the subject of a vast amount of research over the past several decades. This research has resulted in a multitude of approaches to extract ocean wave spectra from Doppler spectrum returns. One common feature of many of these methods is the reduction of the wave spectrum extraction problem from a nonlinear problem to a linear one. In this article, a new approach is introduced, which does not linearize the Fredholm integral equation relating the ocean wave spectrum to the radar Doppler spectrum, but instead maintains its nonlinear nature. Also, unlike previous nonlinear optimization solutions, the proposed method is automatic in the sense that no regularization parameters have to be manually set purely dependent on the radar data from which the ocean wave parameters are being extracted, thereby reducing the need for human intervention in the wave spectrum extraction process. In addition to describing this new method for wave spectrum extraction, this article presents results from a case study on field data from Argentia, NL, Canada, comparing the oceanographic parameters obtained with the proposed method to those recorded by in situ buoy instrumentation. The significant wave height calculated from ocean wave spectra extracted via the method are found to match with those from the buoy, whereas the values of other oceanographic parameters, such as wave period and direction extracted using the proposed method, are less accurate potentially due to the low quality of data available to test the method.
2015 IEEE 14th Canadian Workshop on Information Theory (CWIT), 2015
Shannon entropy is a powerful tool for signal analysis. However, because it is based on a reducti... more Shannon entropy is a powerful tool for signal analysis. However, because it is based on a reductionist worldview, on its own, Shannon entropy cannot properly handle `temporal dynamics' pertaining to nonlinear and nonstationary processes. To remedy this, an extension of Shannon entropy, known as permutation entropy (PE), has been proposed in the literature. In this paper, the utility of PE for signal analysis is demonstrated on a comprehensive and real-world synthetic aperture radar dataset. When compared to conventional methods for signal analysis, the results convey the statistical significance of PE in capturing the dynamics between the constituent values of the signal.
A two-dimensional ensemble empirical mode decomposition (2D-EEMD)-based method is presented to im... more A two-dimensional ensemble empirical mode decomposition (2D-EEMD)-based method is presented to improve wind direction retrieval from rain-contaminated X-band nautical radar sea surface images. 2D-EEMD is first implemented to decompose each rain-contaminated radar image into several intrinsic mode function (IMF) components. Then, a harmonic function that is least-squares fitted to the standard deviation of the first IMF component as a function of azimuth is used to retrieve the wind direction. Radar and anemometer data acquired in a sea trial off the east coast of Canada under rain conditions are employed to test the algorithm. The result shows that, compared to the traditional curve fitting method, the proposed method improves the wind direction results in rain events, showing a reduction of 35.9° in the root-mean-square (RMS) difference with respect to the reference.
2017 18th International Radar Symposium (IRS), 2017
A method for mitigating antenna motion effects in high frequency radar Doppler spectra developed ... more A method for mitigating antenna motion effects in high frequency radar Doppler spectra developed from ocean backscatter is proposed. Based on the established radar cross section models for a fixed antenna and for an antenna on a floating platform, the relationship between these models is developed. Through this relationship, motion compensation can be achieved by deconvolving the radar cross section data with the derived transfer function. A least squares deconvolution (LSD) method is applied in this study and shows good performance.
Knowledge of the ocean wave spectrum, from which many important ocean parameters can be extracted... more Knowledge of the ocean wave spectrum, from which many important ocean parameters can be extracted, is crucial to understand the ocean's behaviour. Due to the intricate nature of ocean wave spectrum extraction from HF radar data, previously-devised methods relied on making a linear approximation to the original nonlinear problem or resorted to constraining the solution space, in order to simplify the solution process. This problem is aggravated in a bistatic configuration due to its geometrical complexity. The present work proposes a change of variables in the second-order radar cross-section from bistatic HF-Radar in order to extract the ocean power spectral density from Doppler HF-Radar data. The main advantage of the proposed method is the possibility of extracting the ocean wave spectrum without assuming any linear approximation to the inverse problem. In this work, it is found that the proposed method can accurately extract the ocean wave spectrum from bistatic HF radar data under a variety of ocean conditions.
The present work proposes the use of a nonlinear inversion technique for the extraction of the di... more The present work proposes the use of a nonlinear inversion technique for the extraction of the directional ocean wave spectrum from bistatic High-Frequency Surface Wave Radar (HFSWR) Doppler data. The extraction method is combined with empirical expressions, solely based on the Doppler data, to retrieve wind speed and direction. Once the initialization parameters have been defined using these empirical expressions, a blind iterative algorithm based on Tikhonov regularization in Hilbert Scales is used to extract the nondirectional spectrum. The extracted spectrum is then used to determine the directional factor, which is assumed to be described by a cosine-power model. The proposed method yields good results with synthetic noise-contaminated HFSWR data with a priori regularization parameters.
2019 IEEE/OES Twelfth Current, Waves and Turbulence Measurement (CWTM), 2019
The effect of sinusoidal platform motion on the first- and second-order high-frequency radar cros... more The effect of sinusoidal platform motion on the first- and second-order high-frequency radar cross-sections per unit area was derived for the monostatic case in the works of Walsh et al. [1]–[2], and more recently for a dual-frequency platform motion model, as well as for a bistatic configuration, in the works of Ma et al. [3]–[4] In all these works, the cross-sections on a floating platform were expressed as a Doppler-domain convolution of the fixed radar cross-section with an infinite weighted sum of Bessel functions of the first kind. Herein, the effect of platform motion is more easily expressed as the product of the time-domain radar cross-section per unit area and a single zeroth-order Bessel function of the first kind for each frequency component of the platform motion. A representative result using this new expression, shows that motion compensation may be performed exactly up to numerical error in the time domain by performing division on the autocorrelation of the received electric field by a known function in the time-domain dependent on the periodic platform motion.
In this paper, the analysis of rain effects on wave height estimation from X-band nautical radar ... more In this paper, the analysis of rain effects on wave height estimation from X-band nautical radar sea surface images is presented. A modified shadowing-analysis-based algorithm is applied to the radar data acquired in a sea trial in the North Atlantic Ocean under both rainy and rain-free conditions. The result shows that rain enhances the image pixel intensity and reduces shadowed areas, leading to the underestimation of wave heights. An increase of about 0.31 m in the bias with respect to in-situ measurements is found in the wave height retrieved from rain contaminated data compared to the results obtained from data without rain.
The Polar Fourier Transform (PFT) can be used to estimate the ocean wave number spectrum. The mai... more The Polar Fourier Transform (PFT) can be used to estimate the ocean wave number spectrum. The main advantage of the PFT over the Cartesian Fourier Transform (CFT) is the ability to be applied on the native radar data without the need for the intermediate stage of scan conversion. However, by definition, the PFT may not be used to detect negative wavenumbers. Therefore, a process of wavenumber mapping is proposed in order to circumvent this problem. In this technique, which is implemented before applying the PFT, the wave number content of the radar signal is compressed by a factor of 1/2 and shifted by pi/2. This mapping migrates all wave numbers to fit into the range of 0 to pi so that the PFT is required to deal with only positive wavenumbers.
Global Oceans 2020: Singapore – U.S. Gulf Coast, 2020
Declining sea ice conditions are often cited as an indicator of climate change, but limited infor... more Declining sea ice conditions are often cited as an indicator of climate change, but limited information is available on sea ice ridges, which comprise up to 50% of ice volume in certain regions. Multi-year (MY) ridges are more hazardous barriers to navigation than first year (FY) ridges and they are more likely to survive the summer melt season, but little effort has been made to identify FY and MY ridges from remote sensing data. This paper describes an analytical method to model electromagnetic scattering from ridges around the VHF range (100–500 MHz) when ridges are modeled as a rough surface over stratified media. Models considering the macroscopic properties of FY and MY ridges relevant to VHF scatter are presented. Simulations show that FY and MY ridges have different scattering characteristics, making it possible to separate the two ice types. Future work will consider how variability in ice ridge characteristics and changes during the ice season affect the separability of FY and MY ridges based on their scattering characteristics.
The extraction of oceanic wave spectrum information from radar data has been a challenging proble... more The extraction of oceanic wave spectrum information from radar data has been a challenging problem that has been the subject of a vast amount of research over the past several decades. This research has resulted in a multitude of approaches to extract ocean wave spectra from Doppler spectrum returns. One common feature of many of these methods is the reduction of the wave spectrum extraction problem from a nonlinear problem to a linear one. In this article, a new approach is introduced, which does not linearize the Fredholm integral equation relating the ocean wave spectrum to the radar Doppler spectrum, but instead maintains its nonlinear nature. Also, unlike previous nonlinear optimization solutions, the proposed method is automatic in the sense that no regularization parameters have to be manually set purely dependent on the radar data from which the ocean wave parameters are being extracted, thereby reducing the need for human intervention in the wave spectrum extraction process. In addition to describing this new method for wave spectrum extraction, this article presents results from a case study on field data from Argentia, NL, Canada, comparing the oceanographic parameters obtained with the proposed method to those recorded by in situ buoy instrumentation. The significant wave height calculated from ocean wave spectra extracted via the method are found to match with those from the buoy, whereas the values of other oceanographic parameters, such as wave period and direction extracted using the proposed method, are less accurate potentially due to the low quality of data available to test the method.
2015 IEEE 14th Canadian Workshop on Information Theory (CWIT), 2015
Shannon entropy is a powerful tool for signal analysis. However, because it is based on a reducti... more Shannon entropy is a powerful tool for signal analysis. However, because it is based on a reductionist worldview, on its own, Shannon entropy cannot properly handle `temporal dynamics' pertaining to nonlinear and nonstationary processes. To remedy this, an extension of Shannon entropy, known as permutation entropy (PE), has been proposed in the literature. In this paper, the utility of PE for signal analysis is demonstrated on a comprehensive and real-world synthetic aperture radar dataset. When compared to conventional methods for signal analysis, the results convey the statistical significance of PE in capturing the dynamics between the constituent values of the signal.
A two-dimensional ensemble empirical mode decomposition (2D-EEMD)-based method is presented to im... more A two-dimensional ensemble empirical mode decomposition (2D-EEMD)-based method is presented to improve wind direction retrieval from rain-contaminated X-band nautical radar sea surface images. 2D-EEMD is first implemented to decompose each rain-contaminated radar image into several intrinsic mode function (IMF) components. Then, a harmonic function that is least-squares fitted to the standard deviation of the first IMF component as a function of azimuth is used to retrieve the wind direction. Radar and anemometer data acquired in a sea trial off the east coast of Canada under rain conditions are employed to test the algorithm. The result shows that, compared to the traditional curve fitting method, the proposed method improves the wind direction results in rain events, showing a reduction of 35.9° in the root-mean-square (RMS) difference with respect to the reference.
2017 18th International Radar Symposium (IRS), 2017
A method for mitigating antenna motion effects in high frequency radar Doppler spectra developed ... more A method for mitigating antenna motion effects in high frequency radar Doppler spectra developed from ocean backscatter is proposed. Based on the established radar cross section models for a fixed antenna and for an antenna on a floating platform, the relationship between these models is developed. Through this relationship, motion compensation can be achieved by deconvolving the radar cross section data with the derived transfer function. A least squares deconvolution (LSD) method is applied in this study and shows good performance.
Knowledge of the ocean wave spectrum, from which many important ocean parameters can be extracted... more Knowledge of the ocean wave spectrum, from which many important ocean parameters can be extracted, is crucial to understand the ocean's behaviour. Due to the intricate nature of ocean wave spectrum extraction from HF radar data, previously-devised methods relied on making a linear approximation to the original nonlinear problem or resorted to constraining the solution space, in order to simplify the solution process. This problem is aggravated in a bistatic configuration due to its geometrical complexity. The present work proposes a change of variables in the second-order radar cross-section from bistatic HF-Radar in order to extract the ocean power spectral density from Doppler HF-Radar data. The main advantage of the proposed method is the possibility of extracting the ocean wave spectrum without assuming any linear approximation to the inverse problem. In this work, it is found that the proposed method can accurately extract the ocean wave spectrum from bistatic HF radar data under a variety of ocean conditions.
The present work proposes the use of a nonlinear inversion technique for the extraction of the di... more The present work proposes the use of a nonlinear inversion technique for the extraction of the directional ocean wave spectrum from bistatic High-Frequency Surface Wave Radar (HFSWR) Doppler data. The extraction method is combined with empirical expressions, solely based on the Doppler data, to retrieve wind speed and direction. Once the initialization parameters have been defined using these empirical expressions, a blind iterative algorithm based on Tikhonov regularization in Hilbert Scales is used to extract the nondirectional spectrum. The extracted spectrum is then used to determine the directional factor, which is assumed to be described by a cosine-power model. The proposed method yields good results with synthetic noise-contaminated HFSWR data with a priori regularization parameters.
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