Analysis of Wave Fields from Temporal Sequences of X-Band Marine Radar Images José Carlos Nieto Borge Dpt. of Signal Theory and Communications University of Alcalá. Spain josecarlos.nieto@uah.es Contents Wind-Generated Waves How wind waves look like? Spectral Description of Wave Fields General solutions of the linear wave theory Dispersion Relation Sea State Gaussian Sea States Three-dimensional Wave Spectrum Lecture within the framework of the project: Inversion of radar remote sensing images and deterministic prediction of ocean waves. University of Oslo (UiO) and Research Council of Norway (RCN) grant 214556/F20. Alternative Wave Spectral Descriptions Sea state parameters derived from the wave spectra 1 2 Sensors for Wave Measurements (I) In-situ sensors: Buoys. Pressure gauges. Wave lasers. Look-down radars. Wave Measurements Current-meter based devices. etc. 3 4
Sensors for Wave Measurements (II) Sensors for Wave Measurements (III) Remote Sensing Sensors: Imaging-based measuring systems present a complementary method to estimate wave properties. These systems are based on remote sensing techniques Video cameras Radar systems These systems can measure 2D (x, y), or 3D (x, y, t) wave properties 2D: Image analysis They use electromagnetic waves to derive sea state parameters. Types: Active. Passive. Bands used for sea state remote sensing 3D: Image time series analysis 5 6 Sensors for Wave Measurements (IV) Remote sensing sensors: High Frequency and Microwave Domain: Altimeter. Synthetic Aperture Radar (SAR). Space or air borne installations Space and Air Borne Radar Systems (I) Altimeters: Radar system looking to NADIR position (vertical incidence). Measurements of Significant Wave Heights. High Frequency Radar. Doppler Radar (X-Band). Coherent Radar (X-Band). On- or off-shore installations (grazing incidence) Marine Radar. Optical Domain: LIDAR. Camera-based sensors. 7 8
Space and Air Borne Radar Systems (II) Space and Air Borne Radar Systems (III) Synthetic Aperture Radars: High resolution radar mounting on moving platforms (e.g. aircrafts, satellites). Variability of the wave propagation direction due to the changes in the bottom topography: The produce 2D information of large areas of the ocean. TerraSAR-X ESA ERS-1/2 SAR TerraSAR-X operational modes Bay of Biscay: Northern coast of Spain 9 10 SAR Examples: Atoll of Funafuti SAR Examples: Oil Spilt Detection Fragile band of land. Prestige accident in the northwest coast of Spain (november 2002). ESA Envisat ASAR Threatened by High swell. Severe storms Typhoons. ESA Envisat ASAR 11 12
SAR Examples: Wind field estimation SAR Examples: Polar ice detection Envisat ASAR ESA Envisat ASAR 13 14 SAR Examples: Polar ice detection SAR Examples: Internal waves detection TerraSAR-X TerraSAR-X Straight of Gibraltar North 15 16
SAR Examples: Complex atmospheric features on the sea surface SAR Examples: Complex atmospheric features on the sea surface TerraSAR-X South Australia TerraSAR-X South Australia 17 18 SAR Examples: Complex atmospheric features on the sea surface SAR Examples: Radar image of harbor areas: Melbourne TerraSAR-X TerraSAR-X Tasmanian Sea North 19 20
SAR Examples: Radar image of harbor areas: Sydney TerraSAR-X Multi-temporal image Resolution: ~ 1 m Radars at Grazing Incidence (I) High Frequency Radars: It measure currents as well as wave spectra EuroROSE Research Project: Gijón Experiment WERA: Receiving Antenna 21 22 Radars at Grazing Incidence (II) Radars at Grazing Incidence (III) Microwave Radars at Grazing Incidence (II): Microwave Radars at Grazing Incidence (I): They normally work at X-Band (electromagnetic wave length of 3cm). The measurement is caused by the backscattering of the electromagnetic waves due to the roughness of the sea surface. A minimum wind speed is needed to obtain a reliable signal for sea state detection. They can operate in vertical (VV) or horizontal (HH) polarization. These systems are easy to be mounted on moving ships, as well as on- and offshore platforms. Most of these systems permit to obtain temporal sequences of radar images using consecutive antenna rotations. Evolution of wave fields on space and time can be derived. Types: Doppler Radars: The measurement is closely related to the pattern of the water particle velocities. Coherent Radars: They measure both amplitude and phase of the backscattered signal. Marine Radars: Typical radar systems used on every moving vessel and maritime traffic control tower. 23 24
Marine Radar Marine Radar Imagery (I) Common radar systems mounted on Moving ships. Off and on shore platforms. Marine traffic control towers. It works on X Band. HH polarisation. Incoherent radar systems. Under various conditions, signatures of the sea surface are visible in marine X-Band radar images. These signatures are known as sea clutter, which is undesirable for navigation purposes. Sea clutter is caused by the backscatter of the transmitted electromagnetic waves from the short sea surface ripples in the range of the electromagnetic wavelength (e.g. ~3 cm). Longer waves like swell and wind sea become visible as they modulate the backscatter signal. It permits to scan consecutive images of the sea surface 25 26 Marine Radar Imagery (II) WaMoS System Some effects are responsible of the radar imagery at grazing incidence and HH polarisation: Shadowing WaMoS II (Wave Monitoring System) Originally developed by the German GKSS Research Centre Nowadays is commercialised Tilt modulation Hydrodynamic modulation Orbital modulation Wind and wave direction... and others (wave breaking, crests, foam, etc.). The radar imaging mechanisms for marine radar are not yet fully understood. Internet/LAN 27 28
WaMoS System Using consecutive antenna rotations, a data set composed of time series radar images is obtained Example of sea clutter time series 4 km Analysis of Wave Fields by using X-Band Marine Radar 29 30 Brief History of the Analysis of Ocean Waves with Marine Radars (I) Late 1950 s: First experiences onboard ships. 1984: First estimation of the directional spectrum and surface current. 1992-1997: Operational system: WaMoS-II 1997: Improvement of the inversion modelling technique: Part I: The marine radar as a remote sensing tool for wave analysis Estimation of the modulation transfer function. Obtention of the higher harmonics. Improvement of the current fit. 1998: Estimation of the significant wave height. Full operational and commercial system: WaMoS-II. 31 32
Brief History of the Analysis of Ocean Waves with Marine Radars (II) Marine Radar Recent developments: Bathymetry estimation. High resolution currents for coastal areas. Local studies of wave fields for variable bathimetry conditions: coastal areas. Estimation of the sea surface: Analysis of individual waves in space and time. Wave groupiness studies in 3D: wave energy propagation. Internal wave detection for harbour locations. Wave breaking. Operational Under research Ordinary marine radars scan the sea water surface at grazing incidence. These systems can be used as a microwave remote sensing tool. Using temporal sequences of sea clutter images it is possible to derive information about wave periods, lengths, and propagation directions. Due to the marine radar response to the sea surface is not calibrated, wave height estimation cannot obtained in a simple way as other wave field parameters. This works deals with a method to estimate ocean wave heights from marine radar data sets. The method is based on the signal-noise ratio due to the speckle background noise due to the sea surface roughness. 33 34 Marine Radar Marine Radar Geometry X-band marine radars operate at grazing incidence: Higher angles of incidence. Typical radar features for wave measurement Feature Value Improvement Antenna Length 6 feet Larger Band X - Output Power 20 kw Higher Azimuthal Resolution Antenna Rotation Period Pulse Repetition Frequency 1 degree Smaller 2.5 s Faster Rotation 2 khz - Sampling Frequency 16 MHz Higher 35 36
Examples of Radar Images of The Sea Surface Wave Field Detection Using Marine Radars 1. Selection of a Rectangular Area. 2. Temporal Sequence Extraction. 3. Computation of the Image Spectrum. Typical rectangle size: 2 x 1 km 2 ~ The wave field within the rectangular area should be statistically homogeneous Deep Waters: Measurement on board a moving vessel Statistically homogeneous wave field Shallow Waters: Measurement from a on-shore radar station Statistically inhomogeneous wave field due to the variable bottom topography Wave Refraction Digitized Radar Image 3D FFT Image Spectrum 37 38 Image Spectrum The radar image is a consecuence of the radar backscattering mechanisms due to the sea surface, rather than an image of the wave field. The 3D FFT of the radar image time series is not an estimation of the wave spectrum, but an estimation of the spectrum of the different radar modulations that performs the image. Part II: The image Spectrum for that reason, the spectrum of the temporal sequence of sea surface radar images is called image spectrum. Inverse modelling techniques are applied to estimate the wave spectrum. Prior to define the steps of the inversion modelling techniques it is necessary to understand the structure of the image spectrum. 39 40
Image Spectrum Structure of the Image Spectrum Wind To define a proper method to estimate the wave spectra it is necessary to understand the structure of the image spectrum. The image spectrum structure implies to link the different hydrodynamic and electromagnetic phenomena responsible of the radar imagery with the different Wave Field Radar Imagery Mechanisms Radar Image (sea clutter) contributions to the image spectrum in the spectral domain of wave numbers and frequencies. 3D FFT 3D FFT Some of these phenomena are still not well understood, mainly because of the grazing incidence and HH polarisation conditions. Wave Spectrum Inversion Modelling Image Spectrum Theoretical results predict that the intensity of the radar image due to the se surface must be weaker than what it is obtained in Nature. This fact implies that ordinary marine radars are a reliable remote sensing tool for oceanic purposes. 41 42 Structure of the Image Spectrum Structure of the Image Spectrum Contributions to the image spectrum: Quasi-estatic patterns due to the constant dependence of radar imagery: Radar equation: P r = P tg t A r F 4 (4 2 )R 4 Background noise due to the sea surface roughness (induced to the local wind). Wave components (within the dispersion shell). 2D transect of a image spectrum measured in the Northern Coast of Spain. Swell conditions Radar Image Time Series 3D DFT Higher harmonics (due to the shadowing and nonlinear wave features). Subharmonic ( group line ): due to the shadowing, nonlinear wave features, wave breaking, etc. 43 44
Structure of the Image Spectrum Structure of the Image Spectrum: Alisaing Effect First Harmonic Including the domain of negative frequencies Dispersion Relation Aliased Wave Components Wave Components (dispersion relation) Group Line Group Line Static pattern First Harmonic (non linear radar imaging) Group Line (non linear wave components) Dispersion Relation Static Patterns (ω <<) (Radar Equation) Background Noise (speckle) First Harmonic 45 46 Structure of the Image Spectrum Structure of the Image Spectrum Higher harmonics Higher harmonics Caused by nonlinear radar imaging process due to shadowing. Weak nonlinearities of the wave field presents spectral components in the same location of the spectral domain. 47 48
Structure of the Image Spectrum Structure of the Image Spectrum Equation of the higher harmonics Harmonics of the dispersion relation: 7 (p + 1) k 7 k (p + 1) p =0, 1,... Fundamental Mode (dispersion relation) Due to shadowing effects First Harmonic s k k =(p + 1) g p +1 tanh p +1 d + k U Harmonics Dispersion Relation 49 50 Structure of the Image Spectrum Structure of the Image Spectrum Background noise (BGN): It is possible to identify nonlinearities in an n-dimensional spectrum Higher harmonics (nonlinear contribution). Due to the sea surface roughness induced by the local wind. BGN permits to derive the Significant Wave Height from the signal to noise ratio. Higher order (summation) of spectral components. Due to nonlinear radar imaging effects (shadowing). Due to weak nonlinearities of the wave field (Stokes waves). How to separate Them? Signal: Energy of the wave field components. Noise: Energy of the BGN components. Research work has been started on that direction 51 52
Structure of the Image Spectrum Structure of the Image Spectrum Spectral noise: Related to the speckle noise in the radar image. Speckle is directly related to the sea surface roughness. Roughness is caused by the local wind. Spectral noise: Independent of the frequency. Normalised BGN Spectrum Angular Frequency ω [rad/s] A parameterisation of the spectral noise would permit a better understanding of the marine radar imaging mechanisms. The existence of the spectral noise permits to estimate Hs. 53 54 Inversion Modelling method Using consecutive antenna rotations, a data set composed of time series radar images is obtained. An inversion modelling method is applied to the image spectrum to estimate the wave spectrum. Hydrodynamic assumptions are considered. Part III: Wave field analysis 55 56
Inversion Modelling method Basics of the wave field measurement by using marine radars Steps of the inversion modelling technique: Current fit. Inversion Modelling method Sea Clutter Time Series 3D FT 3D Image Spectrum Additional option: water depth fit. In addition the water depth could be estimated as well. Phases Surface Current Inversion Modelling Technique 3D pass-band filtering of the wave components within the dispersion shell. Application of an empirical Modulation Transfer Function to correct the wave energy due to radar imaging mechanisms. Scale of the wave spectrum from the Signal to Noise ratio. Derivation of sea state parameters: Sea Surface Estimation 3D Inverse FT Wave Spectrum Directional wave spectrum. Wave heights, periods, propagation directions, etc. 57 58 The basics of the inversion modelling technique assume that ocean waves are dispersive This fact permits to obtain estimations of Sea surface current (current of encounter) U =(U x,u y ) Water depth Inversion Modelling method d Wave spectrum depending on Wave number and frequency Wave number = (k) = p gk tanh(kd)+k U F (2) + (k) F (3) (k, ) Frequency and wave propagation direction E(, ) Only the current that affect the wave field can be measured Inversion Modelling method The inversion modelling technique is based on the hydrodynamic properties of ocean waves Ocean waves are dispersive and they follow a dispersion relation. The inversion model uses Theoretical assumptions: 3D band-pass filter within the dispersion shell. Empirical corrections: transfer function depending on the wave number to correct the wave spectrum estimation. Frequency S( ) 59 60
Current Fit Example of sea surface current estimation (North Sea) Tidal periodicity observed Current Speed FINO 1 Research Platform Wave Number Spectrum Example of a bimodal sea state measured by a WaMoS-II system Current Direction 61 62 Frequency Spectrum Comparison with a directional buoy (Bay of Biscay) Spectral Parameters Comparison with a directional buoy (Bay of Biscay) Frequency Spectrum From the wave number spectrum Frequency Spectrum From the frequencydirection spectrum 63 64
Significant Wave Height Derived from the signal to noise ratio. Significant Wave Height Measurement at the Ekofisk Oill Platform (ConocoPhillips, Norway). a previous calibration campaign is needed 65 66 Significant Wave Height Significant Wave Height EKOFISK Oil and Gas Platform (ConocoPhillips). A set of sensors are deployed in the field area: Wave buoy (used as reference sensor). Neural Network-based methods seems to be a reliable technique to derive SWH. UAH in collaboration with OceanWaveS GmbH is working on this way. 4-array of wave lasers. WaMoS Station. SNR The standard Hs estimation method for marine radar is more accurate than the wave lasers for Hs > 2.5 m (Harald Krogstad*, personal communication). Wave Lengths Wave Periods Neural Network (MLP) Significant Wave Height For Hs < 2.5 m the Hs estimation should be improved: Cases of swell or low winds. Other sea state parameters * Norwegian University of Science and Technology, Trondheim, Norway 67 68
Significant Wave Height Results from EKOFISK. Buoy vs. WaMoS (standard) r = 0.956 r(hs < 2.5m) = 0.890 r(hs > 2.5m) = 0.926 Buoy vs. WaMoS (NN) r = 0.974 r(hs < 2.5m) = 0.948 r(hs > 2.5m) = 0.926 New Developements 69 70 Detection of Individual Waves The method assumes that the shadowing is the dominant modulation mechanism. Detection of Individual Waves Estimation of individual waves The main imagery mechanism for marine radar (e.g. grazing incidence) is shadowing. Sea Clutter Time Series 3D FT 3D Image Spectrum This fact permits to estimate the sea surface for individual wave analysis. Sea Clutter Time Series Sea Surface Inversion Phases Surface Current Inversion Modelling Technique Sea Surface Estimation 3D Inverse FT Wave Spectrum 71 72
Detection of Individual Waves Wave Group Analysis From the wave field elevation kinematic and dynamic features can be derived Wave group analysis from the envelope in 3D (space + time) Estimation of the 3D envelope through the 3D Riesz transform Riesz transform is a n-dimensinal generalization of the Hilbert transform Before only wave grouping information from buoy records could be derived. Analysis of wave energy propagation: Kinetic wave energy per unit of area. Potential wave energy per unit of area. Energy flux. Orbital velocity components (u, v, w): Coastal morphodynamics Analysis of on and off shore marine structures Wave Field Riesz Transform Envelope 73 74 Wave Group Analysis Wave Group Analysis Wave fields present groups or packages of high waves travelling together. 3D Spectrum of the wave envelope. Groups are responsible of the propagation of the wave energy. Sea Surface 3D Wave Envelope Group Train components (responsible of the energy propagation) Pulse Train components (zero mean) 75 76
Orbital Velocity Components Orbital Velocity Components Orbital velocity components (u, v, w) Orbital velocity components (u, v, w) Analysis of the phase speed to estimate wave breaking. Stability of marine systems. Wave field (x, y, t) Velocity Potential (x, y, t) Orbital velocity components u(x, y, t) v(x, y, t) w(x, y, t) 77 78 u-w along the X- axis. Orbital Velocity Components Estimation of bottom topography for coastal areas. Radar derived bathimetry Paul Bell*, 2010, Submerged Dunes and Breakwater Embayments Mapped Using Wave Inversions of Shore-Mounted Marine X-Band Radar Data. IGARSS 2010, Honolulu. Conventional survey (Gridded), Carried out by University of East Anglia, UK Radar Derived Bathymetry * Proudman Oceanographic Laboratory. National Oceanography Centre. UK 79 80
Wind field estimation. J. Horstmann*, M. Coffin*, and R. Vicen-Bueno**, 2010, A Marine Radar Based Surface Monitoring System. IGARSS 2010, Honolulu. Internal waves induced by a moving vessel J. Horstmann*, M. Coffin*, and R. Vicen-Bueno**, 2010, A Marine Radar Based Surface Monitoring System. IGARSS 2010, Honolulu. Wind gusts for wind retrieval * NATO Undersea Research Center. La Spezia, Italy * University of Alcalá, Spain * NATO Undersea Research Center. La Spezia, Italy * University of Alcalá, Spain 81 82 Internal Wave Detection in Isola Palmaria (Italy) J. Horstmann, R. Carrasco, C. Lidó (NURC) http://www.youtube.com/watch?v=cb3j6_9cnky Wave breaking in shallow waters Wave breaking features change the roughness of the sea surface. WaMoS measurement from the German island of Sylt. 83 84
The radar signal is caused by the electromagnetic backscattering phenomenon due to the sea surface roughness. Marine radars can detect sea surface features, such as Wave field parameters including individual waves. Surface currents. Local wind fields. Summary and Outlook Other effects related to the sea roughness. Hs measurements need a previous calibration campaign. Recent improvement permits to obtain Hs even for those cases where the wind speed is lower. The standard analysis of radar images is based on the assumption of spatial homogeneity This is valid for deep or constant water depth conditions. For coastal applications new techniques have to be developed/applied. Recent results permit to estimate individual wave properties. Sea surface estimation. Summary (2) Wave grouping analysis. Orbital velocities. 85 86 Thanks 87