contents analysis of wave fields from temporal sequences ...part i: the marine radar as a remote...

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 [email protected]

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.

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ContentsWind-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

Alternative Wave Spectral Descriptions

Sea state parameters derived from the wave spectra

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Wave Measurements

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Sensors for Wave Measurements (I)

In-situ sensors:

Buoys.

Pressure gauges.

Wave lasers.

Look-down radars.

Current-meter based devices.

etc.

4

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

3D: Image time series analysis

Sensors for Wave Measurements (II)

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Remote Sensing Sensors:

They use electromagnetic waves to derive sea state parameters.

Types:

Active.

Passive.

Bands used for sea state remote sensing

Sensors for Wave Measurements (III)

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Space or air borne installations

On- or off-shore installations

(grazing incidence)

Remote sensing sensors:

High Frequency and Microwave Domain:

Altimeter.

Synthetic Aperture Radar (SAR).

High Frequency Radar.

Doppler Radar (X-Band).

Coherent Radar (X-Band).

Marine Radar.

Optical Domain:

LIDAR.

Camera-based sensors.

Sensors for Wave Measurements (IV)

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Space and Air Borne Radar Systems (I)

Altimeters:

Radar system looking to NADIR position (vertical incidence).

Measurements of Significant Wave Heights.

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Space and Air Borne Radar Systems (II)

Synthetic Aperture Radars:

High resolution radar mounting on moving platforms (e.g. aircrafts, satellites).

The produce 2D information of large areas of the ocean.

TerraSAR-X

TerraSAR-X operational modes

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Space and Air Borne Radar Systems (III)

Variability of the wave propagation direction due to the changes in the bottom topography:

ESA ERS-1/2 SAR

Bay of Biscay:

Northern coast of Spain

!

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SAR Examples: Atoll of Funafuti

Fragile band of land.

Threatened by

High swell.

Severe storms

Typhoons.

ESA Envisat ASAR

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SAR Examples: Oil Spilt DetectionPrestige accident in the northwest coast of Spain (november 2002).

ESA Envisat ASAR

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SAR Examples: Wind field estimation

ESA Envisat ASAR

!

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SAR Examples: Polar ice detectionEnvisat ASAR

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SAR Examples: Polar ice detection

TerraSAR-X

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SAR Examples: Internal waves detection

TerraSAR-X !

Straight of Gibraltar

North

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SAR Examples: Complex atmospheric features on the sea surface

TerraSAR-X !

South Australia

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TerraSAR-X !

South Australia


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Tasmanian Sea

TerraSAR-X

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SAR Examples: Radar image of harbor areas: Melbourne

North

TerraSAR-X

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SAR Examples: Radar image of harbor areas: Sydney

TerraSAR-X !

Multi-temporal image !

Resolution: ~ 1 m

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Radars at Grazing Incidence (I)High Frequency Radars:

It measure currents as well as wave spectra

EuroROSE Research Project: Gijón Experiment

WERA: Receiving Antenna

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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 off-shore platforms.

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Radars at Grazing Incidence (III)Microwave Radars at Grazing Incidence (II):

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.

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Marine Radar

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.

It permits to scan consecutive images of the sea surface

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Marine Radar Imagery (I)

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.

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Marine Radar Imagery (II)

Some effects are responsible of the radar imagery at grazing incidence and HH polarisation:

Shadowing

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.

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WaMoS SystemWaMoS II (Wave Monitoring System)

Originally developed by the German GKSS Research Centre

Nowadays is commercialised

Internet/LAN

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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

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Analysis of Wave Fields by using X-Band Marine Radar

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Part I: The marine radar as a remote sensing tool for wave analysis

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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:

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.

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Operational

Under research

Brief History of the Analysis of Ocean Waves with Marine Radars (II)

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.

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Marine Radar

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.

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Marine Radar

Typical radar features for wave measurement

Feature Value Improvement

Antenna Length 6 feet Larger

Band X -

Output Power 20 kW Higher

Azimuthal Resolution 1 degree Smaller

Antenna Rotation Period 2.5 s Faster Rotation

Pulse Repetition Frequency 2 kHz -

Sampling Frequency 16 MHz Higher

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Marine Radar Geometry

X-band marine radars operate at grazing incidence: Higher angles of incidence.

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Examples of Radar Images of The Sea Surface

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

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Wave Field Detection Using Marine Radars

1. Selection of a Rectangular Area.

2. Temporal Sequence Extraction.

3. Computation of the Image Spectrum.

Digitized Radar ImageImage Spectrum3D FFT

Typical rectangle size: 2 x 1 km2~

The wave field within the rectangular area should be statistically homogeneous

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Part II: The image Spectrum

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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.

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.

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Image Spectrum

Radar Imagery MechanismsWave Field

Wind

Radar Image (sea clutter)

Wave Spectrum

3D FFT 3D FFT

Image SpectrumInversion Modelling

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Structure of the Image Spectrum

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 contributions to the image spectrum in the spectral domain of wave numbers and frequencies.

Some of these phenomena are still not well understood, mainly because of the grazing incidence and HH polarisation conditions.

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.

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Contributions to the image spectrum:

Quasi-estatic patterns due to the constant dependence of radar imagery:

Radar equation:

Background noise due to the sea surface roughness (induced to the local wind).

Wave components (within the dispersion shell).

Higher harmonics (due to the shadowing and nonlinear wave features).

Subharmonic (“group line”): due to the shadowing, nonlinear wave features, wave breaking, etc.

Pr =PtGtArF 4⇥

(4�2)R4

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2D transect of a image spectrum measured in the Northern Coast of Spain.

Swell conditions

Radar Image Time Series

3D DFT

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Including the domain of negative frequencies

Static pattern

Dispersion Relation

Group Line

First Harmonic

Dispersion Relation

Group Line

First Harmonic

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Structure of the Image Spectrum: Alisaing Effect

Group Line (non linear wave

components)

Static Patterns (ω <<) (Radar Equation)

Wave Components (dispersion relation)

First Harmonic (non linear radar

imaging)

Aliased Wave Components

Background Noise (speckle)

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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.

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Higher harmonics

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Equation of the higher harmonics

� = (p+ 1)

s

gk

p+ 1tanh

✓k

p+ 1d

◆+ k ·U

� 7�! (p+ 1)�

k 7�! k

(p+ 1)

p = 0, 1, . . .

Fundamental Mode (dispersion relation)

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Harmonics of the dispersion relation:

Due to shadowing effects

Dispersion Relation

First Harmonic

Harmonics


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How to separate Them?


It is possible to identify nonlinearities in an n-dimensional spectrum

Higher harmonics (nonlinear contribution).

Higher order (summation) of spectral components.

Due to nonlinear radar imaging effects (shadowing).

Due to weak nonlinearities of the wave field (Stokes waves).

Research work has been started on that direction

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Structure of the Image SpectrumBackground noise (BGN):

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.

Signal: Energy of the wave field components.

Noise: Energy of the BGN components.

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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.

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.


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Spectral noise:

Independent of the frequency.

Angular Frequency ω [rad/s]

Nor

mal

ised

BG

N S

pect

rum


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Part III: Wave field analysis

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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.

Inversion Modelling method

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Basics of the wave field measurement by using marine radars


Sea Clutter Time Series 3D Image Spectrum

Inversion Modelling Technique Surface Current

Wave Spectrum

3D FT

Sea Surface Estimation

Phases

3D Inverse FT

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Steps of the inversion modelling technique:

Current fit.

Additional option: water depth fit.

In addition the water depth could be estimated as well.

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:

Directional wave spectrum.

Wave heights, periods, propagation directions, etc.


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)

Water depth

Wave spectrum depending on

Wave number and frequency

Wave number

Frequency and wave propagation direction

Frequency


� = ⇥(k) =pgk tanh(kd) + k ·U

U = (Ux

, Uy

)

d Only the current that

affect the wave field can

be measuredF (3)(k,�)

E(⇥, �)

S(�)

F (2)+ (k)

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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.


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Example of sea surface current estimation (North Sea)

Tidal periodicity observed

Current Fit

Current Speed

Current Direction

FINO 1 Research Platform

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Example of a bimodal sea state measured by a WaMoS-II system

Wave Number Spectrum

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Comparison with a directional buoy (Bay of Biscay)

Frequency Spectrum

Frequency Spectrum

Frequency Spectrum

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Comparison with a directional buoy (Bay of Biscay)

Spectral Parameters

From the wave number spectrum

From the frequency-direction spectrum

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Derived from the signal to noise ratio.

a previous calibration campaign is needed

Significant Wave Height

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Measurement at the Ekofisk Oill Platform (ConocoPhillips, Norway).


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EKOFISK Oil and Gas Platform (ConocoPhillips).

A set of sensors are deployed in the field area:

Wave buoy (used as reference sensor).

4-array of wave lasers.

WaMoS Station.

The standard Hs estimation method for marine radar is more accurate than the wave lasers for Hs > 2.5 m (Harald Krogstad*, personal communication).

For Hs < 2.5 m the Hs estimation should be improved:

Cases of swell or low winds.


* Norwegian University of Science and Technology, Trondheim, Norway

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Neural Network-based methods seems to be a reliable technique to derive SWH.

UAH in collaboration with OceanWaveS GmbH is working on this way.


Neural Network (MLP)

SNR

Wave Lengths

Wave Periods

Other sea state parameters


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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

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New Developements

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The method assumes that the shadowing is the dominant modulation mechanism.

Detection of Individual Waves

Sea Clutter Time Series 3D Image Spectrum

Inversion Modelling Technique Surface Current

Wave Spectrum

3D FT

Sea Surface Estimation

Phases

3D Inverse FT

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Detection of Individual WavesEstimation of individual waves

The main imagery mechanism for marine radar (e.g. grazing incidence) is shadowing.

This fact permits to estimate the sea surface for individual wave analysis.

Sea Clutter Time Series Sea Surface Inversion

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Detection of Individual Waves

From the wave field elevation kinematic and dynamic features can be derived

Wave group analysis from the envelope in 3D (space + time)

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

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Wave Group Analysis

Estimation of the 3D envelope through the 3D Riesz transform

Riesz transform is a n-dimensinal generalization of the Hilbert transform

Wave Field Riesz Transform

Envelope

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Wave Group Analysis

Wave fields present groups or packages of high waves travelling together.

Groups are responsible of the propagation of the wave energy.

Sea Surface 3D Wave Envelope

75

Wave Group Analysis3D Spectrum of the wave envelope.

Group Train components (responsible of the energy

propagation)

Pulse Train components (zero mean)

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Orbital Velocity ComponentsOrbital 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)

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Orbital Velocity ComponentsOrbital velocity components (u, v, w)

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Orbital Velocity Componentsu-w along the X- axis.

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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.

* Proudman Oceanographic Laboratory. National Oceanography Centre. UK

Conventional survey (Gridded), Carried out by University of East Anglia, UK Radar Derived Bathymetry

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Wind field estimation.J. Horstmann*, M. Coffin*, and R. Vicen-Bueno**, 2010, “A Marine Radar Based Surface Monitoring System”. IGARSS 2010, Honolulu.

* NATO Undersea Research Center. La Spezia, Italy

Wind gusts for wind retrieval

* University of Alcalá, Spain

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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.

* NATO Undersea Research Center. La Spezia, Italy* University of Alcalá, Spain

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Internal Wave Detection in Isola Palmaria (Italy)

J. Horstmann, R. Carrasco, C. Lidó (NURC)

http://www.youtube.com/watch?v=CB3J6_9CnKY

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Wave breaking in shallow watersWave breaking features change the roughness of the sea surface.

WaMoS measurement from the German island of Sylt.

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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.

Other effects related to the sea roughness.

Summary and Outlook

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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.

Wave grouping analysis.

Orbital velocities.

Summary (2)

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Thanks

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