CLS-DAR-NT-12-064-1-0_CSKWave_final - Boost

SHOM

Final report PI CSK: Analysis of the

Potentiality and Limitations of Wave spectra inversion using SAR Measurements in X-band from Cosmo-Skymed satellites

Reference: CLS-DAR-NT-12-064

Nomenclature: -

Issue:

Date:

1. 0

Mar. 15, 12

Mid-term report PI CSK: Analysis of the Potentiality and Limitations of Wave spectra inversion using

CLS-DAR-NT-12-064 -

SAR Measurements in X-band

V 2.0 Mar. 15, 12 i.1

Chronology Issues:

Issue: Date:

0.1

1.0

2.0

Reason for change:

02/03/2012 creation

16/03/2012 Final version of mid-term report

27/04/2012 Final version of mid-term report

People involved in this issue:

Written by (*) : F.Collard

Checked by (*) :

Approved by (*) :

Date + Initials:( visa or ref)

Date + Initial:( visa ou ref)


Author

F.Collard

F.Collard

F.Collard

Application authorized by (*) :


*In the opposite box: Last and First name of the person + company if different from CLS

Index Sheet:

Context:

Keywords:

Hyperlink:

[Mots clés ]

Distribution:

Company

SHOM

Means of distribution electronic

Names

Mathilde Faillot, Fabrice Ardhuin (now IFREMER)

Proprietary information: no part of this document may be reproduced divulged or used in any form without prior permission from CLS.


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V 2.0 Mar. 15, 12 i.2

List of tables and figures

List of tables:

Table 1: Characteristics of the available CSK products ...................................................... 5

List of figures:

Figure 1: Omnidirectionnal component of the NRCS in VV and HH polarization with respect to the wind speed. Incidence angles considered are: 30, 40 and 50 degrees ...................... 7

Figure 2: (a) NRCS in VV polarization (b) NRCS in HH polarization (c) Polarization ratio (d)

NRCS difference at X band with respect to azimuth angle for a 40 degrees incidence angle. Grey points are measurements from RENE radar obtained during POLRAD’96 experiment. Dashed-dotted lines, dashed lines and solid lines are given by Kirchhoff

Approximation, Small Slope Approximation and X-MOD (this study) models. .................... 8

Figure 3: (a) NRCS-VV vs NRCS-HH. (b) wind speed from images in VV polarization versus versus wind speeds from images in HH polarization obtained using XMOD GMF and wind direction from ECMWF NWP model. ....................................................................... 9

Figure 4: Histogram of wind speeds given by ECMWF interpolated onto the SAR grid. Each wind speeds is co-located with a NRCS measurement...................................................... 10

Figure 5: Histogram of wind speeds difference between SAR and ECMWF. From images in (a)

VV and (b) HH polarizations ............................................................................... 10

Figure 6: Relative calibration error between calibrated CSK HIMAGE products and XMOD simulation. .................................................................................................... 13

Figure 7 : Incidence angle dependence of NRCS calibration in terms of NRCS difference (upper left), equivalent wind speed difference (upper right) and comparative map of SAR derived wind speed (lower left) and reference ECMWF wind (lower right). HIMAGE VV polarization product on jan 21 2012 at 18:29 UTC .................................................. 13

Figure 8 : NRCS calibration of Wide Region VV product on jan 20 2012 at 18:35 UTC .

Measured vs. expected NRCS (resp. wind speed) on the upper panel (resp. lower panel). left corresponds to the first subswath, center to the middle subswath and right to the third subswath (far range) ................................................................................. 14

Figure 9: NRCS values per incidence angle for no wind scene. .......................................... 15

Figure 10: global NESZ variation function of incidence angle with X-MOD as reference for the three HH Himage products with very little to no wind. The four X-MOD NRCS curves corresponds to 3, 5, 7 and 10m/s wind speed from bottom to top. ............................. 15

Figure 11 : global NESZ variation function of incidence angle with X-MOD as reference for the

VV polarized Huge region products from another project ......................................... 16

Figure 12 : Autocorrelation function for HIMAGE mode. noise (upper left), no swell (upper right), swell low wind (lower left), swell medium wind (lower right) ........................... 17

Figure 13 : Autocorrelation function for Wide Region mode. no swell (left), swell medium wind

(right) ........................................................................................................... 18

Figure 14 : Autocorrelation function for Huge Region mode. no swell (left) ......................... 18

Figure 15 : short scale roughness modulation by long waves ............................................ 21

Figure 16 : Doppler spectra for typical HIMAGE mode SCS-B CSK products. Polarization VV 34 degrees (upper left), VV 57 degrees (upper right), HH 51 degrees (lower left), HH light wind (lower right) ........................................................................................... 22

Figure 17 : Doppler spectra for typical Wide Region (left) and Huge Region (right) SCS-B CSK product ......................................................................................................... 22



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V 2.0 Mar. 15, 12 i.3

Figure 18 : HIMAGE cross-spectrum. Image intensity(top), real part of cross spectra (left), imaginary part of cross-spectra (right). ................................................................ 23

Figure 19 : Wide Region cross-spectra. Image intensity, real part of cross spectra, imaginary part of cross-spectra (from top to bottom). Left is a case with clear imaginary part and right is a similar case but with noisy imaginary part. ............................................... 24

Figure 20 : Himage Wave spectrum inversion. Cross spectra (top). Image intensity (bottom left). Inverted wave spectrum (bottom right) ......................................................... 25

Figure 21 : Wide region Wave spectra inversion for unambiguous (left) and ambiguous case

(right). Cross spectra real and imaginary part, image intensity and inverted wave spectra

(from top to bottom) ........................................................................................ 27

Figure 22 : Map of dominant wave components from inverted wave spectra overlaid on top of sea surface roughness modulation in grey levels. Significant wave height is displayed in color, dominant direction and wavelength by the direction and length of the white arrows. ......................................................................................................... 28

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AD 1 Plan d’assurance produit de CLS

CLS-ED-NT-03-394

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Ocean: Results From Airborne Radar Observations and Comparison With ENVISAT ASAR Data, IEEE

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[R20] P. Janssen, “The interaction of ocean waves and wind”, Cambridge University Press, 300 pp., 2004.

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(IGARSS), Toulouse, France, July 21-25, 2003.

[R23] F. Ardhuin, T. H

. C. Herbers, W. C. O'Reilly and P. F. Jessen, “Swell transformation across the continental shelf. Part II: validation of a spectral energy balance equation”, J. Phys. Oceanogr., 33,

1940--1953, 2003.

[R24] F. Collard, F. Ardhuin and B. Chapron, Extraction of Coastal Ocean Wave Fields from SAR images,

IEEE J. Oceanic Engin., Vol 30.(3), pp. 526-533, Jul. 2005

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[R26] H. E. Krogstad, “A simple derivation of Hasselmann's nonlinear ocean-synthetic aperture radar transform”, J. Geophys. Res., 97 (C2), 2421-2425, 1992.

[R27] V. Kudryavtsev, D. Hauser, G. Caudal and B. Chapron, “A semiempirical model of the normalized radar crosssection of the sea surface 2. Radar modulation transfer function”, J. Geophys. Res., 108(C3),

8055, 2003.

[R28]

K. Hasselmann, and S. Hasselmann, “On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image spectrum and its inversio n”, J. Geophys. Res, 96(C6), 10713-10729,

1991.

[R29]

C. Brüning, S. Hasselmann, and K. Hasselmann, “First evaluation of ERS-1 synthetic aperture radar wave mode data”, Global Atmos. Ocean Syst., 2, 61-98, 1994.

[R30]

S. Hasselmann, C. Brüning, K. Hasselmann and P. Heimbach, “An improved algorithm for the retrieval of ocean wave spectra from SAR image spectra”, J. Geophys. Res., 101, 16615-16629, 1996.

[R31]

C. Mastenbroek, and C.F. de Valk, “A semi-parametric algorithm to retrieve ocean wave spectra from

SAR”, J. Geophys. Res., 105, (C2), 3947, 2000.

[R32]

G. Engen and H. Johnsen, “SAR-Ocean wave inversion using image cross spectra”, IEEE Trans.

Geophys. Remote Sensing, 33(4), 1995.

[R33] Y. Quilfen, B. Chapron, T. Elfouhaily. K. Katsaros, and J. Tournadre, Observation of tropical cyclones by high-resolution scatterometry, J. Geophys. Res. 103, 7767 –7786, 1998.

[R34]

W. C. O'Reilly and Robert T. Guza, “A comparison of two spectral wave models in the Southern

California Bight”, Coastal Engineering, 19, 263--282, 1993.

[R35] P. Wessel and W. H. F.

Smith, “A Global Self-consistent, Hierarchical, High-Resolution Shoreline

Database”, J. Geophys. Res., 101, 8741–8743, 1996.

[R36] A. J. Kuik, G. Ph. van Vledder, and L. H. Holthuijsen, A method for the routine analysis of pitch-and-roll buoy wave data, J. Phys. Oceanogr., 18, 1020-1034, 1988.

[R37]

B. Chapron, F. Collard and F. Ardhuin, “Direct measurements of ocean surface velocity from space: interpretation and validation”, J. Geophys. Res., in revision.

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V 2.0 Mar. 15, 12 i.6

List of Contents

1. Executive summary ....................................................................... 1

2. General project objectives and experiment description .......................... 2

2.1. General context ...................................................................... 2

2.2. Objectives ............................................................................. 2

2.3. Experiment description ............................................................ 2

3.

Integration of COSMO-SkyMed data ..................................................... 4

4. X-band ....................................................................................... 6

4.1. A X-BAND GEOPHYSICAL MODEL FUNCTION ..................................... 6

4.2. Validation ............................................................................. 8

4.2.1. Against numerical weather prediction model ................................................. 8

4.3. Conclusion and recommendations for X-band ................................ 10

5. Quality of COSMO-SkyMed data, adequacy to requirements of the experiment .................................................................................... 12

5.1. Calibration constant................................................................ 12

5.2. Data dynamic wrt XMOD simulation ............................................. 13

5.3. Noise Equivalent Sigma Zero ..................................................... 14

5.4. Effective resolution in azimuth and range .................................... 16

6. Wave spectra inversion ................................................................. 20

6.1. Cross spectra estimation .......................................................... 21

6.2. First wave spectra inversion results ............................................ 25

7. Overall assessment of project preliminary outcome .............................. 29



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V 2.0 Mar. 15, 12 1

1.

Executive summary

Surface waves are known to be observable using satellite SAR imagery. In particular, image mode stripmap SAR products allow for high resolution and sufficient integration time to detect the wave motion. Yet, one of the major challenges remains to push the range of detected wavelength to an acceptable lower limit for the users because of the importance of wind sea information usually associated with smaller wavelength than swell. Significant progress has been achieved to develop understanding of potential and limitations of wave spectra retrieval in C-band using ERS, ENVISAT and

Radarsat-1 measurements. Much effort was devoted to identify the non-linearities and the effect or orbital velocity variance to the so called azimuth cutoff and the way to reconstruct the wave spectra when image spectra is distorted by these random motions within the resolution cell. It is in this context and trying to extend the knowledge gained and methods developed that we analyze today the potential of Cosmo-Skymed data for wave spectra inversion and associated range of validity.

The objective is to study the potentiality of using Cosmo-Skymed (CSK) measurements data to retrieve wave spectra. Although, it is expected that X-band measurements allow better resolution than C-band, still very little is known about the real range of validity and advantages of X band data, configuration parameters like incidence angle, or even intrinsic quality of CSK SAR products

(radiometric and geometric calibration, saturation, scalloping effect, etc).

In order to conduct this study, it was proposed to plan the acquisition of between 60 level1a SCS-B products in HH and VV polarization and the three modes Himage, Wide Region and Huge Region, to perform wave retrieval over areas external in-situ wave measurements are available (ie Pierre Noires buoy). The SARTool software developed by CLS has been upgraded in order to make the first demonstration of CSK SAR level-2 marine products including wave spectra at any location but also map of sea surface winds, and swell (providing that the quality of CSK data is adequate).

Deliverables includes a mid-term report on the wave spectra retrieval feasibility and a final report with buoy validation together with a catalogue of wave signatures such as observed on ordered CSK

SAR data. The final report will not only summarize the potentialities and limitations of wave spectra retrieval using CSK data but also provide clear recommendations for future integration in the existing operational services.



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V 2.0 Mar. 15, 12 2

2.

General project objectives and experiment description

2.1.

General context

With the successful launch, on June 7, 2007, of the first satellite of the Cosmo-Skymed constellation, with, as principal instrument, an X-Band SAR, a call for proposal was setup by the Italian Space

Agency to allow evaluation of Cosmo-Skymed imagery potential. In this framework, a test dataset was requested by SHOM to evaluate the potential of Cosmo-Skymed imagery for wave spectra retrieval. After more than two years waiting, the proposal was accepted and the data were ready to be ordered. At that time, no funding was available anymore and it took some time to budget this activity. Finally in 2011, a window opened with the help of SHOM and CLS was awarded the contract to perform this feasibility study in collaboration with SHOM and IFREMER for the provision of in-situ directional buoy data.

2.2.

Objectives

The objective of this project is to fully explore the capabilities and limitations of COSMO-Skymed

Level-1a products (SCS-B) to retrieve wave spectra in X-band. Performance of the restituted sea state information shall be evaluated on the basis on reference in-situ directional buoy data.

The different steps of this study includes an in depth analysis of the quality of complex SCS-B CSK products, the estimation of modulation transfer functions in X band by the wave motions and a validation exercise using co-located in-situ measurements.

This research project also strongly benefits from the unique capacities of the SARTool software that has been developed by CLS. This software, which consists of 4 modules (SARTool Wind, SARTool

Waves, SARTool Ships and SARTool Oil), aims at producing level2 products from level1-a or Level1b products. SARTool is used today operationally by Telespazio, Kongsberg Satellite Services AS, NOAA,

NATO Undersea Research Centre, CEDRE, etc.

Finally, this project also benefits from two other proposals aiming at exploring more specifically other marine applications:

 Potential and limitations of COSMO-Skymed for ship detection

 Potential and limitations of COSMO-Skymed for oil-spill detection

2.3.

Experiment description

60 CSK Level-1a products (ScanSAR Himage, Wide Region and Huge Region- HR in VV and HH polarization) have been allocated to this project. The coverage (40 x 40 km to 200 km x 200km), the selected polarizations VV/HH as well as the typical ranges of incidence angles (20 to 50°) covers the large range of observational conditions typically used for wave spectra retrieval using SAR imagery.

All products have been ordered as SLC (or SCS 1B for Cosmo-Skymed) to enable cross-spectral technique to be applied. Although the coverage is significantly reduced compared to the typical

ScanSAR products delivered by existing SAR missions operating in C-band, ScanSAR Huge Region products exhibit the closest similarity with existing services (MARCOAST services or CleanSeaNet delivered by EMSA). Up to now, 34 scenes have been acquired and transferred by FTP:

 Over the Golfe of Lion, 3 Huge region archived scenes have been received of the 4 requested.

 Over Iroise sea and the Pierre Noires wave buoy, 6 scenes have been acquired in HIMAGE VV out of the 15 requested. 11 acquired in HIMAGE HH out of the 15 requested. 10 have been acquired in Wide Region VV out of the 10 requested an 0 have been acquired in Wide Region

HH out of the 10 requested.



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The SARTool software developed by the CLS has been upgraded in order to make the demonstration of CSK SAR level-2 marine products including:

 Maps of sea surface winds

 Maps of sea surface waves



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V 2.0 Mar. 15, 12 4

3.

Integration of COSMO-SkyMed data

Scansar Wide SLC

Scansar Wide SLC

Scansar Wide SLC

Himage SLC

Himage SLC

Scansar Wide SLC

Scansar Wide SLC

Himage SLC

Himage SLC

Himage SLC

Himage SLC

Himage SLC

Himage SLC

Himage SLC

Himage SLC

Himage SLC

During the first month of this project, some efforts have been dedicated to the integration of CSK data in the SARTool software. Currently, only Level-1A SCS-B data in the .hdf5 format have been considered.

The available dataset available is composed of 34 scenes detailed as follows:

Type Date Zone Inc. Pol Note

Himage SLC

Scansar Huge SLC

16 fev 2011 19 :15

10 mar 2011 17:51

Bretagne

Golfe Lion

29 HH

VV

400m swell + wind sea 30m

Mistral, no visible waves

Scansar Huge SLC

Scansar Huge SLC

Scansar Huge SLC

Scansar Wide SLC

12 mar 2011 05:29

10 avr 2011 05:28

01 nov 2010 18:22

19 dec 2011 18:12

Golfe Lion

Golfe Lion

Bretagne

Bretagne

VV

VV

HH

VV

South-East wind, no visible waves

Mistral, no visible waves swell light swell

Scansar Wide SLC

Scansar Wide SLC

Scansar Wide SLC

Himage SLC

Himage SLC

Himage SLC

Himage SLC

Scansar Wide SLC

19 dec 2011 06 :10

26 dec 2011 18:24

27 dec 2011 06:04

30 dec 2011 06:16

30 dec 2011 18:17

3 jan 2012 18:17

4 jan 2012 06:10

4 jan 2012 18:11

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

51

48

48

45

VV

VV

VV

HH

VV

VV

HH

VV light swell swell

Large swell, Pierre noires mid swath

Short swell

Large swell and northward current

Very long and large swell

Long swell (but large noise)

Western swell

5 jan 2012 05:58

12 jan 2012 06:04

12 jan 2012 18:11

13 jan 2012 18:29

19 jan 2012 06:10

20 jan 2012 06:10

20 jan 2012 18:35

21 jan 2012 18:29

23 jan 2012 06:10

30 jan 2012 18:23

1 fev 2012 06:04

12 fev 2012 06:10

18 fev 2012 18:05

19 fev 2012 06:15

28 fev 2012 06:09

2 mar 2012 05:27

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

Bretagne

33

46

34

45

41

38

45

57

51

45

19

VV

VV

VV

VV

HH

VV

VV

VV

HH

VV

HH

HH

VV

HH

HH swell

Processing issues, lots of zeros!

Processing issues, lots of zeros !

Nice cross swell

Swell and tidal current

Nice north west swell

Good swell and southward current

Long swell (large noise)

Short swell, low wind

Wind sea

Crossed swell (large noise)

Swell and wind sea

Swell and breaking (large noise)

No wind, noise level !

HH Left looking, cross swell.



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Himage SLC

Himage SLC

7 mar 2012 06:09

10 mar 2012 05:27

Bretagne

Bretagne

45

20

HH Wind sea 80m, current against wind

HH Left looking

Table 1: Characteristics of the available CSK products



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4.

X-band

As for C or L band a GMF is needed to get geophysical parameters from SAR images acquired over ocean scenes at X-band.

Indeed, to retrieve the wind and waves over ocean scenes with a SAR and a scatterometer, it is commonly assumed that the sea surface roughness and thus the normalized radar cross section are related to the instrument characteristics (frequency, polarization, incidence angle) as well as the wind speed and direction. Indeed, as the wind blows over the sea surface, it generates surface roughness generally aligned with wind. Consequently the radar backscattered from this roughened surface is related to the surface wind parameters. The sea surface complexity (in particular its multiscale nature) makes the evaluation of each surface scale contribution to the backscattering mechanism very difficult. The total backscatter has to be seen as a weighted sum of several contributions from a large range of scales (from several meters to few centimeters) with various scattering mechanisms. The relative weight of the surface scale as well as the scattering mechanism depend both on the radar configuration (polarization, incidence angle, frequency) and sea surface conditions. This makes the interpretation of the interactions between electromagnetic and oceanic waves very difficult. To guide the interpretation of the measurements a lot of physically or semi-empirically

models exist [R9][R10][R11][R12][R13]. For wind inversion from SAR and scatterometers in Ku and C bands,

empirical relationships are used. These GMF relates the normalized radar cross section measured by the SAR to the incidence angle, the 10 meters height neutral equivalent wind speed and direction with respect to the frequency and the polarization.

At X band there is no such relationship. But existing empirical relationships could be combined with physically based approaches to get a GMF at X-band for both VV and HH co-polarizations. In order to build an empirical

GMF at X-band for both co-polarizations in a wide range of incidence angles and wind configurations, a large number of measurements of NRCS at X band co-located with wind speed and direction information is required.

By now, as the satellites operating at X-band were launched recently, the amount of data we obtained is limited and its direct use to derive the GMF is not an option for us. Consequently, we propose to use the expertise acquired thanks to existing SAR missions operating at C-band but also thanks to other remote sensing instruments such as scatterometers which also operate in the microwave domain.

The strategy is to combine existing empirical GMFs at other bands to get the expected NRCS at X-band and then use our limited dataset to do the validation.

4.1.

A X-BAND GEOPHYSICAL MODEL FUNCTION

As f

C

< f

X

< f

Ku

(where f is the radar frequency), the resonant wave numbers k r

 k

0 sin



(where k r stands for the resonant wavenumber and k

0

for the incident wave number) at X-Band for incidence angles between 30 and 50 degrees lie between the resonant wavenumbers at C- and Ku-bands. Moreover GMFs to relate NRCS to wind parameters already exist at Ku and C bands and are robust as built empirically on large dataset. We thus assume that for any incidence angles and wind conditions the NRCS at X-band can be related by:



0 pp

( f

X

 u

10

)

 pp

0

( f

Ku

 u

10

)

 pp

0

( f

C

 u

10

) ,



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V 2.0 Mar. 15, 12 7 where

 pp and

 pp are weighted functions to determine using physically based electromagnetic models. To simplify the problem, we first assume that

 pp and

 pp

are only wind speed and incidence angle dependent.

Using RCA model combined with Elfouhaily’s omnidirectional wave spectrum [R14] at Ku-, X and C-band we

estimate

 pp and

 pp

coefficients. At X-band, the NRCS is thus given the previous equation, where

 vv

0 at C

Band is given by CMOD-IFR2 [R15][R17],

 hh

0

at C Band by CMOD-IFR2 combined with the empirical C-band

azimuth angle dependent polarization ratio proposed by [R17] and

 vv

0

and



0 hh

given by the GMF proposed by

[R18]. Thi combination of Ku and C band models to get the NRCS at X-band is called XMOD hereafter.

Figure 1: Omnidirectionnal component of the NRCS in VV and HH polarization with respect to the wind speed. Incidence angles considered are: 30, 40 and 50 degrees

The trend of the omnidirectional component (a

0

) of the NRCS as obtained in X-band using XMOD is presented on

Figure 1

. As for C- and Ku-bands, the NRCS increases with wind speed and decreases when the incidence angle

increases for both polarizations. As defined, the noise equivalent sigma zero for TerraSAR-X is between -19 dB

and -26 dB with an average value of -23 dB [R7]. With respect to this value, it must be stressed that the wind

inversion will be difficult for the highest incidence angles in HH polarization. For example, regarding our results for the a

0 coefficient, it seems difficult to measure any geophysical signature for wind speeds lower than 5 m/s in

HH-polarization at incidence angles higher than 40 degrees. As derived, the range of validity of XMOD is induced by the limitations of the Ku- and C-band GMFs used. Based on these two remarks, we can anticipate optimal performances for wind ranging from 5 to 25 m/s and incidence angles between18 and 40 degrees



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V 2.0 Mar. 15, 12 8

(a) (b)

(c) (d)

Figure 2: (a) NRCS in VV polarization (b) NRCS in HH polarization (c) Polarization ratio (d) NRCS difference at

X band with respect to azimuth angle for a 40 degrees incidence angle. Grey points are measurements from

RENE radar obtained during POLRAD’96 experiment. Dashed-dotted lines, dashed lines and solid lines are given by Kirchhoff Approximation, Small Slope Approximation and X-MOD (this study) models.

4.2.

Validation

4.2.1.

Against numerical weather prediction model

To validate XMOD, we compare the NRCS as observed with RENE airborne radar operating at X-band in both co-polarization. We also compare the polarization ratio and the NRCS difference. The comparisons are presented

on

Figure 2

where the solid lines are the results obtained with X-MOD. In the contrary of the physically based

models we observe that the mean levels of the NRCS, the PR and the NRCS difference as well as the upwind/downwind and upwind/crosswind asymmetries are well reproduced by XMOD. In particular, the difference in the azimuth modulation between VV and HH polarization is well reproduced leading to a realistic modulation for both NRCS difference and PR.

Another approach to validate the XMOD GMF is to take benefit of the dual polarizations mode of TerraSAR-X.

Indeed we have four scenes acquired in both HH and VV polarizations. If the model is consistent between HH and

VV, the retrieved wind fields obtained from the two polarization configurations should be the same. To check this consistency we thus perform a simple wind field inversion using the scatterometry approach with both VV and

HH polarizations for the four scenes and then compare both sets of wind speeds. In this inversion scheme, the wind direction is obtained by interpolating ECMWF (0.5 degre and 6 hours respectively for the spatial and time resolution) but also NCEP (1/3 degre and 3 hours respectively for the spatial and time resolution) wind fields onto

the SAR grid at a resolution of 2 km. The scatter plot on Figure 3 presents (a) the NRCS-VV versus NRCS-HH

and (b) the wind speed deduced from the scenes in VV polarization versus the wind speed deduced from the



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V 2.0 Mar. 15, 12 9 scenes in HH polarization when the prior wind direction is given by ECMWF. As expected, on Figure 3 (a) the

NRCS-VV is found larger than the NRCS-HH. The two sets of wind speeds are also very consistent as the bias is only -0.027 m/s (resp. 0.039 m/s) and the rms 0.38 m/s (resp. 0.39 m/s) when using ECMWF (resp. NCEP).

Figure 3: (a) NRCS-VV vs NRCS-HH. (b) wind speed from images in VV polarization versus versus wind speeds from images in HH polarization obtained using XMOD GMF and wind direction from ECMWF NWP model.

To go further, we process the 20 TerraSAR-X images we have and compare the retrieved wind with NCEP and

ECMWF. The wind direction is given by interpolating ECMWF and NCEP wind fields onto the SAR grid at a resolution of 2 km. The main limitation of such a validation exercise is of course the use of a NWP model with a coarse temporal and spacial resolution to get the wind direction and to be the reference. However, to date we have no other alternative. The histogram of the wind speed as given by ECMWF for the acquired scenes is presented on

Figure 4

. We observe that a wide range of wind speeds is represented. Note that the NWP models give only

slightly different results. After the wind speed inversion, the comparisons with ECMWF (resp NCEP) yield to

0.45 m/s (resp 0.6 m/s) for the bias and 1.57 m/s (resp 1.8 m/s) for the rms in VV and to -0.14 m/s (resp 0.84 m/s) for the bias and 2.31 m/s (resp 2.26 m/s) for the rms in HH. The performance is slightly better in VV than in HH

polarization but still remains satisfying (see Figure 5 ). Indeed, as shown by intensive validations against buoys at

C-band [R16], a rms of 2 m/s is reasonable. To go further on the validation exercise, the dataset should be

enlarged and have co-located TerraSAR-X measurements with in-situ measurements. This will be part of a future work.



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V 2.0 Mar. 15, 12 10

Figure 4: Histogram of wind speeds given by ECMWF interpolated onto the SAR grid. Each wind speeds is colocated with a NRCS measurement.

(a) (b)

Figure 5: Histogram of wind speeds difference between SAR and ECMWF. From images in (a) VV and (b) HH polarizations

4.3.

Conclusion and recommendations for X-band

From this study, it appears that X band can be used for wind inversion using the GMF we have developed and well calibrated data. The range of validity is 18-40 degrees for incidence angles and 2-

25 m/s for the wind speed. At very high incidence angles and for low wind speeds, the noise becomes significant and can affect the wind retrieval.



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As for the other bands, if this study confirms the potential of X-band for wind inversion but it cannot be considered as a complete validation of the method due to the lack of good reference data for validation.

Consequently, we recommend pursuing the investigations.



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5.

Quality of COSMO-SkyMed data, adequacy to requirements of the experiment

5.1.

Calibration constant

This section presents some analysis with regards to the quality of CSK 1A data. Geophysical calibration constant

The first step of this section concerns the absolute calibration of the CSK products. Since no corner reflector has been deployed by CLS, no standard external calibration process could be carried out in this study [Ошибка! Источник ссылки не найден.]. Calibration allows the geophysical interpretation of SAR data by relating its digital number to physical parameters (e.g. soil moisture, wind field ….). Electromagnetic (EM) modeling is often the key component to realize such an interpretation. On the other hand, SAR calibration factor can be assessed if the following two criteria are met:

 The EM model is robust and non systematically biased

 A sufficiently large number of SAR acquisitions is involved: the central limit theorem can be applied.

There has been an increasing interest in the application of microwave remote sensing for ocean wind velocity measurements [Ошибка! Источник ссылки не найден.]. It is well known that the

Normalized Radar Cross Section (NRCS) is a function of polarization, frequency, incidence angle θ, wind speed W, and relative wind direction, the direction 𝜙 being equal to 0 when the wind is blowing towards the radar. The general empirical model for sea-surface NRCS is: 𝜎

0 𝑝

= 𝐴

0𝑝

(1 + 𝐴

1𝑝 𝑐𝑜𝑠𝜙 + 𝐴

2𝑝 𝑐𝑜𝑠2𝜙) where the subscript p denotes the polarization. This kind of modelling is well documented, especially

at C-band (CMOD) for VV polarization [R2] [R3]. In this study, ocean surface backscattering can be modelled at X-band by the so-called XMOD. The model developed in [R4] will be mainly used here. In

view of this section concerning calibration, one may argue this XMOD model is very recent and might not meet the above criteria. However, X-band SAR missions have been launched recently and the proposed XMOD is supposedly accurate.

To assess the calibration factor, it should be noted that some restrictions are applied to ensure that

the EM backscattering is not affected by noise (see section 5.3): the areas where the incidence angle

is above 30° and the wind speed below 5 m/s are discarded of this process. The difference between the calibrated CSK products and the simulated NRCS from XMOD and ancillary ECMWF winds is shown

in Figure 6.



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V 2.0 Mar. 15, 12 13

Figure 6: Relative calibration error between calibrated CSK HIMAGE products and XMOD simulation.

The relative bias is equal to -0.009 dB which can be considered as negligible. However, this process should involve a higher number of acquisitions. In addition to this, the variability of the relative calibration factor is not very small (standard deviation of about 1.13 dB) and is not normally distributed with a maximum around -0.5 dB.

5.2.

Data dynamic wrt XMOD simulation

The above approach can be also performed over the entire range of incidence angles. In this subsection, we would like to compare XMOD simulation (for all wind speed/orientation) with CSK

data. The systematic bias is then computed depending on incidence angle as shown in Figure 7.

Figure 7 : Incidence angle dependence of NRCS calibration in terms of NRCS difference (upper left), equivalent wind speed difference (upper right) and comparative map of SAR derived wind speed (lower left) and reference ECMWF wind (lower right).

HIMAGE VV polarization product on jan 21 2012 at 18:29 UTC



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V 2.0 Mar. 15, 12 14

Figure 8 : NRCS calibration of Wide Region VV product on jan 20 2012 at 18:35 UTC . Measured vs. expected NRCS (resp. wind speed) on the upper panel (resp. lower panel). left corresponds to the first subswath, center to the middle subswath and right to the third subswath (far range)

At this stage, it should be mentioned that, for an a priori random distribution of wind speed and orientation over SAR incidence angle, the EM backscattering over sea surface supposedly strongly decreases with respect to incidence angle. The larger the incidence angle is, the less backscattering power the SAR sensor receives.

Figure 7 and Figure 8 hence shows the goodness-of-fit of the dynamic of CSK data as referred to

XMOD simulation. It should be mentioned that the agreement is in general manner good.

5.3.

Noise Equivalent Sigma Zero

The Noise Equivalent Sigma Zero is an important parameter to assess the quality of SAR products.

Over ocean surface, its estimation can be carried by the measurement of the calibrated NRCS over

the entire range of incidence angles. The following procedure is used [R5]:

 NRCS is evaluated with respect of incidence angle by step of around 0.05 deg over the data products where very low to no wind is observed.



For each incidence angle NRCS is calculated. (see Figure 9)

 For each incidence angle bin, the lowest significant value of NRCS bin is considered as the

NESZ. A NRCS bin is significant when more than 2 values NRCS are found in the bin. Results

are shown in Figure 10.



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V 2.0 Mar. 15, 12 15

Figure 9: NRCS values per incidence angle for no wind scene.

Figure 10: global NESZ variation function of incidence angle with X-MOD as reference for the three HH Himage products with very little to no wind. The four X-MOD NRCS curves corresponds to 3, 5, 7 and 10m/s wind speed from bottom to top.

The retrieved global NESZ values are of the order of the mission specification (< -23 dB).

Comparison with XMOD GMF in HH polarization indicates clearly the limit of using high incidence angles in HH polarization where signal will be dominated by noise. For instance at 45 degrees, noise level is equivalent to a roughness generated by a wind speed of 5m/s at the center of image and

10m/s on the left and right borders of the image.



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V 2.0 Mar. 15, 12 16

Results from previous project of oil spill detection with detected (intensity only) VV pol CSK data (

Figure 11

)

indicates that NESZ values are low enough to ensure the usability of all the incidence angle range at VV polarization for the retrieval of wave information

Figure 11 : global NESZ variation function of incidence angle with X-MOD as reference for the VV polarized Huge region products from another project

5.4.

Effective resolution in azimuth and range

The effective resolution is typically estimated from the width of the autocorrelation function around the maximum at zero lag.



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Figure 12 : Autocorrelation function for HIMAGE mode. noise (upper left), no swell (upper right), swell low wind (lower left), swell medium wind (lower right)



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V 2.0 Mar. 15, 12 18

Figure 13 : Autocorrelation function for Wide Region mode. no swell (left), swell medium wind

(right)

Figure 14 : Autocorrelation function for Huge Region mode. no swell (left)

Effective estimated resolution over ocean

Range ocean resolution Azimuthal resolution ocean

HIMAGE

SCANSAR WIDE

6m

20m

50 to 100m*

50 to 100m*

SCANSAR HUGE 20m 60 to 150m*

*The upper limit is dependent on orbital velocities variance and can be higher than estimated for higher wind situations than the available cases.



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Note that the effective range resolution is much higher than the azimuthal resolution and it is advised to limit the analysis to scales that are correctly resolved in both directions to avoid facing issues of unexpected rotation of the peak direction in any subsequent spectral analysis. Therefore, despite the relatively high resolution of some

Cosmo-Skymed products, only long waves (swell) can be imaged without noticeable distortion. Exceptions can be made if the wave direction is known to be in or close to the range direction from external information.



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6.

Wave spectra inversion

The algorithm proposed here is an extension of the algorithm used to produce level 2 wave spectra products from

ESA’s ENVISAT ASAR wave mode products. In practice the processing of one image block involves the following operations :

(i) The wind speed is estimated from the measured radar cross section (i.e. the image must be calibrated) and an a-priori wind direction, or visual inspection / low wavenumber analysis of the image, using the backscatter model function (XMOD) as described earlier

(ii) The input SLC image is detrended using a Gaussian low pass filter where the width of the filter is set such as to best remove the lower frequencies not related to waves.

(iii) Spectra and cross-spectra are computed corresponding to three extracted looks with time lags of -0.25, 0 and

+0.25 s. An a priori estimation of the speckle noise is used to reduce the variance of the spectra. A weighted sum of the spectra and cross-spectra then provides one single estimation of the spectrum and imaginary part of the cross-spectrum. The weights given to each spectrum are functions of the image clutter noise level estimated from the high-frequency energy in the cross-spectrum.

(iv) Spectra are corrected for nonlinear SAR effects. This operation is performed with a resampling of the image cross-covariance function at short lags (see

[R24]

)

(v) The azimuth cut-off wavenumber k c

is estimated by fitting an Gaussian function to the auto-covariance function of the cross-spectrum image for zero range lag, and the image spectrum (after step iv) is multiplied by a factor exp(k 2 / kc 2 ), where k x

is the azimuthal wavenumber, that corrects for the cut-off effect. This correction is not applied to the highest frequency part of the spectrum.

(vi) The linear system transfer function are estimated and applied (instrument transfer function and image to wave elevation modulation transfer functions), giving a symmetric surface elevation wavenumber spectrum, in which the wave direction is only known with a 180° ambiguity.

(vii) In order to remove this ambiguity a signal to noise ratios (SNR) of the asymmetric spectra is estimated as the cross-spectral level of the resolved wave motion normalized by the spectral level in the high wavenumber part of the cross-spectrum. If this SNR is above certain threshold, then the asymmetric spectrum is smoothed, and the final symmetric and asymmetric wave spectra are obtained from a combination using their clutter noise levels to yield the ambiguity-free wave spectrum. If the SNR is below a certain threshold no ambiguity removal is performed and the symmetric spectrum is kept unchanged.

(viii) Because SAR spectra are originally wavenumber spectra, while in situ observations at fixed positions yield frequency spectra. SAR spectra were thus transformed to frequency-directional spectra using the general dispersion relation. Effects of stronger nonlinearity and changes in the hydrodynamic modulation transfer function may impact the SAR image analysis but are not considered here. The inversion algorithm has not been tuned in any way to the observations.

As described, this inversion procedure primarily estimates the wave spectrum resolved by the SAR (the detected wave pattern in the SAR scene). It is thus mainly adapted to long wave system Note that, although the extraction of the swell is based on the quasi-linear transform, the inversion uses the full theoretical nonlinear SAR mapping through the coupling with the nonlinear part. This algorithm was developed originally for the wave inversion of

ENVISAT ASAR wave mode at a unique incidence angle of 23°, explicitly assuming that observed waves are in deep water. The SAR products tested here are single look complex products with incidence varying from 20 to 55 degrees. These images cover coastal areas where the deep water assumption is no longer valid. The inversion algorithm has therefore been generalized in two ways.

First, the SAR modulation transfer function (MTF) accounting for short wave tilted by larger waves has been generalized to take into account the local variation of backscatter around the changing incidence angle (different from 23°). This is simply implemented by applying for all incidence angles the XMOD empirical relationship relating incidence to X-band backscatter described earlier. Second, the surface orbital velocities for a given wavenumber, entering the velocity bunching MTF, have been modified to take into account the linear dispersion



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V 2.0 Mar. 15, 12 21 relation for surface gravity waves



2 =gktanh(kh), applicable to any water depth h , with g the acceleration of gravity and k and



the wavenumber and radian frequency of the waves, respectively. This replaces the deep water limit



2 = gk. As a result the extra parameter h must be found. Here h is obtained from hydrographic soundings.

Finally, the main modification is related to the fact that a priori look-up tables were not available for incidence angles different from 23° in order to evaluate the nonlinear SAR mapping at different wind speeds and directions.

It is well known that close to its origin, the autocovariance function of the SAR image is generally much broader than the corresponding real aperture radar (RAR) image, and the same thing is true for the cross-covariance of multiple looks. This blurring of short scales is related to surface nonlinearities including velocity-bunching.

Rather than extracting the nonlinear spectral part in the spectral domain, the auto- and cross-covariance functions have thus been re-sampled along their spatial coordinates to minimize the random blurring effects associated with the surface motions

Note however that wave spectra retrieval algorithm is based on the mean wave energy over a selected imagette and the local wave amplitude may easily vary of a factor 2 around this mean. Hereafter a snapshot of short scale

roughness modulation by long wave (

Figure 15

) indicates that modulation is clearly not uniform over this area

covering about 10x15km with clear evidence of wave groups. It is therefore recommended to estimate wave spectra on imagettes no smaller than 10 times the expected dominant wavelength.

Figure 15 : short scale roughness modulation by long waves

6.1.

Cross spectra estimation

Cross spectra estimation requires extraction of different looks from the Doppler spectrum. It is therefore essential that this Doppler spectra is wide enough within the given PRF limits (here of the order of 3300 Hz) to enable

sufficient time between the looks used for cross spectra estimations.

Figure 16

illustrates

.Doppler spectra for HIMAGE mode where a large portion of the PRF (80%) can be used (here PRF is normalized to 1) and therefore the Doppler spectra splinted in three looks of equal bandwidth. Thermal noise level can be seen as a constant of about 0.02 and cross spectra quality, especially the weak imaginary part helping to resolve propagation direction ambiguity, will be affected by noise when the level of signal (Gaussian shape is not

significantly higher than the noise level. For Wide and Huge region (

Figure 17

) the Doppler bandwidth is much

reduced (40% of PRF), causing difficulties to have looks separation time large enough for swell direction ambiguity removal.



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V 2.0 Mar. 15, 12 22

Figure 16 : Doppler spectra for typical HIMAGE mode SCS-B CSK products. Polarization VV 34 degrees (upper left), VV 57 degrees (upper right), HH 51 degrees (lower left), HH light wind (lower right)

Figure 17 : Doppler spectra for typical Wide Region (left) and Huge Region (right) SCS-B CSK product



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V 2.0 Mar. 15, 12 23

Examples of cross spectra are presented on Figure 18 and Figure 19 for HIMAGE and Wide Region

products. Whereas HIMAGE imaginary part of cross spectra has a clear asymmetry at the location where the energy is maximum on the real part, this is not always the case for Wide Region products

where the left panel of Figure 19 indicates a clear imaginary part and the right panel a noisy

imaginary part resulting in the impossibility to retrieve the swell propagation direction.

Figure 18 : HIMAGE cross-spectrum. Image intensity(top), real part of cross spectra (left), imaginary part of cross-spectra (right).



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Figure 19 : Wide Region cross-spectra. Image intensity, real part of cross spectra, imaginary part of cross-spectra (from top to bottom). Left is a case with clear imaginary part and right is a similar case but with noisy imaginary part.



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6.2.

First wave spectra inversion results

Figure 20 : Himage Wave spectrum inversion. Cross spectra (top). Image intensity (bottom left).

Inverted wave spectrum (bottom right)



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V 2.0 Mar. 15, 12 27

Figure 21 : Wide region Wave spectra inversion for unambiguous (left) and ambiguous case

(right). Cross spectra real and imaginary part, image intensity and inverted wave spectra (from top to bottom)

Retrieval of wave spectra from HIMAGE products allow to remove the propagation direction 180

degrees ambiguity in 90% of the cases and generally provide unambiguous wave spectra (Figure 20).

Maps of dominant wave parameters extracted from these wave spectra (Figure 22) are clearly in

agreement with the expected swell patterns in the region of interest even if buoy validation is still needed to quantitatively assess the results. This buoy validation will be available in the Final report.

However, wave spectra retrieved from Wide Region are generally (95%) ambiguous as can be seen on

bottom right spectra of Figure 21 and therefore? Wide Region products, despite their larger swath

coverage, are not recommended for wave retrieval.



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Figure 22 : Map of dominant wave components from inverted wave spectra overlaid on top of sea surface roughness modulation in grey levels. Significant wave height is displayed in color, dominant direction and wavelength by the direction and length of the white arrows.



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7.

Wave spectra Validation

7.1.

Validation dataset

Directional wave spectra observations are required to validate SAR derived 2D wave spectra and only a few number of available waverider buoy data did provide directional information. For instance, the

Meteo-France/SHOM or UK/Meteo-France wave buoy in gulf of Lion and Cote d’Azur or even Brittany or Gascogne did not provide directional information and were not used.

In situ observations from a Datawell directional Waverider buoy were obtained from IFREMER as part of the PREVIMER in-situ observation network. The buoy is anchored by 60m depth near “Les Pierres

Noires” lighthouse at location 48°17,420’N and 4°58,100’W and has WMO identification number

62069. We thank Louis Marié and Fabrice Ardhuin for their great help to identify the data location on

IFREMER archive and to interpret the format.

It was noted that data transmitted to ground recorder only concerns frequency spectrum plus the first two moments of the directional distribution, for a given frequency, namely the peak direction and the directional spread around the peak direction. This limitation is constrained by the transmission link with the buoy and the other directional moments are only available after buoy recovery and therefore were not available for this study. However, in most situations observed in the

CSK SAR dataset, simultaneous swell systems did not have the same frequencies and the first two moments of the directional spectra for each frequency appear to be sufficient for proper validation of the SAR derived wave spectra.

7.2.

Validation method

When comparing wave spectra from SAR and in-situ buoy data, special attention must go to the different quantity measured and to the spectral domain of the two measurement techniques. Firstly, whereas waverider buoys estimate the frequency spectrum, SAR estimates the wavenumber spectrum. The well known water surface waves dispersion relation can be used, for a given water depth, to map frequencies into wavenumber assuming all scales freely propagate according to the dispersion relation. This assumption is however recognized to be valid for long gravity waves.

Secondly, SAR imaging mechanism inherently limits the range of observed wave scales and wind sea spectrum is generally not observed or strongly limited and distorted. Therefore comparison of SAR and in-situ spectra only has a sense when restricted to swell systems.

As a result, prior to comparison with SAR 2D spectra, buoy 2D frequency spectra are transformed into

2D wavenumber spectra and partitioned so that only associated swell partitions from buoy and SAR spectra will be compared in terms of significant wave height, dominant direction and dominant wavenength.



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Figure 23 : Simultaneous observation of directional wave spectra from waverider buoy(left) and from CSK SAR (right). Contour of SAR spectra partitions (blue contour) is over plotted on buoy wave spectra.

7.3.

Validation results

Buoy validation has been undertaken on a subset of all CSK data received. This subset correspond to the cases where the wind speed not too low so that the long waves can be imaged, and to the optimal HIMAGE acquisition mode for wave imaging that was also the only mode where a clear mapping of the location metadata and image was good enough to select the portion of SAR image around the waverider buoy.

Results are separated between HH polarization where the signal to noise was generally poor except for last acquisition with low incidence angles (below 30 degrees), and VV polarization where the signal to noise was found be excellent for all incidence angles.

Integrated parameters from corresponding SAR and buoy directional spectra partitions are estimated

: Hs is the significant wave height, wl is the dominant wavelength for a given partition, and dir is the dominant direction at the partition peak.

HH polarization :

Date SAR Time SAR Hs SAR wl

20111230 06:16 0.89 229

SAR dir Buoy time Buoy hs Buoy wl Buoy dir

115 06:30 2.57 213 100

20120104 06:10

20120119 06:10

20120123 06:10

20120212 06:10

20120219 18:15

20120302 05:27

2.58

1.51

1.31

1.26

1.67

3.62

254

223

240

188

258

252

VV polarization :

Date SAR Time SAR Hs SAR wl

20111230 18:17 5.04 227

110

75

120

125

105

110

SAR dir

110

06:00

06:00

06:00

06:00

18:30

05:30

18:30

2.28

1.56

2.21

0.97

1.54

1.51

2.43

232

212

230

173

116

227

Buoy time Buoy hs Buoy wl

232

120

100

110

120

110

90

Buoy dir

120



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20120103 18:18

20120113 18:30

20120121 18:30

5.25

2.7

4.47

238

166

220

110

110

115

18:30

18:30

18:30

4.23

0.94

1.61

199

171

212

80

120

110

20120130 18:23

20120218 18:05

2.37

2.83

171

205

115

125

18:30

18:00

1.25

1.24

141

161

100

110

For VV polarization dataset, the Normalized Root Mean Square error (NRMSE) observed between SAR and buoy swell partitions integrated parameters is 18.6% for the significant wave height and 12.3% for the dominant wavelength.

For HH polarization dataset, the Normalized Root Mean Square error (NRMSE) observed between SAR and buoy swell partitions integrated parameters is 64% for the significant wave height and 20.3% for the dominant wavelength.

The overall poor results at HH polarization is due to the low signal to noise ratio for incidence angles above 30 degrees and therefore wave inversion from CSK SAR data should only be attempted for VV polarization or HH polarization but low incidence angles (below 30 degrees) despite wave modulation can still be detected on HH CSK data at higher incidence angles.

However, it should be noted that HH polarization data at high incidence angles provides a good detection of wave breaking area where the specular reflection on wave breaking strongly emerges from the noise floor (together with the emerged rocks) with typical bright vertical segments (cf

Figure 24)



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Figure 24 : HH polarized HIMAGE intensity image at high incidence angle (51 deg.) where shirt bright segments highlight the presence of wave breakers around the islands of the Iroise sea.



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8.

Overall assessment of project outcome

In view of the different tasks that were initially planned, this project has been running in a smoothly manner, despite the difficulties in ordering and getting the requested SAR and validation data.

Given the current available dataset, absolute calibration for CSK SCS-B products has been investigated and seems relatively good. The agreement between XMOD model and CSK data seems relatively good as well. The estimated Noise Equivalent Sigma Zero levels meet overall criteria for efficient wave retrieval at VV polarization for all incidence angles and HH polarization for incidence angles < 30 degrees.

The Xband MTF are behaving as expected using the XMOD GMF and wave spectra retrieval is very promising from HIMAGE and in a lesser extend with Wide Region products. No Huge Region product with swell modulation was received but results are expected to be comparable with Wide Region results.

Validation results from the comparison of SAR derived 2D wave spectra and buoy directional spectra highlight the strong impact of the signal to noise ratio in HH polarization at large incidence angle. for

VV polarization, overall results are comparable to those obtained from SAR wave spectra inversion from ASAR instrument in C band and therefore CSK SAR data can be used for wave spectra estimation at the condition of choosing the proper mode (HIMAGE optimal) and the proper combination of polarization and incidence angles. Incidence angles above 30 degrees in HH polarization shall be avoided for spectral inversion but can be used for wave breaking area detection.


CLS-DAR-NT-12-064-1-0_CSKWave_final - Boost

Final report PI CSK: Analysis of the

Potentiality and Limitations of Wave spectra inversion using SAR Measurements in X-band from Cosmo-Skymed satellites

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CLS-DAR-NT-12-064-1-0_CSKWave_final - Boost

Final report PI CSK: Analysis of the

Potentiality and Limitations of Wave spectra inversion using SAR Measurements in X-band from Cosmo-Skymed satellites

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