Use of altimeter data for wave
energy applications
EUMETRAIN Polar Satellite Week 2012
José J. Cândido
8 November 2012
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Linear wave theory
Irregular sea surface
=
Infinite sum of sinusoidal
components
Directional wave spectrum S(f,)
distribution of energy density in
frequency and direction
2

S( f )  S( f , )d
0
Frequency spectrum S(f)
distribution of energy density in
frequency
Characterization of sea waves
Wave parameters
2 
mn 
 
f nS(f ,  )dfd 
n-th spectral moment
0 0
1/2
Hm  4m0
0
 Hs
significant wave height
1/2
Tm02
 m0 

 

 m2 
 Tz
mean zero-crossing period
Characterization of sea waves (cont.)
Wave parameters
m1
Te 
m0
Tp 
P 
1
fp
2
0.5Hs Te
mean energy period
peak period
wave power (deep waters)
(in kW/m when Hs in m and Te in s)
Characterization of sea waves (cont.)
Wave parameters
mean wave direction
2 

  arctan 20 0
  arctan 0
00
0
  S(f ,  ) sin( )ddf
  S(f ,  ) cos( )ddf
 S(f ) sin( (f ))df
 S(f ) cos( (f ))df
Wave data sources
Datawell Directional Waverider
ASAR ScanSAR Wave Mode
Teledyne RD Instruments Workhorse Sentinel ADCP
WAM model (National & Kapodistrian University of Athens)
TOPEX/Poseidon (AVISO)
Satellite altimetry timeline
• 1969 - Space oceanography by radar instrumentation as a new discipline (congress of Williamstown)
• 1973 - Skylab (USA's first experimental Space station) launched in May; first spaceborne altimeter - measurement
of coarse features of the marine geoid
• 1975 - GEOS 3 (Geodynamics Experimental Ocean Satellite) launched in April; improved performance and greater
global coverage - measurements of sea level and its variability over time
• 1978 - Seasat (SEAfaring SATellite) launched by NASA in June; first high-performance altimeter for remote sensing
of the oceans - measured ocean surface and wave heights; mission ended in October 1978, due to malfunction
• 1985 - Geosat (GEOdetic SATellite) launched in March; first mission to provide long-term high-quality altimetry
data (>3yrs)
• 1991 - ERS-1 launched by ESA in July; successively implemented on 3 different orbits, containing several
instruments including a radar altimeter
• 1992 - TOPEX/Poseidon (joint project between NASA and CNES) launched on 10 August; it carried two radar
altimeters and precise orbit determination systems (including DORIS ); laid foundation for long-term ocean
monitoring from Space; supplied world's ocean topography and sea surface height every ten days with high
accuracy
• 1995 - ERS-2 (ERS-1 follow-on) launched in April
• 1998 - GFO (Geosat follow-on) launched in February
Satellite altimetry timeline (cont.)
• 2001 - Jason-1 (TOPEX/Poseidon follow-on) launched on 10 December (CNES and NASA); satellite control and data
processing operations performed by new ground segment
• 2002 - Envisat (Environmental Satellite, ERS-1 and ERS-2 follow-on) launched by ESA on 1 March; carries ten
complementary instruments including radar altimeter and DORIS orbitography and precise location system; offers
near-real-time data access
• 2008 - Jason-2 launched on 20 June (CNES, NASA, Eumetsat and NOAA); takes over and continues TOPEX/Poseidon
and Jason-1 missions; carries Poseidon-3 - next generation of Poseidon altimeter with lower instrument noise and
algorithm enabling better tracking over land and ice; ~2.5 cm accuracy altimeter measurements
• 2010 - Cryosat-2 launched on 8 April (ESA); altimetry satellite dedicated to polar observation - determines
variations in the thickness of the Earth's continental ice
sheets and marine ice cover, tests prediction of thinning
Arctic ice due to global warming; current plans to operate
over oceans for validation purposes in low-resolution mode
• 2011 - HY-2 (HaiYang means 'ocean' in Chinese) launched
in August (China); monitors sea surface wind field, sea
surface height and sea surface temperature
measurement accuracy (credits CNES)
TOPEX/Poseidon
• 1981 - CNES evaluates Poseidon altimeter to be carried onboard the first Spot satellite;
NASA plans TOPEX (Topography Experiment) mission to follow Seasat’s success
• 1983 - Insufficient individual budgets: CNES and NASA begin discussing possibility of
combining the two projects
• 1987 - CNES and NASA formally create partnership for joint project involving French
and American instruments, on an American satellite to be launched by a European rocket
(Ariane 4): TOPEX/Poseidon
TOPEX/Poseidon
Launch
End Date
Altitude
Inclination 66°
Repetitivity
Agency
Frequencies
Improvements to previous altimetry systems:
specially-designed satellite, suite of sensors, satellite
tracking systems and orbit configuration,
development of optimal gravity model for precision
9.9156 days orbit determination and dedicated ground system for
NASA/CNES mission operations
TOPEX: 13.6 GHz - Ku band
5.3 GHz - C band
Poseidon: 13.6 GHz – Ku band
10/08/1992
8/01/2006
1336 km
• 2002 - On 15 September TOPEX/Poseidon assumed a new orbit midway between its original ground tracks; the
former TOPEX/Poseidon ground tracks are now overflown by Jason-1 (this tandem mission demonstrated the
scientific capabilities of a constellation of optimized altimetry satellites)
• 2005 - October, last data acquired, due to failure in a pitch reaction wheel
Altimetry basic principle
Altimetry satellites - distance from satellite to target surface by measuring satellite-tosurface round-trip time of a radar pulse
Satellite orbit accurately tracked (DORIS, PRARE, GPS; laser tracking - calibration);
position determined relative to arbitrary reference surface - ellipsoid; sea surface
height (SSH) - range from sea surface to reference ellipsoid
Water vapour , electrons in the atmosphere, sea state … can affect the radar signal
round-trip time, distorting range measurements – interference correction: supporting
measuring instruments, several different frequencies, modelling
Magnitude and shape of echoes (or waveforms) - characteristics of reflecting surface:
wave height and wind speed over the oceans, backscatter coefficient and surface
roughness for most reflecting surfaces; best results over ocean - spatially
homogeneous, surface conforms with known statistics
Non-homogeneous surfaces, containing discontinuities or significant slopes (some ice,
rivers or land surfaces) - accurate interpretation difficult
Different frequencies used (+ and -)
Ku-band: sensitivity to atmospheric perturbations
Ka-band: better observation of ice, rain, coastal zones, land masses
Comparison between different frequency signals generate interesting results (rain rate over
the oceans, detection of crevasses over ice shelves, etc)
Altimetry requires great amount of information to be taken into account before being able to use the data
Data processing is a major part of altimetry, producing data of different levels for different uses
Radar altimeter data
● Significant wave height - Hs (accuracy comparable to that of in situ measurements)
Wind speed at 10 m height - U10
Backscatter coefficient - σ0
● Wave period - Proposed algorithms:
Relating σ0 with probability distribution of sea surface slopes → variance of the slopes in terms of spatial
spectral moments → dispersion relationship: convert into temporal spectral moments → estimate of
1
m4(σ0), m0=Hs2/16 → altimeter characteristic wave period
m  2
Davies et al. (1997) -
Tz  a  bTA  c  dTA  eTA2  f 2
TA   0 
 m4 
 g 2H s 2
  3.25
 U10




0.31
pseudo wave age
Hwang et al. (1998) - Tp and Tz (more suitable for closed sea, where swell is less dominant)
Gommenginer et al. (2003) - linear relationship between Tz and (σ00.25Hs0.5) based on buoy
observations
2 0.25
 0l
radar cross-section at Ku band in its linear form
Tz  0.895  2.545( 0l Hs )
Quilfen et al. (2004) - neural network to establish Tz(σ0, Hs); two algorithms:
1
Ku band:
Tz  exp(17.1642a  13.5844), a  1  exp(0.6573Hs 0.1084 0Ku 02962  2.2377)

Ku and C bands:

 0Ku 0.3082
2
Tz  exp(5.7474  1.4688a  1.7943b), a 
exp(
1
.
5068
b
),
b

1
1  exp(1.8612  0.08U10 )
 0C 0.2352H s 0.0981
Radar altimeter data (cont.)
● Wave period - Proposed algorithms (cont.):
Kshatriya et al. (2005) - empirical algorithm Tz(ξ, TA)
Tz  a  b  cT A  dTA  e 2  fTA2 ,
a  0.1130, b  0.6090, c  2.4369, d  0.0045, e  0.0487, f  0.2270
Mackay et al. (2008b) - two-piece Tz model (Ku band); threshold level ~13 dB above which σ0 is no
longer related to Tz
  

 1 ln 1   0  A  if  0  
    H s   

Tz  
,
 1  1    A 
 if  0  
 ln 

    H s   
A  17.11,   4.504,   0.1558,   1.658,   12.87
for TOPEX
Radar altimeter data validation
Co-location criteria – Space and time lags
TOPEX/Poseidon
Quasi-polar, non-sun-synchronous orbit
66ºN - 66ºS coverage
9.9156 days repeat cycle
(5 days for tracks intersections)
127 revolutions, 254 passes per cycle
315 km ground track separation at Equator
Buoys:
Wave spectra every 3 hours
(every 30 min, Hs>5 m)
20 min records
Criteria:
Minimum space lag
Maximum space lag
Average criterion
Time interpolation
Space interpolation
Monthly averages
Group velocity criterion
Radar altimeter data validation - Hs & Tz
Moreira et al. (2002)
TOPEX/Poseidon
4 buoys off the west coast of
Portugal
83 - 110 m depths
Sep 1992 - Dec 1999
(1995 on for Tz)
10 - 50 km minimum space lags
▪ Average criteria reduces errors; ▪ Hs: Erms < 0.3 m, r2 up to 0.98; ▪ Local calibrations recommended; ▪ Tz: Davies et al. Erms < 0.7 s with local coeffs.
Radar altimeter data validation - Hs & Tz
in Zhao Dongliang et al. (2012)
NDBC buoys
2001 – 2005
Satellite footprint
within 50 km
Time lag < 1 h
3236 group data
in Cruz et al. (2007)
Mackay et al. (2008b)
TOPEX & NDBC buoy data
T02: Erms = 0.6 s
Radar altimeter data validation - Tz
Pontes et al. (2009)
Quilfen et al. (2004) - Ku & C bands
Jason
NDBC buoys data
Jul-Dec 2005
36 km maximum space lag
30 min maximum time lag
640 group data
Radar altimeter data validation - Hs, Tz, Te & P
M. Teresa Pontes, M. Gonçalves, J. Cândido (2002) - INETI
Empirical algorithm
deduced from buoy
measurements off
the north-west coast
of Portugal
Te  1.1509Tz  1.0882
whole set
< 100 kW/m
TOPEX/Poseidon vs. buoy data
Figueira da Foz
off Portugal NW coast
Radar altimeter data validation and utilization - P
Pontes et al. (2002)
Track 126
P (T/P) = 18.1 kW/m
P (WAM) = 13.5 kW/m
Track 239
P (T/P) = 19.8 kW/m
P (WAM) = 14.9 kW/m
TOPEX/Poseidon
ECMWF WAM model
Rio de Janeiro
off Brazil coast
1999-2001
Radar altimeter data validation - Tz & Te
Te=1.36Tz
Te=1.15Tz
Radar altimeter data validation and utilization - Te & P
Mackay et al. (2008b)
Algorithm to estimate T-10 from Ku-band altimeter data (jointly developed by OPD and NOCS) with Erms≈1.0s
Mean Pelamis WEC power
2ºx2º grid
Global database of altimeter measurements
– 6 missions spanning 14 yrs
Mackay et al. (2008a)
Along track mean Pelamis WEC power
TOPEX/Poseidon & Jason phase A data
Sep 1992 - Sep 2006
Monthly
Annual
Erms=34.3kW
Erms=15.5kW
Mean Pelamis WEC power
2ºx2º square
10 yrs altimeter and NDBC
buoy measurements
Erms for along track mean
Pelamis WEC power
Radar altimeter data utilization
Fugro OCEANOR
Provides metocean data and software packages to the oil, coastal engineering, renewables and other marine
industries
Several different products: WorldWaves global offshore database
Global database – wind and wave time series data
ECMWF models calibrated against satellite data
in situ buoy data where available
0.5º grid; 6 hrs
1996 to date
Global summary of
the WorldWaves
model vs. satellite
correlation coefficient
(for all validation grid
points)
ECMWF WAM model data calibration by Fugro OCEANOR against global buoy and TOPEX database
Correlation coefficient between simultaneous co-located WorldWaves and TOPEX-Jason Hs
Jan 1997- Dec 2006
Radar altimeter data utilization (cont.)
Fugro OCEANOR
World Wave Atlas
Series of wind and wave atlases primarily based on
satellite altimeter data - wind and wave climate
statistics worldwide:
▪ Geosat (1986 - 1989)
▪ Topex-1 (1992 - 2002)
▪ Topex-2 (Sep 2002 –-2005)
▪ Jason-1 (Jan 2002 - 2008)
▪ EnviSat (Oct 2002 – present, ongoing)
▪ Geosat Follow-On (GFO) (Jan 2000 – 2008)
▪ ERS-1 (1991 - 1996)
▪ ERS-2 (1995 - )
▪ Jason-1n (2008 - ongoing)
▪ Jason-2 (2008 – ongoing)
Mean Hs along
TOPEX/Jason ground
tracks off
Western Europe
Hs and wind speed
made ~ each 6 km
along tracks each
satellite passing
Comparison of TOPEX data and simultaneous buoy Hs
Satellite data validation: data set of co-located NOAA buoy and TOPEX data
13 buoys
1365 data records
Data from tracks passing within 100km and 1h with respect to buoy
observations
Radar altimeter data utilization (cont.)
Fugro OCEANOR - Barstow et al. (2009)
Simple Coastal Wave Modelling
Use of satellite data together with long-term offshore WorldWaves model data to
estimate the coastal wave energy resources
Satellite passes from offshore to nearshore → measures Hs profile with along-track
resolution of ~6km
TOPEX: Hs profiles from deep offshore to coast ~every 10 days over 10-year period
Adjust offshore grid point data to various points along the satellite tracks →
reasonably accurate wave height statistics closer to the coast (although data will be
spatial average over altimeter footprint)
Satellite
flying
towards SE
Sep - Nov wave
energy resource
along
Norwegian
Along-track mean Hs (north of Ireland) → estimate long-term wave
statistics closer to the coast
Radar altimeter data utilization - Wave model data validation
ERA-40 WAM model vs. TOPEX/Poseidon - J. Cândido, M.T. Pontes, L. Gato
Conclusions
• Satellite altimeter estimates of Hs accuracy comparable to the
one of in situ measurements
• Several models proposed to estimate Tz from altimetry data with
very reasonable precision
• Assessment of wave energy resource in deep waters requires the
knowledge of Te - algorithms insufficiently accurate
• Use of altimeter data suitable for:
- Preliminary wave energy resource assessment purposes
- Validation of wave model data used in wave energy
resource assessment studies
- Integrating wave atlases - complementary data;
extrapolation of existing data
References
Barstow, S., G. Mork, L. Lonseth, J.P. Mathisen, 2009. WorldWaves wave energy resource assessments from the deep
ocean to the coast. Proc. EWTEC 2009: 8th European Wave and Tidal Energy Conference. Uppsala, Sweden.
Cruz, J., E. Mackay, T. Martins, 2007. Advances in Wave Resource Estimation: Measurements and Data Processing. Proc.
EWTEC 2008: 7th European Wave and Tidal Energy Conference.
Davies, C.G., P.G. Challenor, and P.D. Cotton, 1997: Measurement of wave period from radar altimeters, in Ocean wave
measurement and analysis, edited by B.L. Edge, and J.M. Hemsley, pp. 819-826, Am. Soc. Civil Eng, Virginia, USA, 1997.
Gommenginger, C.P., M.A. Srokosz, P.G. Challenor, 2003. Measuring ocean wave period with satellite altimeters: a
simple empirical model. Geophysical Research Letters, 30(22): 2150, doi: 10.1029/2003GL017743.
Hwang, P.A., Teague, W.J., Jacobs, G.A. and Wang, D.W., 1998: A statistical comparison of wind speed, wave height, and
wave period derived from satellite altimeters and ocean buoys in the Gulf of Mexico region. J. Geophys. Res., vol.103,
No. C5, 10451-10468, May 15.
Mackay, E.B.L., A. Bahaj, C.H. Retzler, P.G. Challenor, 2008a. Wave energy resource assessment using satellite altimeter
data. Proc. International Conference on Offshore Mechanics and Arctic Engineering, OMAE2008, vol. 6, pp. 861-870.
Mackay, E.B.L., C.H. Retzler, P.G. Challenor, C.P. Gommenginger, 2008b. A parametric model for ocean wave period from
Ku band altimeter data. Journal of Geophysical Research, 113: C03029, doi: 10.1029/2007JC004438.
Moreira, N., H.O. Pires, M.T. Pontes, C. Camara, 2002. Verification of TOPEX/Poseidon Wave Data against Buoys off the
West Coast of Portugal. Proc. 21st International Conference on Offshore Mechanics and Arctic Engineering, OMAE2002,
Oslo, Norway.
Pontes, M.T., M. Goncalves, J. Cândido, 2002: Preliminary Assessment of Wave Energy Resource in Brazil and Wave
Energy Plant in Leblon Beach. INETI Report. June.
Pontes, M.T., M. Bruck, S. Lehner, 2009. Assessing the wave energy resource using remote sensed data. Proc. EWTEC
2009: 8th European Wave and Tidal Energy Conference. Uppsala, Sweden. p. 111-116.
References (cont.)
Quilfen, Y., B. Chapron, M. Serre. 2004. Calibration/validation of an altimeter wave period model and application to
TOPEX/Poseidon and Jason-1 altimeters. Marine Geodesy, 27(3): 535-549.
Zhao Dongliang, Li Shuiqing, Song Chaoyang, 2012. The comparison of altimeter retrieval algorithms of the wind speed
and the wave period. Acta Oceanol. Sin., Vol. 31, No. 3, P. 1-9. DOI: 10.1007/s13131-012-0201-4.
AVISO: www.aviso.oceanobs.com
Fugro OCEANOR: www.oceanor.no
www.altimetry.info