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2.7.1.22 Ocean depth/land elevation

The new Global Digital Elevation Model, MACESS, has been developed in ESRIN by merging the ACE land elevation data and the Smith and Sandwell ocean bathymetry data. This new DEM is available at 5min arc resolution for the NRT data and at 2min arc resolution for the offline data.

The ocean depth / land elevation is obtained by bilinear interpolation in space.

If the surface type of the altimeter measurement is set to "open ocean or semi-enclosed seas", only grid points having negative altitude are used in the interpolation. If no such grid points with negative altitude are found, then the four grid points having positive altitude are used. If the altimeter measurement is set to "enclosed seas or lakes", "continental ice", or "land", all grid points are used in the interpolation, regardless of their altitude.

Applicability

  • The ocean depth/land elevation is computed for FDGDR, IGDR and GDR products.
  • The computation of the ocean depth/land elevation is performed continuously for all surface types.

Accuracy

TBD

Reference

Ref 2.31
Defrenne D. and Benveniste J., "A global land elevation and ocean bathymetry model from radar altimetry", QWG meeting minutes, Marsh 2004

2.7.1.23 Total geocentric ocean tide height (solution 1)

The ocean tide solution 1 is based on the GOT00.2 model.

The height of the ocean tide (semi-diurnal and diurnal tidal waves) is the sum of N tidal constituents hi:

image eq 2.91
(i=1,N)

with:
image eq 2.92

Fi is the tidal coefficient of amplitude nodal correction (depends only on the altimeter time)

Ui is the tidal phase nodal correction (depends only on the altimeter time)

Xi is the tidal astronomical argument (depends only on the altimeter time)

σi is the tidal frequency

t, φ and λ are respectively the altimeter time tag, latitude and longitude

Ai(φ,λ) and Bi(φ,λ) are harmonic coefficients bilinearly interpolated at the altimeter location (φ,λ) from the input harmonic coefficients map given by the GOT00.2b model by Ray Ref. [2.32 ] Harmonic coefficients A and B are tidal amplitude x cos(phase) and tidal amplitude x sin(phase) respectively.

The total geocentric ocean tide is the sum of the ocean tide, the tidal loading height and the long period tide equilibrium.

Applicability

  • The total geocentric ocean tide height is computed for FDGDR, IGDR and GDR products
  • The computation of the total geocentric ocean tide height is performed continuously for all surface types (over land and ocean), although it is relevant to ocean surfaces only.

Accuracy

The ocean tide model GOT00.2b, is essentially an update of the one (GOT99.2) described in details in Ray [RD.1]. GOT00.2, is the latest solution in a series beginning with the work described in: E J O Schrama and R Ray, Journal of Geophysical Research, v.99, p 24799, 1994.

GOT00.2b used 286 10-day cycles of Topex and Poseidon data, supplemented in shallow seas and in polar seas (latitudes above 66deg) by 81 35-day cycles of ERS-1 and ERS-2 data., The solution consists of independent near-global estimates of 8 constituents (Q1,O1,P1,K1,N2,M2,S2 and K2).

Reference

Ref 2.32
Ray, R., A Global Ocean Tide Model From TOPEX/Poseidon Altimetry/GOT99.2 - NASA/TM-1999-209478, pp. 58, Goddard Space Flight Center/NASA, Greenbelt, MD, 1999.

Ref 2.33
Discussion, Recommendations and Conclusion, CCVT meeting, 25-27 Mar 2003, ESRIN

2.7.1.24 Total geocentric ocean tide height (solution 2)

The ocean tide solution 2 is based on the FES model.

The height of the ocean tide (semi-diurnal and diurnal tidal waves) is the sum of N tidal constituents hi:

image eq 2.93
(i=1,N)

with:
image eq 2.94

Fi is the tidal coefficient of amplitude nodal correction (depends only on the altimeter time)

Ui is the tidal phase nodal correction (depends only on the altimeter time)

Xi is the tidal astronomical argument (depends only on the altimeter time)

σi is the tidal frequency

t, φ and λ are respectively the altimeter time tag, latitude and longitude

Ai(φ,λ) and Bi(φ,λ) are harmonic coefficients bilinearly interpolated at the location (φ,λ) from the input harmonic coefficients map given by the FES model. Harmonic coefficients A and B are tidal amplitude x cos(phase) and tidal amplitude x sin(phase) respectively.

The total geocentric ocean tide is the sum of the ocean tide, the tidal loading height and the long period tide equilibrium.

FES2002 model is computed for FDGDR, and FES2004 is computed for I/GDR.

 

Applicability

  • The total geocentric ocean tide height FES2002 is computed for FDGDR
  • The total geocentric ocean tide height FES2004 is computed for IGDR and GDR products
  • The computation of the total geocentric ocean tide height is performed continuously for all surface types (over land and ocean), although it is relevant to ocean surfaces only.

Accuracy

FES2002 version of the Grenoble FES hydrodynamical model is used [RD.1] in NRT. FES2002 is a fully revised version of the older FES99 version. The finite element mesh used in the computation was fully rebuilt. Topex/Pos�idon, ERS-2, deep ocean tide gauges and coastal tide gauges data were analyzed so as to be assimilated in the solution. To compute the tidal signal from FES2002, 27 tidal constituents are used. Among these 27 tidal constituents, 9 principal ones are given in input amplitudes and phases maps (M2, S2, N2, K2, K1, O1, 2N2, Q1 and P1). The 18 remaining ones are computed by admittance from the principal constituents 1 to 9, using admittance coefficients.

FES2004 version, used for the Offline, is generated at LEGOS. It is the last update of the FES2002 solution. The altimeter data reprocessing consists in a new atmospherical forcing response correction (mog2D-G) applied to the data before the harmonic analysis.

This new model includes two extra waves, S1 and M4, adding to the 9 waves of FES2002 model. The validation of the FES2004 solutions shows an overall improvement in FES2004 vs GOT00 compared to FES2002 vs GOT00, especially in the mid and hight latitude. Ref. [2.35 ]

References

Ref 2.34
Lef�vre, F., Mod�lisation de la mar�e oc�anique � l'�chelle globale par la m�thode des �l�ments finis avec assimilation de donn�es altim�triques, SALP-RP-MA-E2-21060-CLS, pp. 87, CLS, Ramonville Saint-Agne, 2002.

Ref 2.35
Letellier T, Lyard F. and Lefevre F. The new global tidal solution: FES2004, Proceeding of the Ocean Surface Topography Science Team Meeting, St. Petersburg, Florida, 4-6 November 2004

2.7.1.25 Solid earth tide height and long period tide height

The gravitational potential V induced by an astronomical body can be decomposed into harmonic constituents s, each characterised by an amplitude, a phase and a frequency. Thus, the tide potential can be expressed as :

 

image eq 2.95
 

where the tide potential of constituent s, Vn(s), is given by :

 

image eq 2.96
 

where the phase ω(s).t + φ(s) of constituent s at altimeter time tag t (relative to the reference epoch), is given by a linear combination of the corresponding phases of the 6 astronomical variables ωi.t + φi :

 

eq 2.97
image  

where λ is the altimeter longitude, and where
image eq 2.98
is the associated Legendre polynomial (spherical harmonic) of degree n and order m (
image eq 2.99
, with θ altimeter latitude).

 

The Cartwright's tables provide for degree n=2 and order m=0,1,2, and for degree n=3 and order m=0,1,2,3 the ki(s) coefficients and the amplitudes cn(s) for each constituent s (only amplitudes exceeding about 0.004 mm have been computed by Cartwright and Tayler Ref. [2.36 ] , and Cartwright and Edden Ref. [2.37 ] . This allows for the potential to be computed.

 

The solid Earth tide height and the height of the long period equilibrium tide are both proportional to the potential. The proportionality factors are the so-called Love number Hn and Kn.

 

The solid Earth tide height H_solid is thus :

 

image eq 2.100
 

with : H2 = 0.609

H3 = 0.291

g = 9.80

V2 = V20 + V21 + V22

V3 = V30 + V31 + V32 + V33

 

The height of the long period equilibrium tide H_Equi is thus :

 

image eq 2.101
 

 

with : K2 = 0.302

K3 = 0.093

 

The above described tides contributions do not take into account the permanent tide.

 

Applicability

  • The solid earth tide height and the equilibrium long period ocean tide height are computed for FDGDR, IGDR and GDR products
  • The computation of the solid earth tide height and of the equilibrium long period ocean tide height are performed continuously for all surface types (over land and ocean), although the computation of the equilibrium long period ocean tide height is relevant to ocean surfaces only.

 

Accuracy

The accuracy of the solid earth tide height and of the height of the equilibrium long period ocean tide is better than 1 mm.

 

References

Ref 2.36
Cartwright, D.E., and R.J. Tayler : New computations of the tide-generating potential, Geophys.J.R.Astr.Soc, v23, 45-74, 1971

 

Ref 2.37
Cartwright, D.E., and A.C. Edden : Corrected tables of tidal harmonics, Geophys.J.R.Astr.Soc, v33, 253-264, 1973

 

 

 

2.7.1.26 Tidal loading height according to ocean tide solution 1

The height of the tidal loading is the sum of N constituents hi:

eq 2.102

Ci(φ,μ) and Di(φ,μ) are harmonic coefficients bilinearly interpolated at the altimeter location (φ,μ) from the input harmonic coefficients map. This map has been computed from Cartwright and Ray method Ref. [2.38 ] . This method is based on spherical harmonic approach.

Applicability

  • The tidal loading height is computed for FDGDR, IGDR and GDR products
  • The computation of the tidal loading height is performed continuously for all surface types (over land and ocean).

Accuracy

For the load tide height, other methods have been used for Geosat and TOPEX/POSEIDON missions for the evaluation of the tidal loading. The Ray and Sanchez's method Ref. [2.38 ] for the Cartwright and Ray tide model used a high-degree spherical harmonic method.

References

Ref 2.38
Cartwright and Ray and Sanchez, Oceanic tide maps and spherical harmonic coefficients from Geosat altimetry, NASA tech memo. 104544 GSFC, Greenbelt, 74 pages, 1991.

2.7.1.27 Tidal loading height according to ocean tide solution 2

The height of the tidal loading is the sum of N constituents hi:

image eq 2.103
(i=1,N)

Ci(φ,μ) and Di(φ,μ) are harmonic coefficients bilinearly interpolated at the altimeter location (φ,μ) from the input harmonic coefficients map. This map has been computed from Francis and Mazzega's method Ref. [2.39 ] : this method consists of evaluating a convolution integral over the loaded region (the oceans) with a kernel (so-called Green's function) which is the response of the media (the Earth) to a point mass load. The used ocean tide model is the FES2002 model.

 

Applicability

  • The tidal loading height is computed for FDGDR, IGDR and GDR products
  • The computation of the tidal loading height is performed continuously for all surface types (over land and ocean).

 

Accuracy

For the load tide height, other methods have been used for Geosat and TOPEX/POSEIDON missions for the evaluation of the tidal loading. The Ray and Sanchez's method Ref. [2.40 ] for the Cartwright and Ray tide model used a high-degree spherical harmonic method. The method of Francis and Mazzega is probably more accurate (no cut-off due to spherical harmonics expansion, no ocean to land discontinuities).

 

References

Ref 2.39
Francis, O., and P. Mazzega, Global charts of ocean tide loading effects, J. Geophys. Res., Vol. 95, 11,411-11,424, 1990.

 

Ref 2.40
Ray, R.D., and B.V. Sanchez, Radial deformation of the Earth by oceanic tidal loading, NASA Tech. Memo, 100743, July, 1989.

2.7.1.28 Geocentric pole tide height

The Earth's rotational axis oscillates around its nominal direction with apparent periods of 12 and 14 months. This results in an additional centrifugal force which displaces the surface. The effect is called the pole tide. It is easily computed if the location of the pole is known Ref. [2.41 ] , by :

 

image eq 2.104
 

 

where H_Pole is expressed in mm, and where λ and φ are respectively the longitude and latitude of the measurement. x and y, in arc second, are the nearest previous pole location data relative to the altimeter time and x_avg and y_avg are the averaged pole co-ordinates (in arc second).

A = -69.435 10-3eq 2.105
is the scaled amplitude factor in m:

A = image eq 2.106

where Ω is the nominal earth rotation angular velocity in radian/s, R is the earth radius in m, g is gravity in m/s2,
image eq 2.107
is a conversion factor from arc second to radian, and K2 is the Love number (K2 = 0.302).

x and y are obtained from IERS, and an update of the auxiliary file containing those coordinates is updated every 4-5 days.

 

Applicability

  • The pole tide height is computed for FDGDR, IGDR and GDR products
  • The computation of the pole tide height is performed continuously for all surface types (over land and ocean).

 

Accuracy

IGDR processing uses predicted pole locations, whereas GDR processing use true (measured) pole locations. The use of measured pole locations instead of predicted ones has probably little impact on the pole tide height accuracy.

A pole location accuracy of about 50 cm is needed to get a 1-mm accuracy on the pole tide height.

Reference

Ref 2.41
Wahr, J. : J. Geophys. Res., Vol. 90, pp. 9363-9368, 1985.

 

 

 

2.7.1.29 MWR water vapour content

Vap_Cont is the MWR water vapour content in g.cm-2. It is computed with neural algorithm (see 2.7.1.10. ) from the MWR 23.8GHz and 36.5 GHz brightness temperatures (TB23 and TB36), interpolated to altimeter time, if the MWR land flag interpolated to altimeter time is set to " ocean ", and from σ0_Ku.

where TB23_Int and TB36_Int are the 23.8 GHz and 36.5 GHz brightness temperatures (in K) interpolated to RA-2 time tag, σ0_Ku is the ocean backscatter coefficient for Ku-band (dB).

Applicability

  • The MWR water vapour content is computed for FDGDR, IGDR and GDR products
  • The computation of the MWR water vapour content is performed continuously for all surface types (over land, ice and ocean). Nevertheless, it is applicable only for ocean surfaces.

Accuracy

As this algorithm has been formulated over a representative database Ref. [2.42 ] , a minorant of the error is the rms difference obtained when applying directly the algorithms over the database, i.e. 0.1 g/cm2 for the integrated water vapour content.

As there are no measurements performed, no upper bound of the error can be given.

Reference

Ref 2.42
S. LABROUE and E. OBLIGIS, "Neural network retrieval algorithm for the Envisat/MWR", report CLS/DOS/NT/03.848 of ESA contract n�13681/99/NL/GD, January 2003.

2.7.1.30 MWR liquid water content

Cloud_Liquid is the MWR cloud liquid water contents in kg.m-2. It is computed from the MWR 23.8 GHz and 36.5 GHz brightness temperatures (TB23 and TB36) interpolated to RA2-time, if the MWR land flag interpolated to altimeter time is set to " ocean ", and from σ0_Ku.

Where TB23_Int and TB36_Int are the 23.8 GHz and 36.5 GHz brightness temperatures (in K) interpolated to RA-2 time tag, σ0_Ku is the ocean backscatter coefficient for Ku-band (dB).

Applicability

  • The MWR liquid water content is computed for FDGDR, IGDR and GDR products
  • The computation of the MWR liquid water content is performed continuously for all surface types (over land, ice and ocean). Nevertheless, it is applicable only for ocean surfaces.

Accuracy

As this algorithm has been formulated over a representative database Ref. [2.43 ] , a minorant of the error is the rms difference obtained when applying directly the algorithms over the database, i.e. 0.1 g/cm2 for the integrated water vapour content.

As there are no measurements performed, no upper bound of the error can be given.

Reference

Ref 2.43
S. LABROUE and E. OBLIGIS, "Neural network retrieval algorithm for the Envisat/MWR", report CLS/DOS/NT/03.848 of ESA contract n�13681/99/NL/GD, January 2003.

2.7.1.31 RA-2 wind speed algorithm

First, the atmospheric attenuation is added to the backscatter coefficient to correct it. Then wind speed is computed (in m/s), using a linear interpolation in the input wind table, according to the modified Witter and Chelton algorithm Ref. [2.44 ] .

 

Applicability

  • The RA-2 wind speed is computed for FDGDR, IGDR and GDR products
  • The computation of the RA-2 wind speed is performed continuously for all surface types (over land and ocean).

 

Accuracy

The derived wind speed is considered to be accurate to the 2 m/s level.

 

Reference

Ref 2.44
Witter, D.L., and D.B. Chelton : A Geosat altimeter wind speed algorithm and a method for altimeter wind speed algorithm development, J. Geophys.Res., 96, 8853-8860, 1991

 

 

 


Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry