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 semienclosed 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
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 (semidiurnal and diurnal
tidal waves) is the sum of N
tidal constituents hi:
  eq 2.91 
(i=1,N)
with:
  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 10day cycles of Topex and
Poseidon data, supplemented in
shallow seas and in polar seas (latitudes
above 66deg) by 81 35day cycles of ERS1
and ERS2 data., The solution
consists of independent nearglobal
estimates of 8 constituents
(Q1,O1,P1,K1,N2,M2,S2 and K2).
Reference
Ray,
R., A Global Ocean Tide Model
From TOPEX/Poseidon Altimetry/GOT99.2 
NASA/TM1999209478, pp. 58, Goddard Space
Flight Center/NASA, Greenbelt,
MD, 1999.
Discussion,
Recommendations and Conclusion, CCVT
meeting, 2527 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 (semidiurnal and diurnal
tidal waves) is the sum of N
tidal constituents hi:
  eq 2.93 
(i=1,N)
with:
  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, ERS2,
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 (mog2DG) 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
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,
SALPRPMAE221060CLS, pp. 87, CLS,
Ramonville SaintAgne, 2002.
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, 46
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 :
  eq 2.95 
where the tide potential of
constituent s, Vn(s), is given
by :
  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 :
where λ is the
altimeter longitude, and where
  eq 2.98 
is the associated Legendre
polynomial (spherical harmonic)
of degree n and order m (
  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 socalled
Love number Hn and Kn.
The solid Earth
tide height H_solid is thus :
  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 :
  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
Cartwright, D.E., and R.J. Tayler : New
computations of the
tidegenerating potential,
Geophys.J.R.Astr.Soc, v23, 4574, 1971
Cartwright, D.E., and A.C. Edden :
Corrected tables of
tidal harmonics,
Geophys.J.R.Astr.Soc, v33,
253264, 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 highdegree spherical
harmonic method.
References
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:
  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 (socalled 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
highdegree spherical harmonic method.
The method of Francis
and Mazzega is probably more accurate
(no cutoff due to spherical harmonics
expansion, no ocean to
land discontinuities).
References
Francis,
O., and P. Mazzega, Global charts of
ocean tide loading
effects, J. Geophys. Res., Vol. 95,
11,41111,424, 1990.
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 :
  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
coordinates (in arc second).
is the
scaled amplitude factor in m:
A =
  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,
  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 45 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 1mm
accuracy on the pole tide height.
Reference
Wahr, J.
: J. Geophys. Res., Vol. 90, pp.
93639368, 1985.
2.7.1.29 MWR water vapour content
Vap_Cont is the MWR water vapour content in
g.cm2. 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 RA2
time tag, σ0_Ku is the
ocean backscatter coefficient for
Kuband (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
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.m2. It is
computed from the MWR 23.8 GHz and 36.5 GHz
brightness temperatures (TB23 and TB36)
interpolated to RA2time, 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 RA2
time tag, σ0_Ku is the
ocean backscatter coefficient for
Kuband (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
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 RA2 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 RA2 wind speed
is computed for
FDGDR, IGDR and GDR products

The computation of
the RA2 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
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,
88538860, 1991
