ZIm(t) = t[CIm(t)-iSIm(t)] = I,Z:lm ei8t +Z;;'e- i8t
k
Z!n = FIm[t( C!. - is!.)] ,
C ± - ·S± - C"± i(e:"'+Xt-i)
kim
I kim -
klm e
~ _ 3 Pw (l+k:)
(l+m)!
[
]
~
1m - a e Pe (2/+1) (/-m)!(2/+1)(2-0 0m )
(8)
where Cftm and eflm are the unnormalized tide height amplitude and phase using the
Schwiderski convention, Xk is the Doodson-Warburg phase correction, Ok is the tidal
argument at time t for constituent k, Pw and Pe are the mean densities of the ocean and
solid Earth, a e is the equatorial radius, and k[ is the load Love number, Flm is the factor
converting unnormalized height coefficients into normalized Stokes coefficients and 00m is
the Kronecker delta.
Stokes coefficient variations due to solid Earth tides can be put into the same form by
converting a perturbation in the Love number into its equivalent in tenns of the ocean tide
height field (Eanes et al., 1983; Cheng et al., 1992) as
(9)
where 1C1m = -ymod(l + m,2), okk = okkr + iOkki is the complex, frequency dependent
external potential Love number perturbation defined such that a negative imaginary part
indicates dissipation, Hk is the tidal potential amplitude in the form used in Cartwright and
Tayler (1971) and Cartwright and Edden (1973), oC;"" = oS;1m = 0, and
A". = (-I)m[ae~41C(2 - oom) r·
Long-period (averaged over the argument of latitude and sidereal time) gravitational
excitations of the eccentricity vector are related to the odd degree zonal Stokes coefficients
and odd degree spherical harmonics of the ocean tide height as
'¥ p(t) = I f: . . t[ PZO.¥.-l + P;O.l¥JCIO(t)
=3(ouu)
(10)
where P~ = P!pq(a,e,l) are the prograde and retrograde eccentricity vector excitation
sensitivities, 0; is the low frequency part of the tide argument and is essentially equivalent
to the arguments used in theories of nutation, the ki are the Doodson argument multipliers
for constituent k, and N is the maximum degree, chosen to retain all significant terms given
the satellite's declining sensitivity and the spatial power spectrum of the gravitational
signals.
Long-period gravitational excitations of the node vector are related to the even-degree
zonal Stokes coefficients and even-degree spherical harmonics of the o<:ean tide height as
34
k
Z!n = FIm[t( C!. - is!.)] ,
C ± - ·S± - C"± i(e:"'+Xt-i)
kim
I kim -
klm e
~ _ 3 Pw (l+k:)
(l+m)!
[
]
~
1m - a e Pe (2/+1) (/-m)!(2/+1)(2-0 0m )
(8)
where Cftm and eflm are the unnormalized tide height amplitude and phase using the
Schwiderski convention, Xk is the Doodson-Warburg phase correction, Ok is the tidal
argument at time t for constituent k, Pw and Pe are the mean densities of the ocean and
solid Earth, a e is the equatorial radius, and k[ is the load Love number, Flm is the factor
converting unnormalized height coefficients into normalized Stokes coefficients and 00m is
the Kronecker delta.
Stokes coefficient variations due to solid Earth tides can be put into the same form by
converting a perturbation in the Love number into its equivalent in tenns of the ocean tide
height field (Eanes et al., 1983; Cheng et al., 1992) as
(9)
where 1C1m = -ymod(l + m,2), okk = okkr + iOkki is the complex, frequency dependent
external potential Love number perturbation defined such that a negative imaginary part
indicates dissipation, Hk is the tidal potential amplitude in the form used in Cartwright and
Tayler (1971) and Cartwright and Edden (1973), oC;"" = oS;1m = 0, and
A". = (-I)m[ae~41C(2 - oom) r·
Long-period (averaged over the argument of latitude and sidereal time) gravitational
excitations of the eccentricity vector are related to the odd degree zonal Stokes coefficients
and odd degree spherical harmonics of the ocean tide height as
'¥ p(t) = I f: . . t[ PZO.¥.-l + P;O.l¥JCIO(t)
=3(ouu)
(10)
where P~ = P!pq(a,e,l) are the prograde and retrograde eccentricity vector excitation
sensitivities, 0; is the low frequency part of the tide argument and is essentially equivalent
to the arguments used in theories of nutation, the ki are the Doodson argument multipliers
for constituent k, and N is the maximum degree, chosen to retain all significant terms given
the satellite's declining sensitivity and the spatial power spectrum of the gravitational
signals.
Long-period gravitational excitations of the node vector are related to the even-degree
zonal Stokes coefficients and even-degree spherical harmonics of the o<:ean tide height as
34