The parameters necessary for obtaining a 10 cm accuracy for GEOS-C satellite altimetry are outlined. These data include oceanographic parameters, instrument calibration, pulse propagation, sea surface effects, and optimum design

Weiffenbach, G. C.

English

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AN OBSERVATIONAL PHILOSOPHY
FOR GEOS-C SATELLITE ALTIMETRY
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George C. Weiffenbach
Smithsonian Astrophysical Observatory
Cambridge_ Massachusetts 02138 ._
1 73-  5370
Since the GEOS-C altimetry experiment will be the first of a
series of altimeter missions_ its objectives should be defined within
thG context of the long-term objectives of satellite altimetry. One
definition of these objectives was stated in the report of the
196 9 Williamstown study on Solid Earth and Ocean Physics as the
synoptic measurement of the topography of instantaneous mean sea level
to an accuracy of lO cm. In that report_ emphasis was placed on deter-
mining variations of ocean topography over periods of time ranging from
2 cycles per day to l cycle per year with a spatial resolution of l°
(I00 km) or better.
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The need for establishing the accuracy and reliability of
s_tellite-borne altimeter instruments is self-evident and clearly must
be considered a primary GEOS-C objective. However_ I would like to
suggest that_ although these factors are necessary 3 they are not suf-
ficient for the future design of effective altimetry systems. An
altimetry system is not only comprised of satellite instrumentation
and data acquisition_ but also of all elements of the data analysis
functions_ including computer software and physical models such as
geopotential models_ ocean current and density variation models_ etc.
To fully establish the feasibility of attaining a lO cm system accuracy_
and to provide the inputs needed for the design of efficient altimeter
systems in the future 3 the GEOS-C altimetry experiment must include an
extensive investigation of all the above-mentioned factors. This in
turn implles that another primary objective of GEOS-C must be to acquire
a substantial body of synoptic data to establish the ranges of values
of the various oceanographic parameters that will be encountered in
practice_ to provide the actual experimental data necessary for develo-
ping and evaluating software and analytic procedures_ and to determine
just what ancillary data (e.9._ the geopotential) we will need to
acquire to reach the lO cm accuracy level.
Having stated the broad objectives for the GEOS-C experiment_
I will now outline what I consider to be the major problem areas in
satellite altimetry_ and briefly discuss their current status. I
will then consider some design and operating questions relevant to the
ability of the GEOS-C experiment to contribute to the stated long term
altimetry objectives.
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To makethe subsequent dis_ssion specific enough to provide
useful information we must define somecharacteristics of the alti-
meter instrumentation. I will fi1_t assumethat the GEOS-Cand sub-
sequent instruments will be pulse_ radar altimeters operating in the
X- to K-band region. At this tim_ this choice is clearly the best
from the standpoint of practical _gineering considerations_ since
suitable componentsand systems a_e both available and in an advanced
state of development_ power requ_lements and antenna dimensions are
consistent with satellite constra_ts_ this region of the electro-
magnetic spectrum permits all-we_ner operation 3 and finally_ iono-
spheric propagation errors are at a tolerable level.
With this type of system__he altimeter "footprint" on the
ocean surface will be a circle w_h a diameter in the range l to lO _m.
At wavelengths of l to 3 cmand for ocean-reflecting areas of square
kilometers the radar echo receiv_ at the satellite will be the vector
sumof the echos from a very lar_ number (>lO6) of individual ocean-
surface reflecting elements that ,_ill be distributed in range (height)
over many (r.f.) wavelengths for ell but an extraordinarily smooth
ocean. The resulting distribution} of relative phases among the indi-
vidual echos will cause the amplitude to vary within each (return)
pulse over a very great range. T;_ese amplitude variations_ which will
be distributed according to the _yleigh probability density function_
effectively prevent us from dete_-'ining satellite-to-ocean altitude
from any single pulse. Further_ -here is a minimum time (or distance
travelled by the satellite) that ,_ust elapse between successive pulses
to ensure the decorrelation of this Rayleigh noise that is necessary
before a useful result can be o_tained from the average of many pulses.
For the case we are considering _ere_ the minimum decorrelation tim_ is
of the order of l millisecond_ a_d roughly some lO00 pulses must be
averaged to obtain a reasonable altitude measurement.
Thus the output of the satellite altimeter will be a measurement
roughly once per second of the ve(tical distance between the satellite
and an elongated segment of ocea_ surface with dimensions of the order
of I to lO km perpedicular to t_e satellite subtrack and perhaps lO
to 20 km along the subtrack. Th_ basic observational information from
the altimeter will be a one-dimer_ional profile (averaged over the
elongated footprint) of the ocear_ surface relative to the satellite
orbit as it is traced out in tim_: by the motion of the satellite. In
addltion_ the roughness of the ocean surface will influence the shape
and amplitude of the echo pulses_ and may provide information on
sea state.
Now_ what are the problem areas? They are listed in table I.
First_ there is the instrument _,_:rse_ and its calibration. Although
these are of primary importance_ ] will not discuss them further since
they will be dealt with in detail by later speakers.
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Table I.
Satellite Altimeter Problem Areas.
INSTRUMENTATION
CALIBRATION
PROPAGATION
SATELLITE TRACKING
GEOID
SEA SURFACE EFFECTS
Since the altimeter measures the time interval for a pulse to
travel from satellite to ocean and back_ we must know the pulse propa-
gation velocity to compute altitude. If we assume_ as most everyone
does in practice_ that the light second is our primary length standard 3
we need only be concerned with departures from the vacuum velocity of
propagatlon--viz._ the influences of the ionosphere and troposphere on
microwave propagation velocities.
For radio frequencies below 20 Ghz_ the troposphere produces
an apparent altitude change of about 2-I/2 meters. At any one ocean
location_ the variation of this altitude error with time will have a
peak to peak amplitude of about 30 cm_ and an RMS value of roughly
lO cm_ these variations being the result primarily of variations in
atmospheric water vapor content. There is a water vapor resonance line
at 23 Ghz (_= 1.3 cm) so that should be avoided. There are other mole-
cular absorption lines for radio frequencies above 23 Ghz that will
cause both large altitude errors and loss of signal (e.g. the oxygen
line at _ Ghz)_ so frequencies above 20 Ghz should be avoided. Although
the troposphere will not be serious problem for GEOS-C_ it is clear that
corrections must be devised for a lO-cm system.
At the planned GEOS-C frequency of 13. 9 Ghz_ the uncorrected
ionospheric range error will have a maximum of about 15 cm for daytime
observations and about 3 cm at night, At 20 Ghz these errors would be
halved. Even a rather crude correction can reduce ionospheric altitude
errors to acceptable levels.
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The satellite altitude must be known independently before the
ocean profile can be gotten from the altimeter measurements. In the
I particular case of GEOS-C there will be no dearth of accurate tracking
_":_ observations_ since a substantial number of globally distributed ground
I stations will be available to use the onboard tracking instruments.
Indeed_ if all of the available systems are employed_ GEOS-C will be
the most intensively tracked satellite ever. GEOS-C will be tracked by
laser ranging (12 or more stations with accuracies of 0. 3 to l meter)_
TRANET radio doppler (perhaps 20 stations)_ C-band radar and the
Goddard S-band Range and Range Rate System. As a result the accuracy of
the computed GEOS-C orbits will be limited primarily by the accuracy of
the gravity field model 3 and by the accuracy with which solar photon
pressure and perhaps drag (depending on the GEOS-C orbital altitude) can
be modeled.
The errors that would be introduced into the GEOS-C computed
orbits by the best of the currently available gravity field models is
in the range 3-I0 meters. Improvements in the geopotential model
which are in progress should reduce this uncertainty by a factor of
2 by the time GEOS-C is in orbit. (It should be noted that the GEOS-C
tracking data should themselves lead to further refinement of the
geopotential.)
Taken at face value_ these orbital errors would present an
unduly pessimistic impression. Actually_ the orbit of a satellite
at the altitudes now being considered for GEOS-C (perhaps 800 km or so)
will be controlled almost entirely by the large scale features of the
gravity field_ i.e._ those corresponding to spherical harmnnlcs of
degree and order 20 and lower_ and the corresponding orbital pertur-
bations of any significanoe will have frequencies of lO0 per day or less.
In other words_ there should be no significant orbital perturbations
for GEOS-C which have frequencies greater than lO0 per day--or wave-
lengths shorter than about _000 km. I would estimate that the altitude
uncertainty for GEOS-C for wavelengths less than _000 km will be less
than one meter. Furthermore_ the amplitudes of orbital perturbations
decrease rapidly with decreasing wavelengths.
As a result_ no serious problems should be encountered from
GEOS-C altitude errors when the altimetry data are used to deduce
topographic features with wavelengths less than _000 km_ which is the
area of great_st interest.
Although the fine structure in the gravity field has little
influence on the satellite orbit_ its effect on the geoid is quite
another matter. It will_ of course_ be necessary to separate the
influences of the gravity field on ocean topography from those caused
by oceanographic and meteorological phenomena. One important means
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of effectlng this separation will be to examine altimetry records taken
at different times. Since time variations in the geoid are either ex-
tremely slow or have well defined frequencies (tides)_ it will be
possible to extract from the altimeter data the time varying oceano-
graphic factors. This approach will require substantial data sets
obtained over the full operating life of the altimeter, A different
method will be needed to identify the more stable oceanographic features.
An independent determination of the geoid is obviously one means,
Table 2 lists my estimates of the present errors in geoid topography
for three somewhat arbitrary wavelength regions of the geoid. The
estimates for the short and intermediate regions are quite uncertain
because there are too little data. Indeed_ GEOS-C will provide the
first opportunity for obtaining a. systematic survey of these geold
features over the oceans. A survey of this kind will be very useful
in designing future altimetry experiments. Thus we have another reason
for obtaining a thorough examination of all ocean areas accessible to
GEOS-C.
Table 2,
Present uncertainties in the topogrephy of the gcold,
Short wavelength
Intermediate wavelength
Long wavelength
j'_ < 200 km
20o< # < 2oo0
/_ > 2000
lO to 20 meters
peak.
lO meters
3-_ meters RMS
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Improvements in the long wavelength region of the geoid will
most probably be accomplished through dynamic analyses of satellite
orbits. As noted above GEOS-C will be one of the satellites used
for this purpose. An independent determination of the geoid in the
intermediate region can also be obtained from satellite observations_
either by direct integration of doppler observations of a minimum
altitude satellite_ or through an orbiting gravity gradiometer'. The
only satellite method appropriate for measuring the short wavelength
geoid features is altimetry. An independent measure can only be
obtained through surface observations such as shipboard gravimetry.
One output of the GEOS-C observations which could be important to the
design of future a]timeter experiments would be a survey of these
M.ort wavelength features. This survey would indicate those regions
where acquisition of surface data is most important. This information
_ould be quite valuable_ particularly in the light of the long times
needed to carry out large scale surface observations.
Sea surface effects will not be discussed in any detail here_
as they will be treated at length by subsequent speakers. Briefly
there are two effects of interest, First the shape and amplitude of
the reflected radar pulses are both expected to be influenced by sea
state. This may enable us to obtain synoptic sea state information
from satellite altimetry_ if unique correlations can be deduced from
comparisons of the altimetry data with "ground truth." ]'he second
effect is the altitude bias resulting from the difference between the
electromagnetic and geometric centroids. This difference should not
exceed IO_ of the wave height. Since the median wave height for all
of the oceans is of the order of l._ meters_ the altitude bias should
be acceptable for GEOS-C on an overall basis. H_ever there will be
many occasions_ particularly during winter months at higher latitudes_
when wave heights may be substantially higher. Thus it will be of
considerable importance to monitor echo pulse shape and amplitude to
identify sea state. It would then be possible to at least delete data
when the altitude bias might be unacceptably large. There is also
the possibility of being able to develop suitable corrections for this
source of error.
The final point I wish to consider is the question of how much
coverage--in terms of both geography and time--the GEOS-C experiment
can provide. I consider this point basic to the ability of the GEOS-C
experiment to establish the potential capability of satellite altimetry_
to quantitativeIKdelineate problem areas and to provide a sound basis
for the design of subsequent altimetry missions.
Previous GEOS spacecraft have had three independent power systems:
main_ optical beacon and transponder. I would like to suggest that the
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3main and optical beacon supplies be rearranged to provide maximum
power for the altimeter experiment. Table 3 lists the steady loads
that these two supplies must support. The 0.2 duty cycle for the
telemetry system will provide 5 hours per day of telemetryj which is
generous. Table 4 shows the power budget for 20 sequences (140 flashes)
for 2 lamps flashed simultaneously. Again this should be a generous
allowance for this beacon.
Assuming the GEOS-C solar cell array to be the same as for
GEOS-23 the total average power available at the battery terminals
for the two power systems is 27.7 watts. The power available for
the altimeters is thus 27.7 - 12.9 - 2.0 = 12.8 Watts. The total
energy per day for the altimeters is 307 Watt-hours.
It is presently planned to have two altimeter modes in GEOS-C:
low power synoptic and high accuracy. Estimated power consumption is
40 Watts for the synoptic mode and 80 Watts for the high accuracy mode.
If the available energy is divided equally between the two modes 3 we
have the following duty cycle and total operating times for an 18-month
operating life.
Mode Hours/day Total hours operation
(18-month llfe)
Synoptic 3.84 2100
High Accuracy 1.92 I060
The speed of the satellite over the ground is about 240 ° per
hour. If we assume that the narrow swath traced out by the altimeter
footprint is an adequate sample for a path l° wide 3 the altimeter
sampling rate will be 240 square degrees of ocean per hour. The total
coverage in 18 months under these assumptions will then be 5063000 and
2_3,000 square degrees for the synoptic and high accuracy modes
respectively.
For an orbital inclination of 50°3 the satellite will fly over
some 7_ of the total ocean surface 3 or 223000 square degrees. For an
inclination of 65 °, the corresponding numbers will be 85% and 26_000
square degrees. Therefore 3 on an average 3 each square degree of ocean
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Table 3-
Suggested steady loads for GEOS-C
main and altimeter power systems.
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Doppler Beacon
Command System
Attitude Wheel
Telemetry System
(0.2 Duty Cycle) avg power
Altimeter - continuous loads
Delayed Command System
Data storage memory
Voltage-sensing cutoff switch
Total steady loads .............
5._ Watts
l.O Watts
l.O Watts
1.2 Watts
3.0 Watts
l.O Watts
0.2 Watts
12.9 Watts
Table 4.
Optical beacon power budget for GEOS-C.
Optical beacon
2 lamps
? flashes per sequence
20 sequences per day
Total energy per day
Average power consumption
600 Watt-Seconds
per lamp-flash
from battery
168,000 Watt-seconds
2.0 Watts
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covered by the satellite will be sampled with the following frequency
in the synoptic mode:
Orbit inclination Average number of samples
50 ° 23
6_° 19
If we assume that the high accuracy mode will be concentrated
on more limited "ground truth" areas totaling perhaps _00 square
degrees of ocean_ then some _00 samples will be obtained in 18 months
from this more limited area.
The number of samp|es per square degree in each mode would
seem to provide a quite satisfactory data base for the GEOS-C
altimeter experiment.


An observational philosophy for GEOS-C satellite altimetry

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