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The GEOIK program was started in 1985 to obtain a system
of fitted parameters of the Earth (EP-90) including fundamental geodetic
constants, geocentric reference system, and the parameters of the figure
and the gravitational field of the Earth. Initially, this Program caried
out by the Topography Service of the Ministry of Defense of the Russian
Federation and was classified. In 1992 its many parts were declassified,
and altimetry data processed with the application of the fitted parameters
of the Earth (EP-90) were given to the organizations of the Russian Academy
of Science and World Data Centers to be used.
The Russian geodetic satellite GEOIK carrying a radar altimeter
has been operating since May, 1985. Its main part, satellite GEOIK is one
of the satellies of "Kosmos" series intended for the studies of the Earth
and circumterrestrial space. The satellite is placed on orbit approximately
1500 km high with inclination of 74 or 83 degrees. As of 1996, ten satellites
were launched that were equipped both with radio altimeters (RA) and space-borne
geodetic instruments including Doppler system, radio range system, light
signalling flash system, and laser corner reflectors. Doppler system gives
signals in coherent frequencies of 150 and 400 MHz twelve hours a day to
measure radial velocity; light controlling system produces flashes to photograph
the satellite against the stars; laser corner reflectors of effective area
of 0.024 square meters and relay reflect signals of a ground-based laser
ranger and re-emit signals of ground-based radio ranger.
Ground-based stations measure Doppler radial component of
satellite velocity with respect to the observation station with an error
of 1 - 3 cm/s, determine the satellite position by light flashes with reference
to the stars with an error of 1 - 1.5", and measure distances to the satellite
by laser and radio rangers with errors of 0.5 - 1 and 1 - 2 m respectively.
The bulk of scientific results of GEOIK program includes
the model of geopotential of EP-90 up to the 36th degree and EP-200 up
to 200th degree, the improved coordinates of the geodetic network stations,
and the catalog of the geoid heights in the World ocean.
The program has not been completed yet and collecting altimetry
and tracking data by GEOIK is being in progress now. As of May 1996, the
program allowed making 19.3 million measurements from ten satellites. In
fact each satellite operated from several weeks to 18 months. Sometimes
two satellites operated simultaneously, but it was more often that one
satellite was employed. A list of the satellites, characteristics of their
orbits and their operating time are given in Table 1.
Table. 1
Russian Satellite Altimetry Program GEOIK
|
No Satellite
|
Data Launch
|
Inclination,
deg
|
Period of active work
|
Standard deviation,
cm
|
Calibration correction,
m
|
| 1 |
14.06.85 |
73.6 |
08.07.85 - 31.10.86 |
60 |
-17.0 |
| 2 |
11.02.86 |
73.6 |
03.03.86 - 28.03.86 |
140 |
-25.0 |
| 3 |
02.12.86 |
83.6 |
21.12.86 - 15.12.87 |
166 |
-36.5 |
| 4 |
19.02.87 |
73.6 |
09.03.87 - 12.10.87 |
105 |
-26.0 |
| 5 |
30.05.88 |
73.6 |
20.06.88 - 27.07.90 |
88 |
-22.9 |
| 6 |
28.08.89 |
73.6 |
18.09.89 - 26.09.90 |
|
|
| 7 |
30.07.90 |
73.6 |
19.08.90 - 05.03.93 |
|
|
| 8 |
10 01.93 |
73.6 |
10.01.93 - 23.07.93 |
|
-29.79 |
| 9 |
December 1994 |
73.6 |
18.12.94 - 28.07.95 |
|
-25.42 |
Precision of radar altimeter data
(instrument error) ranged from 0.5 to 0.8 m in various spacecrafts. Frequency
of the altimeter 9.5 Ghz (mean square error of measurements adjusted by
one-second interval and by 10-12 second interval is approximately 0.4 -
0.5 m and 0.1 m respectively); Measurements were conducted in steps of
1 measurement a second. The energetic resurce of altimeter is 10h in one
day.
Radio altimetry measurements data were recorded by space-borne
tape-recorders and once a day sent to ground-based stations by telemetric
channels. Deciphering, preliminary processing, calculating of satellite
ephemerides, applying corrections to RA, and calculating sea-level height
were conducted in Computer Center. Space-borne altimeter operated 10 hours
a day and 5 days a week. The work was planned so that maximal uniformity
of covering the World ocean by sub-satellite tracks could be provided.
With several satellites, the criterion that each altimetry orbit was supported
by tracking data was applied. It resulted in excluding altimetry data obtained
in descending orbits across the Atlantic. The bulk of measurements was
conducted in 1-Hz mode. Owing to technological limitations, some errors
in planning, malfunctions, and space-borne equipment failures, the World
ocean appears to be covered by tracking to a large extent nonuniformly.
In processing altimetry data, calculating satellite ephemerides,
applying corrections, calculating sea-level heights were most important.
Calculations of GEOIK Ephemeris
The ephemeris of GEOIK were calculated by 5-day orbits on
the basis of only tracking data obtained by laser, Doppler, photo measurements,
and distance ranging from the space geodetic network stations.
- Doppler - 1 - 3 cm/s;
- лазер - 0.5 - 1 m;
- distance ranging - 1.5 - 2 m;
- photo measurements - 1 - 1.5 І.
When calculating forces applied to the satellite, the gravitational
field of the Earth, the attraction of the Moon and the Sun, tides in the
solid Earth, light pressure, atmospheric resistance, precessions, nutations,
and poles movements were taken into account.
To calculate orbits the model (EP-90) of gravitational field
of the Earth up to 36th degree was applied. It was obtained by space geodesy
technique, by combining tracking data, including altimetry data, and global
gravimetry and altimetry data on the World ocean presented in catalogs
of 5x5 degrees. Tracking data were used to determine initial conditions
of 16 long (5 days) and 151 short (3 orbits) orbital arcs, geocentric coordinates
of globally distributed network stations, systematic corrections to Doppler,
distance ranging, and altimetry data, elements of mutual transformation
coordinates (reference system of 1942), 167 coefficients of geopotential
expansion by spherical functions most sensitive to the orbits of the given
class. Satellite altimetry measurements (31 5-day orbital arcs) were applied
to improving initial conditions of orbital arcs, the coefficients of the
gravitational field model up to 20th degree, and bias correction to altimetry
data. Catalogs of the heights (1041 blocks) and anomalies (1654 blocks)
were used to improve the model of the gravitational field of the Earth
up to 36th degree. The following parameters of the ellipsoid EP-90 were
obtained:
a = 6378136; b = 1/298.257839303
The research showed that the error of ephemerides calculations
by radius vector is 1 m on 5-day orbits. The estimate of the radial component
of the error by variations of sea-surface heights in the points where altimetry
tracks cross supports the given value. The nominal accuracy of antenna
orientation is 1 degree.
Determination of Altimetry Data Sets of Sea Surface Height
Sets of altimetry data on sea surface were formed after satellite
altimetry data were processed. Processing altimetry data was accompanied
by calculating ocean tides and deviations of the quasistationary heights
from the geoid. Taking into consideration low accuracy of the radio altimetry
measurements, the program GEOIK did not include making corrections to the
measured heights of the sea surface for external conditions (tropospheric
and ionospheric corrections, corrections for waves heights and others).
The systematic component of those effects was supposed to be excluded by
bias correction. It should be noted, however, that satellite 6 had space-borne
altimeter which allowed an accuracy of approximately 0.6 m. It is comparable
to the tropospheric effects.
The calculations of the sea surface were made together with
the calculations of correction for sea-tides heights, which was obtained
with the use of Schwiderski's model for 8 main components given for crossing
points with a space of 1 degree. The program for calculating tides heights
includes correction members for effects of long-period tides in the solid
Earth and takes into account loading and self-attraction.
Values of sea-surface heights were calculated in sessions
on 5-days orbital arcs as a difference of the height component of the satellite
ephemerides and altimetry data like corrections and values of the model
heights of the geoid.
To obtain satellite ephemerides the geopotential model (EP-90)
was applied. To calculate geoid heights above the ellipsoid model EP-200
up to the 200th degree was used. To calculate geoid heights above the ellipsoid
the model EP-200 up to the 200th degree was used. It was derived from harmonic
analysis and fitting of the model EP-90 with the catalog of gravity anomalies
established by averaging initial gravity anomalies by 1x1 degree blocks.
Two types of initial data were used to make gravity anomalies
catalog for the World. These data include geoid heights calculated as mean
values of geoid heights by blocks 1x1 degr. from processed GEOIK altimetry
data, and gravity anomalies catalog compiled by the Topography Service
of Russia jointly with Scientific Recearch Institute of Geodesy and Cartography
by use gravimetric observations on land and in the World ocean. To unite
those two types of data a technique for combining radio altimetry and gravimetry
data was elaborated. This technique is based on local approximation of
the gravitational field of the Earth by a system of mass points. Thus,
56840 values of gravity anomalies were obtained. Other 7960 anomaly
was calculated by foreign data (Model GPM-2).
Nominal accuracy of referring the time to space-borne time
scale is 1 ms. Owing to the elliptical figure of the Earth and the satellite
orbit, the maximal error of sea surface heights calculations caused by
time error is 40 cm.
When using data on differencies of sea-surface heights in
crossing points of altimetry tracks, the time error was estimated for each
5-day altimetry data set. Taking this error into account, we decrease the
mean square error of the differences of sea-surface heights but sufficiently
increase the distribution of error of altimetry data.
Determination of Bias Correction
Direct bias correction (BC) of altimetry data or determination
of systematic instrumental error (calibration) was not included in the
GEOIK program. Therefore, instrumental error was determined by geodetic
(orbital) technique from errors of closure. It was assumed that in a sufficiently
long interval both altimetry data errors and ephemerides and a priori heights
of the geoid were averaged.
For satellites GEOIK-1, GEOIK-5, and GEOIK-6, bias correction was determined,
while the system of fitted parameters of the Earth (EP-90) was being developed.
They were -17, -25, and -36.5 m respectively. These values are sufficiently
stable in the whole interval of the satellite functioning. However, for
GEOIK-6 and GEOIK-7, the spread of errors was not several tens
of decimeters but several tens of meters. It is likely to be related to
switching of subsets of space-borne altimeter and frequency oscillator.
A more accurate BC determination was needed for the above-mentioned two
satellites at the stage of improving ephemerides.
Reference data on failures and switching on board the GEOIK-7
were not sufficient to determine changes in work. Therefore, it was necessary
to analyze all the 53 orbital arcs. Jump variations in bias correction
of more than 3 meters allowed us to divide the whole period of its functioning
into 6 parts. Beginning from 3 august 1992 sharp changes in BC values are noted.
The formats are given in Table 2. Their content corresponds
to the analog formats of Geosat altimetry data records.
Table. 2
GEOIK EP-90 GDR Format
|
Item
|
Parameter
|
Units
|
Bytes
|
| 1 |
Universal Coordinated Time (UTC) |
sec |
4 |
| 2 |
|
microsec |
4 |
| 3 |
|
microdeg |
4 |
| 4 |
|
microdeg |
4 |
| 5 |
|
cm |
4 |
| 6 |
Sea Surface Height (1-s avg) |
cm |
2 |
| 7 |
|
cm |
2 |
| 8 |
|
cm |
2 |
| 9 |
|
cm |
2 |
| 10 |
Type of surface:
0 - if over water
1 - if over land
2 - if over ice surface
3 - if error of the measurement |
|
2 |
| 11 |
|
|
2 |
|
Total number of bytes
|
32
|
Satellite height H above the Reference System EP-90 ellipsoid
H = Orbit (EP-90) + 100000 (1500 km).
Geophysical Center RAS, 1998
Last upgrade 25 September 1999 |
