Post-EPS altimeter mission orbit determination, considering tide
aliasing criteria and applications requirements
L. Carrère, J. Dorandeu, G. Dibarboure, F. Lefèvre (1)
H. Bonekamp, P. Schluessel, F. Parisot (2)
(1) CLS, France
(2) EUMETSAT, Germany
I. Introduction
The aim of the study is to suggest optimal orbit candidates for a Post-EPS (EUMETSAT Polar System)
altimeter mission planned around 2020 and onward.
Optimising future altimeter missions is a complex problem: many conflicting requirements, constraints and
issues must be taken into account. Particularly the aliasing of tides is a crucial issue: it was one of the drivers
of the choice of the TOPEX/Poseidon-Jason’s orbit. Nowadays tidal signals are well known in deep ocean.
However some issues remain in coastal areas and for internal tides. Aliasing of tides by altimeter sampling
remains a challenge as it may pollute other signal estimations, particularly in the aliasing band of 40-90 days
and the semi-annual/annual band for climate purposes.
Some orbit candidates for Post-EPS altimeter mission have been selected and investigated within this
context. Each preliminary post-EPS candidate is assessed in term of sampling capability (temporal and
spatial), and the direct sampling effect of the orbit is investigated thanks to OSSE in a mapping context (for
mesoscale variability of the ocean). The impact of each altimeter sampling on the mean sea level is also
investigated. As Sentinel-3 (S3) is the mission which will most likely fly around the same period, only 2satellites constellations with S3 are considered in the study and are compared to the well-known altimetric
constellations (Jason-1/Envisat, J1/TP, J2/J1N).
II. Global recommendations
A preliminary analysis of passed and planned altimeter missions (GFO, T/P, Jason-, Envisat, Sentinel- …)
allows raising some global recommendations for optimizing future altimeter orbits. These main
requirements are listed below:
 Payload characteristics need to be optimised
 Raw recommendations for optimisation of orbit geometry
o Altitude between 800 and 1400 km, for air-drag and solar radiation exposure trade-off
(Berthias 2008; Ray 2008)
o Repeat cycle between 10 and 35 days, for mesoscale observation and long term continuity
challenge
o High inclination to get more polar ocean observations
o No sun-synchronous orbits because they do not allow aliasing of daily signals (S1)
These requirements induce more than 44000 possible orbit candidates for Post-EPS altimeter mission. Thus
more constraining criteria need to be applied to refine the orbit selection, considering experts and users
requirements in the domains of tides, climate, mesoscale observation, mission cost ...
III. Post-EPS orbit selection criteria
In this section, we describe the criteria which have been applied for selecting a short list of orbit candidates
for post-EPS mission. These criteria concern tides, climate purposes, a good mesoscale observability and
costs.
 Tidal aliasing issues
o No sun-synchronous orbits to allow aliasing of daily signals
o Need to consider main tides and some non-linear tides
o K1 alias is important
o No aliasing at annual or semi-annual frequencies
o No aliasing to very long period: a good aliasing frequency is over 2 cycles per year (cpy)
o Good separability of major tides constituents
 Good mesoscale observability
o Scales of ~150 km, ~15 days
o 3-4 days subcycles are preferred
 Climate issues
o Need to avoid the [4..9 cpy] aliasing band
o No aliasing at annual or semi-annual frequencies and good separation with the Sa/Ssa signals
o No aliasing close to 3 or 6 cpy (60 days climate signals)
 Low altitudes are preferred to reduce mission costs
As all those criteria are very constraining, and trade-off and priorities are needed: two strategies have been
followed, one based on purely tidal aliasing criteria, and a second one relaxing those criteria.
First strategy considers that tide aliasing is a priority, which means that most aliasing frequencies are over 2
cpy, and good separability criteria for most waves
Second strategy considers tide aliasing is not a priority as tides are already well known but climate purposes
are now a priority (good separability criteria with Sa, Ssa and less alias in the [4-9 cpy] band as possible);
mesoscale observation is also a priority (3-4 days sub-cycles only).
Five selected orbits are described in Table 1; the blue lines correspond to first strategy and the green ones to
the second strategy. Notice that many other orbits can be available if relaxing or changing the selection
criteria. The acronyms of the different orbits are given in Table 2.
Table 1: description of the five preliminary orbits selected for post-EPS
TP
J1
J1N
J2
EN
G2
S3
AltKa
S22
A801
A878
A926
A1104
4-sat
Topex/Poseidon
Jason-1
Jason-1’s new orbit (tandem mission with Jason-2)
Jason-2
Envisat
Geosat Follow On (GFO)
Sentinel-3
AltiKa orbit = Envisat orbit
SWOT 22 days orbit in nadir configuration
A801_i71_c22
A878_i66_c10
A926_i67_c13
A1104_i76_c16
constellation of J2-EN-G2-J1N
Table 2 : acronyms of the different satellites / orbits
IV. Geometrical analysis of the proposed orbits
The orbit geometry determines the geographical coverage, the space/time sampling by the altimeter
measurements and thus the type of applications that can be addressed. Figure 1 shows the approximate time
(abscissa in days) and space (y coordinate in km) scales resolved by each post EPS candidate:
 A926 and A923 can resolve smaller scales for 1-5 days time scales;
 A926, A801 and A1104 can resolve smaller scales (< 140 km) for longer period >12-13 days, thus
they are better suited to observe mesoscale structures;
 Constellation with A1104 is the worst constellation case for periods between 5-11 days;
 A878 is interesting for 9-11 days periods, but not as good as the reference TP-J1 case.
2000
Jason+TP
1800
S3+Jason
1600
S3+A878
1400
S3+A801
S3+A926
1200
S3+A923
1000
S3+A1104
S3+S22
800
Delta X (km)
600
400
200
0
1
2 Delta T (days) 3
4
5
300
Jason+TP
280
S3+Jason
260
S3+A878
240
S3+A801
S3+A926
Delta X (km)
220
S3+A923
200
S3+A1104
180
S3+S22
160
140
120
100
5
10
Delta T (days)
15
20
Figure 1 : Approximate space/time scales resolved with post-EPS candidates (2-satellites constellations with S3). The
acronyms of the different orbits are described in Table 2.
The crossover angle (or track angle to equator plane) has a strong impact on geostrophic velocity
observation (meridional velocity is noted V and zonal velocity U): 45° tracks (=90° crossovers) allow an
isotropic velocity observation and lower cross angles create better observations on U and worse on V (EN vs
S3). A878, A923 and A926 are equivalent to J1 with a nearly orthogonal angle at 40-50° latitudes
(geostrophic velocities of western boundary currents) and A801 in the 45-60° range (the circumpolar
current). A1104 has orthogonal angles around 60°, too high to observe the large oceanic currents.
V. Mesoscale application performances (OSSE in a mapping context)
We focus on the ocean mesoscale signal which is modelled thanks to MERCATOR-OCEAN global 1/12°
simulations (ORCA12 model; Le Galloudec et al. 2008). We run OSSE in a mapping context for each orbit
selected for post-EPS, in one satellite configuration and for 2-satellites constellations with Sentinel-3; results
are then compared to the other well-known constellations (J1-EN, J2-J1N, 4-satellites; Le Traon and
Dibarboure 2002). Notice that the SWOT 22 days orbit (nadir configuration) has also been tested here.
The RMS of the sea level mapping error is defined as the RMS of the difference between reconstructed
maps and instantaneous model maps): on the global ocean, this error is correlated with the variability of the
model, with strong errors in high variability areas, like great ocean currents but also south-east of Pacific
and Indian ocean where there is a strong wind induced variability at high and low frequencies (Webb and de
Cuevas 2002, 2003).
In order to validate the approach, we focused on the North Atlantic region which was already simulated by
other authors (Le Traon and Dibarboure 2002). The mean mapping error is computed while averaging on
the areas of variability greater than 15 cm and is given in percentage of model variance for the Sea Surface
Height (noted H), and for the geostrophic velocity’s components U and V. Results given on Figure 2
corroborate other studies although this study has been performed with a different mesoscale model: the 4satellites constellation is the best with an error smaller by more than 42%. Concerning the 2-satellites
constellations, the optimised J2-J1N has very good performances compared to non optimised ones, thanks to
its 10-days repeat period and the 5 days phasing which almost provides a synoptic sampling of the ocean and
makes it less sensitive to HF aliasing. The three post-EPS orbits have similar results, all better than old 2satellites configurations, and A926 shows slighly better performances for H and V. SWOT orbit shows also
similar performances.
Right hand side histograms on Figure 2 compare performances of each orbit in a mono-satellite
configuration: as expected Jason orbit is the worst choice in term of mesoscale mapping likely due its large
blind spots. A878 is a bit better because of its lower altitude (compared to Jason) which induces more
numerous tracks during a cycle. With its 17 days cycle, G2 has very good capability for mapping mesoscale
signals and A926 is even better than G2 for mapping sea surface height.
As far as velocities mapping is concern, A926 has nearly as good performances both for U and V as G2
which is dedicated to mesoscale observation. A878 is the least suited of the three post-EPS potential orbits
to observe geostrophic velocities.
H mapping error in % of mean sea level variance
H mapping error in % of mean sea level variance
7,5
3,5
S3
S2
2
S3
A8
01
S3
A8
78
S3
A9
26
S3
Al
tK
a
N
J2
J1
J1
S3
12,69
10,01
13,08
11,42
13,65
10,41
3,5
J1
EN
4sa
t
6,91
5,5
4,33
4
11,96
4,5
9,5
7,5
5,46
5
7,44
6,87
5,5
6,80
11,5
6,98
6
7,31
13,5
7,49
6,5
15,58
15,5
7
J1
EN
G2
S3
A801
A878
A926
S22
24
U mapping error in % of mean velocity U variance
U mapping error in % of mean velocity U variance
35
23
22
33
30,38
28,87
32,82
30,07
31,46
28,57
30,01
J1
S3
S2
2
N
S3
A8
01
S3
A8
78
S3
A9
26
S3
Al
tK
a
J2
J1
J1
S3
J1
EN
4sa
t
25
V mapping error in % of mean velocity V variance
EN
G2
S3
A801
A878
A926
S22
V mapping error in % of mean velocity V variance
S3
S2
2
N
S3
A8
01
S3
A8
78
S3
A9
26
S3
Al
tK
a
J2
J1
J1
S3
J1
EN
J1
EN
G2
S3
A801
35,51
30,10
33,20
29,91
28
34,09
25,63
26,51
24,81
25,07
32
30
16
4sa
t
34
34,92
18,98
20
22,13
22
25,15
36
25,76
24
27,01
38
35,93
40
26
18
35,44
22,08
23,12
22,59
27
16
28
29
39,44
17
31
17,85
18
22,73
20,51
19
22,46
20
23,23
23,40
21
A878
A926
S22
Figure 2 : Mapping error on SSH (also noted H) and on zonal (U) and meridional (V) velocities on north Atlantic ocean
and for 2-satellites constellations on left panels; on global ocean and for mono-satellites configurations on right panels.
Unit: % of signal variance. The acronyms of the different orbits are given in Table 2.
VI. Mean Sea Level application performances
Monitoring the mean sea level (noted MSL) is one of the most important applications of altimetry and
particularly of long-term and precise missions. We thus investigate the impact of each Post-EPS orbit
candidate’s configuration on MSL applications. The analysis is focused on the Jason-1 period (cycles 1 to
261). The ocean state is modeled by the best observed products available at the present time (weekly PVA
maps available at CLS operationally; Aviso 2006). The maps are interpolated along each satellite tracks and
2° box-averaged maps are computed for each cycle. Then regional and global MSL tendencies can be
deduced for each Post-EPS potential configuration.
The main result of this computation is that the global MSL estimations are weakly impacted by the satellite
tracks definition. Indeed, the global MSL trends are close to 2.65 mm/year for each satellite configuration,
with a maximum difference of 0.05 mm/year between each configuration; such differences are negligible if
we consider that the expected accuracy of the MSL trend from altimetry is 0.6 mm/year (Ablain et al. 2009).
VII. Conclusion and perspectives
A drastic selection on both tidal and climate considerations allowed proposing a few orbits candidates for
Post-EPS reference altimeter mission planned around 2020.
A first preliminary characterisation of the orbits has been made thanks to geometrical analysis of observable
space and time scales: this analysis showed that A1104 is a weak candidate, while A926, A878, A801 are
better suited.
As far as mesoscale observation is concerned, some OSSE analysis in a mapping context allowed a
complementary assessment of each orbit while considering 2-satellites constellations with Sentinel-3. Main
results are summarized below:
 Results are similar to previous studies which used different mesoscale models.
 The optimized 2-satellites constellation J2-J1N is widely better than other 2-satellites constellations.
 The proposed orbits have better scores than the other 2-satellites constellations (J1-EN, J1-S3, S3-EN,
S3-Swot), but they are very similar.
 A926 orbit have slightly better scores.
As monitoring the MSL is one of the most important applications of altimetry, the impact of each Post-EPS
orbit candidate on MSL estimation has been evaluated. This analysis showed that the global MSL
estimations are weakly impacted by the satellite tracks definition.
Evaluation of post-EPS orbits candidates is ongoing for other applications (regional MSL, climate variations
of the ocean), mission costs and POD.
VIII. References
Ablain, M., Cazenave, A., Valladeau, G., and Guinehut, S.: A new assessment of the error budget of global
mean sea level rate estimated by satellite altimetry over 1993–2008, Ocean Sci., 5, 193-201, 2009.
Aviso and PoDaac : User Handbook - IGDR and GDR Jason-1 Products, 2006.
Berthias.JP: Reference altimetry mission orbit selection, Proceedings of the EUMETSAT Ocean Surface
Topography Constellation Workshop, 2008.
Le Traon, P.-Y. and G. Dibarboure: Velocity Mapping Capabilities or Present and Future Altimeter
Missions: the Role of High-Frequency Signals, Journal of Atmospheric and Oceanic Technology, 19, 2077 –
2088, 2002.
Ray, R.: WATER HM and Aliasing Issues, 2008.
http://bprc.osu.edu/water/Meetings_WATERHM/FirstMeetingSWG_Fall2007/RAY_WideSwth.pdf .