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J. Geod. Sci. 2019; 9:48–58
Resea ch A icle Open Access
R. Pail*, J. Bambe , R. Biancale, R. Bingham, C. B ai enbe g, A. Eicke , F. Flech ne , T. G ube ,
A. Gün ne , G. Heinzel, M. Ho wa h, L. Longue e gne, J. Mülle , I. Pane , H. Sa enije,
S. Sene i a ne, N. Sneeuw, T. an Dam, and B. Wou e s
Mass a ia ion obse ing sys em by high low
in e -sa elli e links (MOBILE) – a new concep o
sus ained obse a ion o mass anspo om
space
DOI: h ps://doi.o g/10.1515/jogs-2019-0006
Recei ed Oc obe 5, 2018; accep ed Ma ch 10, 2019
*Co esponding Au ho : R. Pail: Technical Uni e si y o Munich,
Ins i u e o As onomical and Physical Geodesy, Munich, Ge many,
E-mail: oland.pail@ um.de
J. Bambe : Uni e si y o B is ol, School o Geog aphical Sciences,
B is ol, UK
R. Biancale: Cen e Na ional d’É udes Spa iales (CNES), Toulouse,
F ance
R. Bingham: Uni e si y o B is ol, School o Geog aphical Sciences,
B is ol, UK
C. B ai enbe g: Uni e si y o T ies e, Dp m. o Ma hema ics & Ea h
Sciences, T ies e, I aly
A. Eicke : Ha enCi y Uni . Hambu g, Geodesy and Adjus men The-
o y, Hambu g, Ge many
F. Flech ne : GFZ & Technische Uni . Be lin, Chai o Physical
Geodesy, Be lin, Ge many
T. G ube : Technical Uni e si y o Munich, Ins i u e o As onomical
and Physical Geodesy, Munich, Ge many
A. Gün ne : Deu sches GeoFo schungsZen um Po sdam, Sec .
Hyd ology, Po sdam, Ge many
G. Heinzel: AEI, Max Planck Ins . o G a i a ional Physics, Han-
no e , Ge many
M. Ho wa h: Technische Uni e si ä D esden, Ins . o Plane a y
Geodesy, D esden, Ge many
L. Longue e gne: Uni e si é Rennes, CNRS, Géosciences, Rennes,
F ance
J. Mülle : Leibniz Uni e si ä Hanno e , Ins i u e o Geodesy, Han-
no e , Ge many
I. Pane : Ins i u Na ional de l’In o ma ion Géog aphique e
Fo es iè e, Pa is, F ance
H. Sa enije: Technical Uni e si y Del , Wa e Resou ces Sec ion,
Del , Ne he lands
S. Sene i a ne: ETH Zü ich, Ins i u e o A mosphe ic and Clima e
Science, Zü ich, Swi ze land
N. Sneeuw: Uni e si ä S u ga , Ins i u e o Geodesy, S u ga ,
Ge many
T. an Dam: Uni e si y o Luxembou g, FSTC, Luxembou g
B. Wou e s: Uni . U ech , Ins i u e o Ma ine and A mosphe ic
Resea ch, U ech , Ne he lands
Abs ac : As changes in g a i y a e di ec ly ela ed o mass
a iabili y, sa elli e missions obse ing he Ea h’s ime
a ying g a i y ield a e a unique ool o obse ing mass
anspo p ocesses in he Ea h sys em, such as he wa-
e cycle, apid changes in he c yosphe e, oceans, and
solid Ea h p ocesses, on a global scale. The obse a ion
o Ea h’s g a i y ield was success ully pe o med by he
GRACE and GOCE sa elli e missions, and will be con in-
ued by he GRACE Follow-On mission. A comp ehensi e
eam o Eu opean scien is s p oposed he nex -gene a ion
g a i y ield mission MOBILE in esponse o he Eu o-
pean Space Agency (ESA) call o a Co e Mission in he
ame o Ea h Explo e 10 (EE10). MOBILE is based on
he inno a i e obse a ional concep o a high-low ack-
ing o ma ion wi h mic ome e anging accu acy, comple-
men ed by new ins umen concep s. Since a high-low
acking mission p ima ily obse es he adial componen
o g a i y-induced o bi pe u ba ions, he e o s uc u e
is close o iso opic. This geome y signi ican ly educes
a e ac s o p e ious along- ack anging low-low o ma-
ions (GRACE, GRACE-Follow-On) such as he ypical s ip-
ing pa e ns. The minimum con igu a ion consis s o a
leas wo medium-Ea h o bi e s (MEOs) a 10000 km al-
i ude o highe , and one low-Ea h o bi e (LEO) a 350-
400 km. The main ins umen is a lase -based dis ance o
dis ance change measu emen sys em, which is placed a
he LEO. The MEOs a e equipped ei he wi h passi e e lec-
o s o ansponde s. In a nume ical closed-loop simula-
ion, i was demons a ed ha his minimum con igu a ion
is in ag eemen wi h he h eshold science equi emen s o
5 mm equi alen wa e heigh (EWH) accu acy a 400 km
wa eleng h, and 10 cm EWH a 200 km. MOBILE p o ides
p omising po en ial u u e pe spec i es by linking he con-
cep o exis ing space in as uc u e such as Galileo nex -
gene a ion, as u u e elemen o he Cope nicus/Sen inel
p og amme, and holds he po en ial o minia u iza ion
R. Pail e al., Mass a ia ion obse ing sys em by high low in e -sa elli e links (MOBILE) |49
e en up o swa m con igu a ions. As such MOBILE can be
conside ed as a p ecu so and ole model o a sus ained
mass anspo obse ing sys em om space.
Keywo ds: mass anspo – nex -gene a ion g a i y mis-
sion – g a i y ield – high-low acking – sphe ical ha -
monics
1In oduc ion
Clima e change is one o he bigges socie al challenges
oday. The unde lying p ocesses a e mos equen ly e-
la ed o mass a ia ions in he Ea h sys em. Mass is edis-
ibu ed wi hin he Ea h sys em o e a ull ange o spa ial
and empo al scales. As mass a ia ions di ec ly induce
changes o he Ea h g a i y ield, sa elli e missions ob-
se ing he Ea h’s ime a ying g a i y ield a e a unique
ool o obse ing mass edis ibu ion in he Ea h sys-
em, such as he e es ial wa e cycle, a ia ions in he
c yosphe e and oceans, on a global scale. The dedica ed
g a i y mission G a i y Reco e y And Clima e Expe imen
(GRACE) (Tapley e al. 2014) p o ided he i s global de-
e mina ion o Ea h’s mass anspo by measu ing spa-
ial and empo al changes in he g a i y ield caused by
mass a ia ions a all dep hs, while he s a ic g a i y ield
e ie ed om he G a i y ield and s eady-s a e Ocean Ci -
cula ion Explo e (GOCE) mission (D inkwa e e al. 2013)
has imp o ed ou knowledge o he long- e m mass dis i-
bu ion and has p o ided he physical e e ence su ace o
he geoid wi h a esolu ion down o 70-80 km.
This is key in o ma ion, as di ec obse a ions o mass
a ia ions and mass anspo a e di icul o ob ain. Fo
example, almos no di ec obse a ions o e apo anspi a-
ion a e a ailable. S o age changes in deep soil laye s and
g oundwa e a e mos ly inaccessible o con en ional ob-
se a ion echniques. Cu en es ima es o soil mois u e
de i ed om emo e sensing sa elli es a e usually based
on he measu emen o he uppe mos ew cen ime e s
o soil, depending on he pene a ion dep h, lea ing he
la ges pa o he wa e column unexplo ed. The same
holds o he deep ocean ci cula ion, an essen ial bu hid-
den pa o he clima e sys em, playing an impo an ole
in hea anspo and ca bon dioxide seques a ion. Addi-
ional limi a ions o a closu e o he global wa e balance
a e imposed by he sca ci y o da a on eshwa e un-o ,
limi a ions o sa elli e al ime y along coas s and ice shee
ma gins, and in high la i udes.
A esolu ion adop ed by he Council o he In e -
na ional Union o Geodesy and Geophysics (IUGG 2015)
calls o sus ained obse ing o mass anspo p ocesses
om space (Pail e al. 2015a). Unde s anding how ex eme
episodic e en s such as d ough s, loods, ea hquakes and
olcanos, may ela e o he longe - e m e olu ion o he
wa e -cycle o s ess build-up, o esol ing he luxes a he
bounda ies be ween Ea h sys em componen s, equi es
high accu acy ime- a ying g a i y co e age o e a ull
ange o spa ial and empo al scales ha is cu en ly un-
a ailable. Only by mapping ime a ying g a i y wi h a
subs an ially inc eased spa ial esolu ion, we can ully un-
de s and how changes in he Ea h sys em de elop ac oss
scales, how hey modi y he wa e luxes, and how hey
a e ela ed o human ac i i ies. The unde s anding we
may achie e is needed o add ess challenges acing hu-
man socie ies o a sus ainable de elopmen o e he sho
and long e m. They include unde s anding sea le el ise,
and assessing he changing wa e a ailabili y o eshwa-
e supply, ag icul u e and indus y, especially in egions
whe e eshwa e esou ces a e unde se e e h ea , and
an h opogenic demands and s esses a e expec ed o u -
he inc ease in he decades o come. A minimum o 30
yea s o obse a ion is necessa y o disen angle an h o-
pogenic impac om na u al a iabili y (GCOS 2016).
The big success o he GRACE mission led o he im-
plemen a ion o GRACE Follow-On (GRACE-FO) (Flech ne
e al. 2016), which was success ully launched in May 2018
and will con inue he 15 yea s o mass anspo ime se-
ies ob ained om GRACE. Recen ly, he Uni ed S a es Na-
ional Academies o Sciences, Enginee ing, and Medicine
published he decadal s a egy o Ea h obse a ion om
space (NAS 2018), whe e mass change was iden i ied as
one o he op 5 obse ables o be implemen ed by u u e
US Ea h obse a ion missions in o de o ensu e con i-
nui y and enable long- e m mass budge analyses o he
Ea h sys em. Again i is p oposed o plan o a single-
pai mission, which should ollow GRACE-FO. This clea ly
demons a es he impo ance o sus ained g a i y moni-
o ing om space.
On Eu opean side, du ing he las couple o yea s
se e al a emp s ha e been made by he g a i y- ela ed
science communi y o p opose a nex -gene a ion g a i y
ield mission as an Ea h Explo e mission o he Eu o-
pean Space Agency (ESA). The p oposed mission cons el-
la ions di e ed om he ypical GRACE- ype concep o
an in-line pai , wi h which only he along- ack compo-
nen o he Ea h’s g a i y ield can be obse ed, leading
o a e y aniso opic e o s uc u e and he ypical s ip-
ing pa e ns in he esul ing empo al g a i y solu ions. In
2010 he mission p oposal “e.mo ion – Ea h Sys em Mass
T anspo Mission” (Pane e al. 2012) was submi ed in e-
sponse o ESA’s Ea h Explo e 8 call. I was based on a
sa elli e pai in pendulum con igu a ion, whe e he sec-
ond sa elli e pe o ms a pendulum mo ion wi h espec o
50 |R. Pail e al., Mass a ia ion obse ing sys em by high low in e -sa elli e links (MOBILE)
he leading sa elli e, hus obse ing no only he along-
ack, bu also pa s o he c oss- ack componen . In 2016
e.mo ion2(G ube e al. 2015) was p oposed as ESA Ea h
Explo e 9 mission. In he basic con igu a ion, i con ained
one ou o wo in-line pai s o a so-called Bende double-
pai con igu a ion (Bende e al. 2008). This se -up o a po-
la and an inclined pai wi h an inclina ion o 65-70 de-
g ees again esul s in a signi ican ly imp o ed iso opy and
educ ion o s ipes (Da as and Pail 2017).
In his pape we p esen an inno a i e obse a ion
concep o high-p ecision high-low in e -sa elli e anging,
which was p oposed as he MOBILE mission in esponse
o ESA’s Ea h Explo e 10 call. In Sec ion 2 he science
and mission objec i es a e ou line. In Sec ion 3 he ech-
nical concep , including he obse a ion cons ella ion and
he key payload, is p esen ed. The achie able pe o mance
wi h his mission concep is quan i ied by means o a nu-
me ical closed-loop simula ion in Sec ion 4. Finally, in
Chap e 5 he main conclusions a e d awn, and an ou look
o u u e pe spec i es is gi en.
2Science Objec i es and
Requi emen s
2.1 Science Objec i es
The science objec i es and equi emen s o MOBILE
mainly ollow he science and use needs as desc ibed in
(Pail e al. 2015a). The ollowing main science objec i es
ha e been iden i ied:
1. Es ima ing con inen al wa e s o age and eshwa e
luxes
2. Quan i ica ion o la ge-scale lood and d ough e en s
and hei moni o ing and o ecas ing
3. Unde s anding mass balance o ice shee s and la ge
glacie sys ems
4. Deciphe ing sea le el a ia ions and changes in ocean
anspo
5. Valida ion and assimila ion in o global clima e mod-
els
6. Connec ing solid Ea h nea su ace changes o in e -
nal dynamics
7. P ocess couplings and con ibu ion o a consis en
Ea h sys em model
8. P o ision o ime- a iable g a i y e e ence o he
Global Geode ic Re e ence F ame (GGRF)
Wi h hese objec i es, MOBILE con ibu es o an imp o ed
unde s anding o di e en componen s o he Ea h sys-
em, and add esses a numbe o Essen ial Clima e Va i-
ables (ECV; (GCOS 2016)) such as g oundwa e , snow
co e , soil mois u e, ice shee s, glacie s and ice caps, sea
le el, su ace cu en s, and sub-su ace cu en s. Rega d-
ing i em numbe 8, MOBILE would mainly p o ide in o -
ma ion abou he empo al e olu ion o physical e e ence
ames ( o example in egions wi h s ong e ical mo ion
such as glacial isos a ic adjus men e ec s in Fennoscan-
dia o Canada), while i would ha dly be able o compe e
wi h g adiome e missions such as GOCE ega ding he
achie able spa ial esolu ion o he s a ic g a i y ield.
The ele an spa ial and empo al scales o achie -
ing hese esea ch objec i es, as well as he ampli ude o
he signals, a e desc ibed in Fig. 1. An accu acy a he
le el o 10 % o hese signal ampli udes would allow sig-
ni ican ad ances in ou unde s anding o Ea h’s mass
anspo . When app op ia e, hese speci ica ions a e con-
e ed in o equi alen empo al a ia ions o he geoid and
g a i y. Con e sion depends on spa ial scales, o sphe i-
cal ha monic (SH) deg ees. E.g., a mass a ia ion o 1 cm
equi alen wa e heigh (EWH) in a sphe ical cap o a-
dius 2000 km (800 km, 400 km, 200 km, 100 km) maps
o a 0.5 mm ampli ude geoid a ia ion (0.3 mm, 0.15 mm,
0.08 mm, 0.04 mm, espec i ely).
2.2 Science equi emen s and use needs
As he mass signals ela ed o he science objec i es co e
a ange o spa ial and empo al scales, in acco dance wi h
Pail e al. (2015b). and IGSWG (2016) a h eshold scena io
is de ined, which allows us o make a signi ican ad ance
wi h espec o ou cu en knowledge, and a a ge sce-
na io, which means a b eak h ough in he way we use
g a i y da a in Ea h mass anspo moni o ing. Speci i-
cally, he science equi emen s o MOBILE a e:
(1) To eco e empo al g a i y and mass a ia ions in he
Ea h sys em wi h a 150 km spa ial esolu ion o be e ,
wi h a global co e age;
(2) To eco e small ampli ude mass a ia ions wi h an
app oxima ely 5 imes ( h eshold) o 50 imes ( a ge ) in-
c eased sensi i i y as compa ed o cu en knowledge;
(3) To esol e mass a ia ions a daily o decadal ime
scales. While he high empo al esolu ion esul s om he
enhanced da a quali y, he long imescales a e ob ained by
ex ending he exis ing sa elli e g a i y eco ds by a ime
se ies o a leas 5-7 yea s.
The signal cha ac e is ics ha e been s udied in de ail
by Pail e al. (2015b), c . also Fig. 1. Hence mos es ima es
in his sec ion a e based on his e e ence. A highe spa ial
esolu ion han cu en ly achie able is needed in all ields
R. Pail e al., Mass a ia ion obse ing sys em by high low in e -sa elli e links (MOBILE) |51
Fig. 1. Signal ampli udes o mass a ia ions in equi alen wa e heigh (EWH) as a unc ion o spa ial esolu ion, oge he wi h p esen -
day accu acy and esolu ion (GRACE) and wi h MOBILE h eshold and a ge pe o mances. Solid Ea h mass a ia ions a e con e ed o
EWH. Con ibu ions om daily o weekly a ia ions (le panel), om seasonal o in e -annual a ia ions (middle panel), and om long- e m
ends ( igh panel). D awn om (Pail e al. 2015b).
o applica ion. Fo con inen al wa e s o age moni o ing,
10 % o he i e basins wo ldwide ha e cha ac e is ic sizes
la ge han 550 km, 30 % o he basins ha e sizes be ween
550 and 330 km, and 45 % be ween 330 and 180 km, while
he size o global hyd ological modelling g id cells can be
o he o de o 50 km. An inc ease in spa ial esolu ion
down o 150 km would allow o he moni o ing o g ound-
wa e deple ion in smalle scale ho spo s such as many
Eu opean hyd ological ca chmen s. The ine spa ial eso-
lu ion would also allow o he eco e y o mass a ia ions
in elonga ed basins such as he Rhine o Danube ca ch-
men s. In a simila ashion, such an inc ease in spa ial es-
olu ion would mo e han double he numbe o d ainage
basins wi hin ice shee s ha could be esol ed.
Many mass signals in he wa e cycle and wi hin he
solid Ea h a e small in ampli ude, hence demand a high
accu acy. The MOBILE h eshold scena io will allow signi -
ican ad ances in de e mining egional ocean mass a i-
a ions, p ocesses associa ed wi h la ge ea hquakes (Mw
7.8 and abo e) o in sepa a ing la ge glacie complexes
and moni o ing medium-size hyd ological basins wi h a
1.5 cm EWH p ecision. The MOBILE a ge scena io will
p o ide a leap in o signal sepa a ion and leakage educ-
ion om neighbou ing mass sou ces. Fo ins ance, he
glacial isos a ic adjus men (GIA) signal o e An a c ica
leaks by abou 200 km in o he oceans, wi h a 1 cm EWH/y
magni ude (Pail e al. 2015a, Pail e al. 2015b). The a ge
scena io would allow o he sepa a ion o his signal om
he ice mass a ia ions. The high accu acy would also en-
able us o esol e he small ocean ci cula ion signals, such
as in e -annual a ia ions o he A lan ic Me idional O e -
u ning Ci cula ion (AMOC).
Jus he ex ension o he ime se ies beyond GRACE-
FO will allow us o unde s and how an h opogenic o c-
ings in e ac wi h clima e changes in he changing wa e
cycle, and he highe spa ial esolu ion esul ing om MO-
BILE will imp o e he wa e cycle e sus solid Ea h signal
sepa a ion. By p o iding long ime se ies o mass a ia-
ions, MOBILE, as a p ecu so o a sus ained mass ans-
po obse ing sys em om space, will hus also enhance
he alue o da a om p eceding missions.
The analysis o he signal cha ac e is ics enables us o
o mula e, in acco dance wi h (Pail e al. 2015a), he sci-
ence equi emen s o MOBILE h eshold and a ge sce-
na ios, which a e summa ized in Table 1, and g aphically
illus a ed in Fig. 1.
3Technical concep s
3.1 Obse a ion Concep
In o de o achie e he science objec i es as speci ied in
Sec ion 2.1, MOBILE consis s o a cons ella ion o high and
low o bi ing sa elli es. In such a cons ella ion, he main
obse able is he in e -sa elli e dis ance be ween pai s o
sa elli es (as done o GRACE and GRACE Follow-On). How-
e e , ins ead o obse ing g a i y-induced in e -sa elli e
dis ance changes be ween wo low o bi ing sa elli es in
a pea l-s ing con igu a ion, dis ance a ia ions be ween
52 |R. Pail e al., Mass a ia ion obse ing sys em by high low in e -sa elli e links (MOBILE)
Table 1. MOBILE h eshold and a ge science equi emen s and use needs.
Spa ial Resolu ion Equi alen Wa e Heigh Geoid
Mon hly ield Long- e m end Mon hly ield Long- e m end
Th eshold equi emen s
400 km 5 mm 0.5 mm/y 50 µm5µm/y
200 km 10 cm 1 cm/y 0.5 mm 0.05 mm/y
150 km 50 cm 5 cm/y 1 mm 0.1 mm/y
Ta ge equi emen s
400 km 0.5 mm 0.05 mm/y 5µm0.5 µm/y
200 km 1 cm 0.1 cm/y 0.05 mm 5µm/y
150 km 5 cm 0.5 cm/y 0.1 mm 0.01 mm/y
medium (MEO; se e al housand km) and low o bi ing
sa elli es (LEO; se e al hund ed km) a e obse ed. As sec-
ond g a i y obse a ion ype, high-p ecision o bi posi-
ions based on GNSS o bi de e mina ion a e used. This
idea o high-p ecision high-low acking was i s in es i-
ga ed o geos a iona y and GNSS sa elli es, and he main
e o sou ces and he co esponding achie able pe o -
mance was analysed in (Hauk e al. 2017). Howe e , in o -
de o p esen a s and-alone concep wi hou he need o
place addi ional payload o o he space in as uc u e, o
he MOBILE p oposal, dedica ed MEO sa elli es we e in-
cluded in he concep .
The minimum con igu a ion consis s o a leas wo
MEOs (e.g. 10 000 km o highe ) and one LEO (a ound 350-
400 km) in he same o bi al plane. The wo MEOs a e sep-
a a ed by 180-deg ee mean anomaly in o de o maximize
he obse a ion ime. Figu e 2 shows a schema ic o e iew
o his minimum sa elli e con igu a ion.
Fig. 2. MOBILE mission cons ella ion: high-p ecision in e -sa elli e
links be ween LEO and MEOs ( ed), mic o-wa e links om GNSS
sa elli es o MEOs and LEO (black).
All h ee sa elli es ly in a pola o bi in o de o main-
ain a long- e m s able o ma ion (no ela i e d i s o he
o bi planes). The main obse able a e ange measu e-
men s om he LEO o he MEOs, whe e he MEOs a e al e -
na ing a ge s. The main ins umen shall be a lase -based
dis ance o dis ance change measu emen sys em, which
will be placed a he LEO. The MEOs will be equipped
wi h passi e e lec o s o ansponde s. The a ge ang-
ing accu acy is on he mic ome e le el. I shall be empha-
sized ha in his concep he LEO sa elli e will be equipped
wi h he ac i e ins umen a ion, also including di ec ion-
depending poin ing capabili ies. The mo e sophis ica ed
design o he LEO sa elli e has o be done anyway o keep
he sa elli e in a low Ea h o bi . In con as , he design o
he MEO sa elli e can be qui e simple, and ideally i s pay-
load is only o passi e na u e.
On op o his minimum scena io, op ionally he im-
plemen a ion o a hi d o ou h MEO sa elli e could be
conside ed o u he inc ease he mission pe o mance.
In his case he 3 o 4 MEO sa elli es will be sepa a ed by
120 o 90-deg ee mean anomaly, espec i ely. In p inciple,
also a second LEO could be conside ed. Howe e , since he
uppe cos limi o he EE10 call was de ined as 225 mil-
lion Eu os pu ely o he sa elli e(s), i is likely ha a sec-
ond mo e complex LEO sa elli e would no i in o he cos
ame.
The o bi selec ion o he MOBILE cons ella ion needs
o be ca e ully done in o de o ensu e ha he science
goals can be achie ed. In pa icula he o bi al i ude o
he LEO sa elli es d i es he sensi i i y o he Ea h g a -
i y ield, and consequen ly de ines he uppe limi o spa-
ial esolu ion o be achie ed. Figu e 3 shows esul s o a
MOBILE cons ella ion in dependence o he al i ude o he
LEO sa elli e. I iden i ies o example ha by lowe ing he
o bi om 400 o 346 km one can each a gain in spa ial
esolu ion a a le el o abou 30 km ( om SH deg ee 75 o
85 co esponding o spa ial esolu ion 267 km o 235 km).
The cu es in Fig. 3 a e exp essed in e ms deg ee RMS o

R. Pail e al., Mass a ia ion obse ing sys em by high low in e -sa elli e links (MOBILE) |53
equi alen wa e heigh s (EWH), which is compu ed om
ully no malized coe icien s o a sphe ical ha monic se-
ies expansion ¯
Cnm,¯
Snmo deg ee nand o de m, by
σn(EWH)=aρe
3ρw
2n+ 1
1 + kn
u
u
n
X
m= 0
¯
C2
nm +¯
S2
nm ,(1)
whe e ρwand ρe ep esen he a e age densi ies o wa e
and Ea h, a he semi-majo axis o he Ea h, and kn he
load Lo e numbe o deg ee n.
Fig. 3. Residual e o s o mon hly g a i y ield eco e y compa ed
o simula ed signal (black cu e) including only ins umen e o s,
showing he impac o o bi heigh o MOBILE baseline con igu a-
ion. The blue cu e is equi alen o Figu e 5.
Ano he impo an issue ela ed o he choice o op-
imal o bi heigh s is he educ ion o empo al aliasing
due o unde -sampling. In (Mu böck e al. 2015) a numbe
o op imal o bi al i ude bands a e iden i ied, whe e he
impac o empo al aliasing is signi ican ly educed. Se -
e al nume ical simula ions ha e shown, ha ega ding o -
bi choice and ela ed g ound ack co e age he e is some
design eedom, p o ided ha he epea pe iod o he
LEOs is long enough o gua an ee su icien spa ial esolu-
ion and a oiding spa ial unde sampling. Rega ding em-
po al esolu ion, he a ge consis s in compu ing weekly
o mon hly g a i y ield solu ions. Howe e , he “Wiese
pa ame e iza ion” (Wiese e al. 2011) as desc ibed in Sec-
ion 4 will acili a e o es ima e long-wa eleng h g a i y
ields also on a daily o 2-daily basis up o SH deg ee 15 o
20, hus enabling sho la encies o se ice applica ions.
The main ad an age o he high-low acking concep
compa ed o he low-low pea l-s ing con igu a ion imple-
men ed in GRACE and GRACE-FO is, ha mul i-di ec ional
dis ance a ia ions, wi h a s ong dominance o he a-
dial componen , will be obse ed. The esul ing (close o)
iso opic e o beha iou o his concep will educe sig-
ni ican ly he s iping pa e ns caused by ha ing only one-
di ec ional obse a ions, which is one o he key limi -
ing ac o s o nowadays empo al g a i y solu ions, and
inhe en ly will imp o e he spa ial esolu ion. The e o e,
subs an ial pos - il e ing s a egies o educe hese nume -
ical a e ac s can be la gely a oided. The impac o he
high-low obse a ion geome y is nicely isible in Fig. 4.
The iangles in he le column show he o mal e o s
o he MOBILE high-low acking concep (bo om), and
in compa ison GRACE/GRACE-FO low-low acking ( op),
demons a ing ha he i s concep has an almos uni-
o m (iso opic) e o spec um. A pe ec iso opic be-
ha iou implies ha he colou o he iangle in he le
column depends on he deg ee only, bu he e is no a ia-
ion wi hin he o de s o a espec i e deg ee. The imp o e-
men in iso opy is e en be e isible when analysing he
spa ial signa u es o he co a iance unc ion o he g a i-
a ional po en ial, which a e displayed in he middle and
igh columns o Fig. 4. Shown is he co a iance be ween
wo poin s. One o hem is kep ixed a G eenwich me id-
ian (geog aphical longi ude λ=0◦) and ei he a he equa-
o wi h geog aphical la i ude φ=0◦(middle column) o
a a la i ude o φ=45◦( igh column), while he o he one
is a ying in a su ounding a ea o 40◦×40◦. While he
low-low acking concep shows he ypical s ipes caused
by he No h-Sou h obse a ion di ec ion ha a e known
om he GRACE empo al g a i y models, he MOBILE con-
cep exhibi s a qui e iso opic e o s uc u e a bo h la i-
udes, which is qui e close o he ideal iso opic signa u e
o concen ic ings a ound he i s poin .
Fig. 4. Fo mal e o iangle plo s in log10 (le ), and spa ial co a i-
ance unc ions (middle column o equa o , igh column o 45◦
la i ude) o GRACE ype ( op ow), and MOBILE cons ella ion (bo -
om ow).
54 |R. Pail e al., Mass a ia ion obse ing sys em by high low in e -sa elli e links (MOBILE)
3.2 Key payload
The main ins umen o MOBILE is a lase -based dis ance
o dis ance change measu emen sys em, which will be
placed a he LEO. Measu emen o in e -sa elli e anges
by lase ange in e e ome y (LRI) has been es ablished
o he GRACE-FO mission. In his case, he link be ween
he wo sa elli es was gene a ed wi h an ac i e lase on
one sa elli e, and a phase-locked ampli ying ansponde
on he second spacec a . Fo he MOBILE mission con-
cep he ins umen logic needs o be adap ed in wo ways.
Fi s ly, he e will be e y la ge nominal changes in he dis-
ance and ela i e speed, leading o a ange o Dopple
shi s o se e al GHz s. he ew MHz obse ed on GRACE-
FO. Thus a e e ence lase sou ce wi h a la ge ange o
e e ence equencies and a as e phase- acking capa-
bili y han implemen ed o GRACE-FO is equi ed. The
equi ed pa ame e s (<10 GHz ange, <10 MHz/s ack-
ing) a e wi hin he ange o exis ing, space quali ied e -
e ence lase s (e.g., he one used o he ATLID ins umen
on he Ea hCARE mission), bu hei compa ibili y wi h
he needs o an in e e ome ic ins umen has o be sub-
jec o u he s udies.
Secondly, he link implemen a ion has o be modi ied
as he ela i e mo ion o he LEO and MEO sa elli es also e-
qui es poin ing acking capabili ies. The impac on o e -
all mission complexi y and cos is minimised i a acking
mechanism is used on one pa ne only (a LEO), while
he pa ne sa elli es (MEOs) a e equipped wi h passi e
e o e lec o s. Lase acking and anging has been suc-
cess ully pe o med o decades wi h ac i e lase sys ems
on g ound and passi e e o e lec o s on sa elli es in o bi
(e.g., LAGEOS, BLITS). The scien i ic bene i o deploying
a passi e payload in space is he signi ican ly inc eased
mission du a ion when compa ed o complex ac i e pay-
loads. The main echnological challenge in u ilising his
se up o an LRI ins umen is he need o achie e a su -
icien ly high le el o ecei ed powe wi hou he need o
ampli ica ion be ween he wo passes, ideally close o he
80 pW ecei ed by he GRACE-FO implemen a ion, bu a
leas o le els abo e ~1 pW in o de o allow phase ack-
ing. The main design ac o s impac ing he ecei ed powe
a e he ini ial ou pu powe , he size o he e o e lec o ,
and he size o he ecei ing elescope.
Fo he measu emen o non-g a i a ional o ces all
sa elli es a e equipped wi h accele ome e s (ACC), which
a e placed in he cen e o mass o he sa elli es. A ce -
ain le el o compensa ion o non-conse a i e accele a-
ions in along- ack di ec ion is equi ed o he LEO sa el-
li e in o de o emo e he majo pa o he dis u bing sig-
nal, and hus o educe he measu emen ange. Fo MO-
BILE we seek o a esolu ion on he le el o 10−11 m/s2,
ideally wi h he same pe o mance in all h ee di ec ions.
In case only 2 ou o 3 axes a e high-sensi i e, hey should
be o ien ed in ligh di ec ion (la ges signal) and in adial
di ec ion ollowing he concep o he GRACE-FO design.
The implemen a ion o an accele ome e is absolu ely
necessa y on he LEO. Based on he he i age o p e i-
ous g a i y missions an elec os a ic accele ome e wi h
a measu emen bandwid h o 1 o 50 mHz shall be imple-
men ed. Less s ingen equi emen s migh apply o he
MEO sa elli es, because o he subs an ially smalle am-
pli ude o he signal and he ac , ha non-conse a i e
o ces can be modelled much mo e accu a ely in high al-
i udes. To suppo his modelling, also he design o he
MEO could be op imised. As an example, by implemen ing
e y simple geome ical su aces, non-g a i a ional o ces
ela ed o adia i e p essu e ac ing on he sa elli e could be
modelled qui e accu a ely ins ead o ac ually measu ing
hem. In spi e o hese ac s, in he MOBILE concep also
o he MEO sa elli es he implemen a ion o accele ome-
e s was p oposed, bu echnological op ions could be em-
ployed o (one o ) he MEOs by eplacing he elec os a ic
ins umen by inno a i e echnologies. They include:
– Cold a om o hyb id accele ome e : The applicabil-
i y o cold a om in e e ome e s (CAI) o space-bo ne
g a ime y has been ou lined by Ca az e al. (2014).
ONERA is cu en ly de eloping a hyb id ins umen by
combining elec os a ic and CAI accele ome e s (Za-
hzam e al. 2017). The speci ic asse s o elec os a ic
senso s, such as hei low noise le el in a selec ed
measu emen bandwid h and hei space ma u i y, a e
complemen ed by he CAI’s whi e noise spec al be-
ha iou , which is especially bene icial o g a i y e-
co e y in he low- equency ange, and he absolu e
na u e o measu emen , hus a oiding he need o
calib a ion.
– Op o-mechanical accele ome e : No el op o-
mechanical echnologies a e cu en ly being pi-
onee ed by he Ins i u e o Space Sys ems o he
Ge man Ae ospace Cen e (DLR) in collabo a ion wi h
he Chai o Space Technology a he Uni e si y o
B emen. These echnologies consis o monoli hic
pa allelog am mechanical oscilla o s o ex emely
low loss which a e in eg a ed wi h mic o-op ical
displacemen senso s ha moni o he es mass
displacemen (Guzmán e al. 2014), yielding highly
compac and ligh weigh op o-mechanical ine ial
senso s o high sensi i i y.
– MEMS senso s: Mic o-accele ome e s based on mic o
elec omechanical sys em (MEMS) echnology, as hey
a e de eloped by he Impe ial College London, ha e
R. Pail e al., Mass a ia ion obse ing sys em by high low in e -sa elli e links (MOBILE) |55
he po en ial o each noise le els o 10−11 m/s2/√Hz.
MEMS echnology o e s he po en ial o minia u ize
he ins umen and educe he weigh (cu en ly down
o abou 600 g). Fu he a ac i e ea u es a e 3D ca-
pabili ies, and hei use as an angula accele ome-
e suppo ing a i ude de e mina ion (Liu and Pike
2016).
All sa elli es shall be equipped wi h GNSS space ecei e s.
Geo-loca ion o sa elli e obse a ions as well as g a i y
ield e ie al equi e highly accu a e con inuous o bi
de e mina ion. Absolu e kinema ic posi ioning o geo-
loca ion shall be on he cm le el. Using a lase anging
ins umen as main measu emen sys em equi es exac
poin ing o he acking an enna in he o de o 10 µ ad o
less, and he e o e he implemen a ion o sys ems o a -
i ude de e mina ion and con ol. The MEO sa elli es will
e y likely equi e an elec ical p opulsion sys em o mo e
o hei a ge o bi om he lowe sepa a ion al i ude
achie able wi h a low-cos launche .
4Nume ical simula ion and esul s
The science equi emen s o he MOBILE mission ha e
been de i ed in Sec ion 2.2, and a e summa ized in Ta-
ble 1. In o de o e alua e i hese science equi emen s
can be achie ed by he mission cons ella ion desc ibed in
Sec ion 3.1, nume ical closed-loop simula ions including
he main e o sou ces in e ms o ealis ic noise assump-
ions ha e been pe o med. The simula ion app oach is de-
sc ibed in de ail by Hauk e al. (2017).
The ollowing o bi pa ame e s ha e been chosen: The
MEOs o bi in an al i ude o 10798 km and ha e a epea
pe iod o 84 days, while he LEO o bi s in an al i ude o
346 km wi h a epea pe iod o 28 days. All o bi s a e po-
la o a oid ela i e o bi d i s. The MEOs a e in he same
o bi al plane, sepa a ed by 180-deg ee mean anomaly o
he minimum con igu a ion o 2 MEOs, and 120/90 deg ees
in case o 3 o 4 MEOs, espec i ely.
Rega ding e o s o he key ins umen s, he e o
speci ica ions as ou lined in Chap e 3 ha e been used, i.e.
a 1 µm noise le el o he lase anging ins umen , as well
as a noise le el o 10−11 m/s2/√Hz in he measu emen
bandwid h o he accele ome e . In o de o simula e geo-
physical signals, ESA’s Ea h Sys em Model (Dobslaw e al.
2014) has been used, which con ains he i e main geo-
physical signal componen s a mosphe e (A), oceans (O),
hyd ology (H), ice (I) and solid Ea h (S), oge he abb e i-
a ed AOHIS, wi h a ime esolu ion o 6 hou s. Op ionally,
also ocean ide e o s, ep esen ed by a di e ence be ween
wo independen ocean ide models, can be included in he
simula ion.
On op o he ins umen e o s also empo al aliasing
om high- equency geophysical signals is a main e o
con ibu o . I can be signi ican ly educed by enhanced
pa ame e iza ion s a egies such as “Wiese” pa ame e i-
za ion by co-es ima ion o independen daily global g a -
i y ields wi h educed spa ial esolu ion co esponding
o a maximum sphe ical ha monic deg ee and o de be-
ween 10 and 20, depending on he cons ella ion (Wiese
e al. 2011). In con as , due o hei known exci a ion pe-
iods, explici ocean ide pa ame e s can be co-es ima ed
as well (Hauk and Pail 2018). Se e al simula ion uns ha e
been pe o med, by swi ching on and o he di e en e o
sou ces.
A i s i is in es iga ed i he obse a ion equi e-
men s o he co e ins umen s (LRI and ACC) a e capable
o mee he science objec i es o he chosen o bi (mainly
d i en by he o bi al i ude). Fo his ask, simula ions in-
cluding only ins umen e o s we e pe o med. G a i y
ield solu ions ha e been pe o med o he 28-day pe iod,
which coincides wi h he epea pe iod o he LEO. Figu e 5
shows he esul s in e ms o EWH e o s pe deg ee, and
Fig. 6 o cumula i e EWH e o s. The h eshold science
equi emen s as speci ied in Table 1 a e indica ed in o -
ange colou o 400 km (co esponding o SH deg ee 50)
and 200 km (SH deg ee 100), clea ly demons a ing ha
a mission wi h he speci ied ins umen pe o mance, o-
ge he wi h a LEO o bi al i ude o abou 350 km, is sa ely
below he h eshold equi emen s e en o he minimum
con igu a ion o 2 MEOs and 1 LEO (blue cu e). Fu he
imp o ed mission pe o mance can be achie ed by he ex-
ended con igu a ions 3 MEOs/1 LEO (g een) and 2 MEOs/2
LEOs (magen a). As a e e ence, he expec ed pe o mance
o he GRACE-FO mission, assuming an in e -sa elli e ang-
ing accu acy o 50 nm and he same pe o mance o he
accele ome e s as o he MOBILE case, is shown in ed.
E iden ly, e en hough a highe in e -sa elli e anging pe -
o mance o GRACE-FO was assumed, he MOBILE concep
ou pe o ms he GRACE- ype mission especially in low de-
g ees due o he supe io cons ella ion geome y.
F om Fig. 7 one can de e mine he pe o mance one
can achie e wi h he di e en mission cons ella ions when
including also aliasing e o s om hyd ology (H), ice (I)
and solid Ea h (S), oge he abb e ia ed HIS, in he sim-
ula ion. The h eshold science equi emen s a e almos
achie ed o 400 km spa ial esolu ion (SH deg ee 50); in
ac , he 5 mm EHW is eached a deg ees 43 o 46 o
he di e en high-low scena ios. Fo 200 km (SH deg ee
100) he equi ed 10 cm EWH le el is c ossed a deg ee
56 |R. Pail e al., Mass a ia ion obse ing sys em by high low in e -sa elli e links (MOBILE)
Fig. 5. Deg ee (e o ) RMS o ull AOHIS signal (black) and di e en
mission scena ios, when including only ins umen e o s.
Fig. 6. Cumula i e signal o ull AOHIS (black) and cumula i e e o s
o di e en mission scena ios, when including only ins umen
e o s. The h eshold science equi emen s o 400 km (SH deg ee
50) and 200 km (SH deg ee 100) a e included in o ange colou .
96 o he con igu a ion 2 MEOs/1 LEO. As a e e ence, a
GRACE-FO scena io is included ( ed cu e), showing ha
MOBILE, e en in he minimum con igu a ion, will ou pe -
o m GRACE-FO by a ac o o 5 in e ms o mass anspo
obse a ions.
Fig. 7. Cumula i e signals/e o s when including ins umen e o s
and aliasing e o s om hyd ology, ice and solid Ea h (HIS). The
h eshold science equi emen s o 400 km (SH deg ee 50) and
200 km (SH deg ee 100) a e included in o ange colou .
In Fig. 8 he di e ences o he mon hly ue mass
anspo model and he eco e ed signal a e shown in
spa ial domain o he MOBILE minimum con igu a ion,
and he GRACE-FO case as a e e ence. Bo h cases a e e-
sol ed up o SH deg ee 50. As al eady sugges ed by Fig. 4,
he e o pa e n o MOBILE is much mo e homogeneous,
and he ypical s iping o a low-low along- ack anging
sys em is signi ican ly educed.
(a)
(b)
Fig. 8. Global g ids o EWH [m] up o d/o 50 o GRACE (a) and MO-
BILE minimum con igu a ion (b).
The applica ion o ex ended pa ame e iza ion
schemes such as he Wiese app oach as discussed abo e
opens he possibili y o es ima e sho pe iod mass ans-
po signals oge he wi h he a ge ed mon hly solu ions.
In his espec , an in e es ing ques ion o be analysed is
how much signal can be ep esen ed by he 2-daily mass
anspo pa ame e s, which ha e been co-es ima ed up
o SH deg ee 10 in he ame o he g a i y ield e ie al.
In his case he ull AOHIS signal was used as an inpu and
also e ie ed in he simula ion. Figu e 9 shows deg ee
RMS cu es o he ull mass anspo signal (black cu es)
and he de ia ions o he es ima ed 2-daily e ie ed g a -
i y ields (blue cu es) o all 2-day pe iods wi hin he
28-day o bi pe iod. E iden ly he 2-daily g a i y ield can