Astronomical Institute University of Bern

(1) Astronomical Institute, University of Bern, Switzerland (2) Bundesamt für Kartographie und Geodäsie, Frankfurt am Main, Germany

IGS Workshop 2014 – Celebrating 20 Years of Service June 23-27 2014, Pasadena, California, USA

Impact of temporal gravity field parameters determined from GNSS satellites on the

estimated Earth rotation parameters

Krzysztof Sośnica (1), Adrian Jäggi (1),

Rolf Dach (1), Daniela Thaller (2)

Slide 2 Astronomical Institute University of Bern

Sośn

ica

et a

l.: I

mpa

ct o

f tem

pora

l gra

vity

fiel

d pa

ram

eter

s de

term

ined

fro

m G

NSS

sat

ellit

es

on th

e GN

SS-d

eriv

ed E

arth

rota

tion

para

met

ers.

IGS

Wor

ksho

p 20

14, P

asad

ena,

CA,

USA

Table of contents

Introduction: Motivation GNSS sensitivity to low-degree Earth’s gravity field coefficients Solution set-up Temporal Earth’s gravity field from GNSS C20 and correlation with dynamical orbit parameters Other low-degree coefficients

Earth Rotation Parameters (ERPs) & Geocenter Pole coordinates Pole rates Geocenter coordinates Conclusions

Slide 3 Astronomical Institute University of Bern

Sośn

ica

et a

l.: I

mpa

ct o

f tem

pora

l gra

vity

fiel

d pa

ram

eter

s de

term

ined

fro

m G

NSS

sat

ellit

es

on th

e GN

SS-d

eriv

ed E

arth

rota

tion

para

met

ers.

IGS

Wor

ksho

p 20

14, P

asad

ena,

CA,

USA

Three pillars of satellite geodesy

Current status: IGS provides products related to Geometry and Rotation, but not to temporal variations in the Earth’s Gravity field.

Geometry Rotation

Geometry

Gravity Rotation

This solution: Parameters related to all three pillars are simultaneously estimated, because they are strongly dependent on each other.

Are GNSS satellites sufficiently sensitive to variations of gravity?

Slide 4 Astronomical Institute University of Bern

0.0E+00

5.0E-12

1.0E-11

1.5E-11

2.0E-11

2.5E-11

3.0E-11

3.5E-11C2

0C2

1S2

1C2

2S2

2C3

0C3

1S3

1C3

2S3

2C3

3S3

3C4

0C4

1S4

1C4

2S4

2C4

3S4

3C4

4S4

4

Mean a posteriori errors – monthly solutions

GRACE

multi-SLR

CHAMP

GPS+GLONASS

Sośn

ica

et a

l.: I

mpa

ct o

f tem

pora

l gra

vity

fiel

d pa

ram

eter

s de

term

ined

fro

m G

NSS

sat

ellit

es

on th

e GN

SS-d

eriv

ed E

arth

rota

tion

para

met

ers.

IGS

Wor

ksho

p 20

14, P

asad

ena,

CA,

USA

Sensitivity of GNSS solutions to low-degree gravity coeff.

GNSS satellites are very sensitive to gravity field coefficients of degree 2. For coefficients above degree 3, GNSS are typically very sensitive only to resonant gravity field coefficients.

R R R R R R

R: resonant coefficients causing “secular drifts” of GPS semi-major axes

Slide 5 Astronomical Institute University of Bern

Sośn

ica

et a

l.: I

mpa

ct o

f tem

pora

l gra

vity

fiel

d pa

ram

eter

s de

term

ined

fro

m G

NSS

sat

ellit

es

on th

e GN

SS-d

eriv

ed E

arth

rota

tion

para

met

ers.

IGS

Wor

ksho

p 20

14, P

asad

ena,

CA,

USA

List of estimated parameters & solution set-up

We processed 10 years of GPS and GLONASS data using the standard orbit modeling as from CODE with two major exceptions: 7-day solutions are generated

instead of the 3-day long-arc solutions as for the IGS.

The Earth's gravity field coefficients up to degree/order 4/4 and geocenter coordinates are simultaneously estimated along with other parameters.

Estimated parameters

GNSS solutions up to 32 GPS and

24 GLONASS satellites

Orb

its

Osculating elements

a, e, i, Ω, ω, u0 (1 set per 3 days)

Dynamical parameters

D0, Y0, X0, XS, XC – unconstrained DS, DC, YS, YC – constrained at 10-12

(1 set per 3 days)

Pseudo-stochastic pulses

R, S, W (constrained, estimated every 12h)

Earth rotation

parameters XP, YP, UT1-UTC

(Piecewise linear, 1 set per day) Geocenter coordinates 1 set per 7 days

Earth gravity field

Estimated up to d/o 4/4 (1 set per 7 days)

Station coordinates 1 set per 7 days Other parameters

Troposphere ZD (2h),

gradients (24h) and ZTD biases

Slide 6 Astronomical Institute University of Bern

Sośn

ica

et a

l.: I

mpa

ct o

f tem

pora

l gra

vity

fiel

d pa

ram

eter

s de

term

ined

fro

m G

NSS

sat

ellit

es

on th

e GN

SS-d

eriv

ed E

arth

rota

tion

para

met

ers.

IGS

Wor

ksho

p 20

14, P

asad

ena,

CA,

USA

C20 from GPS+GLONASS Offset between SLR and GNSS↓

Semiannual signal is not recovered ↓

GNSS dynamic orbit parameters : D0, Y0, X0, XS, XC

Orbit parameters in the X direction are correlated with C20

GNSS dynamic orbit parameters : D0, Y0, X0, XS, XC

Offset is reduced ↓

Semiannual signal is recovered↓

Slide 7 Astronomical Institute University of Bern

Sośn

ica

et a

l.: I

mpa

ct o

f tem

pora

l gra

vity

fiel

d pa

ram

eter

s de

term

ined

fro

m G

NSS

sat

ellit

es

on th

e GN

SS-d

eriv

ed E

arth

rota

tion

para

met

ers.

IGS

Wor

ksho

p 20

14, P

asad

ena,

CA,

USA

C21, S21, C30 from GPS+GLONASS GNSS-derived gravity field parameters agree quite well with the CSR RL05 results (median difference of 8.2.10-11), but: GNSS-derived

parameters show both: the seasonal signals as well as draconitic periods,

C20 is correlated with orbit parameters in the X direction.

Gravity coefficients benefit from the contribution of GLONASS (after 2008, when the station coverage improves).

↓ Annual signal

↓ 2nd harmonic

↓ 3rd harmonic

Slide 8 Astronomical Institute University of Bern

Sośn

ica

et a

l.: I

mpa

ct o

f tem

pora

l gra

vity

fiel

d pa

ram

eter

s de

term

ined

fro

m G

NSS

sat

ellit

es

on th

e GN

SS-d

eriv

ed E

arth

rota

tion

para

met

ers.

IGS

Wor

ksho

p 20

14, P

asad

ena,

CA,

USA

Question:

How much affected are the GNSS-derived parameters by neglecting the temporal gravity field variations, since GNSS satellites are sufficiently sensitive to

recover the temporal variations of Earth’s low-degree gravity field ?

Slide 9 Astronomical Institute University of Bern

Sośn

ica

et a

l.: I

mpa

ct o

f tem

pora

l gra

vity

fiel

d pa

ram

eter

s de

term

ined

fro

m G

NSS

sat

ellit

es

on th

e GN

SS-d

eriv

ed E

arth

rota

tion

para

met

ers.

IGS

Wor

ksho

p 20

14, P

asad

ena,

CA,

USA

X- pole coordinate

↓ Annual signal

↓ 7th harmonic

Semiannual signal ↓

Differences w.r.t. IERS-08-C04

For the X pole coordinate: • the amplitude of the 7th harmonic is reduced from 15.9 to 12.2 µas, • the amplitude of the annual signal is reduced from 12.8 to 6.9 µas, • the mean offset w.r.t. IERS-08-C04 is reduced from -10.5 to -9.9 µas, for the solutions without and with estimating gravity field parameters, respectively.

Slide 10 Astronomical Institute University of Bern

Sośn

ica

et a

l.: I

mpa

ct o

f tem

pora

l gra

vity

fiel

d pa

ram

eter

s de

term

ined

fro

m G

NSS

sat

ellit

es

on th

e GN

SS-d

eriv

ed E

arth

rota

tion

para

met

ers.

IGS

Wor

ksho

p 20

14, P

asad

ena,

CA,

USA

X- pole rate

For the X pole rate: • the amplitude of the 7th harmonic is reduced from 3.5 to 1.8 µas/day, • the mean offset w.r.t. IERS-08-C04 is reduced from 2.2 to 2.0 µas/day,

for the solutions without and with estimating gravity field parameters, respectively.

Differences w.r.t. IERS-08-C04

↓ 7th harmonic

↓ 3/7 of draconitic year ↓ 6/7 of draconitic year

Slide 11 Astronomical Institute University of Bern

Sośn

ica

et a

l.: I

mpa

ct o

f tem

pora

l gra

vity

fiel

d pa

ram

eter

s de

term

ined

fro

m G

NSS

sat

ellit

es

on th

e GN

SS-d

eriv

ed E

arth

rota

tion

para

met

ers.

IGS

Wor

ksho

p 20

14, P

asad

ena,

CA,

USA

Z component of geocenter coordinates (C10)

When estimating the gravity field coefficients and heavily constraining once-per-revolution orbit parameters in the X direction, the Z geocenter coordinate from GNSS solutions (C10): • is by far less affected by solar radiation pressure modeling, • is closer to the SLR results as compared to GNSS solutions without estimating gravity field.

↓ 3rd harmonic ↓ 5th harmonic

Values shifted by +/-20 mm

Slide 12 Astronomical Institute University of Bern

Summary The GNSS satellites are sufficiently sensitive to low-degree gravity field

parameters, to recover the temporal gravity field variations.

The simultaneous estimation of gravity field parameters along with ERPs, station coordinates, troposphere, and other GNSS parameters is feasible.

The empirical orbit parameters in the X direction are correlated with C20, and thus, the X-parameters partly absorb the C20 variations. However, not all the gravity variations are

absorbed by empirical parameters.

Unabsorbed gravity variations may contaminate the ERP estimates by introducing spurious peaks of seasonal and draconitic signals in the GNSS

solutions when not estimating gravity field parameters.

Spurious seasonal and draconitic signals can be reduced by estimating the gravity field along with other GNSS parameters.

Astronomical Institute University of Bern

(1) Astronomical Institute, University of Bern, Switzerland (2) Bundesamt für Kartographie und Geodäsie, Frankfurt am Main, Germany

IGS Workshop 2014 – Celebrating 20 Years of Service June 23-27 2014, Pasadena, California, USA

Thank you for your attention