Johannes Böhm

Neutral Atmosphere and Geodesy

Acknowledgement: Gregor Möller, Michael Schindelegger, ..

The Atmosphere ...

• .. does not only cause troubles ..

• .. but opens a wide range of possibilities for geodesy

2 wikipedia.org

The Atmosphere ...

.. delays signals in the • ionosphere and • troposphere,

.. influences • Earth rotation, • satellite orbits, • Earth gravity field

3 wikipedia.org

.. moves points due to • loading and • thermal deformation.

The Atmosphere ...

4 wikipedia.org

.. delays signals in the • ionosphere and • troposphere,

Refractivity N = N (p, T, e)

5

[Nilsson et al., 2013]

liquid water

1013 hPa, 300 K, 100%

Troposphere Delays

6

Troposphere Delays

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[Nilsson et al., 2013]

[Saastamoinen, 1972; Davis et al., 1985]

estimated

Vienna

Pressure Values

• Observed values – at epoch

• Numerical weather models – every 6 hours

• Blind models – Berg (1948) – Hopfield (1969) – UNB3m, GPT2, ...

8

3 hPa → 1 mm height

O'Higgins, Antarctica

destructive effect of blind models with loading

e

9

Mapping Functions

Partials Clocks 1 Height sin(e) Zenith delay ≈ mf(e)

e

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Mapping Functions

Partials Clocks 1 Height sin(e) Zenith delay ≈ mf(e)

5 mm @ 5° elevation → 1 mm height

Mapping Functions

• Niell Mapping Functions – blind

• Isobaric Mapping Functions • Vienna Mapping Functions 1

– ECMWF analysis (6 h) • Global Mapping Functions

– ‘averaged VMF1’ – blind – GPT2

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Fortaleza (Brazil)

hydr

. mf a

t e =

5°

GPT2 and GPT2w

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GPT2 GPT2w amendments

2001-2010 monthly mean profiles from ERA-Interim (37 levels) -

5° grid at mean ETOPO5 heights 1° grid

Mean, annual, semi-annual terms; phases estimated -

Pressure, temperature, water vapour pressure, lapse rate and mapping function coefficients

mean temperature Tm and water vapour decrease factor λ

Blind Model for ∆Lwz: GPT2w

• Water vapour decrease factor λ estimated from ray-traced zenith wet delay

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( ) m

sd

m

zw g

eRTkkL

110 3'

26

+

+=∆ −

λ

∫∫∞

∞

=

H

Hm

zTe

zTeT

d/

d/2

( ) 1+= λss ppee

Blind Model for ∆Lwz: GPT2w

• Water vapour decrease factor λ estimated from ray-traced zenith wet delay

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λ semi-annual amplitude []

( ) 1+= λss ppee

Blind Model: GPT2w

• RMS differences w.r.t. IGS ZTDs about 3.4 cm on average

18 RMS differences in cm over 2012

Ray-tracing

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• Great potential but limitations with large number of GNSS observations

• Many active groups, e.g., – GSFC, UNB, NICT, GFZ, GRGS,

Vienna, ... • GSFC has shown improvement for

VLBI baseline length repeatabilities

GNSS Meteorology

• Ground based – precipitable water, tomography

• Space based – radio occulation

• Climate monitoring

20

mm

Nilsson, 2011

Wettzell

The Atmosphere ...

.. delays signals in the • ionosphere and • troposphere,

.. influences • Earth rotation, • satellite orbits, • Earth gravity field

21 wikipedia.org

.. moves points due to • loading and • thermal deformation.

22

Angular Momentum vs. Torque Approach

(1) Conservation of angular momentum in total system (solid Earth + fluids)

(2) Torque approach considers fluids as external layers:

“push-and-pull” interaction with solid Earth

Atmosphere

Pole

Change in fluid angular momentum

[Schindelegger, 2014]

Torque Approach

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Gravitation Friction

Pressure

Total torque of solid Earth (s) on the atmosphere (a)

fmesaas LLLLL ++=−= →→ )()()()(

Ellipsoidal torque Mountain torque Friction torque

Local Torques

0p pp ∆+0

Geophysical Influences on LOD

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[Schindelegger, 2014]

LOD:

cha

nges

in le

ngth

-of-d

ay

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Mass (pressure) or motion (wind) terms?

Geophysical Influences on LOD

puga

volume

dddcos 23

φλφ∫∫∫φλφ ddcos34

∫∫surface

spga

Atmospheric Excitation of Earth Rotation Important ..

• .. for a better understanding of the system Earth • E.g., prograde annual nutation

27 Michael Schindelegger

VLBI residual

Atmospheric Excitation of Earth Rotation Important ..

• .. for a better understanding of the system Earth • .. as boundary condition for NWMs • Predictions of Earth rotation based on NWM forecasts

are of importance for spacecraft tracking (0.1 ms = 1.6 km @ Mars) and real time GNSS orbits

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The Atmosphere ...

.. delays signals in the • ionosphere and • troposphere,

.. influences • Earth rotation, • satellite orbits, • Earth gravity field

29 wikipedia.org

.. moves points due to • loading and • thermal deformation.

Atmospheric Effects on the Earth Gravity Field

• De-aliasing products for CHAMP, GRACE, GOCE • .. for an improved detection of hydrology

30 wikipedia.org

pressure geoid

Maria Karbon

The Atmosphere ...

.. delays signals in the • ionosphere and • troposphere,

.. influences • Earth rotation, • satellite orbits, • Earth gravity field

31 wikipedia.org

.. moves points due to • loading and • thermal deformation.

Radial Deformation ur:

ps Surface pressure pref Reference pressure GR Green‘s functions

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10

mm

5

0

-5

-10

Atmospheric Loading

[Wijaya et al., 2011] Wettzell (non-tidal, IB)

Conclusions

• Atmospheric corrections as determined from Numerical Weather Models play an important role in space geodesy, i.e., for the Earth gravity field, Earth rotation and figure of the Earth

• All parameters are available in real-time when determined from forecast data

• However, more research has to be carried out to reach the goals of GGOS: 1 mm in position and 0.1 mm/year in velocity

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THANKS FOR YOUR ATTENTION

We acknowledge the FWF for funding project ASPIRE (I1479) and ESA for funding project Tropsy.

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