aliasing problems in gravity field recovery and possible ... · jürgen kusche 30.09.2009 1 torsten...

Jürgen Kusche 30.09.2009

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Torsten Mayer-Gürr, Annette Eicker,Enrico Kurtenbach, Jürgen Kusche

Astronomical, Physical and Mathematical GeodesyInstitute of Geodesy and Geoinformation, University of Bonn

Aliasing problems

in gravity field recoveryand possible solutions


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2. While the gravity field changes continously,it takes time to collect satellites data


GRACE

30 days30 days

15 days15 days1 day1 day


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GRACE and ocean tides


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Analyse der GRACE Überflügeund der Gezeitenfrequenzen

2N2

N2 M2

K2

S2

[Zyklen/Tag]

[Tage]

M2


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[Tage]

M2

Analyse der GRACE Überflügeund der Gezeitenfrequenzen

2N2

N2 M2

K2

S2

[Zyklen/Tag]


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GRACE Aliasing Perioden

M2

S2

K2

[1 Jahr]

Alias:14 Tage

Alias:161 Tage

Alias:7.3 Jahre


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Monthly solution: EOT08a vs. FES2004

FES2004 as background EOT08a as background

cm e

qw

h

Amplitude of 161 day fit signal (S2 alias) from 64 monthly GRACE solutions


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Range acceleration residual analysis – M2

EOT08a

FES2004

nm/s

2


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Range acceleration residual analysis – M2

EOT08a

FES2004

nm/s

2

- Ocean tide models must be improved for future satellite missions

- Potential for new gravity missions:with tailored orbits ocean tides can be estimated / improved

(sun synchronous orbits are not a good choice)

- Only possible for effects with known frequency spectrum,(not an option for atmospheric and (non tidal) oceanic mass variations)

- Ocean tide models must be improved for future satellite missions



- Only possible for effects with known frequency spectrum,(not an option for atmospheric and (non tidal) oceanic mass variations)


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While the gravity field changes continously,it takes time to collect satellites data


GRACE

30 days30 days

15 days15 days1 day1 day


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GRACE

30 days30 days

15 days15 days1 day1 dayCommon solution:

- Reduce high frequency signal by models,e.g. atmosphere and ocean dealiasing model (AOD1B)

- Estimate mean solution over a certain time span,e.g. monthly means

Common solution:




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GRACE

30 days30 days

15 days15 days1 day1 dayCommon solution:



Common solution:



Question:

What means high frequency in terms of monthly means?

Question:

What means high frequency in terms of monthly means?


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Simulation

GRACE monthly means

Simulated annual signal


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Simulation

GRACE monthly means

Simulated annual signal

Differences causealiasing errors

(stripes)


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Simulation (1 month, n=60, eq. water height)

Errors in the solutionwithout annual signal:

Basline accuracy is reached

Errors in the solutionwith annual signal:

Well known stripping pattern


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Even long-periodic signals cause aliasing errors in monthly mean fields

Even long-periodic signals cause aliasing errors in monthly mean fields

Time-step representations are not an optimal choice

Time-step representations are not an optimal choice

Other ideas necessary to exploit the increased accuracy of new missions

Other ideas necessary to exploit the increased accuracy of new missions


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Representation of the time variability

1. month 2. month

cnm,snm

time

aliasing errorresulting in stripes

aliasing errorresulting in stripes

schematic picture of the time variations of the gravity field

Estimating monthly meangravity field solutions(GFZ, CSR, JPL)

Estimating monthly meangravity field solutions(GFZ, CSR, JPL)


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1. month 2. month

cnm,snm

time

Estimating 10 or 7 daysmean gravity field solutions(GRGS, GFZ)




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1. month 2. month

cnm,snm

time

increased time resolution:reduced aliasing errorbut reduced redundancy

increased time resolution:reduced aliasing errorbut reduced redundancy





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1. month 2. month

cnm,snm

time


fitting a smooth functionwith only a few parameters

reduced aliasing errornot too much reduced redundancy

fitting a smooth functionwith only a few parameters

reduced aliasing errornot too much reduced redundancy


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Dynamic process

time

Description of the time variable gravityfield as dynamic process

Description of the time variable gravityfield as dynamic process

Current state is determined by previousstates, state change is constrained byphysics (prediction)

Current state is determined by previousstates, state change is constrained byphysics (prediction)

If physics is not exactly known, correlations can be derived by models

If physics is not exactly known, correlations can be derived by models

Kalman FilterKalman Filter

Current state is controlled byobservations

Current state is controlled byobservations


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Kalman filter

daily solutions (degree n=40)daily solutions (degree n=40)

[ cm equivalent water height ]


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Conclusions

Even long-periodic signals cause aliasing errorsin monthly mean fields (stripes)

=> Block mean representations are notan optimal choice

First ideas:- Smooth representations in time by quadratic splines- Description of the time variable gravity field as dynamic process

Further investigations necessary

Even long-periodic signals cause aliasing errorsin monthly mean fields (stripes)

=> Block mean representations are notan optimal choice

First ideas:- Smooth representations in time by quadratic splines- Description of the time variable gravity field as dynamic process

Further investigations necessary

- background models must be improvedfor future satellite missions



- background models must be improvedfor future satellite missions



aliasing problems in gravity field recovery and possible ... · jürgen kusche 30.09.2009 1 torsten...

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