Martin Losch, Helen Snaith, Frank Siegismund, Per Knudsen & the GUTS Team
Scientific Trade off Study and Algor ithm Sp ecificat ion
As part of the GOCE User Toolbox Specification (GUTS) project, the GUTS team has carried out a scientific trade-off study, to select the best algorithms to meet the user requirements for the toolbox. In some cases the selection is straightforward. However, in other cases, the choice depends on scientific applications as well as the algorithm efficiency and more practical considerations. We have looked at the selection of filtering functions used in calculation of a mean dynamic topography from combined GOCE and satellite altimeter data. The trade-off study has also selected the functionality of the toolbox, given the user requirements and the recommended algorithms.
Key outputs for geodetic and solid earth
communities
All default inputs can be replaced with user-supplied
versions
What is the “best”
filter to use?
What is the “best”
way to merge:
retaining features &
reducing errors?
GOCE Level 2 Products Digital Terrain
Model
Altimetric (Mean) Sea Surface
Height
Global a-priori (Mean) Dynamic
Topography
Geoid and Gravity Field Computation
Satellite Only (Mean) Dynamic Topography Calculation and filtering
Combined (Mean) Dynamic Topography
Calculation
Preview and Save
Associated error fields
• Geoid Height
• GravityAnomaly
• Deflections of the Vertical
Satellite only (Mean) Dynamic
Topography (M)DTS
Combined (Mean) Dynamic
Topography (M)DTC
Primary Toolbox Workflow
Short scale features are from both the true dynamic topography and the unresolved short scale geoid:- we need to remove these- but how best to do it?
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h-ND [m], (actual range: [-19m 11m])
... and an “observed” dynamic topography as “altimetric”
sea surface height -
“observed” geoid
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0 50
-100 -50 0
Then we generate an 50
“observed” geoid by
smoothing the “true” geoid
Dynamic Topography Filtering:
a methodology for investigating different proceedures
We choose a “true” dynamic topography from a 1/4˚ ocean model with data assimilation (OCCAM) and generate an “altimetric” sea surface
height = “true” dynamic topography + “true” geoid
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0 50
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We use the 1˚ EGM96 geoid as the “true” geoid
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dynamic topgraphy [m]
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0 50
spectral Pellinen
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0 50
geographical spherical cap
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0 50
spectral quasi-Gaussian (Jekeli)
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0 50
geographical quasi-Gaussian (Jekeli)
Applying filtering in the spectral domain reduces some of the coastal effects
obvious in the geographical filtered fields...
...and corrects the offsets of enclosed seas
We can remove the short scale features by applying
a filter to the obsesrved dynamic topography field.
We can do this is
geographical space, or in spectral space, by
transforming the field to spherical harmonics
Spatial or Spectral Filtering?
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dynamic topgraphy [m]
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0 50
spectral Pellinen
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0 50
geographical spherical cap
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0 50
spectral quasi-Gaussian (Jekeli)
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0 50
geographical quasi-Gaussian (Jekeli)
The RR MDT fields have higher resolution features than the equivalent direct method MDT
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geo-jekeli
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geo-llcap
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geo-sphcap
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0 50
geo-gaubel
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0 50
geo-hann
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0 50
geo-hamm
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0 50
sph-jekeli
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0 50
sph-pellinen
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0 50
sph-boxcar
-1 -0.5 0 0.5 [m]1
The difference between the RR MDT and direct
method MDT for 9 different filters:- 6 spatial and 3 spectral
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0 50
-1 -0.5 0 0.5 [m]1
rms = 11.28 cm
No direct estimate of the errors associated with the
a-priori field are included and these may be large - as shown by the difference
between our “true” and a-priori dynamic topography
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[m]1 The a-priori dynamic topography is taken from a different ocean model
(ECCO) with data assimilation
We can “correct” our altimeter-geoid MDT with high resolution information from an a-priori MDT:- see the poster on “Towards a first prototype” (Rio et al) for an example
The Remove-Restore Method:
Making use of a-priori information
geo−jekeli geo−sphcap sph−jekeli sph−pellinen 0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
error of global mean of MDT [mm]
without
omission error withomission error
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0 50
-3 -2 -1 0 1 2
m x 103 -5 spectral quasi-Gaussian (Jekeli) filter
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0 50
-8-6 -4-2 02 46
m x 108 -3 geographical quasi-Gaussian (Jekeli) filter
The omission error is error due to the part of the signal we don’t include - ie caused by geoid signals at shorter wavelengths
2 orders of magnitude difference
The effect on MDT of geoid omission for a 4˚
geoid calculated using degree and order 20 and filtering in spatial (top) and
spectral (bottom) domains
The omission error is negligible in a global
mean sense when
filtering in spectral space
What about the omission errors?
geo−jekeligeo−llcapgeo−sphcapgeo−gaubelgeo−hanngeo−hammsph−jekelisph−pellinensph−boxcar 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
rms−error [m]
}cutoff:degree & order 25
}cutoff:degree & order 45 RRdirect
RRdirect
A summary of the rms differences between the “true”
and the reconstructed dynamic topograph using 9 different filters (6 spatial and 3 spectral), for both direct and RR techniques, and using 2 different cutoffs
Conclusions
Lower rms differences for lower degree and order cutoff (lower resolution) in all
instances - possibly an artifact of the
methodology
Lower rms differences of RR than direct method in all cases - less
pronounced at higher resolution
Overall lowest rms
differences for spectral quasi-Gaussian (Jekeli) filter using the RR
technique
