Master Thesis

Analysis of seasonal loading-induceddisplacements from GPS and GRACE

Jinwei Zhang

Institute of Geodesy, University of Stuttgart

Supervisor: Prof. Dr.-Ing. Nico SneeuwQiang Chen, M.Sc.

Duration of the Thesis: 6 monthsFebruary 2014

Introduction

Since the masses transport within the Earth system over time, those inducethe mass redistribution on the globe. Hence, the load of masses on thesurface consequently varies, which contributes to the temporal variation ofgravity. Because the geoid of Earth is defined as an equipotential surface ofgravity, the variation of gravity would influence the height displacements.Therefore, the surface loading variation caused by mass redistribution con-sequently leads to the elastic displacements on the Earth’s surface (van Damet al. 2001, De Linage et al. 2007). As we know, the mass load gives pressureon the surface due to the gravitation. As a result of load variation, thesurface displacements occur primarily in vertical direction and in horizontalas well. That is clearly shown in figure 2.The surface deformation could be derived from GRACE through time-variable gravity field and also be observed by IGS stations in GPS 3D co-ordinates (van Dam et al. 2007). The surface deformations derived fromGRACE are spatially smoothed with about 350 km resolution. However, thedeformations of IGS stations observed by GPS are discrete point measure-ments on the globe. Therefore, a validation of the consistency between thedeformations from GRACE and GPS is necessary to be done, which wouldbenefit the further research on mass transport and climate change.

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Surface Mass Transport

Surface Mass Redistribution, i.e. Loading Variation

Temporal Variation of

Gravity

Surface DeformationDerive

Observed by Induce

Figure 1: Process of mass transport and loading variation

Figure 2: Loading variation effects on surface displacements

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Methodology

The 3D surface deformations can be derived from GRACE spherical har-monic coefficients by (Wahr et al. 1998, Kusche & Schrama 2005)

dH(θ, λ) = R ·∞

∑l=0

l

∑m=0

P̄lm(cos θ)(∆Cglm cos mλ + ∆Sg

lm sin mλ)h′l

1 + k′l(1)

dE(θ, λ) =R

sinθ·

∞

∑l=0

l

∑m=0

mP̄lm(cos θ)(−∆Cglm sin mλ + ∆Sg

lm cos mλ)l′l

1 + k′l(2)

dN(θ, λ) = −R ·∞

∑l=0

l

∑m=0

∂

∂θP̄lm(cos θ)(∆Cg

lm cos mλ + ∆Sglm sin mλ)

l′l1 + k′l

(3)For a proper comparison, the spatial and temporal reference of GRACEand GPS need to be unified. Before deriving deformations, the GRACEdata should be filtered in spectral domain. For validation, the correlationcoefficient, the Nash-Sutcliffe efficiency, and WRMS reduction are estimated.In conclusion, the whole procedure of data processing could be graphicallydescribed in figure 3.

Results

To investigate the disagreement between GPS and GRACE, a number of IGSstations in three regions are selected (i.e., Tibetan plateau, Danube basin andGreat Lakes area) with period of 8 years (2003 – 2011).

In figure 4, the eight stations in Danube basin act obviously common annu-ally repeating patterns, that the deformations rise up between spring andautumn, and fall down between autumn and spring. The deformations fromGRACE have quite consistent periodical patterns with ones from GPS. Itstrongly supports the assumption that the annual deformations might bedriven by climate changes.

The mean annual amplitudes from all 15 stations are plotted in figure 5.Only if all the GPS annual signals have completely same amplitudes, thenthe slope of the best fit line would be 1. Therefore, it can be concluded thatmostly deformations from GPS have lager amplitudes than from GRACE,which indicates that not all the deformations contained in GPS signal areinduced by the surface water load variations.

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Monthly static gravity field

Monthly time-variable gravity field

Filtering

Reference frame unification

Non-tidal atmospheric and oceanic effects correction

Monthly deformation time series

Subtracting mean gravity field

Weekly deformation time series

Monthly deformation time series

Time resampling

Joint deformation analysis

GRACE Data Processing

GPS Data Processing

Figure 3: Data processing chain

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2003 2004 2005 2006 2007 2008 2009 2010 2011−10

0

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dH /

mm

BOGO

GLSV

JOZ2

MIKL

ORID

PADO

SULP

PTBB

GRACE monthly GPS monthly GRACE 5−month mean GPS 5−month mean

Figure 4: Comparisons of height deformation time series from GRACE andGPS in Danube basin

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0 1 2 3 4 50

1

2

3

4

5

GRACE amplitude [mm]

GP

S a

mp

litu

de

[mm

]

best fit lineGPS stations

Figure 5: Comparisons of vertical annual amplitudes of signals from GRACEand GPS

Furthermore, the combination of filters would be tested in order to find outthe optimal choice of filtering for GRACE data.

After comparisons, 50% stations filtered by stochastic filter show highercorrelation than other filters, and 52.5% stations filtered by stochastic filtershow larger WRMS reduction than other filters. The maximal difference ofWRMS reduction within Gaussian filter group reaches 10% and normallythe mean difference of the WRMS reduction among different combinationsis only around 1%. However, compared with Gaussian group, the WRMSreduction can be improved by stochastic filter up to maximum 27%, and theaverage improvement is more than 3%.

Conclusion

Based on the work we have done in the thesis, the following conclusionwould be drawn as below:

• GRACE can detect the surface elastic deformations through time-variable gravity field.

• The deformations of all IGS stations in respective regions show strong-ly coherency with common annual patterns, such as on Tibetan plateau,in Danube basin, and in Great Lakes area. That proves the feasibilityof regional loading-induced deformation analysis.

• The loading variations on the surface induce the deformations princi-pally on vertical component.

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Figure 6: GRACE equivalent water height (EWH) after filtering with differ-ent filters

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Longitude

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itu

de

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ANKR

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TLSE

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(a) 500 km

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(b) 300 km

Figure 7: mean annual amplitudes of vertical deformations in Europe filteredby Gaussian isotropic filter

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Figure 8: mean annual amplitudes of vertical deformations in Europe filteredby combination of Gaussian isotropic and destriping filter

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Figure 9: mean annual amplitudes of vertical deformations in Europe filteredby Gaussian anisotropic filter

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Figure 10: mean annual amplitudes of vertical deformations in Europefiltered by combination of Gaussian anisotropic and destriping filter

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Figure 11: mean annual amplitudes of vertical deformations in Europefiltered by stochastic filter

• The mass redistribution and mass load variation can be reflected bysurface deformations from GPS and GRACE. These two independentgeodetic observation systems are potential to estimate the surface loadvariations.

• Filter plays an important role on GRACE data pre-processing, whichinfluences the amplitude of deformations derived from GRACE. Forglobal deformation derivation or inversion of loading, the isotropicGaussian filter with radius of 300 km convolved with destriping filtercan be simply applied for GRACE. However, the stochastic filter is theoptimal choice when we do the regional analysis with several specifiedstations, due to indeterministic property of mass load redistribution.

References

De Linage, C., Hinderer, J. & Rogister, Y. (2007), ‘A search for the ratiobetween gravity variation and vertical displacement due to a surfaceload’, Geophysical Journal International 171(3), 986–994.

Kusche, J. & Schrama, E. J. O. (2005), ‘Surface mass redistribution inver-sion from global GPS deformation and Gravity Recovery and ClimateExperiment (GRACE) gravity data’, J. Geophys. Res. 110(B9), B09409–.

van Dam, T., Wahr, J. & Lavallee, D. (2007), ‘A comparison of annual verti-cal crustal displacements from GPS and Gravity Recovery and ClimateExperiment (GRACE) over Europe’, J. Geophys. Res. 112(B3), B03404–.

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van Dam, T., Wahr, J., Milly, P., Shmakin, A., Blewitt, G., Lavallee, D. & Lar-son, K. (2001), ‘Crustal displacements due to continental water loading’,Geophysical Research Letters 28(4), 651–654.

Wahr, J., Molenaar, M. & Bryan, F. (1998), ‘Time variability of the Earth’sgravity field: Hydrological and oceanic effects and their possible detectionusing GRACE’, J. Geophys. Res. 103(B12), 30205–30229.

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