Flechtner F.M., Gruber Th., G?ntner A., Mandea M., Rothacher M., Sch?ne T., Wickert J. (Eds.) System Earth via Geodetic-Geophysical Space Techniques

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Mass Variation Signals in GRACE Products

and in Crustal Deformations from GPS:

A Comparison

Martin Horwath, Axel Rülke, Mathias Fritsche, and Reinhard Dietrich

1 Introduction

Geophysical mass variations are reﬂected not only in variations of the gravity ﬁeld

which are sensed by GRACE but also in solid Earth deformations. In particular, load

variations (e.g. due to the global hydrological cycle) induce an elastic deformation

which can be modeled by the load Love number formalism. Such elastic deforma-

tions can be, in turn, observed by geodetic GPS observations. A cross-comparison

with GRACE results and GPS results (cf. Davis et al., 2004; King et al., 2006;

van Dam et al., 2007) may validate either technique and may ﬁnally contribute to

the improvement of mass transport estimates. This article describes results from

analyses following this strategy.

2 Crustal Deformation Time Series from GPS in a Consistent

Reference Frame

With regards to GPS and other space geodetic techniques, site speciﬁc time series

of residual crustal deformations are in general considered as displacements w.r.t. an

a priori deﬁned reference network geometry. Here, we make use of homogeneous

results from a reprocessing of a global GPS network (Steigenberger et al., 2006)

in order to realize a terrestrial reference system in a consistent way including sta-

tion coordinates and velocities and low-degree spherical harmonics for surface load

variations as well (Rülke et al., 2008). Given the corresponding frame, a reference

network geometry can be derived for any arbitrary epoch by propagating the solved

for site coordinates and velocities as well the low-degree deformation terms. Daily

global GPS network solutions are then compared according to that reference on

the basis of a 6-parameter similarity transformation (3 translations, 3 rotations).

For each individual site, transformation residuals together with the deformation

M. Horwath (B)

Institut für Planetare Geodäsie, Technische Universität Dresden, 01219 Dresden, Germany

e-mail: martin.horwath@legos.obs-mip.fr

399

F. Flechtner et al. (eds.), System Earth via Geodetic-Geophysical Space Techniques,

Advanced Technologies in Earth Sciences, DOI 10.1007/978-3-642-10228-8_34,

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Springer-Verlag Berlin Heidelberg 2010

400 M. Horwath et al.

time series converted from the low-degree harmonics compose the overall crustal

deformation time series represented by GPS.

3 Comparison of Low-Degree Deformations from GPS

and GRACE

Reprocessed GPS observations are used to directly infer spherical harmonics for

surface loads (see Sect. 2). Unlike GPS, related degree-1 terms cannot be derived

from GRACE only measurements as the origin of the underlying reference system

coincides with the center of mass of the Earth system, i.e. CM. But higher degrees

of loading are captured by both techniques. Exemplarily, Fig. 1 shows changes in

C_20 obtained from the global GPS reanalysis and from GRACE (GFZ Release

04) where background ﬁelds (see Sect. 4.1) were re-added to the GRACE solution

so that both the GPS and the GRACE curve show estimates of the full non-tidal

variations. In this case, we ﬁnd good agreement between the completely independent

and complementary results.

2002 2003 2004 2005 2006 2007 2008

−5

x 10

−10

Time

Fig. 1 Changes in C_20

obtained from the global GPS

reanalysis (gray line)and

from GRACE (GFZ Release

04, black line)

4 Comparison of Point-Wise Deformation Time Series

4.1 Daily GPS Versus Geophysical Models

In order to validate the GRACE background models (given in high temporal reso-

lution), daily surface mass variations according to these models were converted to

crustal load deformation time series (using the load Love number theory) and com-

pared to daily deformation time series from GPS. The background models include

the atmospheric and oceanic models routinely applied in GRACE processing and, in

addition, the WGHM hydrology model (Döll et al., 2003) which was experimentally

applied as a background model within the TIVAGAM project. Degree-one deforma-

tions which are present in either datasets were included using the ‘Center of Figure’

reference frame.

Figure 2 (left) illustrates the comparison in the vertical dimension for sample

stations on all continents and on Greenland for the year 2003. Generally, the GPS

time series show larger day-to-day variations. This predominantly reﬂects noise in

Mass Variation Signals in GRACE Products and in Crustal Deformations from GPS 401

Vertical, daily

–20

–10

–20

POTS

ARTU

KUNM

ALIC

MCM4

KULU

DRAO

BRAZ

HRAO

01 03 05 07 09 11

Month of year 2003

Vertical, monthly

2002 2004 2006

Year

Horizontal, monthly

2002 2004 2006

Year

Fig. 2 Comparisons of station-wise nonlinear crustal deformations (mm) from GPS (gray)and

from computed load deformations according to models and GRACE results (black). The considered

GPS sites are indicated in the far left. Left: Daily vertical deformations in 2003. Black curves

show GRACE background model results. Center: monthly vertical deformations over the GRACE

period. Black curves show GRACE results. Right: Same as in the center, but for the North and East

components. North components are shifted by +5 mm

the daily GPS time series. On a time scale from days to weeks where the mod-

eled variations are dominated by atmospheric mass variations, there are remarkable

agreements between both types of observations: see, e.g., the POTS and ARTU sites.

This shows that the GPS vertical deformations well reﬂect geophysical load effects.

On an annual scale, there is a clear correlation in the behavior of either time series

402 M. Horwath et al.

but the differences are also considerable, most remarkably at the BRAZ site. Errors

of the hydrology model, local effects, and systematic effects in the GPS time series

(see Sect. 5) are possible causes of such differences.

4.2 Monthly GPS Versus Grace

Monthly averages of GPS site displacements were compared to modeled defor-

mations according to the GRACE monthly solutions. Here, the GRACE monthly

solutions had to be ﬁltered to dampen high-degree error effects. To avoid smooth-

ing of hydrological signals, the WGHM hydrology model was removed before

smoothing and restored afterwards. Also, the atmospheric and oceanic background

models were re-added. Since degree-one components are not given by the GRACE

solutions, those components were also excluded from the GPS deformations.

Figure 2 (center) illustrates the respective comparisons for the vertical compo-

nent. There is a clear resemblance between GPS and GRACE at all shown sites. At

the same time, signiﬁcant differences remain.

For a more quantitative comparison, statistical parameters were computed: the

standard deviations (STDs) of the GPS and GRACE time series as well as of their

difference, σ

GPS

,σ

GRACE

and σ

Diff

; the correlation coefﬁcients between GPS and

GRACE; and the percentage of GPS variance explained by the GRACE time series,

(σ

GPS

− σ

Diff

)/σ

GPS

. These parameters are shown globally for every involved sta-

tion in Fig. 3. The GPS variability is typically higher than the GRACE variability

(Fig. 3a). This is true for almost all continental sites and is particularly pronounced

for sites on small ocean islands where the geophysical signal ought to be small due

to the inverse barometric compensation of atmospheric pressure variations and due

to the smallness of land hydrology domains. Also, the GPS-GRACE differences are

far larger than the expected error in the GRACE-derived time series (Fig. 3b).

Nonetheless, the GPS-GRACE agreement is good for most of the continental

sites. There, the correlation (Fig. 3c) is typically between 50 and 80% and the

percentage of explained GPS variance (Fig. 3d) is typically between 20 and 60%.

For horizontal components, examples of time series comparisons are shown in

Fig. 3 (right). The GPS variability is far larger than the GRACE variability. Apart

from a few exception (including KULU), there is hardly any similarity between the

two kinds of time series.

5 Systematics in GPS-GRACE Discrepancies

To further illuminate the nature of the GPS-GRACE discrepancies, a principal com-

ponent analysis (PCA) of these discrepancies was performed in selected regions.

Here, we concentrate on the results for the analysis of the horizontal components.

Figure 4 shows the PCA results for a European, an Australian and a North American

sub-network. The ﬁrst empirical orthogonal functions (EOFs) are almost uniform

Mass Variation Signals in GRACE Products and in Crustal Deformations from GPS 403

12345678910

STD of GPS and GRACE [mm]

(a)

123456

STD of (GPS-GRACE) and of GRACE error effect [mm]

(b)

0 20 40 60 80 100

GPS-GRACE correlation [%]

(c)

0 20 40 60 80 100

Percentage of explained variance [%]

(d)

Fig. 3 Statistical parameters for the comparison of GPS and GRACE vertical deformation time

series. (a) STDs of the GPS signal (circles) and the GRACE signal (background image). (b)STDs

of the GRACE-GPS discrepancy (circles) and an assessment of GRACE error effects (background

image) following the approach of Horwath and Dietrich (2006). (c) Correlation between GPS and

GRACE. (d) Percentage of GPS signal variance explained by the GRACE signal

–2

–1

–2

–1

–2

–1

2002 2004 2006

52% of total variance

2002 2004 2006

47% of total variance

2002 2004 2006

40% of total variance

2mm horizontal

Fig. 4 Results of a principal component analysis of the horizontal GPS-GRACE discrepancies

performed for regional sub-networks. The maps show the patterns of the ﬁrst EOFs, the time

series show the corresponding PCs. That is, multiplying the time series with the mapped patterns

yields variations that make up 52, 47 and 40%, respectively, of the total variance of GPS-GRACE

discrepancies

404 M. Horwath et al.

displacements of almost all involved sites. These patterns are responsible for about

50% of the variance of the GPS-GRACE discrepancies. The respective principal

components (PCs) contain a large seasonal signal without being purely seasonal.

The next EOFs (not shown) also contain spatially coherent patterns. In conclusion,

the GPS-GRACE discrepancies are dominated by variations that are correlated over

large distances.

At the moment, we address these remaining discrepancies to be caused by a

remaining systematic GPS mismodeling. In fact, there are a number of possi-

ble aspects i n the modeling of GPS observations such as solar radiation pres-

sure or Earth albedo that are suitable to induce common large scale residual

pattern.

6 Regionalized Comparison Studies

As a way to circumvent the systematic errors apparently present in the GPS time

series we want to consider regional networks and remove their common displace-

ments since, according to our previous analyses, we suspect systematic errors to

dominate these common displacements in the GPS results. We thus aim at isolating

the internal deformations of regional networks.

We choose the following realization of this general approach: For every month

we perform a Helmert transformation of the monthly network geometry onto the

mean network geometry. We set up four transformation parameters with respect to

geocentric coordinates: three rotations and one scale parameter. By not allowing for

translations, we effectively estimate independent ‘shifts’ in the horizontal and in the

vertical directions. We then consider the residuals of the Helmert transform as the

internal deformations of the regional network. We perform this procedure equally

for the GPS and for the GRACE time series.

Figure 5 illustrates the procedure for the example of the Australian regional

cluster. For two selected sites, the coordinate time series from the global analysis

–4

East North

KARR

–10

Up [mm]

2002 2004 2006

Time

TOW2

From global analysis

2002 2004 2006

Time

–4

KARR

–10

2002 2004 2006

Time

TOW2

From regional analysis

2002 2004 2006

Time

Fig. 5 Illustration of the regionalization approach outlined in Sect. 6. Left half: Horizontal and

vertical deformation time series (mm) from GPS (gray)andGRACE(black) for two Australian

sites. Right: The same kind of time series after regionalization

Mass Variation Signals in GRACE Products and in Crustal Deformations from GPS 405

(shown in the left half of the ﬁgure) show relatively large GPS-GRACE discrep-

ancies in the horizontal directions which are similar for both sites. The right half

of the ﬁgure shows the regionalized deformation time series. For the horizontal

directions, much of the presumably spurious GPS variations is reduced by the

Helmert transform and the remaining variations better resemble the GRACE vari-

ations. These GRACE variations are also changed by the regionalization, but not

much, because the dominant horizontal signal of the GRACE time series is a con-

traction and dilatation of the whole network due to continental load changes and

this signal is not absorbed by the Helmert transform. For the vertical component,

the regionalization reduces the (absolute) differences between the GPS and GRACE

time series but it also dramatically reduces the presumable signal in both time

series. This is because the dominant geophysical signal in the vertical is a unidirec-

tional upward and downward displacement which is well absorbed by the Helmert

transform.

Figure 6 shows statistical parameters of the GPS-GRACE comparison per site as

in Fig. 3c and d but now for horizontal time series in six regions, converted following

our regionalization approach. Table 1 shows the mean values of these parameters for

each of the six regions. The GPS-GRACE resemblance after regionalization is still

weak but was, nevertheless, considerably improved by the regionalization.

0 20 40 60 80 100

GPS-GRACE correlation [%]

(a)

0 20 40 60 80 100

Percentage of explained variance [%]

(b)

Fig. 6 Statistical parameters as in Fig. 3c, d, but now for the horizontal components after

regionalization in the outlined six regional sub-networks

Table 1 Regional mean values of the statistical parameters shown in Fig. 6. In parentheses, the

respective values before regionalization are shown

Region Correlation (%)

Percentage of explained

variance (%)

North America 17 (8) 0 (–4)

Europe 24 (–4) 5 (–21)

Asia 22 (15) 5 (2)

South America 46 (23) 17 (3)

Africa 51 (39) 26 (17)

Australia 38 (11) 14 (–1)

406 M. Horwath et al.

7 Conclusions

GRACE and GPS are complementary ‘sensors’ for surface mass variations. A

comparison between both shows encouraging results. In the vertical dimension,

there is typically good agreement between GPS observations and modeled defor-

mations from GRACE-derived mass variations. This can be seen as a progress

compared to previous studies using standard GPS products (e.g., van Dam et al.,

2007). The remaining discrepancies, however, by far exceed expected errors in

the GRACE-derived deformations. This is even more evident in the horizontal

dimensions.

A likely cause of these discrepancies lies in remaining systematic errors in the

GPS solution. The problem of systematic differences can be partly circumvented by

analyses of internal deformations of regional subnetwork.

The work illustrates that there remain large challenges in consistently combining

different space geodetic techniques into one Global Geodetic Observing System

(Drewes, 2005).

References

Davis JL, Elosegui P, Mitrovica JX, Tamisiea ME (2004) Climate-driven deformation of the solid

Earth from GRACE and GPS. Geophys. R es. Lett. 31, L24605, doi:10.1029/2004GL021435.

Döll P, Kaspar F, Lehner B et al. (2003) A global hydrological model for deriving water availability

indicators: model tuning and validation. J. Hydrol. 270, 105–134.

Drewes H (2005) Science rationale of the global geodetic observing system (GGOS). In: Tregoning

P, Rizos C (eds.), Dynamic Planet: Monitoring and Understanding a Dynamic Planet with

Geodetic and Oceanographic Tools, Vol. 130 of IAG Symposia, Springer, Berlin, pp. 703–710.

Horwath M, Dietrich R (2006) Errors of regional mass variations inferred from GRACE monthly

solutions. Geophys. Res. Lett. 33, L07502, doi:10.1029/2005GL025550.

King M, Moore P, Clarke P, Lavallée D (2006) Choice of optimal averaging radii for temporal

GRACE gravity solutions, a comparison with GPS and satellite altimetry. Geophys. J. Int.

166(1), 1–11, doi:10.1111/j.1365-246X.2006.03017.x.

Rülke A, Dietrich R, Fritsche M, Rothacher M, Steigenberger P (2008) Realization of the

Terrestrial Reference System by a reprocessed global GPS network. J. Geophys. Res. 113,

B08403, doi:10.1029/2007JB005231.

Steigenberger P, Rothacher M, Dietrich R, Fritsche M, Rülke A, Vey S (2006) Reprocessing of a

global GPS network. J. Geophys. Res. 111, B05402, doi:10.1029/2005JB0037472.

van Dam T, Wahr J, Lavallée D (2007) A comparison of annual vertical crustal displacements from

GPS and Gravity Recovery and Climate Experiment (GRACE) over Europe. J. Geophys. Res.

112, B03404, doi:10.1029/2006JB004335.

Monthly and Daily Variations of Continental

Water Storage and Flows

Kristina Fiedler and Petra Döll

1 Introduction

Continental water storage is an essential part of the global water cycle, being par-

ticularly important for the existence of many ecosystems and for the satisfaction

of human demands, including water for agricultural, industrial and domestic use.

Total continental water storage is the sum of water stored as snow and ice, in and on

vegetation cover, in the unsaturated soil zone, in groundwater and surface waters

like rivers, wetlands, lakes and reservoirs. Little is known about the spatial and

temporal variability of water storage on a global scale although this information

is important for understanding the global hydrological cycle. Direct estimations of

storage change are often restricted to the point scale and to single components of

total water storage, such as groundwater or lakes, due to the lack of an adequate

monitoring network. With the GRACE satellite mission launched in 2002, estimates

of the Earth’s dynamic gravity ﬁeld became available with unprecedented accuracy.

Over land, the time variable gravity data mainly contain a hydrological signal rep-

resenting continental water storage changes. In order to evaluate GRACE results,

the state-of-the-art WaterGAP Global Hydrological Model (WGHM) was applied

to calculate monthly continental water storage changes on a global scale during

the period for which GRACE data were available. Simulated daily water storage

values were intended to be used as a means to improve de-aliasing of GRACE

data. To improve estimates of both water storage and river discharge, the repre-

sentation of ﬂow velocities and man-made reservoirs in WGHM was improved.

Finally, a best estimate of continental water storage variations and water ﬂows was

derived.

K. Fiedler (B)

Institute of Physical Geography, Goethe University Frankfurt am Main,

60438 Frankfurt am Main, Germany

e-mail: ﬁedler@em.uni-frankfurt.de

407

F. Flechtner et al. (eds.), System Earth via Geodetic-Geophysical Space Techniques,

Advanced Technologies in Earth Sciences, DOI 10.1007/978-3-642-10228-8_35,

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408 K. Fiedler and P. Döll

2 Modelling of Global Continental Water Storage and Flows

with WGHM

2.1 Model Overview

The WaterGAP global hydrological model (WGHM) has been developed at the

Centre for Environmental Systems Research at the University of Kassel. Ongoing

model development is done both in Kassel and at the University of Frankfurt. A

detailed model description can be found in Döll et al. (2003). WGHM operates with

an internal time step of one day and a spatial resolution of 0.5

◦

lat/long. Calculations

are based on spatially distributed physiographic characteristics and on time series

of monthly climate data. A global database of lakes and wetlands is integrated to

supply information on large surface water bodies. Anthropogenic water use is cal-

culated externally: water needed for irrigation, industrial and domestic purposes is

taken into account but it is assumed to be taken out of surface water bodies only.

Within the model, total water storage is calculated as the sum of canopy, snow, soil

and groundwater storage as well as water stored in surface water bodies (rivers, wet-

lands, l akes and reservoirs). A global-scale analysis of long-term average seasonal

storage variations in the different compartments (for the climate normal 1961–1990)

was performed by Güntner et al. (2007).

2.2 Improved Representation of Lateral Flows

In order to improve the representation of river discharge and terrestrial water stor-

age changes in WGHM, the globally constant river ﬂow velocity was changed to a

dynamic approach and a new reservoir algorithm was introduced.

2.2.1 Variable Flow Velocity

In the standard version of WGHM, river ﬂow velocity is set constant at 1 m/s for

the whole globe. Following the work of Schulze et al. (2005), a new algorithm to

calculate the ﬂow velocity as a function of slope and discharge was applied, using

the Manning-Strickler-Formula

v = n

−1

· R

2/3

· S

1/3

(1)

where v is ﬂow velocity (m/s), n is river bed roughness (–), R is the hydraulic

radius and S is river slope (m/m). The slope is derived using elevation data from

the GTOPO30 global digital elevation model with a horizontal grid spacing of 30

arc seconds (approximately 1 km). The hydraulic radius is calculated based on river

width (W) and depth (D). Because information on W and D is not available on a

global scale, these values are estimated as a function of discharge according to

Allen et al. (1994). River bed roughness is not directly measurable and varies on

a very small scale. Based on data listed by Mays (1996), a global value of 0.04

is applied. Ongoing work will focus on a spatially distributed roughness value as