Optimal locations for absolute gravity measurements and sensitivity of GRACE observations for constraining glacial isostatic adjustment on the northern hemisphere

Geophysical Journal InternationalGeophys. J. Int. (2012) doi: 10.1111/j.1365-246X.2012.05563.x

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Optimal locations for absolute gravity measurements and sensitivityof GRACE observations for constraining glacial isostatic adjustmenton the northern hemisphere

Holger Steffen,1 Patrick Wu1 and Hansheng Wang2

1Department of Geoscience, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4 Canada. E-mail: [email protected] Key Laboratory of Geodesy and Earth’s Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China

Accepted 2012 June 1. Received 2012 May 31; in original form 2012 March 1

S U M M A R YGravity rate of change is an important quantity in the investigation of glacial isostatic adjust-ment (GIA). However, measurements with absolute and relative gravimeters are laborious andtime-consuming, especially in the vast GIA-affected regions of high latitudes with insufficientinfrastructure. Results of the Gravity Recovery And Climate Experiment (GRACE) satellitemission have thus provided tremendous new insight as they fully cover those areas. To betterconstrain the GIA model (i.e. improve the glaciation history and Earth parameters) with newgravity data, we analyse the currently determined errors in gravity rate of change from abso-lute gravity (AG) and GRACE measurements in North America and Fennoscandia to test theirsensitivity for different ice models, lithospheric thickness, background viscosity and lateralmantle viscosity variations. We provide detailed sensitivity maps for these four parametersand highlight areas that need more AG measurements to further improve our understanding ofGIA. The best detectable parameter with both methods in both regions is the sensitivity to icemodel changes, which covers large areas in the sensitivity maps. Also, most of these areas areisolated from sensitive areas of the other three parameters. The latter mainly overlap with icemodel sensitivity and each other. Regarding existing AG stations, more stations are stronglyneeded in northwestern and Arctic Canada. In contrast, a quite dense network of stationsalready exists in Fennoscandia. With an extension to a few sites in northwestern Russia, acomplete station network is provided to study the GIA parameters. The data of dense networkswould yield a comprehensive picture of gravity change, which can be further used for studiesof the Earth’s interior and geodynamic processes.

Key words: Satellite geodesy; Gravity anomalies and Earth structure; Composition of themantle; Dynamics of lithosphere and mantle; Europe; North America.

1 I N T RO D U C T I O N

Glacial Isostatic Adjustment (GIA) describes ongoing processeson the Earth induced by the last ice age. During the last ice age,the enormous weight of the large-scale ice sheets, for example,in North America and Fennoscandia, depressed the crust and pro-duced the so-called peripheral forebulge around the ice sheet. Sincethe melting of the ice sheets, the Earth has been readjusting byviscous flow and returning slowly to its equilibrium shape, lead-ing to uplift in the formerly glaciated area and subsidence in thesurrounding.

Detailed knowledge of the GIA process is indispensable inadvancing our understanding of mantle rheology and dynamics,glaciation history and climate change. In general, GIA investiga-tions employ dedicated GIA models simulating the dynamic re-sponse of the Earth by applying a load history from ice models

(see Steffen & Wu 2011, for an overview). To improve such a GIAmodel, four parameters turned out to be most important—they arethe chosen ice model, lithospheric thickness, radial viscosity pro-file [or a background viscosity profile for three-dimensional (3-D)modelling] and lateral viscosity contrasts (Wu et al. 2010). Theseparameters can be constrained with the help of geodetic measure-ments as well as relative sea levels. However, due to economic,logistic and ecological (e.g. in polar regions) reasons, these mea-surements and data points do not and cannot cover the whole Earthwith sufficient density and accuracy. Hence, new geodetic data needto be acquired at optimal locations so that the four parameters canbe better resolved. An optimal location is thereby defined by wheresensitivity of the data lies above the current accuracy of a selectedmeasurement method.

Wu et al. (2010) studied the optimal locations for GPS mea-surements in North America and Fennoscandia. They showed that

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2 H. Steffen, P. Wu and H. Wang

Figure 1. Gravity rate of change (a) in Canada (Pagiatakis & Salib 2003, PGC solution) from combined absolute (blue triangles) and relative gravitymeasurements (black dots), and in Fennoscandia [(b) Gitlein (2009); (c) Engfeldt et al. (2006)] from absolute gravity measurements (blue triangles). Units areμGal a−1. The full names of the absolute gravity stations used in Mazzotti et al. (2011) and marked by the red squares in (a) are: CHUR Churchill, MB; FLINFlin Flon, MB; DUBO Pinawa, MB; INTF International Falls, MN; WAUS Wausau, WI; NLIB Iowa City, IA; SASK Saskatoon, SK; PRDS Priddis, AB. Thegrey frame in (a) marks the size of the Fennoscandian area shown in (b) and (c) to highlight the difference in size between the two GIA-affected regions andthe AG station density. Further AG stations in Fennoscandia and the Baltic States where measurements may be used for a combined solution are marked by redsquares in (b) (modified and updated from Timmen et al. 2006; Gitlein 2009; Steffen & Wu 2011).

more permanent GPS stations are needed in northern Canada espe-cially in a region west of the Hudson Bay until the Rocky Moun-tains. In Fennoscandia, the almost adequate GPS network shouldbe extended to the last known GIA-affected areas in the Russianpart of East Europe and to Central Europe. However, uncertaintiesin GPS absolute rates can be up to 1–2 mm a−1 due to the poorresolution of GPS to Earth’s centre of mass variations (Mazzottiet al. 2011). This is not the case for absolute gravity (AG) mea-surements as they are measured relative to the Earth’s centre ofmass.

In this study, our focus will be on terrestrial and space-borngravity data in northern Europe and North America. Since adding

new AG stations is costly and since taking the measurements istime-consuming (Wilmes et al. 2005; Timmen et al. 2006; Gitlein2009), a key question is to find the optimal locations for new AGobservations that are most sensitive to the four GIA parametersabove. One aim of this study is to show locations of prospectiveAG sites that are sensitive to all four parameters and locationsthat are sensitive to only one, two or three parameters. Thus, theresults are useful for the inversion of one individual parameteror for the separation of the effects of two or more parameters ininversions.

In North America, AG measurements in the GIA area have beenundertaken since 1987 (Lambert et al. 2001), but mainly in highly

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Geophysical Journal International C© 2012 RAS

Optimal absolute gravity locations 3

Table 1. Model parameters for the reference model and the other models used to compute sensitivity in Figs 3–6.LT, lithospheric thickness; UM, upper-mantle viscosity (above 670 km depth); LM1, shallow lower-mantle viscosity(670–1171 km depth); LM2, deep lower-mantle viscosity (1171 km to core–mantle boundary).

Effect of Figures Ice LT UM LM1 LM2Subplot Model [km] [Pa s] [Pa s] [Pa s]

Reference Model ICE-4G 115 6 × 1020 3 × 1021 6 × 1021

Ice model 3–4 a ICE-5G 115 6 × 1020 3 × 1021 6 × 1021

5–6 a FBKS8 in Fenno 115 6 × 1020 3 × 1021 6 × 1021

ICE-4G elsewhere

Lat. Heterogeneous 3–6 b ICE-4G Lat. Het. Lith 6 × 1020 3 × 1021 6 × 1021

Lithosphere (Wu et al. 2005)

Background Viscosity 3–6 c ICE-4G 115 7 × 1020 1022 1022

Lat. Heterogeneous 3–6 d ICE-4G 115 Lat. Het. Mantle RF3S20 withViscosity β = 0.4 (Wang et al. 2008)

Table 2. Used observation errors for discussion of current sensitivityof selected GIA parameters in Fig. 7. Units are μGal a−1.

Best AG Average AG GRACE

Fennoscandia 0.11 0.16 0.11North America 0.09 0.18 0.10

populated regions south and southwest of Hudson Bay (Fig. 1a).Different types of instruments have been used, thus differentcorrection factors are applied because the instruments show differ-ences in intercomparisons and may also present shifts after upgradesor repairs (Lambert et al. 2001). After a thorough data analysis,Lambert et al. (2001) found that the combination of the once pop-ular ICE-3G global ice model at the time (Tushingham & Peltier1991) and a laterally homogeneous standard earth model needscorrections—either a 2 to 3-fold increase in lower mantle viscosityor a 50 per cent increase in Laurentide ice sheet thickness west ofLake Superior. The potential of AG measurements for correctingice histories was supported again in a later study with a longer time-series (Lambert et al. 2006). This is in contrast to investigations byLarson & van Dam (2000), who noted after comparison of AG withGPS that GPS is the better system for monitoring GIA. The authorsreached this conclusion on the basis of the instrument and deploy-ment costs and the difficulty of eliminating systematic errors in AGmeasurements. Recently, Mazzotti et al. (2011) reported that a com-bination of GPS and AG measurements can provide significant con-straints to global geodetic, geodynamic (e.g. GIA), and hydrologicalstudies.

First AG measurements in Fennoscandia date back to 1976 withmeasurements at several sites in Norway, Sweden, Finland andDenmark by Italian scientists whose aim was to improve the worldgravity standard, and to establish new absolute references (Cannizzoet al. 1978). Repeated AG measurements began in 1988 at three sitesin Finland (Bilker-Koivula et al. 2007). Since then, measurementshave been performed at more than 60 stations in Fennoscandiaby different institutes from Norway, Sweden, Finland, Denmark,Germany and USA (Wilmes et al. 2005; Gitlein 2009). A major co-operation was realized in 2003 with annual AG measurements fromdifferent FG5 absolute gravimeters (Timmen et al. 2006). Prelimi-nary and regional results of this co-operation have been presentedat different venues in the world, but a combined result for the manyaccessed stations in Fennoscandia, however, has not been publishedyet. Breili et al. (2010), for example, determined AG values for 16

stations in Norway obtained with the FG5-226 instrument of theNorwegian University of Life Sciences. Fig. 1(b) shows a recentresult by Gitlein (2009) obtained with one instrument (FG5-220)for the centre-of-rebound area. Engfeldt et al. (2006) presentedcombined values including measurements before 2003 from differ-ent instruments for 11 stations covering a larger area (Fig. 1c),which have been recently used in a GIA analysis by Pettersen(2011). Note that the trend value for Joensuu in eastern Finland(−1.7 μGal a−1 ± 0.8 μGal a−1) is most likely too low, which isdue to a measurement time span of only 6 yr. Other stations havetime spans up to 18 yr.

Another aim of this study is to analyse the sensitivity of datafrom the Gravity Recovery and Climate Experiment (GRACE) twin-satellite mission to the four GIA parameters and discuss the datareliability in the determination of the parameters. Similar to thestudy on AG measurements, we will show regions that are sensitiveto only one, two, three or all four parameters. Launched in 2002,GRACE has also greatly facilitated investigations on GIA, and sev-eral studies have addressed the affected areas in North America(Paulson et al. 2007; Tamisiea et al. 2007; Rangelova & Sideris2008; Van der Wal et al. 2008; Wang et al. 2008; Steffen et al.2009a; Sasgen et al. 2012) and Fennoscandia (Muller et al. 2005,2006a,b, 2012; Steffen et al. 2008, 2009a,c, 2010; Van der Wal et al.2011). The studies range from the detection of the GIA effect itself toestimation of lithospheric thickness and mantle viscosity, and com-parison of ice and hydrology models as well as different GRACEsolutions. It is also noted that AG measurements offer a unique op-portunity for validating and testing the results of GRACE (Timmenet al. 2006). Steffen et al. (2009b) compared GRACE results to AGmeasurements in six selected locations in Fennoscandia. Althoughland hydrology clearly affects results from both GRACE and AGmeasurements, the authors concluded that AG measurements area valuable tool for GRACE data evaluation and validation. Mulleret al. (2012) recently combined GRACE with AG measurementsand developed a land uplift model. It is hoped that such a combina-tion may help increase the low resolving power of geodetic data inFennoscandia, because they are currently not capable to determinethe lower-mantle viscosity (Steffen & Wu 2011).

In the next section, we will summarize the earth and ice modelsused in the sensitivity study. This is followed in Section 3 by adiscussion of current accuracies of gravity measurements on groundand in space as well as the dedicated trend error in gravity rate ofchange. In Section 4, we show our results and discuss them inSection 5. Finally, we conclude in Section 6.




Figure 2. Gravity anomaly trend (a) in Canada and (b) in Fennoscandia as derived from GFZ GRACE observations between 2003 July and 2010 Decemberusing a Gaussian filter of 400 km. Corresponding trend errors are shown in (c) and (d), respectively. Units are μGal a−1. The GRACE trend errors used in theactual analysis are not those in the figure but are constant by region to account for the maximum value arising from the figure.

2 G I A M O D E L L I N G

The results in this investigation are based on model calculationsthat employ the Coupled Laplace-Finite Element method of Wu(2004). We compute the response of a non-rotating, spherical, self-gravitating, Maxwell visco-elastic earth which includes materialcompressibility and self-gravitating oceans. For the sensitivity wefollow the approach described in Wu et al. (2010): we take thedifference between the predictions of two models that only differin one of the former discussed parameters and thus compute thesensitivity of AG or GRACE measurements to a specific modelparameter. An overview of the different ice and earth models isgiven in Table 1. One should caution that the model parametersused here only represent ‘typical’ cases and the results in this paper

give us a feel of what sensitivity one may expect in general. Thus,there is no claim that the results are ‘definitive’.

In our study regarding the sensitivity to ice histories, we use theICE-4G model (Peltier 1994) as basic model and keep the earthmodel to be the same. A comparison is then made between ICE-4G and ICE-5G (Peltier 2004) predictions in North America, andbetween ICE-4G and FBKS8 (Lambeck et al. 1998) in Fennoscan-dia. The usage of different ice models for the two regions is due tothe fact that each combination gives the highest sensitivity in thoseareas (Table 1).

In all other studies ICE-4G is used with different earth models,but we note that ICE-5G would give similar results. The referenceearth model is the laterally homogeneous model RF3 from Wanget al. (2008) parametrized according to the values listed in Table 1.




Figure 3. Sensitivity of absolute gravity measurements in North America to changes in (a) ice model (see text), (b) lithospheric thickness, (c) backgroundviscosity and (d) viscosity structure (homogeneity vs. heterogeneity). Units are μGal a−1.

For sensitivity to lithospheric thickness, the response of RF3 iscompared with a similar earth model except that the lithosphericthickness varies laterally with thickness exceeding 200 km over thecontinental cratons. The thickness then gradually thins to 75 kmover the oceans (see Wu et al. 2005, for this model).

For sensitivity to background viscosity profile, the response ofRF3 is compared with model RF2 from Wang et al. (2008). The twomodels differ mostly in the lower mantle, where RF2 has a viscosityvalue of 1022 Pa s (see Table 1).

For sensitivity to lateral viscosity variations, the response of RF3is subtracted from the response for model RF3S20. The latter is ob-tained by superposing lateral viscosity perturbations inferred fromseismic tomography model S20A (Ekstrom & Dziewonski 1998)on the background viscosity profile of RF3. In addition, the lateralviscosity variations are scaled with a certain beta value to take careof the contribution of thermal versus chemical origin of seismictomography (see Wang et al. 2008, for details). Here, we use a betavalue of 0.4 because it gives the highest sensitivity and also fits bestgeological and geodetic data sets (Wang et al. 2008).

3 A C C U R A C Y O F M E A S U R E M E N T S

The sensitivity of GIA parameters and thus its interpretation is lim-ited by the accuracy of the geodetic measurements and the currenttrend errors determined from the measurements. The trend errorof geodetic measurements generally depends on several factors,

for example, spatial factors such as geometry and size of network,number of stations, distribution of stations in a network, choiceof reference station etc., and temporal factors such as time spanof network, time span of each individual instrument in a network,relation of different instrument time spans in a network and manymore. Also, the chosen mathematical approach in the analysis andtrend calculation is of importance (see e.g. Van Camp et al. 2005).The size of a network and the choice of the reference stations have,for example, a significant effect on the estimated velocity field fromGPS observations (Legrand et al. 2010), which strongly influencesgeodynamic interpretations.

The time span of measurements and the relation of time spansof all instruments in a network also affect the accuracy of a GPSvelocity field and/or its point values (Wu et al. 2010). This is alsoobserved for point measurements from AG (Van Camp et al. 2005).Nonetheless, with repeated AG campaigns one should be able toconstrain gravity rate of change with an uncertainty of 0.1 μGal a−1

after 15 to 25 yr (Van Camp et al. 2005). Lambert et al. (2001)calculated a trend error in the gravity rate of change between 0.2and 0.4 μGal a−1 for six stations in North America. The lower valuewas achieved for two stations (Churchill and International Falls)with long records of about 12 yr, while the other four stations (FlinFlon, Pinawa, Wausau, Iowa City) with the higher value had (only)5 yr of observation. Adding four more years, the error decreased tovalues between 0.13 and 0.27 μGal a−1 (Lambert et al. 2005). Lateron, Lambert et al. (2006) presented an error of 0.11 μGal a−1 for17 yr of measurements in the station of Churchill. Recently, new




Figure 4. Same as Fig. 3, but for GRACE observations.

AG results for eight stations in North America (see Fig. 1a) havebeen published by Mazzotti et al. (2011). The two stations with thelongest record of now about 21 yr, Churchill and International Falls,have trend errors of 0.09 and 0.13 μGal a−1, respectively. Valuesfor Flin Flon, Pinawa, Wausau, and Iowa City with 14–15 yr recordrange between 0.18 and 0.28 μGal a−1. Mazzotti et al. (2011) alsoshowed errors for the two stations Priddis and Saskatoon, whichhave only 7 and 8 yr, respectively, of record. The error with at least0.4 μGal a−1 is significantly higher than that for the older stations.Comparing the average error for the six stations shown in Lambertet al. (2001) to the average value presented for those stations inMazzotti et al. (2011), an improvement from 0.35 to 0.18 μGal a−1,almost 50 per cent, has been achieved.

Based on a combination of absolute and relative measurementsdating back to the 1960s, Pagiatakis & Salib (2003) generated amap of gravity rate of change in Canada. The authors provided twosolutions, called GSD and PGC (Fig. 1a), that differ in the usedconstraints (repeated AG measurements) of gravity rate of changeat six locations during the adjustment. The calculated errors arebetween 0.06 and 0.90 μGal a−1 for GSC solution and 0.08 and0.90 μGal a−1 for PGC solution.

Since 2003, northern Europe has been annually investigatedwith absolute gravimeters purchased by the northern countries andGermany (see table 2 in Steffen & Wu 2011). Gitlein (2009) givesa comprehensive overview, especially of the German activities. Atentative map of gravity rate of change determined from the mea-surement campaign between 2003 and 2008 using the FG5-220 ofthe Institut fur Erdmessung in Hanover is shown in Fig. 1(b). Note

that we only plot results for stations that have enough measure-ments allowing an adequate trend calculation. Gitlein (2009) alsoprovides standard deviations for calculated trends of nine stations.The values vary between 0.24 and 1.10 μGal a−1 for time spans of3–5 yr (not every location has been accessed from 2003 to 2008).In a further study, those measurements have been combined for sixstations with earlier measurements of the Bundesamt fur Kartogra-phie und Geodasie (BKG), Frankfurt, Germany, and the NationalOceanic and Atmospheric Administration (NOAA) dating back to1993. The trend errors decrease for time spans between 11 and 14 yrto values ranging from 0.11 to 0.24 μGal a−1. The average error forthe six stations drops from 0.62 to 0.16 μGal a−1 (Gitlein 2009),which is an improvement of 74 per cent. The errors of computedgravity rates of change by Engfeldt et al. (2006) for 11 stationsin Fennoscandia from observations with different FG5 instrumentsbracket values from 0.1 to 0.4 μGal a−1, with the exception of Joen-suu (0.8 μGal a−1). Pettersen (2011) noted that the gravity ratesof change from different literature sources only presenting a fewvalues such as Engfeldt et al. (2006) or Gitlein (2009) deviate nomore than 0.3 μGal a−1 from each other.

In view of the different values for the best and the average trenderror mentioned in the studies above, the sensitivity discussion ofAG measurements will be subdivided into one for the best and theaverage trend error that can be currently achieved in North Americaand Fennoscandia. The values are listed in Table 2. Note that weadopt the error values from different studies. Thus, the errors areconditional on the assumption made for error estimation in therespective studies. In general, the error is calculated by fitting a




Figure 5. Same as Fig. 3, but for Fennoscandia.

linear trend to the data (statistical scatter, standard deviation) and thetrend is mainly assumed to be related to GIA only. Hence, any othercalculation method and/or correction for other contributions (suchas hydrology, atmosphere, ocean loading, local/regional tectonics)will affect the used values.

The accuracy of GRACE and the trend error estimation is, ofcourse, very different from AG, although it is also here well knownthat a longer time span generally decreases the errors. Wahr et al.(2006) give an overview of possible contributions to GRACE errors.They subdivided the errors into two categories: (i) errors in monthlyGRACE gravity field solutions, and (ii) errors due to changes in thetrue monthly mass averages caused by things other than a quantityunder consideration (e.g. GIA or continental water storage). The firstcategory includes measurement, processing and aliasing errors, thesecond depends among other things on the ground track of GRACEin a month (Wahr et al. 2006).

Using GRACE for GIA investigations in North America,Tamisiea et al. (2007) estimated an uncertainty of the trend of atleast 0.115 μGal a−1 for 48 monthly solutions. Paulson et al. (2007)showed errors of at least 0.2 μGal a−1 for 53 monthly solutions.The analysis of Van der Wal et al. (2008) of 60 monthly solu-tions gave errors of at least 0.55 μGal a−1. Note that these errorsinclude contributions due to the removal of hydrological effects.Similar studies have also been pursued for Fennoscandia. Whiletrend estimates from 56 months of observation had an error of0.23 μGal a−1 (Steffen et al. 2008), the error for 69 months alreadydecreased to 0.1 μGal a−1 (Steffen et al. 2010). In both investiga-tions the hydrological effect on the trend has been assumed to benegligible.

In Fig. 2 we show the determined trends of gravity change and theerror for 90 months (2003 July to 2010 December) of GRACE ob-servations in North America and northern Europe. The calculationfollows the approach described in Steffen et al. (2010). The resultsare obtained from GRACE solutions of the Helmholtz-ZentrumPotsdam, Deutsches GeoForschungsZentrum (GFZ) with 400 kmGaussian filter. The maximum error values are 0.11 μGal a−1 inNorth America (Fig. 2c) and 0.10 μGal a−1 in northern Europe(Fig. 2d), which is at most 10 per cent of the maximum GIA signalsin these areas (Figs 2a and b). Tests with solutions of other solutioncentres and filter techniques yielded comparable results. Therefore,these error values will be used in our discussion in Section 5 basedon the assumption that the effect of hydrology in the observationscan be neglected. Currently, hydrological effects can only be cor-rected with hydrological models, which, however, do not provideerror bars and thus an adequate error estimation would be beyondthe scope of this paper.

4 R E S U LT S

The sensitivity of AG measurements in North America to thefour parameters in discussion is presented in Fig. 3. Changingthe ice model from ICE-4G to ICE-5G (Fig. 3a) leads to nega-tive sensitivity values of up to −1.5 μGal a−1. The affected areabasically envelopes Canada east of the Rocky Mountains. Valuesof less than −1 μGal a−1 are found west of Hudson Bay wherethe biggest differences especially in ice thickness between thetwo used models are known (Peltier 2004). A laterally varying




Figure 6. Same as Fig. 3, but for GRACE observations in Fennoscandia.

lithosphere shows distinct areas of sensitivity, for example, northof Vancouver and in Labrador, with values up to −0.2 μGal a−1

on the continent (Fig. 3b). Lower values are only reached in thenorthwest from Baffin Island to Greenland. If the backgroundviscosity is increased at 670 km depth, most of Canada high-lights a sensitivity peaking southeast of the Hudson Bay at about−0.2 μGal a−1 (Fig. 3c). A change from laterally homogeneous toheterogeneous viscosity structures results in a sensitivity between−0.2 and −0.1 μGal a−1 in two large areas south and southwestof Hudson Bay as well as in Labrador and around Prince EdwardIsland (Fig. 3d).

The sensitivity of GRACE observations in North America (Fig. 4)shows similar patterns as the AG sensitivity, but the values changetheir sign. This similarity is a result of the calculation methodof these vertical rates within the modelling, which will be dis-cussed in the next session. In general though, the absolute valuesof sensitivity are up to 50 per cent higher, and thus the affectedareas increase. This can be seen, for example, in the maximumarea east of Hudson Bay for a different ice model (Fig. 4a) andin the southern Canadian part for background viscosity change(Fig. 4c).

In Fennoscandia, the change from ICE-4G to FBKS8 shows twomajor peaks in sensitivity for AG measurements (Fig. 5a). Oneis located in the Scandinavian Peninsula with −0.4 μGal a−1, theother one in central Finland with 0.3 μGal a−1. A laterally varyinglithospheric thickness yields sensitivities exceeding −0.1 μGal a−1

in most parts of the peninsula (Fig. 5b). Whole Scandinavia is en-veloped with values less than −0.1 μGal a−1 when increasing back-ground viscosity below 670 km depth (Fig. 5c). This again confirms

that GIA data in Fennoscandia are sensitive to the viscosity of atleast the shallow part of the lower mantle. Negligible sensitivitiesare found for lateral viscosity changes in the mantle (Fig. 5d).

As for North America, the differences between the sensitivityof AG measurements and GRACE observations in Fennoscandiamainly exists in the changed sign for GRACE (Fig. 6). The patternis comparable but slightly smaller areas are affected.

5 D I S C U S S I O N

For future planning of AG measurements intended to help in GIA in-vestigations it is advisable to look for optimal sites on land in NorthAmerica and Fennoscandia that are sensitive to all four parameterssimultaneously, or, for separation of effects of these parameters, tohighlight areas that are sensitive to only one, two or three of theparameters. Such separation is possible only if these effects are in-dependent and do not interact. For this purpose, we superpose thefour results of Figs 3–6, but only highlighting the sensitivity (inabsolute values) which is above the current values for trend errorscalculated from AG and GRACE measurements (Fig. 7). Based onthe discussion in Section 2, we show the sensitivity for the AG mea-surements for the currently best value and the average (see Table 2)in both North America and Fennoscandia (Figs 7a–d). The sensi-tivity discussion for GRACE (Fig. 7e and f) is based on the upperlimits present in Fig. 2.

Assuming an average value of 0.18 μGal a−1 of AG measure-ments in North America, the gravity rates are already sensitiveto all four GIA parameters (Fig. 7a). Here, Vancouver, parts of theRocky Mountains, a large area west of the Rocky Mountains around




Figure 7. Sensitivity of absolute gravity (a–d) and GRACE (e and f) measurements in North America (a, c and e) and Fennoscandia (b, d and f) above thetrend error of absolute gravity and GRACE measurements to changes in ice model (see text, red area, lines from top left to bottom right), lithospheric thicknessvariations (green, lines from top right-hand side to bottom left-hand side), background viscosity (blue dots), and lateral viscosity variations (pink, horizontallines). Units are μGal a−1. The trend error used is listed in Table 2. If a colour does not appear, then the sensitivity of this parameter either lies in the sea/lakeor is below the trend error.




Hudson Bay and a narrow band in northern USA are well suited toresolve especially the ice model alone. Sensitivity to lithosphericthickness variations encircles western British Columbia, BaffinIsland and Labrador with only small overlaps with other sensitivityareas. Changes in background viscosity present four significant sen-sitive regions in Canada, which, however, overlap by the majoritywith the other areas, especially the ice model. A similar result isfound for lateral viscosity variations. Ice model and lateral litho-spheric thickness variations are thus the best resolvable parametersfor the assumed trend errors.

In Fennoscandia (Fig. 7b), AG measurements are also sensitive toall four GIA parameters for an average trend error of 0.16 μGal a−1.Almost the whole region shows areas sensitive to at least one param-eter. The western part of Fennoscandia, Finland and northern coastlines of the White Sea are sensitive to the chosen ice model. Sensitiv-ity to background viscosity covers the central part of Fennoscandia,mainly overlapping with ice model sensitivity. The sensitivity areafor lithospheric thickness changes overlaps with both ice model andbackground viscosity in the Scandinavian Peninsula making it hardto separate. Lateral viscosity changes may only be significant onnorthern coastlines.

More overlaps are visible in both North America and Fennoscan-dia when assuming the currently best possible gravity trend errors,0.09 μGal a−1 in North America and 0.11 μGal a−1 in Fennoscan-dia, from the measurements. This is clearly related to the fact thatall sensitivity areas become larger and also new sensitive regionsappear with dropping errors. There are a few areas in North Amer-ica which are sensitive to only one parameter (Fig. 7c). Most of theareas show a sensitivity to the ice model. This holds for northernUSA, a narrow band in southern central Canada, in the Yukon Ter-ritory and in the northernmost continental parts of Canada. Areassensitive to lithospheric thickness changes are isolated in Alaska,Yukon, southwestern USA, northeastern Canada and Baffin Island.Background viscosity is only covered in the Rocky Mountains, lat-eral viscosity changes in northern parts of the USA and CanadianMaritime. The other areas are mostly sensitive to two and threeparameters. An overlap of all four sensitivity areas is only found ina small area in Labrador.

The areas of ice model and background viscosity sensitivity dom-inate in Fennoscandia (Fig. 7d). The latter reduces the area that isonly sensitive to lateral viscosity variations in the north. The sensi-tivity to lithospheric thickness variations cannot be isolated and thusdistinguished from other parameters. In general, the ScandinavianPeninsula is mainly sensitive to two or three parameters. Regionssensitive to all four parameters can be found north and west of theGulf of Bothnia.

The sensitivity of the GIA parameters in GRACE observationin North America shows similar patterns as the AG measurementswith best error (Fig. 7e). Interestingly, there is no overlap of allfour parameters. The ice model and background viscosity havethe largest areas sensitive to one single parameter. Lithosphericthickness is isolated in Baffin Island. South of the Hudson Bay andin Labrador three parameters overlap, the rest of Canada is mainlysensitive to two parameters.

The GRACE sensitivity map in Fennoscandia (Fig. 7f) is almostidentical to the one for the best AG error with two exceptions: thearea for ice model sensitivity in northwestern Russia almost van-ishes and lateral viscosity changes are only detectable near Lofotenarchipelago.

The similarity of AG measurements and GRACE patterns is alsofound in comparison to patterns of vertical velocity rates shownby Wu et al. (2010). This is due to fact that terrestrial

( dgdt

)AG

and

space-borne( dg

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)GRACE

gravity rate of change and vertical rate of

deformation(

dhdt

)GPS

for a certain location (φ, λ) are connected by(see e.g. Muller et al. 2012)(

dg

dt

)GRACE

=(

dg

dt

)AG

− γ f

(dh

dt

)GPS

, (1)

with γ f = −3.086 μGal cm−1 the free air gradient. Eq. (1) is used inour modelling and as a consequence GPS, GRACE and AG rates asderived with the modelling are interchangeable predictions. Thus,we cannot take advantage of using multiple techniques, for ex-ample, to check technique-dependent errors and phenomena otherthan GIA. However, model parameters can be verified and improvedwith co-located sites and therefore, multiple techniques are indis-pensable.

6 C O N C LU S I O N S

In this paper, we have studied the sensitivity of terrestrial and space-born gravity measurements in North America and Fennoscandia tofour selected parameters of interest in GIA modelling. The resultsshow that both the terrestrial AG measurements and the GRACEtwin-satellite mission observations sense the four parameters withintheir currently determined trend errors. The best detectable param-eter in both regions is variation of the ice model, which covers alarge sensitivity area and also shows broad regions of no overlapwith sensitivity areas of the other three parameters. Sensitivity areasof lithospheric thickness variation, background viscosity and lateralviscosity variations tend to overlap with ice model sensitivity andeach other. Only a few isolated regions can be identified in bothNorth America and Fennoscandia where only one of these param-eters can be addressed with the measurements. However, this alsodepends on the used trend error. Areas that are only sensitive tolateral viscosity variations appear to be the hardest to detect withgravimetric methods.

Comparing the sensitivity maps with existing AG stations andnetworks (Fig. 1a), there are definitely more stations needed innorthwestern and Arctic Canada. Critical gaps are found in thenorthern parts between the Rocky Mountains and Hudson Bay aswell as in Baffin Island and Labrador. In addition, more stationsare needed to densify the network in the areas of interest. A quickcomparison of Figs 1(a) and (b) (the grey frame in Fig. 1a indi-cates the area size of b) illustrates the different station density inNorth America and Fennoscandia. A quite dense network of sta-tions already exists in Fennoscandia. However, it is unfortunatethat a comprehensive data combination of all measurements so farhas not been published yet. The potential is indicated in the workby Gitlein (2009). An extension of the network to northwesternRussia with a few more sites (in addition to Lovozero station inKola Peninsula, which also needs a continuous occupation) wouldhelp to resolve the parameters addressed in this study. The results ofsuch a full study would provide a comprehensive picture with goodresolution of gravity change in Fennoscandia, and would be usefulfor studies of the Earth’s interior and geodynamic processes. Hence,it would complement the existing BIFROST GPS network (seeLidberg et al. 2010, for more information) and would therefore bean important component of a combined GIA model for Fennoscan-dia as proposed in e.g. Hill et al. (2010) and Muller et al. (2012). Itwould also allow a better correction of the GIA effect in AG mea-surements in surrounding regions such as western Europe, whereslow intraplate vertical deformation may then be monitored (VanCamp et al. 2011).




A complete terrestrial data set would also deliver the groundtruth for GRACE (Muller et al. 2005). The comparability of the twomethods is obvious when comparing the sensitivity maps. GRACEgives almost the same result as AG measurements, which is, as dis-cussed earlier, a result of the calculation method. The coverage isarea-wide, but one has to keep in mind that the accuracy and there-fore the trend error are affected by several overlapping processes inthe geosphere, which cannot be easily separated. Removing oneof the effects may result in higher errors due to the provided errorof the model or data used in the separation. Taking the current trenderror into account, the ice model is the best resolvable parameterwith GRACE. This agrees with findings by Tamisiea et al. (2007),who found that GRACE constrains the ancient ice history, and Vander Wal et al. (2009), who noted that the ICE-5G model (Peltier2004) is too thick west of Hudson Bay. The other three parame-ters also exclusively appear on the sensitivity map, but in smallerand unevenly distributed areas. Nonetheless, the results are readyfor investigation as they present the current GRACE-derived trenderrors.

To sum up, gravity measurements provide an important quantityin GIA investigations. The current accuracy of the measurementsand the calculated errors in the gravity rate of change allow thoroughstudies of glaciation history and the Earth’s structure. GRACE dataare ready to use, but terrestrial measurements, however, need morestations in North America. Moreover, an analysis of the completestation network including a combination of all AG measurementsby different instruments in Fennoscandia is also needed.

A C K N OW L E D G M E N T S

We are grateful for the constructive comments by two anonymousreviewers. We thank Joe Henton and Anthony Lambert (PGC Sid-ney) for helpful discussions. Many thanks also go to Kurt Lambeckfor providing the RSES ice model. The Finite-Element calculationwas performed with the ABAQUS package from Hibbitt, Karlssonand Sorensen Inc. This research is supported by an Operating Grantfrom NSERC of Canada to Patrick Wu and Hansheng Wang is sup-ported by National Natural Science Foundation of China (Grant No.40825012, 41021003), National Key Basic Research Program ofChina (973 Program, grant No. 2012CB957703) and CAS/SAFEAInternational Partnership Program for Creative Research Teams.The figures in this paper are drawn using the GMT graphics pack-age (Wessel & Smith 1998).

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Optimal locations for absolute gravity measurements and sensitivity of GRACE observations for constraining glacial isostatic adjustment on the northern hemisphere