JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, B02406, doi: /2010jb007776, 2011

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2010jb007776, 2011 The influence of decadal to millennial scale ice mass changes on present day vertical land motion in Greenland: Implications for the interpretation of GPS observations Matthew J. R. Simpson, 1 Leanne Wake, 2 Glenn A. Milne, 3 and Philippe Huybrechts 4 Received 15 June 2010; revised 8 November 2010; accepted 22 November 2010; published 10 February [1] We show predictions of present day vertical land motion in Greenland using a recently developed glacial isostatic adjustment (GIA) model, calibrated using both relative sea level (RSL) observations and geomorphological constraints on ice extent. Predictions from our GIA model are in agreement with the relatively small number of GPS measurements of absolute vertical motion from south and southwest Greenland. This suggests that our model of ice sheet evolution over the Holocene period is reasonably accurate. The uplift predictions are highly sensitive to variations of upper mantle viscosity. Thus, depending on the Earth model adopted, different periods of ice loading change dominate the present day response in particular regions of Greenland. We also consider the possible influence of more recent changes in the ice sheet by applying a second ice model; specifically, a surface mass balance (SMB) model, which covers the period 1866 to Predictions from this model suggest that decadal scale SMB changes over the past 140 years play only a small role in determining the present day viscous response (at the sub mm/yr level in most locations for a range of Earth model parameters). High rates of peripheral thinning from 1995 to 2005 predicted using the SMB model produce large elastic uplift rates ( 6 mm/yr) in west and southwest Greenland. This suggests that in some areas close to the ice margin, modern surface mass balance changes have a dominant control on present day vertical land motion. Citation: Simpson, M. J. R., L. Wake, G. A. Milne, and P. Huybrechts (2011), The influence of decadal to millennial scale ice mass changes on present day vertical land motion in Greenland: Implications for the interpretation of GPS observations, J. Geophys. Res., 116,, doi: /2010jb Introduction [2] The ongoing deformation of the solid Earth, in regions of past and present glaciation, records the Earth s response to surface load change. The development of space geodetic techniques over the past two decades has enabled us to image this pattern of deformation to a high degree of precision; Global Positioning System (GPS) measurements are able to determine the rate of present day Earth deformation to within a mm/yr [King et al., 2010]. In North America and Eurasia, GPS observations show that the Earth is deforming in response to past ice mass loss that occurred following the Last Glacial Maximum (LGM, 21 ka B.P.) up until the eventual demise of ice in the early Holocene [e.g., Milne et al., 2001; Calais et al., 2006; Sella et al., 2007]. Present day Earth 1 Geodetic Institute, Norwegian Mapping Authority, Hønefoss, Norway. 2 Department of Geography, University of Calgary, Calgary, Alberta, Canada. 3 Department of Earth Sciences, University of Ottawa, Ottawa, Ontario, Canada. 4 Earth System Sciences and Department of Geography, Vrije Universiteit Brussel, Brussels, Belgium. Copyright 2011 by the American Geophysical Union /11/2010JB deformation in these regions is dominated by the continuing viscous relaxation of the Earth s mantle in response to past ice mass changes. Generally speaking, the highest rates of uplift correspond to areas of thickest ice at the LGM. [3] In areas currently glaciated, like Greenland, the rate of present day deformation is complicated by the additional signal associated with the Earth s elastic response to contemporary ice mass changes. Recent GPS observations, for example, have revealed very high rates of elastic uplift caused by current ice mass loss from outlet glaciers in the southeast of Greenland [Khan et al., 2007] as well as other areas peripheral to the ice sheet [Jiang et al., 2010; Khan et al., 2010]. Thus, the accurate interpretation of GPS data from Greenland requires the elastic and viscous components of the motion to be isolated. Khan et al. [2008] demonstrated one method for achieving this goal: Altimetry and interferometry satellite data [e.g., Rignot and Kanagaratnam, 2006; Stearns and Hamilton, 2007] can be used as a basis to estimate contemporary ice mass change and therefore the corresponding elastic term. If the elastic term is then removed from the observed rate of uplift, we can assume that the remaining signal is the viscous component, which can then be compared to glacial isostatic adjustment (GIA) model predictions [e.g., Fleming and Lambeck, 2004; Peltier, 2004; Simpson et al., 1of19

2 2009] to place constraints on both past ice mass changes and Earth viscosity structure. An alternative approach to that adopted by Khan et al. [2008] involves the reverse procedure; the use of a GIA model to predict and remove the viscous component of the signal so that the residual can be employed to infer contemporary ice mass changes [e.g., Khan et al., 2007, 2010]. Contemporary ice mass variation and the elastic term can also be better constrained using a combination of satellite gravity data and GPS observations [Khan et al., 2010] and/or by extracting accelerations rather than velocities from the GPS time series [Jiang et al., 2010]. Regardless of the approach taken, GIA models have a central role to play in arriving at a robust understanding of contemporary land motion in Greenland observed using GPS. [4] There are only a small number of GPS stations in Greenland that have been operational for more than a few years and have therefore yielded useful results [e.g., Wahr et al., 2001a, 2001b; Dietrich et al., 2005; Khan et al., 2007, 2008, 2010; Jiang et al., 2010]. However, as part of the Greenland GPS Network project (GNET), 51 continuous GPS stations have recently been installed around the periphery of the ice sheet (Figure 1) [Bevis et al., 2009] (also see The number and spatial coverage of GPS observations, therefore, is set to dramatically increase in the coming years, resulting in a far more extensive data set. With this in mind, it seems a timely exercise to revisit the issue of present day vertical land motion in Greenland from a modeling perspective. Several past modeling studies have examined predictions of presentday uplift rates in Greenland [e.g., Le Meur and Huybrechts, 1998, 2001; Huybrechts and Le Meur, 1999; Wahr et al., 2001a, 2001b; Tarasov and Peltier, 2002; Khan et al., 2008]. We build on these works (1) by showing results from a new Greenland GIA model [Simpson et al., 2009] and (2) by considering the influence of recent decadal to century scale ice mass variations on present day uplift rates. [5] This analysis has two main aims. The first aim is to use the recently developed GIA model of Simpson et al. [2009] to generate predictions of present day vertical land motion in Greenland. We show how different aspects of the loading history (in both time and space) contribute to the predicted present day uplift rates. Deconstructing the signal in this manner will be useful when using the model for the future interpretation of GPS observations. We also show the sensitivity of the uplift predictions to changes in Earth model parameters, which has only been partially explored in past studies [Wahr et al., 2001a, 2001b; Khan et al., 2008]. It is well established that predicted present day uplift rates are highly sensitive to changes in Earth viscosity structure [e.g., see Mitrovica et al., 1994a]. The predictions from our GIA model are also compared to some of the existing GPS observations. [6] The second aim of this analysis is to examine the possible influence of ice mass variability over the last century (or so) on present day vertical land motion. It is generally assumed that ice mass change over this time plays a minor role in determining the present day viscous Earth response in Greenland. (Although, in other parts of the world, observed high rates of uplift have been attributed to ice mass loss over the last few centuries [e.g., Larsen et al., 2005; Dietrich et al., 2010].) Indeed, ice mass variation over recent centuries may be important; Ivins and James [2005] showed that predicted present day uplift rates are potentially very sensitive to ice loading variations over the last two millennia (depending on Earth structure). Further, Tarasov and Peltier [2002] demonstrated that submillennial ice mass changes over the last 1000 years may play a significant role in determining the present day Earth response in southwest Greenland. Current Greenland GIA models used to generate uplift predictions are calibrated using observations of relative sea level (RSL) [e.g., Tarasov and Peltier, 2002; Fleming and Lambeck, 2004; Simpson et al., 2009]. It is interesting to note that even the highest quality RSL data used in these modeling studies cannot resolve changes over several centuries (or less) [e.g., Long et al., 1999, 2003, 2006, 2008; Bennike et al., 2002; Sparrenbom et al., 2006]. Thus, for existing Greenland GIA models, there is little constraint on changes over decadal to century timescales, and so this has clear implications for interpreting uplift rates correctly. Recent analyses, however, have considered changes of the Greenland Ice Sheet (GrIS) over the last 100 years or so [e.g., Huybrechts et al., 2004; Hanna et al., 2005; Rignot et al., 2008; Ettema et al., 2009; Wake et al., 2009]. Therefore, improved models of recent ice sheet behavior are available to allow us to consider what role ice mass changes over the past few centuries play in determining the present day Earth response. Of these new models, we use the surface mass balance (SMB) reconstruction of Wake et al. [2009], which covers the period 1866 to Data and Model Description 2.1. GPS Observations [7] Figure 1 shows the locations of the GPS stations established as part of the GNET project and also those considered in past studies. Initial GPS work in Greenland was conducted by Wahr et al. [2001a]; they analyzed data from Kellyville and Kulusuk and determined uplift rates of 5.8 ± 1 and 2.1 ± 1.5 mm/yr, respectively. The high rate of subsidence observed at Kellyville was attributed to a neoglacial regrowth of the southwest margin of the GrIS over the last 3 to 4 kyr. A following study included GPS data from Thule, in northwest Greenland, which determined an uplift rate of 0.7 ± 0.9 mm/yr [Wahr et al., 2001b]. Dietrich et al. [2005] showed results from a GPS network of 10 sites, spread across the ice free coast of southwest Greenland. Campaign style (repeated) observations were made at these sites; the locations of which are shown by the circles in Figure 1. Data from the central site (Kangerlussuaq), situated close by to Kellyville (see Figure 1), produced an absolute uplift rate of 3.1 ± 1.1 mm/yr. They also computed relative rates of uplift and established that the southwest region has an east west gradient of present day vertical Earth motion. Areas close to the ice margin are subsiding but this changes to uplift as one moves west toward the outer coast [Dietrich et al., 2005, Figure 8]. This pattern of response was also ascribed to a readvance of the GrIS in southwest Greenland over the last 3 to 4 ka. [8] More recently, Khan et al. [2008] extended the work of Wahr et al. [2001a, 2001b] by reanalyzing longer time series from Kellyville, Kulusuk and Thule. They also had access to data from GPS stations at Scoresby Sund in east Greenland, Qaqortoq in the south and data from a tide gauge at Nuuk, which is on the southwest coast. We show the tide 2of19

3 Figure 1. Locations of GPS sites discussed in the text. Figure 1 (left) is a zoom of boxed area in Figure 1 (right). Observations made by Khan et al. [2008] and Dietrich et al. [2005] are marked by stars and circles, respectively. Inverted triangles mark the locations of the newly established GNET sites. In reality, the tide gauge and GPS campaign position at Nuuk lie in the same location; the star has been moved slightly to make sure both symbols are distinguishable. gauge and GPS locations (Figure 1, stars) and corresponding secular uplift rates (Table 1) determined by Khan et al. [2008]. Note that the error terms reported in Table 1 are based on one sigma formal errors, but include other effects to provide a more realistic error estimate [Khan et al., 2008]. The results from the GPS data reanalysis by Khan et al. [2008] differ significantly from the earlier results of Wahr et al. [2001a, 2001b], most notably for Kellyville. The rate determined for Kellyville is also different to that obtained by Dietrich et al. [2005] for the nearby station ( 20 km) at Kangerlussuaq. These differences have been attributed to the use of different reference frames for these separate analyses and/or the use of different processing techniques [Dietrich et al., 2005; Khan et al., 2008]. Furthermore, Khan et al. [2008] corrected for elastic uplift arising from present day ice mass change when calculating secular uplift rates. They account for the large contemporary ice mass loss occurring principally at the major outlet glaciers of Helheim, 3of19

4 Table 1. Observed and Predicted Absolute Rates of Uplift at the GPS Sites and Tide Gauge at Nuuk a Observed Uplift Rates Predicted uplift rates (mm/yr) GPS Location Corrected for Elastic Term (mm/yr) Huy2 (Best Fit Earth Model) Huy2 (Best Fit East Earth Model) Kellyville 1.2 ± NA Nuuk 2.2 ± NA Qaqortoq 0.3 ± NA Kulusuk 0.4 ± Scoresby Sund 0 ± Thule 3.6 ± NA a Observed rates are as analyzed by Khan et al. [2008]. See Figure 1 for sites locations. The best fit Earth model is characterized by a 120 km thick lithosphere, upper mantle viscosity of Pa s and lower mantle viscosity of Pa s. The best fit Earth model for regions across east Greenland is characterized by a 120 km thick lithosphere, upper mantle viscosity of Pa s, and lower mantle viscosity of Pa s [see Simpson et al., 2009]. NA, not applicable. Kangerlussuaq and Jakobshavn Isbrae and also from coastal glaciers in the southeast [see also Khan et al., 2007]. [9] The very latest work has shown that significant accelerations of vertical land motion in Greenland have occurred during the past decade [Jiang et al., 2010; Khan et al., 2010]. Vertical accelerations signify an elastic Earth response and thus can be used to infer present day ice mass change [e.g., Jiang et al., 2010]. Jiang et al. [2010] reexamined GPS data from Kellyville, Qaqortoq, Kulusuk and Thule, using the same time series as Khan et al. [2008], but, as opposed to this latter study, found an acceleration of uplift at these sites. Indeed, they indicate that at all of these locations the Earth is now rapidly uplifting, even if it was subsiding at earlier times. As discussed in Jiang et al. [2010], this methodology can potentially be used to better constrain the viscous term. [10] In this study we analyze only vertical rates of uplift as observed horizontal rates are, as yet, unpublished; furthermore, determining horizontal rates requires a correction for plate motion. Given that there is a significant range of past solutions for absolute uplift rates in Greenland, we are cautious when comparing GPS data to model results. As mentioned, this range may be attributable to the use of different realizations of the global reference frame in the separate analyses [e.g., see also Dietrich et al., 2005, Table 6]. Our model generates predictions in the center of mass of the solid Earth reference frame (CE). Thus, in terms of absolute rates, we focus on the results presented by Khan et al. [2008] as they provide rates which are in a realization of the CE frame [Argus, 2007] and they correct for the contemporary elastic term (i.e., these results can be directly compared with our GIA model predictions). We also compare our results to the relative rates presented by Dietrich et al. [2005], who give rates in the IGb00 frame of Ray et al. [2004]. In this case, it is important to note that for vertical velocity differences within a regional network, reference frame uncertainties are largely canceled out [Dietrich et al., 2005]. We can therefore use these relative rates as an additional model constraint Description of the GIA Model [11] We generate predictions of present day vertical land motion using the Greenland GIA model of Simpson et al. [2009], which, as discussed in section 2.1, uses the center of mass of the solid Earth reference frame. In general terms, the GIA model employed in this study is composed of three components: a model of grounded ice evolution (for Greenland and other ice sheets), a sea level model to compute the redistribution of ocean mass for a given ice and Earth model, and an Earth model to compute the solid Earth deformation associated with the ice ocean loading history. Each of these components is described in this section The Ice Sheet Models [12] Typically, GIA models use observations of relative sea level change in the near field of past or presently glaciated regions to quantitatively infer the loading history of grounded ice sheets [e.g., Tushingham and Peltier, 1991; Peltier, 1994; Lambeck et al., 2006]. Note that in most GIA studies, this calibration procedure involves the application of ice models that include little in the way of glacier or ice sheet physics (i.e., no treatment of surface mass balance or ice flow; at best simplistic parabolic equations are used to determine the geometry of the past ice load). This is not the case for the GIA model of Simpson et al. [2009], which, following the methodology of Tarasov and Peltier [2002, 2004], was developed using a relatively sophisticated, threedimensional ice sheet model. The ice model of Simpson et al. [2009] was calibrated to 214 observations of RSL as well as field data on past ice extent: the resultant Greenland deglaciation history is hereafter referred to as Huy2. Note that the background (non Greenland) component of the ice model is represented by the ICE 5G model [Peltier, 2004]. [13] The three dimensional thermomechanical ice sheet model used in developing Huy2 is based on that detailed by Huybrechts [2002]. There are 31 layers in the vertical and a horizontal grid resolution of 20 km, which corresponds to horizontal grid cells for Greenland. This ice sheet model simulates the evolution of the Greenland ice sheet over the last two glacial cycles in response to changes in past climate and eustatic sea level (the temperature forcing is inferred from the GRIP d 18 O ice core record [Dansgaard et al., 1993]). The model is composed of three parts; calculating ice dynamics, solid Earth (isostatic) response and surface mass balance (see Huybrechts and de Wolde [1999] for a full description). Ice dynamics are simplified to the shallow ice approximation for large ice masses [Hutter, 1983]. Grounded ice flows through internal deformation and basal sliding. Longitudinal stress gradients are ignored and grounding line dynamics are not modeled explicitly. Instead, the position of the marine margin is diagnosed from a simple calving parameterization. The Earth model is typical of that used in ice sheet modeling studies; it has an asthenosphere with a single relaxation time (3000 years) overlain by an elastic lithosphere [Le Meur and Huybrechts, 1996]. 4of19

5 It should not be confused with the Earth model employed in the GIA modeling presented in this analysis (described in section 2.2.3) which is significantly more complex. Overall mass balance is considered as the net contribution of the mass input (snowfall accumulation) and output (meltwater runoff and calved ice) to the ice sheet system. Meltwater runoff is calculated using the positive degree day method [e.g., Braithwaite, 1995] which takes the melt rate to be proportional to the surface air temperature (the model makes use of the recalibrated runoff and retention model of Janssens and Huybrechts [2000]). [14] In the latter part of the analysis (section 4.2) we go on to consider the model of Wake et al. [2009], which is a surface mass balance reconstruction of the GrIS covering the period 1866 to To calculate SMB, Wake et al. [2009] use a similar method to Huy2 (see above) except that the model was forced using monthly temperature and annual precipitation data. From 1866 to 1957 they input climatic data from Box et al. [2006, 2008] and from 1958 to 2005 data from Hanna et al. [2008]. The horizontal grid resolution is 5 km, which corresponds to horizontal grid cells for Greenland. Thus, in comparison to Huy2, the Wake et al. [2009] model benefits by having both a more accurate and higher resolution climate forcing and a finer model resolution (in both time and space). Note, however, that potential recent ice loading changes from dynamic flow variations of outlet glaciers are not part of the Wake et al. [2009] model The Sea Level Model [15] The sea level model predicts the vertical deflection of both the ocean surface and the Earth s solid surface due to changes in ice ocean mass configuration. Height shifts of the ocean surface are determined by computing perturbations to the geopotential. Perturbations to the rotation vector and the resulting feedback of this forcing on sea level and land motion are computed as described by Milne and Mitrovica [1998] and Mitrovica et al. [2001]. Global ice/water mass is conserved in the model. For more detail on the sea level algorithm used to compute the ocean loading in this analysis, see Mitrovica and Milne [2003] and Kendall et al. [2005] The Earth Model [16] Following Peltier [1974], the GIA ice ocean forcings are convolved, in space and time, with the impulse response Love numbers to give the solution for a generalized surface load. A Maxwell viscoelastic rheology is used and the Earth model is spherically symmetric, self gravitating and compressible. The elastic and density structure are taken from seismic constraints [Dziewonski and Anderson, 1981] and depth parameterized with a resolution of 15 to 25 km. The radial viscosity structure is depth parameterized more crudely in to three layers: an elastic lithosphere (i.e., very high viscosity values are assigned), an isoviscous upper mantle bounded by the base of the lithosphere and the 670 km deep seismic discontinuity, and an isoviscous lower mantle continuing below this depth to the core mantle boundary Calculating Vertical Land Motion Rates [17] For the Huy2 GIA loading computations, the iceocean loading increments are every 6000 years from 122 to 32 ka B.P., every 1000 years from 32 to 17 ka B.P. and every 500 years from 17 to 0.5 ka B.P. The final loading step before present is 100 years B.P. (Note that the timing of the loading increments is the same as with the ICE 5G model [Peltier, 2004].) To compute vertical land motion, we adopted an algorithm based on that described by Mitrovica et al. [1994b]. Uplift rates are calculated over the last loading step prior to present day (i.e., the last 100 years). Thus, the elastic component of land motion is computed from the last 100 years of averaged ice thickness changes and therefore will not reflect transient changes during this period (see also section 4.1). For the Wake et al. [2009] model, which covers the period 1866 to 2005, ice loading changes are discretized every 10 years for input to the GIA model. In this case, the elastic term is calculated using ice loading changes from 1995 to 2005 (see also section 4.2). The reader should note that as some of the ice loading changes are highly localized, this leads to a considerable influence of the Gibbs phenomenon in the computed elastic component of the land motion (this is evident in Figures 2, 7b, 8b, 9b, and 9c). Spherical harmonic expansions were truncated at degree and order 256 for the Huy2 calculations and 512 for the Wake et al. [2009] calculations. 3. Uplift Predictions Generated Using the Huy2 Deglaciation History [18] In this section we address the first aim of our analysis and use the Huy2 ice history to generate predictions of present day vertical land motion in Greenland. We first show the total viscoelastic signal, which includes the viscous response to past changes as well as the elastic response to contemporary changes (section 3.1). To aid in our interpretation of this signal, we show how different aspects of the loading history (in both time and space) contribute to the predicted present day uplift rates (sections 3.2 and 3.3). We also show the large sensitivity of the uplift predictions to changes in Earth model parameters (section 3.4). Finally, results from sections 3.2 to 3.4 are used to interpret the existing GPS observations (section 3.5). (Uplift predictions for the GNET sites, shown in Figure 1, are not discussed here but are included in Table S1 in the auxiliary material.) 1 [19] The reader should note that the predictions of presentday uplift shown in sections are generated using the Huy2 ice loading history with its corresponding best fit Earth model. This Earth model produced the best fit to the sea level data considered by Simpson et al. [2009] and is characterized by a 120 km thick lithosphere, an upper mantle viscosity of Pa s and a lower mantle viscosity of Pa s. We recognize that using RSL data to constrain a GIA model is a nonunique inversion problem and, therefore, there is an inherent trade off when determining Earth structure and the ice history [e.g., Peltier, 1994; Lambeck et al., 1998] Predicted Present Day Uplift Rates From the Huy2 Model [20] Figure 2 shows predicted present day uplift rates generated using the complete Huy2 ice loading history (122 ka B.P. to present day) with its corresponding best fit Earth model. This prediction also takes into account changes in non Greenland ice (the ICE 5G model of Peltier [2004]) and the ocean load. 1 Auxiliary materials are available in the HTML. doi: / 2010JB of19

6 Figure 2. Predicted present day vertical crustal velocities (mm/yr) generated using the Huy2 ice history, including non Greenland ice evolution (ICE 5G) and ocean load changes. The adopted Earth model is characterized by a 120 km lithosphere, an upper mantle viscosity of Pa s, and a lower mantle viscosity of Pa s. Observations made by Khan et al. [2008] and Dietrich et al. [2005] are marked by stars and circles, respectively (predictions for these locations are shown in Table 1 and Figure 6). [21] Inspection of Figure 2 shows the Earth is largely uplifting across the north and east of Greenland, with highest rates of uplift in the northeast that are in excess of 4 mm/yr. In contrast, the southwest is subsiding, with the lowest rates around 5 mm/yr. Generally, we find the Huy2 best fit prediction exhibits a pattern of response broadly similar to that produced by the ICE 5G(VM2) global model of Peltier [2004] [Khan et al., 2008, Figure 9]. The term VM2 denotes the viscosity profile that accompanies the ICE 5G ice model. In comparison to our best fit Earth model the VM2 profile has, broadly speaking, similar values for upper mantle viscosity and higher values (factor of 2 to 3 for most depths) for lower mantle viscosity. Note that the Greenland component of the ICE 5G model is represented by the model of Tarasov and Peltier [2002]. However, although the spatial pattern is similar, the magnitude of our predictions are somewhat smaller than those generated using ICE 5G(VM2) Stages of Post LGM Ice Load Change in Greenland [22] Le Meur and Huybrechts [1998] showed how the viscous and elastic contributions to predicted present day uplift rates in Greenland can be considered separately. Figure 3a is a plot of the present day viscous uplift rate generated using the complete ice load history of the Huy2 Greenland model (122 ka B.P. to present day). To better understand how the ice load history produced this result, we examine how different periods of post LGM ice evolution contribute to the present day rate of viscous deformation (Figures 3b 3e). In other words, we show how specific periods of past ice loading influence vertical land motion today. (We address the elastic term in section 4.) Note that the predictions shown in Figure 3 are generated using only Greenland ice and do not account for ocean load changes. [23] Figure 3b shows that GrIS mass changes between the LGM and beginning of the Holocene (the period 21 to 10 ka B.P.) generate present day vertical velocities which are not much larger than ±1 mm/yr. At the LGM, the Huy2 ice model has a volume of 4.1 m excess ice equivalent sea level (i.e., relative to present day, the modeled LGM ice sheet contains an increased volume which is equivalent to a global sea level change of 4.1 m) [Simpson et al., 2009]. This is larger than previous estimates [e.g., Clark and Mix, 2002; Fleming and Lambeck, 2004]. The larger LGM volume is based on new evidence which indicates that the ice sheet grounded farther out on the continental shelf in the east [Evans et al., 2002, 2009; Kuijpers et al., 2003; O Cofaigh et al., 2004; Jennings et al., 2006; Wilken and Mienert, 2006; Håkansson et al., 2007; Long et al., 2008; Roberts et al., 2008]. Subsequent to the LGM, the modeled ice sheet increases in volume and reaches its maximum post LGM volume at 16.5 ka B.P.; when it contains 4.6 m excess ice equivalent sea level [Simpson et al., 2009]. The volume is predicted to be a maximum at this time as increased accumulation rates in Greenland [Cuffey and Clow, 1997] still outweigh the increased ablation from rising temperatures. The resultant thickening of the central dome produces a central region of subsidence (Figure 3b). The modeled marine retreat of GrIS begins around 12 ka B.P. and is driven by rising sea levels [Simpson et al., 2009]. The marine breakup occurs very rapidly so that ice sheet is inland of the present daycoastlineby10kab.p.[bennike and Björck, 2002]. This retreat produces a belt of uplift around the coastline of Greenland (see Figure 3b). [24] Once land based, the Huy2 ice model follows a pattern of continuous but slower Holocene retreat [Simpson et al., 2009]. This is largest and most well recognized in now ice free areas of southwest Greenland [e.g., van Tatenhove et al., 1995, 1996]. Figure 3c shows that for ice mass changes between 10 and 4 ka B.P., the largest contribution to present day vertical velocities is in the southwest. In this region the plot shows a bull s eye of uplift that exceeds 6 mm/yr. This retreat, and associated uplift, can be attributed to the reaction of the ice sheet to the Holocene Thermal Maximum. This occurred, broadly, between 9 and 5 ka B.P. in Greenland [Kaufman et al., 2004], over which time temperatures were 2.5 C warmer than at present [Dahl Jensen et al., 1998]. In response to this warming the 6of19

7 Figure 3. Predicted present day vertical crustal velocities (mm/yr) generated using the Huy2 ice history only, i.e., no non Greenland ice or ocean load changes are included. Illustrations of how different periods of past loading contribute to the present day viscous Earth response for (a) the full ice model history from 123 ka B.P. to present, (b) 21 to 10 ka B.P., (c) 10 to 4 ka B.P., (d) 4 to 1 ka B.P., and (e) 1 ka B.P. to present. The Earth model is the same as that used to generate Figure 2. modeled ice sheet reduces in size and reaches a minimum post LGM volume between 4 and 5 ka B.P. (with a smaller volume of 0.17 m ice equivalent sea level relative to the present ice sheet). In some areas the ice margin retreats behind its present day position, most notably in the southwest sector of Greenland where the retreat is as large as 80 km [Simpson et al., 2009]. A smaller retreat in the north produces uplift rates of around 2 mm/yr (Figure 3c). 7 of 19

8 Figure 4. Predicted present day vertical crustal velocities (mm/yr) generated using the non Greenland components of the ICE 5G model and corresponding ocean load changes. The Earth model is the same as that used in Figure 2. [25] Following the Holocene Thermal Maximum cooling occurred and the GrIS underwent a neoglacial regrowth [Kelly, 1980; Weidick et al., 1990] before reaching its present day state. Modeled Huy2 ice mass change between 4 ka B.P. and present day thus marks a switch from retreat to regrowth of the ice sheet. The neoglacial readvance of the GrIS in the southwest over this period generates present day subsidence rates in excess of 10 mm/yr. In Figure 3, we partition this response into that for the period 4 to 1 ka B.P. (Figure 3d) and 1 to 0 ka B.P. (Figure 3e). Results for the latter period show that, even for this relatively short loading period, the contribution to the present day signal is significant with rates reaching a magnitude of up to 3 mm/yr. [26] Generally speaking, results from the Huy2 model suggest the following: The present day viscous Earth response in the north of Greenland reflects the ice sheet s early to mid Holocene evolution, while vertical rates in the east tend to reflect changes from the LGM to beginning of Holocene period. The present day viscous signal in the southern sectors of Greenland (especially in the southwest) strongly reflects ice thickness changes throughout the Holocene period and, in particular, the neoglacial Non Greenland Ice Load Changes [27] Past GIA modeling studies have shown that non Greenland ice load change significantly influenced land motion in Greenland over the last 10 ka [Fleming and Lambeck, 2004; Simpson et al., 2009]. Thus, it is not surprising that non Greenland ice load change also plays a role in determining present day uplift rates in Greenland. Previous studies have examined this issue using predecessors of the ICE 5G model; Wahr et al. [2001a, 2001b] showed results from the ICE 3G model [Tushingham and Peltier, 1991], and Tarasov and Peltier [2002] showed results from the ICE 4G model [Peltier, 1994]. [28] Figure 4 shows predicted present day uplift rates generated using only the non Greenland ICE 5G ice history [Peltier, 2004]. In general, we find that the pattern of response is broadly similar to that shown in the earlier investigations. Uplift rates in Greenland are generally less than ±1 mm/yr. In west and ice free southwest Greenland the Earth is subsiding, with rates here reaching as low as 1.5 mm/yr. This response is due to the collapse and migration of a forebulge developed during the evolution of the North American ice sheets. It is worth noting that the nature of land motion associated with forebulge collapse is strongly controlled by the adopted mantle viscosity structure [e.g., Peltier, 1974; Wu and Peltier, 1982; Mitrovica et al., 1994a]. In the northwest of Greenland the solid surface is uplifting as a result of past ice mass loss on Ellesmere Island Sensitivity of Uplift Predictions to Changes in Earth Viscosity Structure [29] Figure 5 shows the range in the predicted present day uplift rates for changes in Earth model parameters. For this, we use the Huy2 ice loading history (122 ka B.P. to present day). The prediction also takes into account non Greenland ice (the ICE 5G model of Peltier [2004]) and the ocean load. All changes were made relative to a reference Earth model which has intermediate parameter values: a 96 km thick lithosphere, upper mantle viscosity of Pa s and lower mantle viscosity of Pa s. Each Earth model parameter was varied independently; lithospheric thickness from 71 to 120 km (Figure 5a), upper mantle viscosity from to Pa s (Figure 5b) and lower mantle viscosity from to Pa s (Figure 5c). The range in parameter values is the same as explored by Simpson et al. [2009]. [30] The results shown in Figure 5 indicate that the predictions are strongly dependent on the adopted Earth model. The predictions appear most sensitive to changes in upper mantle viscosity structure (Figure 5b); the range is largest (over 12 mm/yr) in the southwest where modeled ice thickness changes during the Holocene are larger than anywhere else in Greenland (see section 3.2. and Simpson et al. [2009]). This occurs because an Earth model with a relatively weak upper mantle ( Pa s) will reflect late Holocene ice mass changes (i.e., the neoglacial regrowth of the GrIS in that region over the last 4 ka) and predict subsidence. Whereas, an Earth model with a relatively stiff upper mantle (10 21 Pa s) is more sensitive to ice ocean loading changes that occurred between the LGM and early Holocene and, therefore, predict uplift (figures not shown). In some coastal and now ice free areas of Greenland, we 8of19

9 Figure 5. The range in predicted present day uplift rates (mm/yr) generated using the Huy2 ice history and a range of Earth models. Earth model parameters were varied independently for (a) lithospheric thickness, (b) upper mantle viscosity, ands (c) lower mantle viscosity (see text for details). find that the predictions are also sensitive to changes in lithospheric thickness (Figure 5a). The northwest coast is also sensitive to variations in lower mantle viscosity values (Figure 5c), this sensitivity appears to be associated with the forebulge of the North American ice sheets. Uplift rates in central Greenland appear equally sensitive to changes in all the Earth model parameters. These results are broadly comparable to Earth model sensitivities shown in studies of the Antarctic Ice Sheets [Ivins et al., 2000; Ivins and James, 2005] Comparison of Predicted Present Day Uplift Rates From the Huy2 Model to the GPS Data [31] Table 1 shows observed secular uplift rates (corrected for the contemporary elastic term) from the GPS receivers and tide gauge at Nuuk analyzed by Khan et al. [2008]. Errors in the estimated elastic correction, however, could influence the observed secular rates significantly. For example, it is in southeast Greenland where the largest contemporary ice mass loss has been observed [e.g., Rignot and Kanagaratnam, 2006]. Khan et al. [2008] calculate the elastic uplift resulting from this recent mass loss to be 5.6 mm/yr for the GPS site at Kulusuk. This elastic signal is removed from the GPS data to determine an observed secular uplift rate of 0.4 mm/yr. We note that the latest work of Jiang et al. [2010], in which accelerations are extracted from the GPS time series, suggests a different elastic response. Thus, uplift rates (i.e., those comparable to GIA model predictions) calculated using the methodology of Jiang et al. [2010] will give different results to the previous analyses. For comparison with the observations of Khan et al. [2008], rates of uplift generated using the Huy2 model and its corresponding best fit Earth model are also shown in Table 1. [32] At Kellyville and Nuuk, the Huy2 best fit model predicts subsidence of 0.73 and 1.94 mm/yr, respectively; these results are within error of the observations. We note that if we consider the viscous term only (i.e., ignore the elastic component of land motion which is computed from the last 100 years of averaged ice thickness changes), then for Kellyville and Nuuk the model predicts vertical rates of 1.19 and 2.11 mm/yr, respectively. These predictions are therefore in better agreement with the observed values (see Table 1). Overall, our results suggest that the Huy2 model of Holocene ice evolution in southwest Greenland, with a readvance of up to 80 km over the last 4 ka, is reasonably accurate. In their analysis, Khan et al. [2008] compared their GPS observations from across Greenland to predictions from the ICE 5G(VM2) model of Peltier [2004]. They showed that the ICE 5G(VM2) model overestimates subsidence in southwest Greenland which leads them to suggest that the ICE 5G modeled readvance that occurs from 8 ka B.P. in southwest Greenland is too large or mistimed. In the south of Greenland at Qaqortoq, the Huy2 best fit model predicts subsidence of 0.73 mm/yr; this is also within error of the observations ( 0.3 ± 1.1 mm/yr). Huy2 predicts subsidence in this area as the modeled ice margin undergoes a read- 9of19

10 Figure 6. Relative rates of uplift across southwest Greenland. The observations of Dietrich et al. [2005] are marked by vertical error bars (which denote the RMS error value). The predictions of the Huy2 best fit Earth model (see Figure 2) are marked by dark gray squares. The predictions made for the hybrid Huy2 Wake model (using the Huy2 best fit Earth model) are marked by the light gray crosses (see sections 4.3 and 4.4). vance of 20 km over the last 4 ka.khan et al. [2008] indicate that a similar sized 33 km readvance of the Qassimuit lobe during the past 3 ka is required to reconcile data model misfits between the ICE 5G(VM2) model and their GPS observations. [33] In southeast Greenland at Kulusuk, the Huy2 best fit model predicts uplift of 0.41 mm/yr; this is within error of the observations which indicate a slight subsidence of 0.4 ± 1.1 mm/yr. Simpson et al. [2009] showed that the RSL data from across the east Greenland coast favor a distinctly different Earth model to that determined for the Huy2 best fit model (i.e., the Earth model which gives best fit to the complete RSL data set). Thus, we also show in Table 1 predicted uplift rates using the east Greenland best fit Earth model, which is characterized by a 120 km thick lithosphere, upper mantle viscosity of Pa s and lower mantle viscosity of Pa s (as before, viscosity changes only as a function of depth with this model). For Kulusuk, the Huy2 east best fit model predicts subsidence of 1.23 mm/yr; this result is just within the error of the observed value of 0.4 ± 1.1 mm/yr. At Scoresby Sund in east Greenland, the Huy2 best fit model predicts uplift of 1.54 mm/yr; too large when compared to the observed value of 0 ± 1.1 mm/yr. In comparison, the Huy2 east best fit model predicts subsidence of 1.04 mm/yr for Scoresby Sund; in this case the model slightly underpredicts the observed uplift velocity. We note that the Huy2 model is constrained by only a single RSL reconstruction in this area [Long et al., 2008], which remains the only RSL data available along the entire southeast coast. [34] At Thule in northwest Greenland the Huy2 best fit model underpredicts uplift by 4 mm/yr. A similar discrepancy was found for the ICE 5G(VM2) model, which suggests that for both models past ice thicknesses are insufficient and/or the timing of maximum ice extent is inaccurate in this region [Khan et al., 2008]. In the Huy2 model, ice extends only to the axis of Nares Strait at the LGM, although observations have shown Greenland and Ellesmere Island ice coalesced at this time [England, 1999]. It is also possible the GrIS extended farther onto the continental shelf west of Thule at the LGM and this may explain the misfit between the GPS data and our predictions. A recent analysis of ice cores has shown that the ice sheet in northwest Greenland experienced a large elevation decrease during the Holocene, which strongly supports this hypothesis [Vinther et al., 2009]. It is also worth noting that the Huy2 model is not well constrained in the northwest as the temporal coverage and height precision of the RSL data in this region is poor [Bennike, 2002; Simpson et al., 2009]. [35] On considering the observations of Dietrich et al. [2005] we find that the Huy2 best fit model does not show agreement to most of the data. Figure 6 shows their observed and our predicted relative rates of uplift for the network of GPS sites in southwest Greenland. As an example, observations show that relative to Sisimiut (SIS1) on the outer coast, the GPS site at Kangerlussuaq (KAN1) is subsiding by 4.1 mm/yr. For these same sites Huy2 predicts a far smaller relative subsidence rate of 0.28 mm/yr. This could suggest that some aspect of the modeled ice sheet regrowth in the southwest is inaccurate. Although predicted relative rates of uplift for specific GPS sites are not in agreement with the observations, our prediction (Figure 2) exhibits a similar east west pattern as shown by Dietrich et al. [2005, Figure 8]. We note that our Earth model sensitivity study (section 3.4) shows that uplift rates in southwest Greenland are strongly dependent on the adopted value of both the lithospheric thickness and upper mantle viscosity. A reduction of either of these parameters, from our best fit values, will improve the fit to the relative observations of Dietrich et al. [2005]. 4. The Influence of the Past 100 Years of Ice Load Change on Present Day Uplift Rates [36] As outlined in the Introduction, the second aim of this analysis is to examine the possible influence of ice mass variability over the last century (or so) on present day vertical land motion. We begin by examining the Huy2 model [Simpson et al., 2009]. As mentioned in the model description, the 100 year B.P. ice ocean loading increment marks the last time step prior to present day for this GIA model (over which uplift rates are calculated). For the purpose of comparison with Huy2, we also show uplift predictions for the Wake et al. [2009] surface mass balance reconstruction, which covers the period 1866 to 2005 and is forced by more accurate climate data The Huy2 Model (Past 100 Years) [37] As with other millennial scale ice sheet models, the temperature record used to force Huy2 is derived from ice core d 18 O isotope data. The time resolution of the GRIP d 18 O data [Dansgaard et al., 1993] as input to the ice model is 100 years and so subcentury scale surface mass balance (SMB) variability is not captured. For Huy2, the average rate of ice volume change over this period is 16 km 3 /yr; indicating that the ice sheet is in negative mass balance. 10 of 19

11 Figure 7. (a) Predicted present day vertical crustal velocities (mm/yr) generated from the Huy2 model for the past 100 years of ice load change (the last time step prior to present day in the GIA model). The viscous response is shown for our best fit Earth model (as used to generate Figure 2). (b) The elastic component of the present day response. (Note the different scale bars used.) Modeled ice thickness changes over the last 100 years are mostly less than ±20 m; the spatial pattern is characterized by accumulation of <10 m in the interior with ice mass loss around the majority of the margin. In some marginal areas this ice thinning is as large as 80 to 100 m; the most extensive and largest negative changes are in central west Greenland. The largest mass gain is in southwest Greenland, ice thickness increases here are between 20 and 40 m (we do not show a figure of these spatial changes here). Previous studies that have used millennial scale ice sheet models to predict the most recent evolution of the GrIS have shown similar patterns of ice thickness change [e.g., Huybrechts, 1994; Huybrechts et al., 2004]. The Huy2 model exhibits essentially the same pattern of ice thickness change as shown by Huybrechts et al. [2004, Figure 8a] This is not surprising as the Huy2 model is adapted from the ice model presented by Huybrechts [2002] and we would not expect the ice sheet s evolution over the last 100 years to differ significantly from these earlier results. [38] Modeled ice thickness changes over the past 100 years are thought to largely reflect the response of the GrIS to increased temperatures following Little Ice Age cooling [Huybrechts, 1994]. It should be noted that predicted ice thickness changes over the last 100 years, to some extent, will also reflect longer term changes to the GrIS. It is well accepted that the ice sheet is still reacting to past ( 10 ka B.P.) climate change [e.g., Abe Ouchi et al., 1994; Huybrechts, 1994; Huybrechts and Le Meur, 1999]. Indeed, it has been suggested that the thickening that occurs in southwest Greenland may represent a long term ice dynamic trend arising after the last deglacial transition [Huybrechts, 1994]. For the Huy2 model, it is possible that some part of this thickening may also be due to the continued recovery of the GrIS following the Holocene Thermal Maximum. However, we note that Huybrechts [1994] demonstrated that the ice sheet s evolution over the last 100 years appears insensitive to this period of warming. [39] Figure 7 shows both the elastic and viscous components of uplift generated using the last 100 years of ice load change in the Huy2 model (to clarify, these predictions do not take into account changes in non Greenland ice or ocean load). The pattern of Earth response broadly reflects the ice thickness changes as detailed above. Figure 7a shows the pattern of viscous response for the Huy2 best fit Earth model; predicted uplift rates are around ±0.2 mm/yr. We also examined the viscous response for an Earth model with a relatively weak upper mantle of Pa s (figure not show). In this case, the predicted pattern is the same as in Figure 7a, but rates are around ±1.2 mm/yr. Figure 7b shows that the elastic response to modeled ice mass changes over the last 11 of 19

12 Figure 8. Predicted present day vertical crustal velocities (mm/yr) generated using the surface mass balance reconstruction of Wake et al. [2009] with a steady state ice dynamic field. (a) The viscous response to ice loading changes from 1866 to 2005 for our best fit Earth model (as used to generate Figure 2). (b) The elastic response to ice loading changes from 1995 to (Note the different scale bars used.) century is around ±2 mm/yr (an order of magnitude larger than the viscous response for the Huy2 best fit model). Note that this is the elastic component of the total viscoelastic predicted signal shown in Figure The Wake et al. [2009] Model [40] It is important to note that SMB values shown by Wake et al. [2009] are presented as anomalies with respect to the 1961 to 1990 average SMB. Over this period, the ice sheet is assumed to be in balance everywhere, as suggested by the results of Hanna et al. [2005] for the whole ice sheet. Therefore, mass gained by accumulation or lost by ablation is balanced locally by downward flow of ice. Assuming that ice dynamics have remained stable over the 140 year modeling period, the time series of Wake et al. [2009] may be interpreted as a fair approximation of the total mass changes of the ice sheet over this period. [41] The SMB record presented by Wake et al. [2009] shows that over the 140 year study period the GrIS has generally been in a state of slight negative mass balance, albeit with considerable temporal variability. Between 1866 and 1922 the ice sheet is mainly in a state of positive SMB with respect to the 1961 to 1990 average. From 1922 to 2005 this changes to a state of largely negative mass balance, although several years in this latter period show the ice sheet having a high amplitude mass gain (see Wake et al. [2009, Figure 3] for the SMB time series). The Wake et al. [2009] SMB model also exhibits a considerable degree of spatial variability. In general, most ice is lost at the margins in the more southerly areas of Greenland; up to 100 to 200 m over the study period (see Wake et al. [2009, Figure 4] for the cumulated SMB changes over the period 1866 to 2005). In contrast, in the far southeast of Greenland, ice thicknesses have increased by 100 to 200 m due to the high accumulation rates that characterize this region. [42] Unlike Huy2, we note that the Wake et al. [2009] model has yet to be validated against RSL observations and so we are less confident in the accuracy of the uplift predictions, particularly in areas where the climate forcing is not well constrained (e.g., regions where observations are limited). However, the model is consistent with a number of observed changes in the GrIS over the past century as well as the past decade (see section 5 for the latter). Several studies have detailed observed changes to the GrIS over the last 100 years, but these are limited to only a few regions of Greenland. In west Greenland, the frontal of recession and subsequent inland ice thinning of Jakobshavn Isbrae ( 25 km) since 1900 is well recognized [Weidick and Bennike, 2007] and geomorphological evidence from southwest Greenland indicates that the ice front has retreated by 12 of 19

13 Figure 9. Predicted present day vertical crustal velocities (mm/yr) showing (a) the present day viscous response generated using the Huy2 ice history for the loading period 122 ka B.P. to 140 years B.P.; including non Greenland (ICE 5G) ice evolution and ocean load changes. (b) The combined elastic and viscous response generated using the surface mass balance model of Wake et al. [2009] (i.e., the sum of Figures 8a and 8b); note that ocean load changes are not included. (c) The sum of Figures 9a and 9b, representing the results for our hybrid model. The Earth model is the Huy2 best fit model. Observations made by Khan et al. [2008] and Dietrich et al. [2005] are marked by stars and circles, respectively (predictions for these locations are shown in Table 2 and Figure 6). 1 to 2 km over the last 100 years [Forman et al., 2007]. Wake et al. [2009] find that the observations of Forman et al. [2007] agree qualitatively quite well with their modeled ice thickness changes, suggesting that part of the observed thinning must also be surface mass balance driven. [43] Figure 8a shows the viscous response to ice loading changes over the period 1866 to 2005 (the Earth model is the Huy2 best fit model). The spatial pattern is characterized by subsidence of around 0.2 mm/yr in southeast Greenland with the highest rates of uplift between 0.1 and 0.2 mm/yr in the central west and north. As expected, the viscous term appears to largely reflect the general trend of ice mass change predicted by the Wake et al. [2009] model. We note that this pattern of vertical land motion shows broad similarities to the prediction generated using the Huy2 model (see Figure 7a). The size of the signal is also similar to that predicted using Huy2, with neither set of predictions exceeding ±0.2 mm/yr. We also find that for an Earth model with a relatively weak upper mantle (1020 Pa s), the magnitude of the predictions for each model is also similar, around ±1.2 mm/yr (figure not shown as pattern of response the same as in Figure 8a). Thus, when compared to the results of Huy2 (for the past 100 years), making use of the Wake et al. [2009] model makes little difference in determining the amplitude of the viscous response but there are some significant differences in the spatial pattern. [44] Figure 8b shows the elastic response, which was calculated using the averaged ice loading changes for the period 1995 to This is approximately the same timeframe over which the GPS data were recorded [Dietrich et al., 2005; Khan et al., 2008]. The spatial pattern is characterized by large rates of uplift (over 6 mm/yr) in some areas close to the margin of the ice sheet, most notably in west and southwest Greenland. These are driven by rates of peripheral thinning as high as 5 to 10 m/yr [see Wake et al., 2009, Figure 5]; which dominate the SMB signal and result in an average mass loss rate of 69 km3/yr for this 10 year period. As mentioned, the Wake et al. [2009] model does not account for nonsteady state ice dynamic features. Therefore, for areas of the GrIS where observations show that outlet glaciers are losing mass from specific ice dynamic responses [e.g., Joughin et al., 2004; Howat et al., 2005; Rignot and Kanagaratnam, 2006; Stearns and Hamilton, 2007], our predictions will miscalculate elastic uplift (see also section 4.4). While the Wake et al. [2009] model has this limitation, it does show that surface mass balance changes are generating a large elastic response. The highest rates of elastic uplift are around 3 times larger than those generated using the Huy2 ice history 13 of 19