Geophysical Journal International Geophys. J. Int. (2011) 186, 1036–1044 doi: 10.1111/j.1365-246X.2011.05116.x Ongoing glacial isostatic contributions to observations of sea level change Mark E. Tamisiea National Oceanography Centre, Joseph Proudman Building, 6 Brownlow Street, Liverpool, L3 5DA, UK. E-mail: [email protected] Accepted 2011 June 15. Received 2011 May 30; in original form 2010 September 8 Downloaded from https://academic.oup.com/gji/article/186/3/1036/589371 by guest on 28 September 2021 SUMMARY Studies determining the contribution of water fluxes to sea level rise typically remove the ongoing effects of glacial isostatic adjustment (GIA). Unfortunately, use of inconsistent ter- minology between various disciplines has caused confusion as to how contributions from GIA should be removed from altimetry and GRACE measurements. In this paper, we review the physics of the GIA corrections applicable to these measurements and discuss the differing nomenclature between the GIA literature and other studies of sea level change. We then ex- amine a range of estimates for the GIA contribution derived by varying the Earth and ice models employed in the prediction. We find, similar to early studies, that GIA produces a small (compared to the observed value) but systematic contribution to the altimetry estimates, with a maximum range of −0.15 to −0.5 mm yr−1. Moreover, we also find that the GIA contri- bution to the mass change measured by GRACE over the ocean is significant. In this regard, we demonstrate that confusion in nomenclature between the terms ‘absolute sea level’ and GJI Gravity, geodesy and tides ‘geoid’ has led to an overestimation of this contribution in some previous studies. A component of this overestimation is the incorrect inclusion of the direct effect of the contemporaneous perturbations of the rotation vector, which leads to a factor of ∼two larger value of the degree two, order one spherical harmonic component of the model results. Aside from this confusion, uncertainties in Earth model structure and ice sheet history yield a spread of up to 1.4 mm yr−1 in the estimates of this contribution. However, even if the ice and Earth models were perfectly known, the processing techniques used in GRACE data analysis can introduce variations of up to 0.4 mm yr−1. Thus, we conclude that a single-valued ‘GIA correction’ is not appropriate for sea level studies based on gravity data; each study must estimate a bound on the GIA correction consistent with the adopted data-analysis scheme. Key words: Satellite geodesy; Sea level change; Time variable gravity. to the Earth model employed in the analysis, and the plausible range 1 INTRODUCTION of values has not been established. A number of recent studies have investigated the sea level budget The impact of GIA on the estimates of ocean mass change derived using three complementary measurements: altimetry (e.g. Jason- from GRACE has caused much debate. Indeed, ocean mass balance 1), gravity (Gravity Recovery and Climate Experiment, GRACE) studies have used estimates near −1mmyr−1 (Willis et al. 2008; and thermosteric variations (Argo) (Willis et al. 2008; Cazenave Leuliette & Miller 2009) or −2mmyr−1 (Cazenave et al. 2009). et al. 2009; Leuliette & Miller 2009). The ongoing effects of glacial These values are based on GIA model predictions developed by isostatic adjustment (GIA), that is, the continuing response of the Paulson et al. (2007) and Peltier (2004), respectively. The significant viscoelastic Earth to the loading from the ice age, impact the first discrepancy in the value adopted in previous studies is surprising two of these measurements. In this regard, the contribution of GIA given that the GIA predictions were both derived using the ICE- to altimetry is generally cited as −0.3 mm yr−1 (thus, subtracting 5G ice model with some form of VM2 Earth model (Peltier 2004; the GIA contribution implies adding 0.3 mm yr−1 to the observed Paulson et al. 2007). Peltier (2009) derived a value of −1.8 mm yr−1 altimetry rate), following the value derived by Peltier (2001). Peltier from the ICE-5G(VM2) (Peltier 2004) and explored the sensitivity (2009) found same value based upon ICE-5G(VM2) (Peltier 2004), of this estimate to different smoothing values and exclusion of but a slightly more negative value of −0.32 mm yr−1 when averaging particular spherical harmonic components of the model prediction. over a reduced latitude range of ± 66◦.However,thisrateissensitive It is interesting to note that several of the studies (Leuliette & Miller 1036 C 2011 National Environment Research Council (NERC) Geophysical Journal International C 2011 RAS Isostatic contributions to sea level change 1037 2009; Cazenave et al. 2009; Peltier 2009) have claimed closure of Classically, GIA models have focused on predictions of sea level the sea level budget using the three observation techniques despite because many of the time-series used as constraints in GIA mod- using these significantly different estimates of the GIA contribution elling are from (broadly defined) paleoshoreline data. [A compre- to the mass estimate derived from GRACE. In the effort to better hensive discussion of the general concepts involved in the prediction constrain the mass flux into the oceans, it is important to understand of GIA-induced sea level changes, and the first modern theoretical the range of uncertainty in the GIA contribution to the GRACE treatment of these changes, may be found in the canonical work of observation. Farrell & Clark (1976).] Given the relatively long time scale of GIA, This paper addresses three issues. First, GIA studies of sea level sea level variations driven by this process are predicted under the often use the term geoid interchangeably with absolute sea level or assumption that the evolving ocean is in static equilibrium (surfaces sea surface. We begin by reviewing these GIA calculations to rig- of constant pressure and density are equipotentials). This static sea orously describe the physical meaning of the predicted quantities. level theory treats the sea surface as an equipotential surface (i.e. This discussion clarifies the GIA contribution to ongoing changes no dynamic effects are taken into account). However, it is impor- in sea level as measured by either altimetry and gravity missions. tant to note that the value of the potential that defines the surface This review also demonstrates that a GIA correction to GRACE will be time dependent (e.g. Dahlen 1976; Farrell & Clark 1976), estimates of ocean mass balance based upon absolute sea level pre- as becomes evident when one considers that sea level was over Downloaded from https://academic.oup.com/gji/article/186/3/1036/589371 by guest on 28 September 2021 dictions (e.g. Peltier 2004) is inconsistent with the observation it is 120 m lower at the Last Glacial Maximum. It is the time dependence correcting and is thus in error. Secondly, for both altimetry and grav- of the potential value that has lead to confusion of terminology in the ity observations we estimate a plausible range of values associated past. Note that we also assume the density of water is constant, both with uncertainties in Earth and ice sheet models. Understanding spatially and temporally. These assumptions will hold throughout the uncertainty in these predicted contributions is vital to assessing the paper. the constraints imposed by the altimetry and gravity observations. The sea level predictions in GIA literature are typically a measure Finally, we illustrate that the GIA correction to a GRACE esti- of ‘relative sea level’, SR(θ, φ, tj), which is a globally defined field mate of ocean mass change will vary significantly depending upon at co-latitude θ, east-longitude φ and time tj. As an example, if the analysis techniques and averaging regions applied to the data. tide gauges could be deployed globally and were only affected by We will conclude that a universally applicable ‘GIA correction’ to GIA, they would observe S˙ R (θ,φ,tp), where the dot indicates a mass change measurements over the ocean is neither possible nor time derivative and tp is the present-day time (see Fig. 1a). The appropriate. ocean is bounded by two surfaces, the sea surface and the crust, and relative sea level refers difference between these two boundaries (see Fig. 1b) 2 TERMINOLOGY SR (θ,φ,t j ) = SA(θ,φ,t j ) − R(θ,φ,t j ). (1) Studies of global sea level aim to quantify changes to both the total In this equation, SA(θ, φ, tj) is the absolute sea level or sea surface ocean volume and mass. If the Earth was rigid and the observa- and R(θ, φ, tj) is the height of the solid surface, assuming that these tions were made in a well-realized reference frame, then altimetry are measured relative to a common datum (e.g. the centre of mass would measure changes in the sea surface (or ocean volume), while of the Earth system, CM). Examples of S˙ A(θ,φ,tp)andR˙ (θ,φ,tp) GRACE would measure changes in ocean mass. In practise, nei- are shown in Figs 1(c) and (d). As indicated by the time derivative ther of these conditions is met. However, part of Earth’s non-rigid of eq. (1), in Fig. 1 the panels (a) = (c) − (d) The shoreline at t character is frequently incorporated into such studies. For example, = tj is a location where SR(θ, φ, tj) = 0, or, alternatively, where the GRACE observations of geopotential change are generally reported height of the sea and solid surfaces are the same. in terms of change in equivalent water height (EWH) (e.g. Wahr In GIA models, the solution to eq.