Next to steric and dynamic changes, redistribution of mass between land and ocean is one of the major components driving global and regional sea level change (Chambers et al., 2016; Stammer et al., 2013). The redistribution causes distinct regional sea level change patterns, known as sea level fingerprints, which are caused by gravitational effects, changes in the Earth rotation parameters, and by deformation of the solid Earth (Clark & Lingle, 1977; Milne & Mitrovica, 1998). A substantial part of the regional pattern is caused by vertical deformation of the solid Earth that affects both land and the ocean bottom (King et al., 2012; Riva et al., 2017). Due to changes in the land ice mass balance and land hydrology, the oceans have gained mass over the past decades (Chambers et al., 2016), which results in an increase of the total load on the ocean bottom. Under this increasing load, the ocean floor will subside due to elastic deformation. This subsidence will increase the ocean basin capacity, given a constant geocentric ocean surface. Note that this elastic deformation has to be considered in addition to the viscoelastic response to past ice ocean mass changes, known as Glacial Isostatic Adjustment (GIA), for which sea level reconstructions are routinely corrected (Tamisiea, 2011). Ray et al. (2013) shows that the ocean bottom deformation caused by changes in ocean dynamics, atmospheric pressure, and land water storage (LWS) results in a substantial effect on the seasonal cycle in sea level derived from altimetry. However, in that study, ice mass changes, which have been the main cause of the ocean mass increase over the last two decades (Chambers et al., 2016), were excluded. In this paper, we examine how elastic deformation due to present-day ice mass and LWS changes has affected the shape of the ocean bottom over the last two decades and whether this deformation does affect trends in regional and global sea level reconstructions from tide gauges and altimetry.
Sea level changes are generally expressed in two distinct reference frames: either relative to the local ocean floor (relative sea level change) or relative to the Earth’s center of mass (geocentric or absolute sea level change). Global mean sea level (GMSL) changes due to mass redistribution are called barystatic changes. These barystatic changes are defined as the total volume change of the ocean, divided by the ocean surface area. With this definition, barystatic changes are equal to relative sea level changes, integrated over the whole ocean. However, because of the deformation of the ocean bottom due to the changing load, global mean geocentric sea level changes resulting from mass changes are not equal to the barystatic changes. Since the solid Earth deformation is not uniform over the oceans, the regional or basin mean difference between relative and geocentric sea level change may deviate from the global mean difference.
The emergence of satellite altimetry has given a near-global overview of sea level changes (Nerem et al., 2010). However, because satellite altimetry observes sea level in a geocentric reference frame, global mean sea level estimates derived from altimetry will not observe the increase in ocean volume due to ocean bottom subsidence, and hence, they may underestimate GMSL rise. A correction associated with the elastic response to present-day mass redistribution is almost never applied (see Fenoglio-Marc et al., 2012; Kuo et al., 2008; Rietbroek et al., 2016 for exceptions), and altimetry-derived global mean sea level changes resulting from mass redistribution may thus differ from associated global ocean volume changes.
The launch of the Gravity Recovery And Climate Experiment (GRACE) satellite mission has allowed more detailed global and regional estimates of ocean mass changes and comparison with sea level changes (Chen et al., 2017; Kleinherenbrink et al., 2016; Leuliette & Willis, 2011). GRACE observations show ocean mass changes and hence show relative rather than geocentric sea level changes (Kuo et al., 2008; Ray et al., 2013), and the direct comparison between altimetry and GRACE will thus also introduce a bias when the effect of ocean bottom deformation is not corrected for.
On centennial timescales, sea level change estimates are mainly based on tide gauge data. As land-based instruments, they observe relative sea level. In the ideal case, when tide gauges sample the full ocean, they observe global ocean volume changes. In reality, tide gauges do not sample the whole ocean, and local vertical land motion (VLM) unrelated to large-scale sea level processes affects the observations, and therefore, correcting tide gauge records for VLM is desirable (Wöppelmann & Marcos, 2016). Traditionally, only the GIA component of VLM was modeled and corrected for. More recently, GPS, altimetry, and Doppler orbitography and radiopositioning integrated by satellite observations have been used to correct tide gauge records for VLM (Ray et al., 2010; Wöppelmann & Marcos, 2016). This correction brings tide gauges into a geocentric reference frame, and hence, the resulting global and regional sea level rise estimates may be biased due to ocean bottom deformation in the same way satellite-based estimates are.
In this paper, we study the difference in relative and geocentric sea level rise due to elastic deformation, given realistic estimates of present-day water mass redistribution to see to what extent the different observational techniques are affected. Based on recent estimates of mass changes related to ice, land water storage, and dam retention, we compute the resulting global mean and regional ocean bottom deformation. The impact on tide gauge-based sea level reconstructions is estimated by computing a synthetic “virtual station” sea level solution (Jevrejeva et al., 2006).
2 Methods and Data
The spatially varying response of the geoid, the solid Earth, and relative sea level to present-day mass exchange is computed by solving the elastic sea level equation (Clark & Lingle, 1977), which includes the Earth rotational feedback (Milne & Mitrovica, 1998). We solve the sea level equation using a pseudo-spectral method (Tamisiea et al., 2010) up to spherical harmonic degree 360 in the center of mass (CM) of the whole Earth system frame. The load Love numbers used to determine the geoid and solid Earth response are computed from the Preliminary Referenced Earth Model (Dziewonski & Anderson (1981)). The resulting relative sea level change η(θ,ϕ,t) at longitude θ, latitude ϕ, and time t can then be expressed as follows:
G(θ,ϕ,t) is the deformation of the geoid, R(θ,ϕ,t) is the change of the solid Earth height, and is a global mean term, which is required to ensure mass conservation. Hence, regional variations in relative sea level are both caused by changes in the local geoid and solid Earth deformation. R(θ,ϕ,t) and G(θ,ϕ,t) evaluate to zero when integrated over the whole Earth. However, they do not necessarily evaluate to zero when integrated over the global ocean or over the altimetry domain (±66∘S). Therefore, is generally not equal to the total barystatic change.
Local geocentric sea level change ζ(θ,ϕ,t) only differs from local relative sea level change by the local solid Earth height change. Therefore, geocentric sea level change can be expressed as follows:
Since geoid variations have more power at longer wavelengths than solid Earth deformations, the spatial patterns of relative sea level changes (equation (1)) can substantially differ from those of geocentric changes (equation (2)).
We compute the sea level response to mass redistribution related to glaciers, the Greenland and Antarctic ice sheets, and LWS over the period 1993–2014. We use the mass redistribution data from Frederikse et al. (2017), which provides estimates of the temporal and spatial distribution of the mass changes from the aforementioned processes, which we review here briefly. Glacier mass loss is based on a surface mass balance model (Marzeion et al., 2015). The Greenland and Antarctic ice sheet contributions are based on an input-output approach, where the surface mass balance (SMB) contribution is based on RACMO2.3 (van den Broeke et al., 2016; van Wessem et al., 2016). The ice discharge is modeled as a constant acceleration departing from long-term equilibrium between SMB and discharge before 1993. The acceleration is 6.6 Gt/yr2 for the Greenland ice sheet and 2.0 Gt/yr2 for the Antarctic ice sheet. The total mass change is partitioned over each ice sheet by normalized GRACE mascon solutions (Watkins et al., 2015). For LWS, we include groundwater depletion, based on modeled estimates from Wada et al. (2012), and dam retention, based on the GRaND dam database (Lehner et al., 2011), with reservoir filling and seepage rates from Chao et al. (2008). For a more complete description of the data and the associated uncertainties, we refer to Frederikse et al. (2016, 2017).
The barystatic contribution associated with each process is depicted in Figure 1a. To assess the impact on regional estimates, we have separated the ocean in six regions, as depicted in Figure 1b, which also shows the domain covered by the TOPEX/Poseidon and Jason 1/2/3 altimeters, which is between ±66∘S.