Australia: The Land Where Time Began

A biography of the Australian continent 

Ocean Bottom sinking as a Result of Increasing Mass of Extra Water in the Ocean from Melting Ice Sheets and Glaciers

The total ocean mass is increased by the mass distribution that is occurring at present, and on average, is causing the bottom of the ocean to subside elastically. Barystatic sea level rise is, therefore, larger than the global mean geocentric sea level rise which is observed by satellite altimetry and tide gauges that are GPS-corrected. In this study Frederikse et al. used realistic estimates of the redistribution of mass from ice mass loss and land water storage in order to quantify the ocean bottom deformation that results and its effect on global and regional ocean volume change estimates. The resulting globally averaged sea level change is 8% smaller than the barystatic contribution over the period 1993-2014. The difference is about 5% over the altimetry domain, and barystatic sea level rise will be underestimated by more than 1 mm/year between 1993 and 2014. Regional differences are often larger: up to 1 mm/year over the Atlantic Ocean and 0.3 mm/year in the South Pacific. When regional sea level changes are observed in a geocentric reference frame deformation of the ocean bottom should be considered.

Next to steric and dynamic changes, mass redistribution between land and ocean is one of the major components that drive global sea level change (Chambers et al., 2016; Stammer et al., 2013). Distinct regional patterns of sea level changes, called sea level fingerprints, are caused by the mass distribution, which are the result of gravitational effects, changes in the rotation parameters of the Earth, and by deformation of the solid Earth (Clark & Lingle, 1977; Milne & Mitrovica, 1998). A vertical deformation of the solid Earth that affects both land and the floor of the ocean causes a substantial part of the regional pattern (King et al., 2012; Riva et al., 2017). The oceans have gained mass over the past decades due to changes in the land ice mass balance and land hydrology (Chambers et al., 2016), which has resulted in an increase of the total load on the floor of the ocean. Given a constant geocentric ocean surface, this subsidence will increase the capacity of the ocean basin. According to Frederikse et al. this elastic deformation has to be considered as well as the viscoelastic response to past ice ocean mass changes, known as glacial isostatic adjustment (GIA), which sea level reconstructions are routinely corrected for (Tamisiea, 2011).  It has been shown (Ray et al., 2013) that the deformation of the ocean floor caused by changes in ocean dynamic, atmospheric pressure, and land water storage (LWS) results in a substantial effect on the seasonal cycle in sea level derived from altimetry. In that study, however, changes in ice mass, which have been the main cause of the increase in ocean mass over the last 2 decades (Chambers et al., 2016), were excluded. In this paper Frederikse et al. examined how elastic deformation resulting from ice mass loss at present and changes in land water storage has affected the shape of the ocean floor over the last 2 decades and whether the deformation does affect trends in the regional and global sea level reconstructions that used tide gauges and altimetry.

There are 2 distinct reference frames that are generally used to express sea level changes: either relative to the local ocean floor (relative to sea level change) or relative to the centre of mass of the Earth (geocentric or absolute sea level change). Global mean sea level (GMSL) changes that are due to redistribution of mass are barystatic changes. Barystatic changes are defined as the total change of volume of the ocean, divided by the surface area of the ocean. Barystatic changes are equal to relative sea level changes by this definition, integrated over the entire ocean. However, as the deformation of the floor of the ocean that is due to changing load, global mean sea level changes that result from changes of mass are not equal to the barystatic changes. As the deformation of the solid Earth is not uniform over the oceans, the regional or basin mean difference between relative sea level changes and geocentric sea level change may deviate from the global mean difference.

A near-global overview of sea level changes has been achieved by the emergence of satellite altimetry (Nerem et al., 2010). However, as the sea level changes are observed is a geocentric reference frame by satellite altimetry, global mean sea level estimates that have been derived from altimetry will not detect the increase in volume of the ocean that is due to subsidence of the ocean floor, and therefore they may underestimate the GMSL rise. A correction that is associated with the elastic response mass redistribution of the present is almost never applied (see Fenoglio-Marc et al., 2912; Kuo et al., 2008; Rietbroek et al., 2016 for exceptions), and altimetry-derived global mean sea level changes that result from the redistribution of mass may therefore differ from associated global changes of ocean volume.

Since the launch of the Gravity And Climate Experiment (GRACE) satellite mission it has been possible to attain more detailed global and regional estimates of mass changes of the ocean and comparison with changes in sea level (Chen et al., 2017; Kleinherenbrink et al., 2016; Leuliette & Willis, 2011). GRACE observations have shown ocean mass changes and therefore show relative rather than geocentric sea level changes (Kuo et al., 2008; Ray et al., 2013), and therefore a bias will be introduced by direct comparison between altimetry and GRACE when the effect of ocean floor deformation is not corrected for.

Estimates of sea level change on centennial timescales are based mainly on tide gauge data. As they are land-based instruments they observe relative sea level. When gauges sample the full ocean in the ideal case, they observe global ocean volume changes. In reality, tide gauges do not sample the entire ocean, and local vertical motion of land (VLM) which is not related to large-scale sea level processes affects the observations, and therefore, correcting records from tide gauges for VLM is desirable (Wöppelmann &Marcos, 2016). Traditionally only the GIA component of VLM was modelled 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). Tide gauges are brought into a geocentric reference frame by this correction, the global and sea level rise estimates that result may be biased due to ocean floor deformation in the same way that satellite observations are.

In this paper Frederikse et al. studied the difference in relative and geocentric sea level rise that results from elastic deformation, given realistic estimates of redistribution of water mass at present to determine to what extent the different observational techniques are affected. They computed the global mean and regional ocean floor deformation based on recent estimates of mass changes related to ice, land water storage, and dam retention. The impact of sea level reconstructions based on tide gauges is estimated by computing a synthetic “virtual station” sea level solution (Jevrejeva et al., 2006).

Discussion and conclusions

Frederikse et al. quantified the effect of mass loss of the present on deformation of the ocean floor. Many sea level observations are affected by this difference. Global mean geocentric sea level has risen by about 8% less than the barystatic equivalent between 1993 and 2014. Therefore, due to the redistribution of mass at present the total volume of increase would be underestimated by about 0.13 mm/year, if the sea level was observed by satellite altimeters with global coverage. As a result of the orbits of satellites, that area that is covered by altimetry observations is generally limited, with the highest latitudes often not being observed. The underestimation of the total volume of change becomes about 0.10 mm/yr or 6% of bathymetric contribution, when global mean sea level is estimated from the range covered by the TOPEX/Poseidon and Jason altimeters. According to Frederikse et al. next to barystatic sea level rise, steric changes are present, and therefore, total GMSL rise for the period 1993-2014, which is in the order of 3 mm/yr (Chambers et al., 2016; Chen et al. 2017) and is larger than the barystatic contribution alone. The uncertainty of the correction is largely the result of uncertainties in the redistribution of mass, as the elastic response of the Earth is reasonably well defined (Mitrovica et al., 2011).

The global mean deformation of the ocean floor resulting from elastic deformation which is caused by redistribution of mass at present is still smaller than the deformation of the ocean floor bias that results from the viscoelastic response to changes in ice mass in the past (GIA), which is in the order of -0.15 to -0.4 mm/yr (Tamisiea, 2011). Also, the bias is still within the uncertainty range of GMSL trends that are derived from altimetry, which are in the order of 0.4 mm/yr (Chen et al., 2017). The effect is, nevertheless, systematic and relatively easy to account for. The sea level rise that results from ice sheets in a future warming climate will increase (e.g. Kopp et al., 2014), and therefore, the magnitude of the bias that is due to elastic deformation of the ocean floor will grow. When no changes in the altimetry trend uncertainty are assumed, the bias becomes larger than the uncertainty when the bathymetric sea level rise reaches 6.5 mm/yr. Under high-end scenarios of sea level rise, such barystatic contributions could be reached in the 21^st century (DeConto & Pollard, 2016; Jevrejeva et al., 2016).

Deformation of the ocean floor varies spatially, and on regional and basin mean scales, the difference between geocentric sea level and relative sea level can deviate substantially. The largest differences can be recorded in the Arctic Ocean: as a result of the location being close to many sources of melting, relative seal level in the Arctic drops, though geocentric sea level rises, with the result that there can be a difference of 1.3 mm/yr between both metrics. Basin mean differences up to 0.4 mm/yr or 23% of the regional relative sea level changes occur outside the Arctic Ocean. The differences between geocentric sea level and relative sea level are in the same range as uncertainties in the basin mean sea level that are estimated from altimetry, which are on the submillimetre level in many basins, though substantially less variability is shown by the spatial patterns compared to the patterns related to ocean dynamic change (Kleinherenbrink et al., 2016; Purkey et al., 2014). In reconstructions that do not use VLM observations or satellite altimetry (e.g. Hay et al., 2015; Jevrejeva et al., 2006), the effects on the deformation of the ocean floor will not affect the reconstructions, though a bias may result in the sampling of the spatially varying sea level field by the limited number of tide gauges (Thompson et al., 2016). Tide gauge observations that are VLM-corrected have been used recently to reconstruct regional and global sea level changes (Dangendorf et al., 2017; Wöppelmann et al., 2014). Geocentric sea level changes are observed in tide gauge reconstructions when the records are corrected for VLM. Deformation of the ocean floor could, therefore, affect these reconstructions as well. The use of virtual station techniques that use all locations of the PSMSL RLR database with 70% data availability over the area of the altimetry, only a small difference was found by Frederikse et al. between the reconstructed global mean geocentric sea level and the relative sea level. Frederikse et al. did not find that the reconstruction of global mean relative sea level underestimates the underlying basin mean value, which was also found by Thompson et al. (2016). When the Arctic Ocean is omitted from tide gauge reconstructions it results in a larger difference between geocentric sea level changes and relative sea level changes, though the bias that was mentioned previously with the underlying basin mean sea level changes is still present. Frederikse et al. found that on regional scales similar differences between relative and geocentric sea level changes for the synthetic tide gauge reconstructions as for the averaged fields, though in some basins, especially in the South Atlantic Ocean, differences with the underlying fields result from the sparse sampling. In global and regional tide gauge reconstructions the difference between relative and geocentric sea level changes are not independent from the station selection and method of reconstruction, and the values that were mentioned previously cannot be used blindly to quantify the effect of ocean floor deformation in a specific reconstruction. E.g., the global reconstruction (Church & White, 2011) uses patterns of spatial sea level change that were estimated from altimetry, which are also affected by the deformation of the ocean floor, though in a way that differs from that mentioned here.

It is suggested by Frederikse et al. that the differences between relative and geocentric sea level change should be observable in VLM estimates at coastal locations as these differences are the result of deformation of the solid Earth. The uncertainties of individual VLM observations, however, and 20 year linear trends in observations from tide gauges are still generally larger than the rates that are considered here (Dangendorf et al., 2014; Hughes & Williams, 2010; Wöppelmann & Marcos, 2016). When multiple independent observations on regional scales can be combined, it is suggested that deformation of the ocean floor that results from mass loss of the present can be observed in GPS and tide gauge records (Galassi & Spada, 2017; Pfeffer et al., 2017).

Altimetry and tide gauge observations that are corrected by VLM also underestimate the global mean sea level acceleration, as acceleration over the last 2 decades has been shown by barystatic sea level rise (Chen et al., 2017). It is expected that the contribution to sea level rise will increase further in a warming climate, and therefore, this bias will also increase towards levels that might possibly exceed the uncertainty margins at the locations of individual tide gauges.

The effect of deformation of the ocean floor should be taken into account in order to increase the accuracy of sea level estimates, as was done in this study, or by using more direct observations. E.g. direct estimates of global mass redistribution is allowed by the GRACE mission, from which deformation of the ocean floor can be computed (Ray et al., 2013), though with the uncertainty that is associated with models of global isostatic adjustment (King et al., 2012). When tide gauge and altimetry observations are compared on a regional scale or when regional volume changes are estimated from observations in a geocentric reference frame, caution is required with the large regional differences.

Frederikse, T., et al. (2017). "Ocean Bottom Deformation Due To Present-Day Mass Redistribution and Its Impact on Sea Level Observations." Geophysical Research Letters 44(24): 12,306-312,314.