3.1 Thermosteric sea level rise

Global thermosteric sea level rise is the simplest contribution to global sea level rise. Thermosteric sea level can be computed from the density profile over depth, which is derived from temperature and salinity data (Dangendorf et al., 2014). Changes in temperature dominate steric sea level variability. A reduction in total radiative forcing, no matter if it comes from a reduction in GHG forcing or from solar geoengineering, will produce the same reduction in heat transfer to the ocean and so the same reduction in thermosteric sea level rise.

Bouttes et al. (2012) explore the reversibility of thermosteric sea level rise using a coupled climate model for a range of CO₂ ramp-up and ramp-down scenarios, though the results apply equally to the case of solar geoengineering. They find that the thermosteric sea level rise response to their scenarios can be roughly approximated by the integral of radiative forcing, which closely corresponds to the total heat uptake of the oceans over the simulations. This implies that to halt thermosteric sea level rise, radiative forcing would need to be restored to preindustrial conditions. As the total forcing is ramped down, the warmed oceans become out of equilibrium with the now-cooled atmosphere and slowly give off the heat they absorbed, gradually reversing the thermosteric sea level rise that had occurred during the ramp-up (see Fig. 1 of Bouttes et al., 2012).

3.2 Surface mass balance

Many ice sheet and glacier models use a simple parameterization of surface mass balance, using a positive degree-day factor to estimate the amount of melt per degree above freezing at the glacier surface (Ohmura, 2001). Degree-day factors are determined empirically and vary due to surface albedo, meaning that a weathered ice surface such as the Greenland ice margin is rather dark and has high degree-day factors, while pristine snow cover has a low factor. This degree-day approach has been used in all studies of solar geoengineering's effect on surface mass balance to date but it has some important limitations.

Fundamentally the surface melt rate depends on the availability of energy at the surface; this means that net shortwave radiation, net longwave radiation, sensible heat, and latent heat fluxes all matter. Despite only accounting for temperature, degree-day approaches generally produce results similar to more complete energy balance models for surface melt; this is because downwelling longwave radiation, which typically is the dominant contributor to the energy flux, correlates well with surface air temperature since much of the downwelling longwave radiation is emitted in the first 1 km of the atmosphere (Ohmura, 2001). However, degree-day approaches cannot capture the full response to changes in energy fluxes and a look at some case studies reveals that changes in insolation can have outsized impacts which will be underestimated by degree-day approaches.

Increased summer insolation at high latitudes during the Eemian interglacial period (115–130 kyr BP) raised temperatures but also directly affected surface melt. Van de Berg et al. (2011) made an attempt to separate the contributions of elevated temperatures and increased solar forcing and suggested that 45 % of the change in surface mass balance could be attributed to the changed solar forcing alone.

Volcanic eruptions provide a more contemporary analogy to the potential effects of solar geoengineering on surface melt. Fettweis et al. (2007) simulated the surface mass balance of Greenland between 1979 and 2006 and find maxima for surface mass balance in 1983 and 1992, the years after the El Chichón and Pinatubo eruptions, respectively. Hanna et al. (2008) combine observations and modeling to evaluate the surface mass balance of Greenland over a longer period, finding that the years following El Chichón and Pinatubo have the third lowest and the lowest runoff and the third and sixth greatest surface mass balance, respectively, between 1958 and 2006.

In an analysis of recent changes over Greenland, Hofer et al. (2017) found that the substantial reduction in cloud cover over Greenland in the past 2 decades is the likeliest cause for the accelerated mass loss from the ice sheet over this period. To arrive at this result they simply calculated how much melt would result from the change in downward surface shortwave energy received over the melt season as a result of the change in cloud cover and compared this against the other contributions to melt and accumulation. They find that the ∼10 % reduction in summer cloud cover over Greenland in the past 2 decades led to a ∼4000 Gt loss of mass making it the dominant driver of surface mass balance change in this period. In Svalbard the opposite has been seen, with less melt than projected by degree-day models of glacier mass balance due to an increase in cloud cover partially offsetting the increased temperatures (Slangen et al., 2017). Giesen and Oerlemans (2012) and Lang et al. (2015) use glacier mass balance models that account for this change in surface shortwave radiation and produce a better fit to observations.

These examples suggest that solar geoengineering could be more effective at changing surface melt than achieving the same reduction in temperature with a reduction in GHG forcing. To evaluate the differences in the drivers of surface mass balance, we conduct a simple analysis of the well-studied GeoMIP G1 experiment, in which the radiative forcing from an instantaneous quadrupling of CO₂ concentrations is offset by a reduction in the solar constant sufficient to restore the preindustrial radiative balance and global-mean temperature (Kravitz et al., 2011). Kravitz et al. (2013) provide an overview of the climate response to this experiment from 12 Earth system models, and we analyze data for these same 12 models.

The models that ran the GeoMIP G1 experiment did not perfectly restore global-mean temperatures to the preindustrial levels, although the differences in top-of-atmosphere radiative forcing were specified to be less than 0.1 W m⁻². As we are interested in the relative efficacy of solar geoengineering compared to an equivalent reduction in CO₂ forcing, it is necessary to rescale these results so that they match the models' preindustrial global-mean temperature.

where F is the ratio between the global-mean temperature (GMT) anomaly of 4×CO₂ − control and of 4×CO₂ − G1. This ratio is greater than 1 if G1 is warmer than the control and less than 1 if it is cooler than the control. This ratio can then be used to rescale the effects of the reduction in solar constant to produce a synthetic scenario G1^* in which global-mean temperatures would be identical to the control case:

where X is the variable to be rescaled. We apply this equation to all variables in our analysis. We also generate scenarios in which regional, annual-mean temperatures are restored using the same approach (G1-Greenland and G1-Antarctica).

Figure 1Regional-mean anomalies (a–e) and efficacies (f–j) of G1^* and G1-Greenland at offsetting 4×CO₂ − control regional-mean anomalies for Greenland for each model within the GeoMIP G1 ensemble. In (a–e), the upper points show the 4×CO₂ − control anomaly, the middle row of points show the G1^* results, which restore global mean temperature, and the lower points show the results for G1-Greenland, which restores local temperature. The ensemble median is shown with a plus symbol. The results from some outlier points have been displayed as text in the color of the corresponding model. SFC_heat is the net heat flux into the surface, i.e., net SW + net LW − sensible heat − latent heat, and SFC_rad is the net radiative flux into the surface, i.e., net SW + net LW. Efficacy is defined in the text. Where data were unavailable these models have not been plotted for those variables.

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Figures 1 and 2 compare the regional-mean anomalies from the control for the 4×CO₂, G1^*, and G1-local experiments and the efficacy of G1^* and G1-local at offsetting 4×CO₂ trends for Greenland and Antarctica, respectively. Efficacy is defined as the fraction of the 4×CO₂ trend offset:

As an example, many studies have shown that solar geoengineering is more effective at offsetting global-mean precipitation than global-mean temperature. Tilmes et al. (2013) find that compared to the control the GeoMIP ensemble mean showed a 6.9 % increase in global-mean precipitation in 4×CO₂ and a 4.5 % reduction in G1. Taking these numbers we find an efficacy of 165 %; that is, whilst 100 % of the global-mean temperature response has been offset, 165 % of the global precipitation response has been offset. When comparing the global-mean temperature and local-mean temperature efficacies, we find if 100 % of the global-mean temperature has been offset, 90 % of the Greenland mean temperature has been offset (90 % efficacy relative to global temperature) and if 100 % of the Greenland-mean temperature has been offset 111 % of the global-mean temperature has been offset (111 % efficacy relative to local temperature).

In Greenland (Fig. 1), G1^* offsets most of the effects of 4×CO₂, bringing climate much closer to the control conditions with a median efficacy that is within 10 % of 100 %. However, this result is a combination of G1^* being under-effective at offsetting local temperatures, offsetting 90 % of the annual mean and 91 % of the summer mean, and being over-effective at offsetting the other fields relative to local temperatures, as seen in G1-Greenland results. There is a wide range of annual-mean precipitation responses across the ensemble in G1^* but the ensemble median is close to 100 %, i.e., the substantial increase in precipitation in 4×CO₂ has been offset. The global-mean hydrological cycle has been weakened substantially but it seems local temperatures have been the dominant driver of the local hydrological response. The ensemble median shows a large increase in net downward surface radiation and surface heat flux of greater than 10 W m⁻² for the 4×CO₂-control anomaly, though some models show considerably larger changes. Relative to local temperature change, solar geoengineering is over-effective at offsetting these changes in all models, with the ensemble median offsetting 116 % of the net downward surface radiation and 111 % of the net downward surface heat flux increases that were seen in 4×CO₂. These results suggest that positive degree-day melt schemes which do not account for these radiation and energy flux changes could underestimate the effectiveness of solar geoengineering at offsetting melt in Greenland by approximately 10 %.

In Antarctica (Fig. 2), a similar picture emerges as for Greenland with G1^* being under-effective at offsetting local temperatures but relative to local temperature change being over-effective at offsetting the other fields. However, the implications of these results are different as melt plays only a small role in Antarctic surface mass balance, with accumulation dominating and with the surface mass balance contribution of Antarctica to future sea level rise projected to remain negative for the foreseeable future. Ligtenberg et al. (2013) predict an increase in Antarctic surface mass balance of 98 Gt yr⁻¹ K⁻¹ using the RACMO2 model and Lenaerts et al. (2016) predict an increase of 70 Gt yr⁻¹ K⁻¹ using the CESM model. The ensemble median precipitation response is close to control values in the G1^* experiment, though there is substantial model spread, which suggests that regional temperatures dominate the Antarctic hydrological response rather than the state of the global hydrological cycle, which is significantly weaker in G1^*. These results suggest that the negative contribution to sea level rise of the positive surface mass balance response of Antarctica to global warming would decline roughly in line with temperatures if solar geoengineering were deployed, though more work is needed to explore this issue.

This simple assessment supports the view that solar geoengineering would have a greater potential to reduce surface melt, and hence the sea level rise contribution from surface mass balance changes of glaciers and the ice sheets, than previous studies have suggested. However, several factors would need to be accounted for in future work to make a robust estimate of the efficacy of solar geoengineering at offsetting surface melt. First, the impacts of a reduction in incoming sunlight will be greater where the albedo of ice is lowest. A large and growing fraction of the ablation zone of Greenland in summer is darkened by distributed surface impurities and snow algae revealed when the snow layer is melted; these darkened areas typically have an albedo half that of clean ice (Ryan et al., 2018). The impact of reduced sunlight will also be greater in low-latitude regions where the shortwave flux makes up a greater fraction of the total contribution to the surface energy flux, e.g., in high-mountain Asia. For tropical and midlatitude glaciers, changes in accumulation due to changes in precipitation will also be an important factor to consider.

Figure 2As in Fig. 1 but for Antarctica and Antarctic summer.

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The results described here apply to a uniform reduction in incoming sunlight but the response to other more realistic forms of solar geoengineering could be tailored to produce different outcomes. For example, whilst a uniform reduction in incoming sunlight would not offset all warming at high latitudes, stratospheric aerosol geoengineering could be deployed to produce a thicker aerosol cloud at high latitudes to reduce high-latitude temperatures in line with global mean temperatures or to cool them further (Dai et al., 2018; Kravitz et al., 2018). However, it is important to note that the effects of solar geoengineering cannot be limited to the area of application and there would be remote impacts even if stratospheric aerosol geoengineering was limited just to polar regions (Robock et al., 2008).

3.3 Ice shelf collapse and dynamic mass loss

The other mechanism by which ice sheets lose mass is by calving icebergs from marine-terminating glaciers and here the effects of solar geoengineering are harder to anticipate. The rate of discharge depends on how fast the ice flows across the grounding line. The rate of ice flow depends on several factors that are affected by changes in climate. Warmer ice is less viscous, allowing it to flow faster, though this changes only very slowly and is negligible for the ice sheets on centennial timescales (Slangen et al., 2017). Increased meltwater can penetrate to the bed of the glacier and lubricate it, which may speed up the flow, although this “Zwally effect” seems not especially important in Greenland where surface meltwaters are efficiently drained in channelized drainage systems such that changes in surface runoff have little impact on basal friction (de Fleurian et al., 2016), and in Antarctica surface melt is not as of yet significant in fast-flowing glaciers (Joughin et al., 2009). For Antarctica where ice discharge is the dominant loss mechanism, the most significant effect of climate change is to thin and weaken ice shelves which provide a buttressing effect, pushing back against the glaciers and slowing their flow into the ocean.

Antarctica is so cold that little surface melt occurs on the ice shelves; however, relatively warm waters have been observed penetrating below the ice shelves, melting them from below (Pritchard et al., 2012). The water mass responsible for this melt is not the surface water around Antarctica but rather the circumpolar deep waters (originating around 500 m below the surface) that surround Antarctica. Surface winds have acted to pump this relatively warm circumpolar deep water up and into the ice shelf cavities. Here this relatively warm water can reach the grounding line where the ice starts to float and where pressure requires the ice to have the lowest melting point temperature. This ocean-driven melt has been observed to be thinning ice shelves, at rates as large as 50 m per year at the grounding line and as high as 14 m per year averaged over some of the larger ice shelves (Rintoul et al., 2016), weakening their buttressing effect and increasing the rate of discharge of glaciers into the ocean (Favier et al., 2014). It is generally believed that the fate of the ice shelves is likely to be determined by the degree to which this circumpolar deep water is able to penetrate into the deep ice shelf cavities rather than by surface melt (Liu et al., 2015; Pritchard et al., 2012).

A recent study (DeConto and Pollard, 2016) has challenged this view, suggesting that the atmospheric warming that led to the breakup of some Antarctic Peninsula ice shelves would, if the warming continued, destabilize the larger southern ice shelves in the future. The process is through the hydrostatic head of meltwater-filled crevasses, which results in “hydrofracture” and the rapid disintegration of the ice shelf (Scambos et al., 2013). Furthermore, they suggest that once large ice shelves begin to retreat, the large unstable ice cliffs formed could promote further rapid retreat, in a process dubbed marine ice cliff instability (Pollard et al., 2015). Together these processes combined to produce a substantially greater Antarctic contribution to sea level rise than seen in earlier studies which did not account for these highly uncertain processes (DeConto and Pollard, 2016).

Climate change and solar geoengineering will affect the ice shelves, and hence the rate of discharge of marine glaciers, primarily by changing surface air temperature and wind patterns that affect the upwelling of circumpolar deep water. Solar geoengineering could lower surface air temperatures and hence reduce the likelihood of surface-melt-induced hydrofracturing of the ice shelves as assessed by DeConto and Pollard (2016). Whilst solar geoengineering could lower surface air temperatures and surface ocean temperatures around Antarctica, this would have a limited impact on the temperature of the deep circumpolar water mass responsible for thinning the ice shelves in the near future as it is deep below the surface. As noted above, ocean-driven melt is primarily controlled by the upwelling of these deep waters, which is driven by Southern Ocean winds. A recent study of the effects of stratospheric sulfate aerosol geoengineering in a scenario of future GHG emissions found that it would warm the stratosphere, changing both atmospheric and oceanic circulation patterns (McCusker et al., 2015). They simulated a greater upwelling of circumpolar deep water relative to a scenario without an increase in GHG forcing but that ocean temperatures were significantly lower than in the GHG-forcing-only scenario. If this result proves robust, then it suggests that whilst stratospheric aerosol geoengineering – or at least geoengineering using aerosols like sulfates, which strongly alter stratospheric heating rates – could lower surface melt considerably it may have a limited ability to reduce ice shelf basal melt rates.

The dynamical response of marine glacier ice flow to changes in the buttressing effect of ice shelves is not simple and there is the potential for runaway responses which would limit solar geoengineering's potential to slow or reverse this contribution to sea level rise. Fürst et al. (2016) show that ice shelves in the West Antarctic Amundsen and Bellingshausen seas are extremely sensitive to calving, meaning that even a small amount of increased calving will trigger dynamical responses in the feeding ice streams, increasing their flow rate. Furthermore, West Antarctica's geography makes its ice sheet especially vulnerable to such changes. Much of the ice sheet rests on bedrock below sea level, which becomes deeper further from the coast. This arrangement makes many of Antarctica's glaciers susceptible to “marine ice sheet instability” (Mercer, 1978), in that if the boundary layer begins to retreat, the ice flow across the grounding line increases, prompting a self-sustaining retreat that would continue until a bedrock ridge further inland. In fact, observations suggest that recent increases in the temperature of water around Antarctica may have already triggered a process that will lead to the collapse of the Pine Island and Thwaites glaciers (Favier et al., 2014; Joughin et al., 2014). Unless an ice stream has exceptionally strong lateral buttressing (Robel et al., 2016), a marine ice sheet instability, once started, may only be stopped by modifying bathymetry to provide extra buttressing, as simulated by flow-band modeling on Thwaites Glacier (Wolovick and Moore, 2018). However, initial results from the BISICLES model evaluating the response of an idealized vulnerable marine glacier to imposed warming found that returning the entire water column to cooler conditions reversed the retreat that had begun during the warming (Asay-Davis et al., 2016). It seems reasonable to expect that solar geoengineering, like emissions cuts, may help to prevent other marine glaciers from becoming unstable by limiting surface melt that could lead to ice shelf collapse but would have a limited ability to reverse subsurface warming on decadal timescales. It may be that significant losses from some West Antarctic glaciers are unavoidable by simply returning climate and oceanic driving conditions to the preindustrial conditions and perhaps that even doing so would not be sufficient to arrest the retreat.