Projections of sea level rise are based on mathematics. That is a pragmatic statement rather than a profound one. Insurance actuaries assessing flood risk in Norfolk, Virginia, coastal planners in Miami, and infrastructure engineers in Bangladesh all rely on figures that ultimately stem from physics equations explaining how water behaves as it warms. The issue that an increasing amount of oceanographic research has been addressing is that those equations have been based on oversimplified assumptions about the expansion of deep ocean water, which introduce mistakes that increase over decades. The thermal expansion coefficient, which is effectively the amount that a specific volume of saltwater expands when its temperature rises by one degree, is the crucial variable.
This coefficient is seen as roughly constant across ocean depths, or at least as fluctuating in ways that are manageable to average out, in the simple models that have traditionally supported IPCC sea-level estimates. The issue is that as it heats up, water under the intense hydrostatic pressure of the abyssal plain—the crushing weight of three to six kilometers of water above it—behaves differently from surface water. The combination of temperature, salinity, and pressure in those conditions causes non-linear variations in the expansion coefficient at depth. Warm water close to the surface reacts differently to a given temperature increase than cold, dense, highly pressured water at 3,000 meters, and this difference is not insignificant for figuring out how much the whole ocean volume is expanding.
The modeling problem is made more difficult by the measuring problem. Oceanographers’ understanding of the upper two kilometers of the ocean has been revolutionized by the Argo float program, which consists of roughly 4,000 autonomous floats that circle the world’s oceans, diving and emerging on regular cycles and radioing their temperature and salinity profiles. However, the abyss is not two kilometers.
Situated between three and six kilometers below the surface, the abyssal plain encompasses much of the ocean floor and contains a substantial portion of the entire ocean volume. Although Deep Argo is expanding the program’s reach beyond 6,000 meters, the data density is still significantly lower below 2,000 meters than it is above. Because there are so few historical temperature records from the deep ocean, it is necessary to work with limited data, which increases uncertainty, in order to identify trends there.
Additionally, some important physics has been absent from the models. The deformation of the solid Earth under varying water loads has historically not been properly taken into account in IPCC sea-level estimates. The ocean floor itself reacts when ocean water redistributes, such as when ice melts, when ocean mass transfers from one basin to another, or when thermal expansion causes water to migrate horizontally across pressure gradients. When weight is added, it flexes slightly, and when weight is withdrawn, it rebounds slightly. These solid-earth reactions alter the seafloor’s local height, which has an impact on sea-level observations in ways that the simplified models don’t fully account for.
The local gravitational field is also altered by dispersing vast masses of water; since the sea surface follows gravity, variations in gravity result in variations in sea level that are completely independent of variations in temperature and ice melt. Although these gravity changes have been directly measured by the GRACE satellite program, it is technically challenging to incorporate them into regional estimates.
When you carefully examine this, the aspect that yields the most unexpected outcomes is the horizontal redistribution of enlarged water. Sea level in one ocean basin is not simply raised uniformly by thermal expansion. Sea levels in locations that may be thousands of kilometers away from the warming are impacted by the sideways movement of water mass caused by pressure gradients brought on by the expansion. For instance, events in the deep Pacific have an impact on the dynamics of the North Atlantic. Even if the worldwide average is handled rather effectively, regional sea-level predictions that do not take these redistribution effects into account may incorrectly predict the direction of change for certain coastlines.
The research is refining the uncertainty rather than coming to the conclusion that earlier estimates were alarmingly incorrect. There is no doubt about the direction of sea level rise caused by thermal expansion. There is nothing subtle about the physics of water expanding when heated. In order to generate more accurate estimates at the regional level, where choices concerning coastal infrastructure and flood planning are really made, the recalculation effort is bringing back the real-world complexity that simpler models omitted.
Miami, Jakarta, or Amsterdam would benefit more from a regional sea-level rise forecast that takes into consideration local gravity, local land movement, and the unique pattern of water mass redistribution that will impact their specific shoreline than from a global average. This recalculation effort aims to improve the deep-ocean physics, which is necessary to get those regional values correct.
