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CrustalTrudger t1_iudj1fq wrote

I assume you're asking about the surface elevation of the topography beneath the ice sheet, like those constrained in papers like Morlighem et al., 2017? In short, the reason for the below sea level elevations are the mass of the ice and the isostatic response of the crust to this mass.

In detail, the Earth's crust behaves somewhat like a giant elastic sheet. When a surface load, like an ice sheet, is placed on the crust, it deflects downward analogous to how if you put a weight on the center of a trampoline, the surface of the trampoline would deflect downward by an amount proportional to the mass, the distribution of that mass, and the 'rigidity' of the trampoline itself. The added extra complication is that in the analogy, the trampoline is the crust and the air is the mantle, but in reality the mantle is extremely viscous, so the flexural response to a mass is not instantaneous (like it effectively is in the trampoline example, because air can flow out of the way beneath the trampoline very quickly), i.e., it is dictated by both the elastic properties of the crust, but also the viscosity of the mantle as the mantle has to flow (reminder the mantle is a solid, but behaves like a fluid on long timescales, i.e., it's a rheid) away from the depression to accommodate the deflection. Similarly, when the surface mass is removed (or reduced), there will be an isostatic/flexural response, i.e., the surface elevation will 'rebound'. When this is discussed in reference to reduction of ice sheet mass, this is described as glacial isostatic adjustment (GIA) or 'glacial rebound'. Because of the moderating effect of the high viscosity of the mantle (i.e., it takes time for the mantle to flow back to allow for rebound), GIA is actually still occurring from large ice sheet reductions during the end of the last glacial period, and we can measure the vertical rate at which the Earth's surface is still rebounding in response to melting of the large northern hemisphere ice sheets.

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ILikePenguinss OP t1_iudkizm wrote

Replying to CrustalTrudger (#344,823)

Interesting!

Edit: Ok someone had to point out that I should reply with more, so: Interesting how that works! If I understand what you said correctly, it’s kind of like dropping a giant ball of whatever into an ocean and the waves splashing out in all directions. Funny how both complicated and simple geography can be at times!

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CrustalTrudger t1_iue9g0y wrote

Replying to ReddFro (#350,104)

They're definitely included in terms of detailed projections for local relative sea level rise in certain areas. Relative sea level change is the rate of sea level change relative to a local datum, which differs from global eustatic sea level change, which is the change relative to a fixed global datum (e.g., the center of the Earth). For example, in a hypothetical scenario where global eustatic sea level rise is 3 mm/yr, but the local rate of surface uplift at the coast in a particular area is 5 mm/yr from isostatic or tectonic forces, the rate of relative sea level change would actually be a 2 mm/yr apparent sea level fall in that location.

With respect to projections of global eustatic sea level rise over time frames like 50-100 years, most won't necessarily include projections of isostatic responses to recent (i.e., anthropogenically related) ice mass redistribution and resultant changes to ocean basin volume, because the effects will be relatively small given the time frame of responses (see correction by u/agate_ below) and the pretty large uncertainties in other aspects like the "right" concentration pathways and associated ice sheet responses (e.g., Horton et al., 2020) or steric components of projected eustatic sea level change (e.g., Camargo et al., 2020).

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ReddFro t1_iuecypi wrote

Replying to CrustalTrudger (#350,575)

Huh, so no help on sea level rise expected from this. I wondered.

Well here’s hoping scientists underestimated the short term impact an unprecedented amount of ice sliding into the ocean over a short period has on crust deflection and we get a fast enough rebound to reduce the impact of sea level rise (without, you know, massive earthquakes and the like)

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agate_ t1_iuetd4b wrote

Replying to CrustalTrudger (#350,575)

> With respect to projections of global eustatic sea level rise over time frames like 50-100 years, most won't necessarily include projections of isostatic responses to recent (i.e., anthropogenically related) ice mass redistribution and resultant changes to ocean basin volume, because the effects will be relatively small

It's rare I get to correct /u/CrustalTrudger ! Modern sea level rise predictions do include the effects of vertical land motion, because that effect is significant over 50-100 year time frames.

The IPCC has released a sea level rise interactive map that shows its projections for the rest of the century, and lets you compare the various terms.

In New York City, for example, sea level is projected to rise about 40% more than the global average. Much of this extra sea level rise is because the crust beneath New York is currently moving downward due to the glacial isostatic adjustment process Crustal described. The rest of the extra sea level rise in New York is due to the changing gravitational pull of Greenland as it melts. (!)

In a few areas, such as Hudson Bay, the crust is moving upward fast enough to completely cancel out the effects of sea level rise caused by global warming. But that's pretty rare.

Anyway, point being that modern sea level forecasts do include isostatic response, and while it's not a dominant effect, it is big enough to make a difference.

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agate_ t1_iueuo0w wrote

Replying to agate_ (#354,523)

Oh, and to follow up on my followup: the case of New York shows one important subtlety, namely that glacial loads can cause both downward and upward motions at the same time.

/u/CrustalTrudger described the earth as a viscous trampoline. I'd like to suggest you think of it as a viscous air mattress. The overall volume of the mantle remains unchanged, so if the weight of glaciers pushes one area down, nearby areas must move up, as the mantle displaced under the glacier has to go somewhere. When the glacial load is removed, the opposite effect occurs.

This means that while most of Canada is currently rising as it recovers from the weight of the Laurentide ice sheet being removed, much of the United States is currently sinking by the same effect.

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CrustalTrudger t1_iuhloty wrote

Replying to Fukkinchilll (#369,903)

> This may be a silly question, but how much weight would it take to cause this?

Mathematically, there's not a minimum threshold, but in practice, there's going to be mass distributions that are going to produce such a small predicted deflection they are not really measurable. The math for flexure is laid out in a variety of places, Wickert, 2016 provides a pretty complete view if you can't get your hands on a copy of Turcotte & Schubert. Thus, you can calculate the predicted flexure for any mass, but in practice, that mass may be insufficient to produce a measurable flexure. The other big complication here is that the response also depends on the duration of the load and/or the rate of change of the load through time as the way the lithosphere responds to loads (i.e., purely elastic, viscoelastic, etc.) depends on the rate of change of the load (e.g., Watts et al., 2013).

> Also, does it depend on the makeup of earth that sits below said weight?

Yes. If you look through the math in Wickert, you'll see a few terms that potentially vary with location, specifically the density contrast between the infilling material and the mantle and the flexural rigidity (D). For the former, this means that the density of the load (i.e., is it rock, water ice, liquid water, etc) matters, but also that theoretically the density of the mantle in that location matters. In practice, we often assume a standard density for the mantle (not necessarily always) so we don't often consider this term to vary by location (but in reality, it might). However, flexural rigidity definitely does vary by location. If you go to the appendix, you'll see a definition for D that includes Young's modulus, the Poisson ratio, and the effective elastic thickness (Te). We typically assume Young's modulus and Poisson's ratio are constants for the lithosphere, but Te can vary a lot by location (e.g., Watts, 1992, Burov & Diament, 1995, Burov, 2011), e.g., the oceanic lithosphere generally has a narrow range of Te with most being ~10-20 km whereas continental lithosphere has a pretty wide range of Te with some in similar ranges as oceanic lithosphere but others being significantly thicker. The effective elastic thickness is kind of what the name implies, i.e., it's an approximation of the thickness of a purely elastic sheet that would explain the observed deflection for a given mass distribution. Te is generally not a physical thing (many of the cited papers are trying to find relations between Te and something we can actually measure like crustal thickness, temperature profiles, age, etc) but is something we estimate from observed deflections (though for oceanic lithosphere, it is more explainable as a function of lithosphere age/temperature). In general, for the same surface mass and mass distribution lower Te means more "local compensation", i.e., larger deflections with much shorter wavelengths, whereas larger Te means less deflection distributed over a much longer wavelength. In practice, Te is the main thing that we consider to vary as a function of location (and in turn, flexural ridigity) and this has a pretty important influence on how that area responds to a given load.

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