Lectures 9-10: Sea level

• Coastal geology wrap up
• Relative sea level
• Glacial isostatic adjustment
• Viscoelasticity
• Earth as a viscoelastic solid
  • Elastic response (ongoing melt)
    • Fingerprints of ice melt
  • Viscous response (after melting ends)

We acknowledge and respect the lək̓ʷəŋən peoples on whose traditional territory the university stands and the Songhees, Esquimalt and W̱SÁNEĆ peoples whose historical relationships with the land continue to this day.

Hawaii

Linear features in lithified carbonate dunes at 6.7 meters and 8.2 meters

The Bahamas

The Bahamas

Relative Sea Level

Relative Sea Level

Glacial isostatic adjustment

• Postglacial rebound: viscoelastic response of the solid Earth after ice melt
• Glacial isostatic adjustment: the viscoelastic response of the Earth's solid surface, its gravity field, and rotation axis to changes in ice and ocean load

Glacial isostatic adjustment

• Postglacial rebound: viscoelastic response of the solid Earth after ice melt
• Glacial isostatic adjustment: the viscoelastic response of the Earth's solid surface, its gravity field, and rotation axis to changes in ice and ocean load

Glacial isostatic adjustment

• Postglacial rebound: viscoelastic response of the solid Earth after ice melt
• Glacial isostatic adjustment: the viscoelastic response of the Earth's solid surface, its gravity field, and rotation axis to changes in ice and ocean load

Our previous considerations of isostasy

Viscoelastic deformation

Stress is proportional to strain and a constant of proportionality (the Young's modulus or spring constant, k)

$$ \sigma = k \frac{\Delta L}{L}=ke $$ Hooke's law

$$ \sigma = \mathrm{stress}\\ e = \mathrm{strain} $$

Viscoelastic deformation

Stress is proportional to strain rate and a constant of proportionality (the coefficient of viscosity, $\eta$)

$$ \sigma = \eta \frac{d}{dt}\left(\frac{\Delta L}{L}\right)=\eta\frac{de}{dt} $$ For a fluid whose viscosity is not dependant on strain rate (Newtonian fluid)

$$ \sigma = \mathrm{stress}\\ e = \mathrm{strain} $$

Viscoelastic deformation

In the simplest model of viscoelastic deformation (a Maxwell body), the total strain is the sum of a viscous term and an elastic term that feel the same stress.

$$ \frac{de}{dt} = \frac{1}{k}\frac{d\sigma}{dt} + \frac{1}{\eta}\sigma $$ An instantaneous elastic response and a time-dependant viscous response for a fluid whose viscosity is not dependant on strain rate (Newtonian fluid)

$$ \sigma = \mathrm{stress}\\ e = \mathrm{strain} $$

Why is the spring constant paired with the time-dependant term? Consider the end-members of infinitely stiff springs or infinitely high viscosity.

Viscoelastic deformation

In the simplest model of viscoelastic deformation (a Maxwell body), the total strain is the sum of a viscous term and an elastic term that feel the same stress.

$$ \frac{de}{dt} = \frac{1}{k}\frac{d\sigma}{dt} + \frac{1}{\eta}\sigma $$ An instantaneous elastic response and a time-dependant viscous response for a fluid whose viscosity is not dependant on strain rate (Newtonian fluid)

$$ \sigma = \mathrm{stress}\\ e = \mathrm{strain} $$

Why is the spring constant paired with the time-dependant term? Consider the end-members of infinitely stiff springs or infinitely high viscosity.

Earth as a viscoelastic solid

• Maxwell time: time after which half of the deformation is elastic and half is viscous. A body is often considered elastic for $t<<t_{\mathrm{Maxwell}}$ and mainly viscous for $t>>t_{\mathrm{Maxwell}}$.

Earth as a viscoelastic solid

• Load change at the top (a change in stress)
• instantaneous elastic response
• time-dependant viscous response

Elastic response

Sea level response to rapid melting of ice sheets and glaciers:

Elastic response

Sea level response to rapid melting of ice sheets and glaciers:

Sea level fingerprints

The instantaneous spatial pattern of sea level rise will be different depending on which ice sheet is melting

Sea level fingerprints

The instantaneous spatial pattern of sea level rise will be different depending on which ice sheet is melting

Viscous response

What is the ongoing viscous response during an interglacial (after most ice melting is complete)?

Viscous response

Numerical prediction of present-day rate of local sea-level change due to ongoing glacial isostatic adjustment

Describe the general pattern you see. What gives rise to this pattern?

Viscous response

Viscous response

Viscous response

Viscous response

Viscous response

Viscous response

Viscous response

Viscous response

Try to draw the temporal evolution of sea level during an interglacial (with no excess melt) for Hawaii and The Bahamas.

Past warm periods can tell us how sensitive ice sheets are to warming

Past warm periods can tell us how sensitive ice sheets are to warming

Sea level reconstructions are uncertain largely due to uncertainties in GIA, but more data and better inversions can help.