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In the model, two processes impact the sea level:
- Thermal expansion, which depends on the ocean temperature .
- The ice sheet melting, which depends on the ice sheet extent .
We note by the sea level anomaly with respect to the present-day
level:
, where is the
average sea depth
The average sea depth is calculated as:
where
is the volumetric mass of water at temperature
, is the global-mean ocean temperature, which
is supposed to be an average of the global surface temperatures over
the previous 100 years , the total sea water mass and
the surface of ocean basins.
- We calculate
assuming a linear relationship as
a function of , given the thermal expansion coefficient
:
- We calculate
by a mass balance: let
be the total mass of the water in the system {ice sheets + ocean},
and the fraction of this water trapped in ice sheets.
We have:
Assuming that the surface of the ocean basins is constant, we get:
where id the average sea depth if all ice sheets had melted.
We take =3.8km ([Herring and Clarke, 1971]).
Therefore:
We parameterize by a 3rd-degree polynomial function
so as to respect the constraints summarized in section 2.1.
Next: Acknowledgments
Up: 5 Appendix: equation details
Previous: 5.4 Albedo and ice
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Camille RISI
2023-07-24