Couple the Halfar dome model previously created using the CISM documentation section 8.1.1, with the Mohamed et al. 2016 exterior calculus solution of incompressible Navier-Stokes as the ocean component. For more information about the Halfar dome, refer to the climate starter kit scenarios, Halfar 1984, and Buehler’s notes provided as a file in the starter kit. Place Greenland on a spherical ocean world with no other landmasses. The size of the spherical world should be comparable to the size of the Earth. Let the bottom of the ocean at a constant sea floor depth have impermeable boundary conditions. Let the lateral boundary conditions of the ocean be periodic. Assume this spherical world is non-rotating.
Using 1970 data for initial conditions, calibrate the coupled ice-ocean model parameters $A$, $\rho$, and $n$, using ice thickness data for Greenland from the year 1999. You will need to search for Greenland mesh data for 1970. Are the calibrated parameter values reasonable? What are the limitations of this model? How do these results compare to a standalone Halfar model calibration? For all questions, assume you are still in the spherical ocean world.
What will Greenland (in the spherical ocean world) look like in 20 and 50 years? Plot Greenland’s ice loss over the mesh, as a function of time.
(Challenge) Add salinity as a tracer to the coupled model in the manner Oceananigans does, simplifying where possible. Decompose fluid density into three components: the reference density, a background density, and a buoyant tracer - salinity. The buoyant acceleration of the fluid becomes $b = -\frac{g \rho'}{\rho_0}$. Also add the tracer conservation equation $\partial_t c = -u \cdot \nabla c - U \cdot \nabla c - u \cdot \nabla C - \nabla \cdot q_c + F_c$. Map salinity as a function of ocean depth.
Scenario 4: Ice and Ocean Modeling
Couple the Halfar dome model previously created using the CISM documentation section 8.1.1, with the Mohamed et al. 2016 exterior calculus solution of incompressible Navier-Stokes as the ocean component. For more information about the Halfar dome, refer to the climate starter kit scenarios, Halfar 1984, and Buehler’s notes provided as a file in the starter kit. Place Greenland on a spherical ocean world with no other landmasses. The size of the spherical world should be comparable to the size of the Earth. Let the bottom of the ocean at a constant sea floor depth have impermeable boundary conditions. Let the lateral boundary conditions of the ocean be periodic. Assume this spherical world is non-rotating.
Using 1970 data for initial conditions, calibrate the coupled ice-ocean model parameters $A$, $\rho$, and $n$, using ice thickness data for Greenland from the year 1999. You will need to search for Greenland mesh data for 1970. Are the calibrated parameter values reasonable? What are the limitations of this model? How do these results compare to a standalone Halfar model calibration? For all questions, assume you are still in the spherical ocean world.
What will Greenland (in the spherical ocean world) look like in 20 and 50 years? Plot Greenland’s ice loss over the mesh, as a function of time.
(Challenge) Add salinity as a tracer to the coupled model in the manner Oceananigans does, simplifying where possible. Decompose fluid density into three components: the reference density, a background density, and a buoyant tracer - salinity. The buoyant acceleration of the fluid becomes $b = -\frac{g \rho'}{\rho_0}$. Also add the tracer conservation equation $\partial_t c = -u \cdot \nabla c - U \cdot \nabla c - u \cdot \nabla C - \nabla \cdot q_c + F_c$. Map salinity as a function of ocean depth.