Upper boundary condition of the dynamic scheme

[pat-schmitt]

During the development of a new dynamic scheme (see PR) a discussion about the upper boundary condition (at the highest point of the glacier bed) arose. The question is: What should we do with the ice flux at the highest point of the glacier? (The ice flux to the left at distance 0 in Figure 1).

Two possibilities:

1. Set the flux to zero: We do not allow any ice flux to the left at the highest point. (The current default)
2. Define one extra grid point at the left and set this ice thickness to zero all the time, but allow an ice flux to the left. (Suggested by @dngoldberg)

An advantage of the first approach is that no untracked ice gets lost at the highest point. Also, when we think about ice caps (Figure 2), it could be that there is also a glacier flowing down the other side of the mountain.

On the other side, if we think of pure valley glaciers, it is unphysical to have a high vertical wall of ice (like for the blue line in Figure 1 at distance 0). And probably, this should be included as a limit for glacier growth. Presumably, it has not a large influence when dealing with today's glacier states (like the dashed line in Figure 1), but could be important for equilibrium experiments like @juliaeis is conducting (blue line in Figure 1).

An idea also would be to use condition one for ice caps and condition two for pure valley glaciers. But I am not sure how easy it is to get the information if the flowline starts at an ice divide, and implementing two boundary conditions will add quite some complexity to the code. Not sure if this is worth it...

Figure 1, made by @juliaeis

Figure 2, from Maussion et al. 2019