How useful is a new roof on a shabby house? An example from glacier modeling

Coming from geosciences, we hopefully know what we want to do. Coming from numerics, however, we often know quite well what we are able to do and look for a way to sell it to the community. A few years ago, deep-learning techniques brought new life into the glaciology community. These approaches  allowed for simulations of glacier dynamics at an unprecedented computational performance and motivated several researchers to tackle the numerous open questions about past and present glacier dynamics, particularly in alpine regions. From another point of view, however, it was also tempting to demonstrate that the human brain is still more powerful than artificial intelligence by developing a new classical numerical scheme that can compete with deep-learning techniques concerning its efficiency.

Starting point was, of course, the simplest approximation to the full 3-D Stokes equations, the so-called shallow ice approximation (SIA). Progress was fast and the numerical performance was even better than expected. The new numerical scheme enabled simulations with spatial resolutions of 25 m on a desktop PC, while previous schemes did not reach simulations below a few hundred meters.

However, the enthusiasm pushed the known limitations of the SIA a bit out of sight. Physically, the approximation is quite bad on rugged terrain, particularly in narrow valleys. So the previous computational limitations have been replaced by physical limitations since high resolutions are particularly useful for rugged topographies. In other words, a shabby house has a really good roof now.

What are the options in such a situation?

• Accept that there is no free lunch and avoid contact to the glacialogy community in the future.
• Continue the endless discussion about the reviewers' opinion that a spatial resolution of 1 km is better than 25 m.
• Find a real-world data set that matches the results of the model and helps to talk the problems away.
• Keep the roof and build a new house beneath. Practically, this would be developing a new approximation to the full 3-D Stokes equations that is compatible to the numerical scheme and reaches an accuracy similar to those of the existing approximations.
• Take the roof and put it on one of the existing solid houses. Practically, this would be an extension of the numerical scheme towards more complicated systems of differential equations. Unfortunately, efficient numerical schemes are typically very specific. So the roof will not fit easily and it might leak.

The story is open-ended, but there will be at least a preliminary answer in the presentation.