Compose Budyko-Sellers with Halfar

[lukem12345]

Budyko-Sellers-Halfar

This PR composes the Budyko-Sellers 1D energy-balance climate model with the Halfar model of glacial dynamics.

Motivation

We wish to demonstrate an Decapodes multiphysics composition in which "the coupling occurs in the bulk... through source terms or constitutive relations that are active in the overlapping domains of the individual components" as described by Keyes et al. in their survey "Multiphysics simulations: Challenges and opportunities"1 . Keyes et al. note that there are in fact many classifications of multiphysics, although in practice this first one is the one that most people refer to.

Composition Pattern

We do so with the composition pattern:

In our composition, Halfar's A is computed at each time-step according to the temperature T at each point on the domain. The chosen formula is inspired by the relation between A and T given in the table on page 2 of Halfar's 1981 "On the Dynamics of the Ice Sheets"2.

This composition of models should be revisited in the context of "ice albedo feedback", such as that examined in Widiasih's "Dynamics of the Budyko Energy Balance Model"3. As currently written, the warming Decapode updates the "A" power-law variable considered by the Glen's Law component of the Halfar model, but does not connect it this back to the albedo considered by the Budyko-Sellers model. Thus, the current warming Decapode "feeds", but does not "feed back" at this time. (This is stated concisely and diagrammatically in the following section.) Note that there is no limitation to the Decapodes approach that prevents this. (I just need to spend more time looking at Widiasih's paper to figure out which equations to use.) In fact, the models could be composed with the following composition diagram now, and using the current warming Decapode, but the physical validity of this is questionable.

Feedback Composition Pattern

Diagrammatically, we say that the complete feedback Decapode that composes a model like Widiasih's is:

The result of the above composition would be the Widiasih Decapode to follow the current trend of naming Decapodes after the first author of the paper inspiring them.

Appendix

A.1: Decapodes

The Budyko-Sellers and Halfar Decapodes are not repeated here.

Warming

A.2: Simulation Results

Citations

GitHub may automatically replace these citations with hyperlinks.

[codecov]

Codecov Report

Patch and project coverage have no change.

Comparison is base (2dfdd4b) 88.40% compared to head (81fb989) 88.40%.

Additional details and impacted files

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