Add attributes to WMT diagnostics

[hdrake]

The WMT rate variables output by xwmt currently either have no attributes or–even worse–inherit attributes from the input budget diagnostics, meaning that the units and other metadata are wrong and misleading.

These should have descriptive attributes, at the very least explaining what each term is and what its units are (e.g. kg s-1).

[cspencerjones]

I think this would be really helpful! We are using the package again and I find that I am confused about some of the terms. For example, I am confused about what "negative rhs" means - I think you have told me but I have forgotten. Is this written down anywhere? Even a descriptive list of terms would be helpful, so that I am not having to dig through code and the paper to figure out what is going on.

[gmacgilchrist]

Agreed, improved documentation in general, and attributes attached to variables, would be nice. This should be easier since @hdrake's paper was published. We are back working on this more regularly in St Andrews, so can contribute some of these improvements.

FYI, @cspencerjones, for the negative LHS terms, see the derivations in Appendix A of the paper, arriving at equations A15-17. It's all about reverting from conservation equations for extensive quantities into those for intensive quantities (which is what's relevant for WMT).

[hdrake]

Just a quick note to let you know that I’m recovering from a broken collarbone so not writing much code right now. I’ll be checking GitHub to answer questions and comment on PRs though.

Like Graeme said, the “negative rhs” term is what people usually call the freshwater forcing term. I found it really confusing that people don’t usually explain where that term come from, so I went in a lot of detail for it. The reason it’s important is because it’s not actually a term in MOM6 tracer budgets so you need to add it to both side of the equation to maintain conservation.

[hdrake]

In terms of documentation, the challenge is that we don’t want to prescribe a rigid form of the water mass budgets, because different models and different tracers have different terms represented.

I think the appropriate places for more documentation of attributes describing each term are either upstream of xwmt source code (in xbudget) or downstream (in model-specific example notebooks).