Back when I was a student, I took a course on environmental modelling. Well, that’s what it said in the guidebook – it was almost entirely about modelling water flows in river catchments. (Either way, if you’re studying maths at ANU, I recommend looking into it.)
Early in the course, we looked at a very simple model. It worked like this:
- Get a reading from the rain gauge
- Assume rain is even over the entire area, and work out how much water that is
- Stick in a delay (maybe half a day) before the water reaches the river
- Assume that the water will come fast at first, and gradually tail off
- After a few days, assume all the water that hasn’t come yet will all come in a pulse, so you don’t have to keep calculating things.
So essentially, the entire model is delay, then decay. No consideration for the season, temperature, soil, vegetation or anything. An entire river summed up with just two numbers.
We moved on to more complex models, some with multiple decay functions, some with rudimentary soil hydrology. Obviously, since they modelled the mechanisms more accurately, they’d give better results, right?
Turns out they gave different results, but they weren’t necessarily any better. A single rain gauge doesn’t give particularly good information about rainfall over a whole area, especially when it’s only being checked once a day. River flow measurement wasn’t particularly accurate either.
Since no model was particularly good, the lecturers used the simplest one when doing field work. It gave useful results, and it was easier to explain. And that’s an important point – if you want people to use your model, make sure they can understand it.