Week 9: The month the tank runs dry

Week 9 — the monthly storage balance, why annual averages hide drought, and a synthetic dry-year dataset to test your design against

3 May 2027

Open slides — week 9

The question#

You have a supply curve from week 7 and a demand curve from week 2. What size tank turns one into the other, what does it cost, and what still fails?

The last clause is the week. Every storage design fails somewhere; the question is whether you know where before your marker does.

The method: the monthly balance#

V(t) = min( capacity, V(t−1) + inflow(t) − demand(t) )

Run it over a repeating average year with a three-year spin-up and report year three, so the starting volume you guessed stops mattering. Three rules:

1. Domestic demand has first call. A domestic shortfall is carted in, and carted water counts as an import in the closure denominator.
2. The garden gets greywater first, then whatever the tank still holds. A garden shortfall lowers garden water satisfaction, not water closure — which is exactly why the two are always published together.
3. When the tank is full, inflow overflows. Overflow is reported. It is not a loss you can spend.

Storage comes out of the same $30,000 as everything else, at $130 per kL for the shell plus $1,000 per tank for pad, plumbing and overflow.

Worked example: Darwin, where the annual balance lies#

Darwin’s numbers, all from the excellent reference design:

Read those last two rows together. The site throws away 245 kL and buys 48 kL, in the same year, with a surplus on paper of 192 kL. 1.4 % of Darwin’s rain falls in its driest four months. The annual balance is not merely imprecise here; it is the wrong question.

The obvious response is a bigger tank. Test it: raising new-storage spend from $4,000 to $9,000 buys 38 more kilolitres and moves Darwin’s water closure by 0.06, while consuming $5,600 of a $30,000 allowance once establishment is counted. That result is why this course’s own reference designs were re-costed and their storage reduced — the earlier recipe was buying capacity the wet-dry cycle could not use.

Storage saturates. Find where yours does before you spend the budget.

The drought-year dataset#

Average-year monthly means contain no droughts, so a design tuned to them is tuned to a year that never happens. The course supplies a clearly labelled synthetic dry-year dataset for each site — monthly rainfall scaled from that site’s Bureau of Meteorology statistics toward a low decile, then perturbed.

It is synthetic. It is not a historical drought and must not be described as one. Its job is to make your design fail somewhere visible, so you can say what fails first and what you would do about it.

Five sites: storage, imports and overflow at the excellent design#

What this week hands you#

A sized storage system with the month it empties named, the volume imported, the volume overflowing, and the same figures re-run against the dry-year dataset. A design that never fails on the dry year has not been tested hard enough.

Back to week 9 overview