## Monday, 14 October 2019

### HSC General Maths questions

Every year the HSC General Maths exam in NSW has some question about a roof with rainwater and a cylindrical tank to hold it in.

I just created three sample questions (with worked answers) if anyone else has students / family / self wanting to get some practice questions that aren't already in a past paper.

## Monday, 11 February 2019

### What's happening to the rain in the city of the endless summer?

I hear that my friends and colleagues in the USA are having a cold winter. Could we swap? We've got enough heat to spare this summer.
I've started pining for the cold season -- April to September in Sydney.
I remember the "cold season" from my childhood having sport cancelled a little bit more regularly than it is for my children. By the way if anyone else from my soccer team is reading this, do any of you remember us ever scoring a goal or winning a game? Maybe we didn't practice enough.
Anyway, I don't remember the droughts being as bad back then either.
So how much less rain are we getting?
Looking at the left-hand graph, it's a very noisy signal, so I went with a Theil-Sen regressor to try to find a good trend line. Theil-Sen should be more robust to noise than using ordinary least squares regression. It's not super-accurate, but roughly 0.6mm per year looks about right. 30mm difference since the 1960s is roughly 5% less rain. That sounds (and looks) about right.
Normally I wouldn't want to do a 50 year rolling average on a data set that only goes back to 1859, but anything much less than that and the trend wasn't very clear. Even using a 50 year trend (the graph on the right) it's still quite lumpy.
So what's going on? Is it raining less heavily than it used to?

Nope -- that's the opposite of what we expected. When it rains in the cold months, it actually rains harder than it used to.
In 2001, a typical cold-season storm dropped 8.8mm of rain. The median rainfall on a rainy day was 8.8mm. In 1901, a typical storm deposited just 2.8mm.
So is it raining less often?

Yep -- a lot less. Winter drought is a serious thing now. Back in 1891 it rained for 120 days (out of the 183 days in what I call the "cold season"). Last year (2018) it was 50.
Out of the top 10 driest winters (fewest days of rain), 4 of them happened since 2000; and if we discount the extremely dodgy-looking measurements from 1858 (the first year the Bureau was taking measurements) then 5 out of the top 10 have occurred since 1995.
(Silly extrapolation: the regression trend suggests one less rainy day per decade. 2409 will be on track to have no winter rain at all. I think that would make Sydney into a desert.)
Droughts are getting longer (through winter and summer), and then when the drought breaks, we get smashed with a deluge of rain in a short burst. Winter wasn't like this when I was younger: ask some older people about their experiences too. It was just regular constant drizzle.
Summer rain patterns are more complex, and I'll do a post about that another day. Preview: summer rain isn't solving the winter drought problem.
If anyone wants to do Melbourne (the city that rained that little bit more than Sydney), I've put the jupyter notebooks on github here: https://github.com/solresol/endless-summer/blob/master/rainfall.ipynb