Comments on the last post speculated that rainfall in Australia might show a trend if one looked at smaller regions than the entire continent. In particular, some wondered about the history of precipitation in New South Wales (NSW, one of the areas hardest hit by bushfires), and one reader was kind enough to point to data from Australia’s BoM (Bureau of Meteorology), featuring this map of the trends in rainfall since 1970 throughout NSW:
Almost every part of the state shows a declining trend. But how significant is the trend?
Their data for precipitation throughout the state of NSW actually begin back in 1900; here are annual averages:
I’ve shown a linear trend (by least squares) as a red line, but that does not mean the trend is necessarily a straight line; that’s just what the linear trend is. It’s upward, but the statistics say it’s not “statistically significant” — the uncertainty (shown by the pink area) is big enough that the real trend could be flat, or even slightly downward, or not even a straight line.
The straight-line model is great when the trend is a straight line, or even close. But when it isn’t, I like to look for more general patterns with a smoothing fit, and if you’re a regular reader you know I like the lowess smooth:
Now we see hints (but not conclusive) of a possible downward trend recently. Hence I fit a linear spline, a model consisting of two straight-line segments joined at their endpoints. I chose the time at which the trend changes direction by changepoint analysis (adapted to this model), and it turned out to be 1974 — not far from the 1970 starting point for the trends given in the map from BoM. Here’s the best-fit such model as a blue line (with dashed blue lines outlining the uncertainty) compared to the linear model (red line with pink uncertainty range):
The changepoint analysis doesn’t just identify the optimal time of the trend change, it also provides a test statistic to determine whether or not such a trend change is statistically significant. The result indicates that it definitly is not. It might look so, but you can almost always find a changepoint time that makes it look that way even with random noise (the essence of the multiple testing/selection bias problem).
Even if I use only the data from 1974 onward and fit a straight line, I still don’t get statistical significance. This isn’t really the right test, it’s too likely to say “significant” when it isn’t really — but even cheating in favor of significance doesn’t make it happen.
The bottom line is: I don’t see evidence for a trend in precipitation in New South Wales, at least not in the annual average data.
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Open Mind 
I appreciate this clarification.
Beautiful number work! So clear, comprehensive and honest imho.
I see that there are regular spikes up or down that seem to happen in a 3 or 4 year cycle: 3 up in mid 1980s, 3 down in mid 90s, 4 down start around 1998, 4 down again start around 2010, 4 down again start 2016. If there is trend down that is stat significant, we may need a couple more decades of data to nail that down. I don’t expect to be around to see it and I hope it doesn’t happen because the fire conditions are simply hell on earth for the resident beings.
Thanks for your work!
Thanks for this analysis. It shows me that data is evidence and that data tells a story. I look at the parched landscape burning and while the dryness of the last few years has given this tinder dry landscape vs the statistics of your graphs suggest more.
I recall ‘pan evaporation’, being the evaporation levels of an open pan of water, being used to compare the water that leaves a landscape with that of the rainfall, being the water that enters the landscape. Cloudy days reduce the evaporation, leaving more water for nature and for farming. Blue Sky days with light breezes increase pan evaporation.
I also recall that torrential rainfall with overland floodwater flows (such as from storm events) enters rivers, and steady rainfall wets and hydrates the landscape – not really entering the rivers until the land is saturated. What type of evaporation and what type of rainfall is therefore important, and that is a complexity that I would not know how to approach.
What if you remove outliers caused by ENSO…[and is there a way of meaningfully deciding where on the index that cut-off should be, and does that leave enough data for anything genuinely informative?].
1973-74 were big la Nina years [as with 1950 and 2010-11].
>The bottom line is: I don’t see evidence for a trend in precipitation in New South Wales, at least not in the annual average data
Which backs up what the BoM has said in the past.
They have also said there IS a trend in the SW of Western Australia of reduced rain fall and they have suggested that the NW of Australia will get increased rain fall and the SE will get reducued rainfall in the long term. Where their delination for SE is, I am not sure ? About Port Macquarie and south I think but am unsure.
I live in the SW of Western Australia, and it seems that more cold fronts pass too far south to provide rainfall for us. This is due to trends in the southern annular mode, see https://youtu.be/KrhWsXCB3u8.
For us in the west, our source of rain is either cold fronts, or tropical moisture sucked in from our north. And we do seem to get a bit more rain from this source these days.
The east coast of Australia is a more complex system than ours.
Looks like NSW also may have had the driest year on record, besides Australia, as a whole. Regardless of what the longer term trend is, this must have an effect for this extended fire season. The short term “trend” makes me wonder if Australia is hitting a tipping point.
MR says: “The short term “trend” makes me wonder if Australia is hitting a tipping point.”
Tipping point or exponential growth, doesn’t matter too much. The precautionary principle suggests that we be careful about problems that appear to grow in a linear fashion because we will have trouble discerning the early stages of exponential growth from linear growth. So, we look back and see steady or slowly accelerating growth and we project forward based on the linear trend when we are actually in a system of exponential growth or a system that include positive feedbacks/tipping points that will cause systems to behave in a manner that we do not anticipate.
So, yes… it’s worthwhile asking if we want to take chances with what appears to be linear growth or appears to have no statistical significance in an area where a miscalculation has disastrous consequences.
Lot of fire in Australia, but no statistical significance detected. Do you feel safe knowing that the stats don’t ring the alarm bells? Grab a flight and spend a week at the beach in Mallacoota and then get back to us with your thoughts.
Warm regards,
Mike
@smallbluemike,
Not to throw cold water on Tamino’s technique, which is good and standard, but just to point out that one of the problems with classical significance and other tests is that it goes into analysis with the Let’s pretend we know absolutely nothing else mindset, which is not only unrealistic, it’s just not true. Accordingly, it is no surprise that “tests” often return nulls, because they have no power to detect anything.
Of course, a denier or else skeptic might say use of priors — which is one alternative — is putting a finger on the scale. But I’d counter that failing to do so is putting a finger on the scale in another direction. Moreover, there are principled ways of constructing these. Y’might, for example, take the complement of land in Australia to form a broad band of prior for precipitation trends, or even all the non-NSW land in the latitude band of Australia to form a broad prior for precipitation trends.
Or you might work in the frequency domain instead of the time domain, recommending in particular the work of Rosen, Wood, and Stoffer (2012) in “AdaptSPEC: Adaptive spectral estimation for nonstationary time series” JASA, 107, 1575-1589, as realized in the BayesSpec package of R, or Roever’s somewhat famous bspec package which riffs off psd (see overview), which is a frequentist standard. bspec is famous because it was used in the Nobel-winning LIGO work.
Trend in the areas that are burning…
http://www.bom.gov.au/climate/change/#tabs=Tracker&tracker=trend-maps&tQ=map%3Drain%26area%3Daus%26season%3D0112%26period%3D1920
Also, around Australia there is a common thread that in the 70s rainfall patterns changed, with less in the south especially. The CSIRO climate models suggest this will continue.
How long before this is significant?
Yep. I live here and have looked at the data … a lot. Neitehr you nor BOM nor CSIRO would/have find trends in a region such as NSW. Maybe in a few years if you combine NSW VIC SA and TAS (SE Austrailia, a climatic region not a political grouping, such as looking for trend in Nevada climate as opposed to great plains, Rockies etc.) I believe the SW WA trend crossed into significance.
Click to access SWSY_Climate_TechRpt.pdf
And a different style of test. one that tried to identify how far south the southern rain band was. (AKA what is the latitude track of the high lows and cold fronts) and have they moved south and offshore (taking the rain with them). variability in our country is damn high. We are the land of droughts and flooding rains always were, even if they are getting worse that makes it hard to prove on restricted subsets not the overall pattern effect. There would also be the question of causation as the ozone hole apparently also played a role.
Thanks Tamino, very interesting.
All the best to you & ‘Pamina’ – especially in the health corner – for this year.
@Tamino (h/t @Bindidon),
Yes, heartiest of wishes and luck from me, too!
@smallbluemike, @Tamino,
By the way, the “latest and greatest” appears to be the bsplinePsd package of R documented in:
M.C.Edwards, R.Meyer, N.Christensen, “Bayesian nonparametric spectral density estimation using B-spline priors“, Statistics and Computing, January 2019, 29(1),67-78.
I have not tried this yet. However, I’m planning on diving in to analyses of some streamflow and riverflow series this first quarter, and I’ll try it and report on my experiences at my blog.
My 50 odd years experience in North East NSW leads me to have the hunch that the rainfall has become/is becoming increasingly seasonal and more intensely episodal. Spring and early summer are drier than they were – hence fires. Late summer early autumn makes up the difference for the annual average with cyclonic activity or monsoonal troughs bringing brief heavy dumps Also when there is rain in spring summer it is 2 inches overnight which runs straight off the bone dry ground rather than regular light soaking showers. A trend or not in average annual rainfall will tell you nothing about soil moisture, which is a big factor in flammability of vegetation and ecosystem health. Of course this is just me talking out my arse (ass). I’m not a data and stats head (despite frequently lurking in this blog)…but I do find my arse often makes sense.
I think Mary Potter has asked the right question: does the data indicate the pattern of rainfall has changed?
You should revisit these gems from your past Tamino:
http://web.archive.org/web/20080914072308/https://tamino.wordpress.com/2008/05/30/drought-in-australia/
http://web.archive.org/web/20080803024223/tamino.wordpress.com/2008/06/08/victoria-rainfall-fall-rain/