# Statistical prediction

The correlations with the oceanic and other climate variation modes described in the previous post can be used to build a simple statistical prediction model using multiple linear regression:

Spencers Creek peak depth (cm) = 1438 – 0.61 x year – 24.8 x AAO + 0.86 x SOI – 13.2 x IOD – 10.4 x PDO – 0.17 x last year’s depth

AAO, SOI & IOD are the June-July-August averages and PDO is the 2-year average to August.  I also include the calendar year to model the downtrend and last year’s depth to implement a weak 2-year cycle like that seen in the Fourier analysis.  The resulting model explains 31% of the variance (~27% detrended), which is not a lot, but not nothing either.  As a result the estimate is only good for about +/-50 cm at 1-σ (range includes about two-thirds of years).

For 2013, my guesses for the parameters are AAO 1.0, SOI 0.0, IOD -0.2 and PDO -1.4.  That gives a “best estimate” peak depth of 170 cm.

Historically, this “new” model goes like this (vs the “old” regression model I used in previous years and a popular cycle-based model from Bruce Peterson at ANU):

More:  It’s worth noticing one of the perils of statistical prediction there.  The first five parameters (year, AAO, SOI, IOD and PDO) all carry solid physical reasons why they should affect our snow, and in the direction modelled.  Global warming tells us to expect a downtrend, and –0.61 x year implements one.  We live in an ENSO climate, so +0.86 x SOI is no surprise.  The point is that correlation by itself is never reliably predictive.  It is correlation plus understanding that justifies the inference of causation, and only then is statistical prediction valid.

Which leaves us with that last parameter, –0.17 x last year’s depth.  The data does show some weak negative auto-correlation (tech speak for what that does), and it does show a weak 2-year cycle in Fourier analysis (last year bad — this year good).  The trouble is, I can’t think of a single physical mechanism which could possibly make that happen.  Most likely it’s just chance; some statistical artifact.  If so, there’s no way it can be predictive and no justification whatever for including it in a predictive model.  So why’s it there?  Err, guilty your honour … anyway, the effect is pretty minor here.

### 4 comments to Statistical prediction

• Michael

best estimate seen yet – means Vic should hit about 140cm at Hotham and 80cm at Buller

• Gerg

Thanks. A couple more paragraphs there you might be interested in.

• Michael

Why is it that average snow fall is Hotham (3m), Falls (4m), Thredbo (2.4m) and Perisher (2.5m) yet NSW always has higher snow base?

• Gerg

Resort dishonesty … seriously, few resorts are entirely honest about their snow. Years ago the competitive dishonesty between Thredbo and Perisher got so absurd that a truce was declared and both agreed to use Snowy Hydro’s depth from Spencers Creek, half way between the two. (In recent years they seem to have reneged on that deal and are back to reporting separately.) I expect you’ll find that the 2.4/2.5 m is not aggregate snowfall but the average aggregate week-on-week increases in Spencers depth over the season, which is not quite the same thing.

One way to check is to look at the average precipitation for June-July-August, when most of our snow falls. You need to be careful though, because not all winter precipitation is snow (unfortunately), some records are too short, and snow precipitation gauges can be unreliable. For Charlotte Pass (near Spencers Creek, half way between Perisher and Thredbo), the JJA average is 570 mm (1930-2013, pretty reliable). If all of that fell as dry snow (it sure doesn’t), that would be about 5.7 m of aggregate snowfall based on the general “1 cm per mm” rule. That’s a whole lot more than 2.5 m. Unfortunately the Falls Creek record is too short and unreliable to compare, but the equivalent for Hotham Heights is about 470 mm (1925-1991) so 3 m snowfall there is believable; 4 m close by at Falls Creek seems a touch high.

My take would be that all four resorts probably average between 3 and 4 m snowfall a season, with Perisher / Thredbo a bit higher than Hotham / Falls.