Spencers Creek snow depth prediction model - mark V

As you may know, for many years I have attempted to predict the season peak snow depth at Spencers Creek¹, midway between Perisher Valley and Thredbo, NSW, using a simple multiple regression model based on well-known climatic modes and influences.

 
It’s time for another rework. I’ve hit the thing fairly hard this time — for a relatively small improvement in absolute performance but I think a substantial gain in structure and understanding. As often occurs with such things, the result is overall a simpler model.

 

Deletions

1. Pacific decadal oscillation

The correlation of PDO with our snow season has always been tenuous. In fact the contribution it has been making to prediction outcomes is remarkably slight. Gone!

Spencers Creek season peak snow depth vs PDO

 

2. Indian Ocean dipole

To the controversial ones…    The simple fact is that, despite anecdotal commentary and a big rap in season 2016 (and not just from me!), there just isn’t statistical support for including IOD. It shows a moderate correlation with peak snow depth in a straight one-on-one, but put together in a multiple regression it just doesn’t rate.

Spencers Creek season peak snow depth vs IOD

‘All-in’ multiple regression stats

 
I still don’t know exactly why that is, but two things seem to contribute:

  • IOD and SOI are correlated, and SOI is winning in the multiple regression with peak snow depth.
     
  • Available IOD estimates for much of our snow depth record are of poor quality. I’ve written about this before, but this graph showing IOD estimates from three different sources tells the story: IOD’s from Saji et al (he invented it!) are nothing like more recent estimates from BOM. That doesn’t seem to be a definitional difference; I’ve been told it arises from the quality of the Indian Ocean SSTs used to compute it. Fine resolution is necessary, especially in the eastern upwelling region, and that isn’t available before about 2000.
  • Various IOD estimates

Regardless, gone!

 

3. Calendar year

What the…    Yep, look at the stats above. In the latest generation of my model the ‘calendar year’ term just isn’t contributing. That is not because its effect is subsumed by the SST terms, because I’m using detrended SSTs (more later). It appears to be mainly because the obvious downtrend in peak snow depth is adequately modelled by the strong uptrend in AAO.

Gone!

 

Additions

4. Sunspots

I’ve written at length before about why I don’t include sunspots in my snow depth prediction model, but given the silliness that is regularly sprouted in ‘mainstream’ media about sunspot-based prediction, I thought it would be fun to plug them in, to show how irrelevant they are. Yes there is a positive correlation between sunspots and our snow depth — a remarkably weak one:

Spencers Creek peak snow depth vs sunspots

And yes there is a putative explanation for that (see my earlier post) — an unconvincing one. But because sunspots are uncorrelated with other effects, mutiple regression loves them and bumps them up in the stats (therein likely lies a trap). Nevertheless, adding them to my model actually makes little difference, here:

MkV model with and without sunspots

I just can’t get excited one way or the other about this ‘influence’. It’s in. For now.

 

5. Split sea surface temperatures

This is the important change. I’ve been using a one-box local sea surface temperature parameter combining influences from the Great Australian Bight and from the north-west Tasman Sea (land areas are excluded):

MkIV prediction model sea surface temperature influence box

The challenge for that is the Tasman has been warming much faster than the Bight, culminating in this summer’s record high temperatures there (and a record hot summer for NZud).

2017 SSTs

January Tasman Sea SSTs

 
It has become obvious that these two influence regions need to be treated separately — if not right now, then likely in the near future. The risk with that of course is overfitting — adding cherry-picked parameters to the model for the sake of it rather than for good physical reasons, so building a behemoth with nice performance figures but little connection to reality. I’m confident that splitting the local SST influences is not that.

I have chosen to use two influence areas — one sampling the western Great Australian Bight, south-east of Perth, and another a broad area of the north-west Tasman Sea:

SST influence boxes

 
Both were chosen by manual optimisation of the correlations of the winter average SST across the box with peak snow depth — itself a form of over-fitting. I do not know whether the chosen bounds represent a physical influence, or a region of higher data quality in the historical record (more ship passes) … or perhaps just arise by chance (which would make them poorly suited to prediction). Future model performance may tell.

 
The correlations look like this (not detrended):

Spencers Creek season peak snow depth vs Perth SST

Spencers Creek season peak snow depth vs Tasman Sea SST

 
Both SST samples show strong uptrends; the Tasman very strong. For the model proper I’m again using linearly detrended SSTs, this time rotated about 2020. Without detrending the model needs its calendar year term again — with a positive coefficient (depth increasing with time!). Presumably that is because the uptrends in the SST series are a little too strong relative to the correlation of their year-to-year variations with peak snow depth. Linear detrending doesn’t alter the model outcome at all (with the calendar year term in — because it is a completely linear model).

 

Outcome — the MkV model

The new six-parameter model equation is:

  Spencers Creek peak depth (cm) = 263 – 16.6 x AAO + 2.59 x SOI – 46.5 x SST_Perth – 84.9 x SST_Tasman + 585 x aerosol + 0.02 x sunspots

 
Compared to the previous MkIV model it goes like this:

MkV model vs old MkIV model

 
As said, the improvement is slight. The standard deviation of the residuals falls by about 2 cm from 44 cm to 42 cm. I think it’s a better model.

 
The 2018 prediction will be out shortly.

 

Notes

1. Snow depth at ~1830 m elevation at Spencers Creek near Charlotte Pass, NSW, midway between Perisher Valley and Thredbo; data from Snowy Hydro Limited.

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