One of a series; also see editions: #1, #3, #4

Well that’s easy … why not just take the peak depth trend (from Spencers Creek, near Charlotte Pass, Australia) and extrapolate? Hey, zero in 2270, no worries:

I can think of at least four things wrong with that (below) but it’s enough to notice that the trend is rather poorly defined statistically (*knowing nothing else**), so simple extrapolation is seriously dubious. If we just consider the uncertainty in the *slope* of the trend (and ignore the uncertainty in position), we get a range of possible zero dates that is near uselessly wide (the range shown is ±1 standard deviation, which only covers about two-thirds of possibilities; there’s another third even further out):

### Issues:

- As explained, the peak depth series is so variable (“noisy”) that the trend is not well enough defined to provide a useful estimate by extrapolation.
- Global warming is not linear anyway, so linear extrapolation of an outcome is a dopey choice. Both the increase in temperature to date and the predicted future increases show major acceleration, like this:

- The response of snow depth to warming is not likely to be linear either. Warming affects our snow in multiple synergistic ways: by decreasing the winter proportion of snow vs rain precipitation, by decreasing total winter precipitation (overall drying in SE Australia), and by increased and earlier melt (already observed). See the Hennessy report.
- We’re after the date of the first zero snow depth season, or rather the chance of that happening by a particular date. That is not the same thing as the date when the peak depth trend reaches zero. The spread of likely future depths about the trend will begin to intersect zero long before the trend itself gets there. Aggregating that intersection over a number of years, the cumulative probability of getting at least one zero is going to become large long before the midline intersects:

But it’s not even that simple. We showed earlier that the band of variability about the trend is unlikely to be of constant width over time. It’s more likely to be at least partly proportional to the current trend estimate; something like this:

It’s pretty obvious that we’re kidding ourselves here. But there may yet be a way, next time.

### Notes:

* We sure do know lots else; see for example the Hennessy report and recent update.

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