One of a series, also see editions: #2, #3, #4, #5
Readers will know that I don’t make my peak depth prediction for the Australian snow season until April, when the required parameters become clearer, but I see that Mr Peterson’s prediction for the 2014 Spencers Creek peak depth is in at a generous 201.2 cm.
Peterson’s method users cycles he detects in the Spencers Creek (near Charlotte Pass, Australia) peak snow depth record applied to its long term trend. Given that I’ve previously argued that the record contains no discernible cycles (other than a weak 2-year one, probably a chance artifact), I don’t expect Peterson’s method to have much more skill than say just picking the mean trend estimate. That said, my own method using regressions with well-known climatic variation modes isn’t exactly wildly skillful either. Prediction is difficult, especially about the…
Here’s how we’ve gone in the past¹:
Trend significance
Peterson also has things to say this year about the significance of the downtrend in the Spencers Creek peak snow depth record. By reference to the confidence limits on the trend slope, he estimates the probability that there is “no slope at all” at 32%². What he fails to say is that that is the probability (actually of zero or positive slope) knowing nothing else. I submit that we most emphatically do know lots else, so the finding is not interesting. (It arises because the peak depth series is highly variable — noisy — and the record is relatively short given the amount of noise.)
Kolmogorov–Smirnov
Peterson’s interpretation of this statistical test is odd. What he really seems to be testing is whether the annual peak depth readings, taken as a whole, fit a normal distribution with the same mean and variance as the sample. The relatively high probability that the peak depths are not normally distributed (31%) is coincidentally similar to the (incorrect²) “no trend” probability he calculates. The high result is very likely due to smearing of near normally distributed residuals by the effect of the trend, but by itself says nothing much about presence or absence of trend. For example, it could just be that the depths really aren’t normally distributed; not everything in nature is.
Notes:
1. The comparison isn’t a completely fair one. My “predictions” plotted are really hindcasts using the actual observed parameters through each season. Most of Peterson’s are true a priori predictions, I think. Some early ones might be a posteriori.
2. Update: His estimate of this probability appears to be way high. The least squares slope over 1954-2013 is -0.70 cm/year and its standard error is 0.47 (uncorrected for slight negative autocorrelation), so the probability that the slope is actually zero or positive is only about 7%. Knowing nothing else.
