The maximum depth of the winter snow in the Australian Alps varies from year to year. If these variations were random, then the best guess for next year's maximum snow depth would be the average depth. If a linear trend and some cyclical factors are present, then it should be possible to quantify these, and make a better guess. However see the Trend Analysis, especially the final paragraph.
From inspection of Figure 1, it appears that an exceptionally good year is often (but not always) followed by several poor years,
and that there appears to be a systematic decrease in snow depth with time. I have analyzed the year to year fluctuations assuming that, in addition to a purely random component, there are periodic components which can be derived from the historical measurements, and
that these can be used to predict future behavior.
In addition to random fluctuations, a decrease of 7.6 cm/decade and
cyclic components with periods of about 4 years were found, and
used to predict the maximum snow depth for next year.
As can be seen in Figure 2, years with below average snow depths occur more often than expected from purely random variations, as do exceptional years with depths exceeding the average by more than 100 cm. Slightly above average years occur less frequently than expected.
The prediction for 2018, based on the measurements from 1954 through 2017, is for a maximum snow depth of 192.3 cm, which is 5.0 cm less than the 64 year average of 197.3 cm, 16.4 cm above the 175.9 cm expected from the decreasing linear trend, and 12.6 cm below the actual 204.9 cm in 2016.
We can expect the 2018 snow depth to be slightly below the long term average, alightly above the liner trend, but not as good as last year.
I computed the maximum entropy and linear prediction values made with a varying number of poles, and found that the minimum of root-mean-square differences between the predicted and actual values was obtained using only 4 or 5 poles.
The line has a slope of 7.6 cm/decade. With a probable error of 4.3 cm/decade.
The data were divided into three periods, plots made of the snow depth distributions for each period, and some statistics calculated from the data of each period.
Note that the first two periods (1955-1975 and 1976-1996) have an excess of years with high snowdepths, while the latest period (1997-2017) has a
more random distribution of snowdepths peaked at 176.9 cm.
Snow Depth Trends
|Average||Variance||Median||2-3 meters||> 3 meters|
Column 5 gives the number of years, and the percentage of years, in the interval given in Column 1, where the maximum snow depth was between 2 and 3 meters.
Column 6 gives the number of years, and the percentage of years, in the interval given in Column 1, where the maximum snow depth was above 3 meters. Fewer years had maximum snow depths above 3 meters in the later periods, leading to a drop in the average and median depths, as
well as to a smaller spread in depths about the average. This can be seen in the plots of the distributions as well as in the above table.
The Kolmogorov-Smirnov Test is used to obtain the probability that two data samples are drawn from the same underlying distribution.
First, I compare
the distribution of measured snow depths with normal distribution which with the same average and variance as that found
for all the snow depth data.
This probability is inversely related to the maximum vertical separation between the two lines in Figure 6.
The result of the Kolmogorov-Smirnov Test is that there is 46% probability that the snow depth distribution from 1955 through 2017 represents a
random distribution with average 197.3 and a standard deviation of 61.8 with no linear trend.
However, there is a clear difference between the early data and more recent data, as seen in Figure 5 and the table of Snow Depth Trends.
The result of this second Kolmogorov-Smirnov Test is that there is only a 27% probability that the snow depth distribution from 1954-1984 comes from the same underlying distribution as the snow depth distribution from 1985-2016.
Even more striking is a comparison with the snow depth distribution from the last 10 years, which has an average of 180.9 and a variance of only 8.7 as compared with an average of 177.6 and a variance of 40.3 for the past 31 years given in the table Snow Depth Trends. With such a small variance, I expect that snow depth for 2017 will not be much different than the average of the last 10 years, 173.3 cm, essentially the same as the linear trend, and the same as last year.