Snow Depth Prediction

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. However, if some cyclical factors are present, then it should be possible to quantify these, and make a better guess.

From inspection of Fig. 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 can be used to predict future behavior. In addition to random fluctuations, cyclic components with periods of 3.4 years and 5.4 years were found, and used to predict the maximum snow depth for next year.

Figure 2. -- Distribution of maximum snow depths. Actual values are represented by the solid line histogram. For comparison, a random distribution with the same average value and variance is represented by the dashed line. The predicted 2008 value is shown as a filled circle.

As can be seen in Fig. 2, years with low snow depths occur more often than expected from purely random variations, as do exceptional years with depths exceeding 300 cm. Average and slightly above average years occur less frequently than expected.

The prediction for 2008, based on the measurements from 1954 through 2007, is for a maximum snow depth of 242 cm, 21% more than the 54 year average value of 200.3 cm, and more than the 2007 actual depth of 164.4 cm

Figure 3. -- Comparison of actual (open circle) and predicted (solid dot) snow depths.

The depths from 2005 are over predicted, and with 2008, are part of a predicted rise in snow depths, while the actual depths had a deep minimum in 2006.