Snowfall Frequency Expressed by Regression Analysis with Logarithms

The frequency of phenomena that cause natural hazards is an important factor in planning measures against those phenomena. In the frequency analysis, probability distributions of extreme values are commonly used to ascertain the return period, but complex procedures such as parameter setting are necessary in order to fit the data to the probability distribution. On the other hand, it has long been known that the relationship between the frequency and the magnitude of natural phenomena exceeding a certain threshold can be simply approximated by exponential and/or power-law distributions. We examined the suitability of an approximation using an exponential function for snowfall events in order to obtain a simple method (i.e, one not using the probability distributions) for determining the frequency of snowfall events exceeding a certain snowfall amount.
The frequencies of snowfall events were analyzed using hourly snow depth observed at 237 stations of the Japan Meteorological Agency in the past few decades. Snowfall amount was defined as the cumulative value of the positive difference in snow depth each hour. Each snowfall event was regarded as ending when snowfall (i.e., the hourly difference in snow depth ? 0 cm) ceased for more than 6 hours. The cumulative numbers of snowfall events from classes of large snowfall amounts at intervals of 5 cm were counted for cases of snowfall amounts exceeding 30 cm. Dividing the cumulative number of events by the years of observation provides the frequency of snowfall events. This frequency means the number of event occurrences per year for snowfall exceeding a certain value. To obtain the estimation equation for the frequency of snowfall events exceeding a certain snowfall, regression analysis between the common logarithm of frequencies and the snowfall amounts was carried out.
The regression analysis for each station revealed a strong linear correlation between the logarithm of frequency and the snowfall amount at a statistically significant level of 1%. The frequencies estimated from the regression equations at all stations were compared with observed values at 5-cm snowfall intervals. In the range of snowfall amounts between 40 cm and 100 cm, the coefficients of determination exceed 0.9 and the root mean squared errors (RMSEs) are less than 0.5. In cases of snowfall amounts exceeding 65 cm, the RMSEs are less than 0.1. Consequently, using the regression analysis with the logarithm of snowfall frequency enables the easy evaluation of the frequency of snowfall events exceeding a certain snowfall amount.