To observe or predict changes in the frequency and/or severity of a hazard (or of a related event such as heavy rainfall), it is necessary to quantify these properties. Parameters for measuring frequency include the interarrival time (the time between successive events), the return period (the mean interarrival time) and the mean annual frequency (the reciprocal of the return period in years). The severity of a weather-related hazard (or related parameter) is usually quantified mainly in terms of its magnitude or intensity (e.g. river discharge, wind speed, rainfall rate, temperature). Sometimes an index of severity is used, reflecting a number of intensity measures, or incorporating the duration and spatial extent of the event.
For any particular climatic conditions, the distribution of events in magnitude or intensity (often extended to include non-hazardous magnitudes) largely summarises the statistical properties of that particular type of event, and forms the basis for most other indices. For weather-related parameters, these frequency-magnitude distributions have a wide variety of shapes (for example, see Brooks and Carruthers, 1953, chapter 8, and von Storch and Zwiers, 1999, chapters 2 and 3). They are sometimes normalised to form probability distributions. For natural hazards, however, the most extreme events must also be rare, so the distributions will always have a low and/or high extreme value tail. The above frequency parameters generally refer to the cumulative (exceedance) frequency - that is, including all events that are equal to or less than (greater than) some intensity level in the low (high) value tail. In some cases, only the most extreme event within a certain time period (e.g. the maximum value of river discharge each year) is considered. The resulting distribution can then be modelled using extreme value analysis (e.g. von Storch and Zwiers, 1999, chapter 2; Bedient and Huber, 1992).
In using frequency-magnitude distributions to investigate extreme events, however, it is important to be aware of a number of potential problems (Smith and Ward, 1998, pp. 188-191; Essenwanger, 1976, pp. 143-189). First, it is possible for the data to be undersampled (missing some events) or oversampled (including events that are not independent). Second, the distributions themselves may be changing over the period of the observations (e.g. owing to climatic variations). Finally, there may be more than one population of events (i.e. events with different source mechanisms), leading to a mixed frequency distribution.
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