Fire rotation

The fire rotation, introduced by Heinselman (1973), is equal to the spatial extent of the study area divided by the mean annual proportion of the study area that burned. This measure has been commonly used by foresters and ecologists as a means of expressing how long it would take to burn a large proportion of the study area (e.g. references in Johnson and Gutsell (1994)). The area-burned data could be obtained using historical records, satellite data or tree-ring records. For example, if satellite data suggested that, within one year, 100 km2 of a 1000 km2 area had burned, the fire rotation would be:

Assuming that the rate of burning would remain the same in subsequent years, this suggests that in ten years, an area equal in size to the whole 1000 km2 study area would burn.

Further, assume that the satellite study was extended to cover 10 years of data, that 100 km2 of area was burned every year, and that only 700 km2 of the landscape had been burned during that time period. (The latter observation would be true because some portions of the land will have been burned two or three times.) If the fire rotation over the 10-year period was calculated using the proportion of the landscape that had been burned, the fire rotation would be underestimated as: 1000 km2 / 700 km2 * 10 yr"1 = 1000 years / 70 = 14.3 years. It is thus important to calculate the natural fire rotation using the mean annual proportion of the study area that burned, and not the proportion of the landscape that burned at least once over thetemporal extentof the study. Indeed, even an annual resolution would underestimate the fire rotation if fires over-burn sections of the study area within a single year.

Although the fire rotation can be calculated using one year of data, as the annual area burned can vary markedly due to inter-annual variations in factors such as climate, the measure will become more meaningful as more years of data are employed.

The fire cycle is the number of years required to burn an area equal in size to the study area (Van Wagner, 1978). It is equivalent to the fire rotation but, while the fire rotation is typically calculated using historical records, the fire cycle is calculated usingtree-agedata. The different terms are thus used to indicate that they have been calculated using different types of data. The frequency distribution of time-since-last-fire points or areas, reconstructed usingtree-ages, can be analysed using statistical methods adopted from survival analysis (e.g. Reed, 1994; Reed et al., 1998). These methods enable the fire cycle in different time periods and spatial locations to be estimated and tested for significant differences. The value of using tree-age data is that it enables the fire cycle to be calculated for time periods hundreds of years into the past.

A fire interval is the time between two consecutive fires. For example, if a tree contained fire scars in the years 1800 and 1810, the fire interval was 10 years. The mean fire interval (MFI) is equal to the sum of individual intervals divided by the number of intervals. For example, assume that a tree contained fire scars in the years 1800, 1810, 1860 and 1900. The intervals are 10, 50 and 40 years, for a sum of 100 years, and there are 3 intervals; the mean fire interval is thus 33.3 years. More accurate estimates of the MFI are obtained through the use of parametric methods that are more appropriate to the data (e.g. Clark, 1989; Johnson and Gutsell, 1994).

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