Fractal dimension as an indicator for quantifying the effects of changing spatial scales on landscape metrics

While geographers and ecologists are well aware of the scale effects of landscape patterns, there is still a need for quantifying these effects. This paper applies the fractal method to measure the scale (grain or cell size) sensitivity of landscape metrics at both landscape and class levels using the Gold Coast City in Southeast Queensland, Australia as a case study. By transforming the original land use polygon data into raster data at eleven aggregate scales, the fractal dimensions of 57 landscape metrics as defined in FRAGSTATS were assessed. A series of linear log-log regression models were constructed based on the power law to obtain the coefficient of determination (COD or R2) of the models and the fractal dimension (FD) of the landscape metrics. The results show that most landscape metrics in the area and edge, shape and the aggregation groups exhibit a fractal law that is consistent over a range of scales. The six variations of several landscape metrics that belong to both the area/edge and shape groups show different scale behaviours and effects. However, the metrics that belong to the diversity group are scale-independent and do not accord to fractal laws. In addition, the scale effects at the class level are more complex than those at the landscape level. The quantitative assessment of the scale effect using the fractal method provides a basis for investigating landscape patterns when upscaling or downscaling as well as creating any scale-free metric to understand landscape patterns.