A revised coastal sensitivity index for Canada’s marine coasts calculated using nonparametric statistics

A coastal sensitivity index (CSI) is a measure of the sensitivity of a coastline to its physical environment, which provides information useful for coastal management. Traditionally, a CSI is calculated as the mathematical aggregation of coastal sensitivity indicators, which may include factors such as coastal material, relief, and wave energy. The indicators differ depending on study area, but generally are assigned a score ranging from one to five in order of increasing sensitivity. These scores are then aggregated using either the square root of the product mean (the “classic” method) or the geometric mean. Both of these methods are limited by mathematical assumptions, lack of comparability, and the need for empirical validation. In this study, we applied an alternative nonparametric method of calculation, known as μ-statistics, to Canada's marine coasts to provide an improved measure of coastal sensitivity. μ-statistics, which offer a mathematically sound method of aggregating ordinal indicators, have a number of theoretical advantages over the classic and geometric mean methods. In practice, when applied to Canada’s marine coasts, we find that the μ-statistics method (1) compresses the mid-range variability in the resulting sensitivity index, (2) accentuates positive and negative distribution tails, and (3) minimizes propagated errors by 190% and 50%, respectively, compared with the classic and geometric mean methods. Additionally, the μ-statistics method has a theoretical foundation that relieves the necessity to empirically validate the aggregating assumptions and relies only on the assumptions inherent in the scoring method. μ-statistics thus provide a new, rigourous method for the calculation of coastal sensitivity indices when the underlying variables have ordinal scores.