A non-uniqueness problem in the identification of power-law spectral scaling for hydroclimatic time series

Abstract

Power-law spectral scaling violates assumptions of standard analyses such as statistical change detection. However, hydroclimatic data sets may be too short to differentiate the spectra of 1/f α vs low-order linear memory processes, an ambiguity exacerbated by the ubiquity of both process types. We explore this non-uniqueness problem by applying a heuristic tool to four examples from each of four hydroclimatic data types: circulation indices, station climate, river and aquifer conditions, and glacier mass balance. This selection spans much of the globe and includes some of the longest instrumental data sets available. The most common outcome is that power-law scaling is apparent, but the record is insufficiently long to discriminate between underlying mechanisms. The use of palaeoclimatic data to extend the instrumental record was investigated, but produced mixed results. Conversely, a balance-of-evidence approach, additionally incorporating physical process considerations, may help us recognize variate classes for which 1/f α scaling can be concluded. Practical recommendations are offered.Editor D. KoutsoyiannisCitation Fleming, S.W., 2013. A non-uniqueness problem in the identification of power-law spectral scaling for hydroclimatic time series. Hydrological Sciences Journal, 59 (1), 73–84.