Hurst Analysis of Hydrologic and Water Quality Time Series

Abstract

A continued important area of research in hydrologic modeling is the issue of spatial and temporal scaling of biogeochemical properties and processes. Hurst analysis, which is a fractal-based scale invariant approach for analyzing long-term time series data, can provide insight into this issue as a quantitative approach for evaluating temporal scale in time series. The objectives of this paper were to compute the Hurst coefficient (H) for hydrologic and water quality variables, to study the effects of seasonality on H, and to determine how the H for the water quality indicators are related to that of the hydrologic parameters (e.g., discharge and rainfall). Two sites were investigated, Little River and Walker Branch, both located in east Tennessee. The water quality indicators include total coliform for Little River data and nitrate, chloride, sulfate, and calcium concentrations for Walker Branch data. H was estimated using spectral analysis. It was found that H for water quality indicators were significantly different from hydrologic parameters in an untransformed series, whereas it is not different in deseasonalized series (except total coliform). The comparison of untransformed and deseasonalized data series showed that there is no statistically significant value to deseasonalize the data, although the data series appears to shift toward random scaling after deseasonalization.