The wavelet packet transform: A technique for investigating temporal variation of river water solutes

Abstract

Understanding factors influencing river water quality is of increasing importance. We are now able to intensively monitor water variables resulting in large time series which can be used to facilitate this understanding. These time series represent the aggregation of many complex processes driven by external factors and occurring at different temporal scales. The challenge is to use the time series to elucidate the dominant climatic, hydrological and biogeochemical processes occurring at each temporal scale (or frequency). The time series are typically non-stationary and so classical methods, such as Fourier analysis, are not suitable. In this paper we demonstrate that the Discrete wavelet packet transform (DWPT) and an adaptation of this (the Maximal Overlap DWPT—MODWPT) are appropriate tools for analysing these complex signals. We exemplify this by considering measurements of nitrate and chloride concentration, temperature and discharge from the Taw River, Devon, UK. The wavelet analysis is able to distinguish frequency specific behaviour as well as intermittent events that were not visually apparent in the original time series. We find supporting evidence for observations made on similar systems by other workers and make some additional observations. We conclude that the MODWPT is an important tool which can help hydrologists and biogeochemists gain insight into the complex behaviour of catchment systems.