A Multiscale Approach to Timescale Analysis: Isolating Diel Signals from Solute Concentration Time Series.

Solute concentration time series reflect hydrological and biological drivers through various frequencies, phases, and amplitudes of change. Untangling these signals facilitates the understanding of dynamic ecosystem conditions and transient water quality issues. A case in point is the inference of biogeochemical processes from diel solute concentration variations. This analysis requires approaches capable of isolating subtle diel signals from background variability at other scales. Conventional time series analyses typically assume stationary or deterministic background variability; however, most rivers do not respect such niceties. We developed a time-series filtering method that uses empirical mode decomposition to decompose a measured solute concentration time series into intrinsic mode frequencies. Based on externally supplied mechanistic knowledge, we then filter these modes by periodicity, phase, and coherence with neighboring days. This method is tested on three synthetic series that incorporate environmental variability and sensor noise and on a year of 15 min sampled concentration time series from three hydrologically and ecologically distinct rivers in the eastern United States. The proposed method successfully isolated signals in the measured data sets that corresponded with variability in gross primary productivity. The strength the diel signal isolated through this method was smaller compared to the true signal in the synthetic series; however, uncertainty analysis showed that the process-model-based estimates derived from these signals were similar to other inference methods. This signal decomposition method retains information that can be used for further process modeling while making different assumptions about the data than Fourier and wavelet analyses.