On detrending stream velocity time series for robust riverine flow turbulence characterization

The impact of various detrending techniques on turbulence quantities estimation of riverine and tidal flow data obtained from field experiments was investigated, with particular focus on their autocorrelation function, ρuu, and velocity spectrum, Φu. Standard detrending methods were examined, including frequency-based (high-pass filter) and regression-based (polynomial detrend) filtering techniques. Our results show that intervals of flow acceleration and deceleration, typical in tidal and riverine flows, significantly affect the estimation of turbulence quantities using high-pass frequency filtering and polynomial detrending of varying orders, which can strongly condition ρuu and Φu, affecting the estimation of derived turbulence quantities. Also, frequency- and regression-based filters require heavy parameter tuning in filter design, making them inefficient for detrending turbulence data. We propose an alternative detrending method, utilizing the intrinsic model function (IMF) obtained from empirical mode decomposition (EMD). Two variations of detrending data using EMD were tested; the first removes only the EMD residue, and the second removes both the EMD residue and the largest scale intrinsic mode function. We demonstrate that the second EMD detrend variation (i.e., removing residue and the largest scale IMF) successfully removes the large-scale unsteady trend of the data while retaining the energy of other scales, producing a more representative velocity spectrum.