Seepage velocities derived from thermal records using wavelet analysis

Abstract

Summary The main objective of this study was to determine if wavelet analysis can be used as a band-pass filter for non-stationary time series of temperature records. It was demonstrated that this new processing technique is efficient in calculating seepage velocities by using a virtual experiment and field data measured in the Mess Stream, Grand Duchy of Luxembourg, Europe. Temperature time series were measured continuously over a 2-year period in the streambed sediments. The seepage velocity was derived from the one-dimensional analytical solution of Stallman. However, the ubiquitous property of the temperature signal is that it is non-stationary, i.e. the frequency component of the signal becomes a function of time. Instead of applying traditional filtering techniques based on the Fourier transform, we introduce the continuous wavelet transform (CWT) as a band-pass filter to extract the daily component from raw temperature data. For the analysed time series, the estimated seepage velocities based on the amplitude ratio were always negative and within the range of −0.7 to −2.5 m d −1 , indicating gaining conditions prevailing in the Mess Stream. The uncertainty associated with the seepage velocities was calculated by the Monte Carlo analysis allowing several physical parameters of the model to vary over pre-defined intervals with normal distribution. Auxiliary hydraulic measurements in the stream and in the riverbank confirm the dominance of gaining stream conditions. However, the seepage rates based on the thermal records were much higher than the calculated Darcy velocities. This study demonstrates the applicability of continuous wavelet transform as an alternative method to Fourier transform for the analysis of non-stationary temperature time series.