Extracting the properties of Earth and atmospheric tidal harmonics from groundwater level records: a least-squares approach

Groundwater resources are under increasing threat from human activity and climate change, making sustainable management critical. However, appropriate management generally requires extensive knowledge of the properties and characteristics of aquifers. In recent years, research into passive investigation methods utilising the impact of Earth and atmospheric tides (EAT) on the groundwater response have gained momentum. EAT occur at known frequencies of daily and sub-daily cycles per day (cpd) and present an inexpensive and viable opportunity for the characterization of groundwater systems at an unprecedented spatial and temporal resolution (McMillan et al., 2019). However, quantifying aquifer properties relies on accurate and reliable extraction of the harmonic properties (amplitude and phase) of tidal components embedded in groundwater level and atmospheric pressure records that are dominated by larger magnitude variations as well as other noise. Here, we use synthetic signals and real measurements to test and compare the performance of the Discrete Fourier Transform (DFT) with a generalised harmonic least squares amplitude and phase estimation (APES) approach for the harmonic tidal components. APES was implemented in Python in conjunction with a windowed de-trending function that serves as a high pass filter. The analysis focuses on three realistic aspects often encountered in groundwater monitoring: (1) the minimum record length required to reliably separate tidal components at nearby frequencies, (2) signal quantisation as a proxy for measurement resolution, and (3) the amount of sampling gaps or irregularly spaced sampling. Results indicate that APES outperforms DFT in quantifying the amplitude of the major tidal components M2 (1.93227 cpd) and S2 (2.0 cpd) on regularly sampled data, because it is not subject to spectral leakage. Furthermore, APES is superior in handling data gaps, missing values and outliers, yielding accurate amplitude estimates even for comparably small amounts of data and without requiring pre-processing such as data interpolation or resampling. This increases the data volume for the tidal analysis considerably and enables a much more extensive use of tidal analysis. Further investigation will focus on the methods’ performance in quantifying the phase of the M2 and S2 components.

 

McMillan, T. C., Rau, G. C., Timms, W. A., & Andersen, M. S. ( 2019). Utilizing the impact of Earth and atmospheric tides on groundwater systems: A review reveals the future potential. Reviews of Geophysics, 57, 281– 315. https://doi.org/10.1029/2018RG000630.