The groundwater response to Earth tides and atmospheric pressure changes can be used to understand subsurface processes and estimate hydraulic and hydro-mechanical properties. We develop a generalised frequency domain approach to disentangle the impacts of Earth and atmospheric tides on groundwater level responses. By considering the complex harmonic properties of the signal, we improve upon a previous method for quantifying barometric efficiency (BE), while simultaneously assessing system confinement and estimating hydraulic conductivity and specific storage. We demonstrate and validate this novel approach using an example barometric and groundwater pressure record with strong Earth tide influences. Our method enables improved and rapid assessment of subsurface processes and properties using standard pressure measurements.

The groundwater response to barometric pressure and gravity changes caused by Earth tides has long been observed and is a powerful yet underutilised tool to passively characterise subsurface systems

Overview of the major tidal components found in well water levels

The method by

In this technical note, we generalise the method by

Since the extension of the method published in

Throughout this paper, subscripts refer to the considered tidal components

The method by

The complex groundwater response to the Earth-tide-only driver for the

For some tidal components, for example

Since the measured well water level response for

It is important to note that our extended approach given in Eqs. (

Amplitude ratio and phase shift relationship between subsurface pore pressure and well water level for harmonic forcing under fully confined conditions

Figure

The strongest modification of the harmonic response occurs for fully confined and not for leaky conditions (Fig.

both amplitude damping and phase shifts are mainly controlled by the subsurface hydraulic conductivity. For the confined case,

Using Eqs. (

The tidal disentanglement further enables estimation of the subsurface hydraulic conductivity (

The first step towards tidal disentanglement is to extract the tidal harmonics from the time series. Since the frequencies of the main tidal components are well known

Before extracting tidal harmonics, lower frequency variations should be removed. We suggest first applying a de-trending filter with a cut-off frequency of

The three BE

Time series of

Figure

As a next step, we extracted the tidal harmonic components from all three time series (BP, ET and GW in Fig.

Figure

Polar plots showing amplitudes and phases derived from the fitting coefficients using Eqs. (

To illustrate the tidal disentanglement, we use polar plots to visualise the key components. Figure

Well water level response to pore pressure for BLM-1 (well radius of 0.127 m and length of 106 m) and

To account for the amplitude damping and phase shifting of the well in response to the harmonic pore pressure changes, we have used the dimensions of the well BLM-1 (see previous details) to calculate the solution space of the analytical solution for confined conditions (Appendix

The damping of the amplitude in the well in this case is only

Using Eq. (

The BRF-based BE

Summary of the parameters, values and uncertainties calculated in this work.

The negative phase shift between Earth tides and groundwater pressure (

Previous works have reported that a phase difference of 180

We present a frequency domain method to disentangle the groundwater response to Earth and atmospheric tides. It is a more general solution than that previously presented by

Our method enables an improved and rapid estimation of BE in general but especially for cases where the borehole water level is strongly influenced by Earth tides. Under such conditions, the influence of the phase difference between Earth tides and its groundwater response also has to be considered when revealing the atmospheric tide embedded in the

The following differential equation describes water flow in and out of a well under semi-confined (leaky) conditions:

The fluctuating water level and the drawdown are related by the following:

For fully confined conditions, when

The well water level response to barometric pressure forcing in the time domain is referred to as the barometric response function (BRF). A BRF can be used to indicate confinement and estimate barometric efficiency

When HALSs optimisation (Eq.

The code and data set are available on Figshare under

GCR conceived the idea for this work, analysed the data, made the figures and wrote the first draft. MOC contributed to method development through intensive technical discussions and reviews. RIA and PB improved this work by providing useful suggestions and edits.

The authors declare that they have no conflict of interest.

This technical note is based on a presentation given at the European Geosciences Union (EGU) General Assembly in the year 2020, which was reorganised as Sharing Geosciences Online due to the Covid-19 pandemic. We thank Paula Cutillo and Shannon Mazzei from the National Park Service (NPS) in California (USA) for providing the barometric and groundwater pressure data set. We acknowledge support from the KIT Publication Fund of the Karlsruhe Institute of Technology.

This research has been supported by the European Commission Horizon 2020 Marie Skłodowska-Curie Actions (SubTideTools; grant no. 835852), an Independent Research Fellowship from the UK Natural Environment Research Council (grant no. NE/P017819/1), and the KIT Publication Fund of the Karlsruhe Institute of Technology. The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.

This paper was edited by Insa Neuweiler and reviewed by Todd Rasmussen and two anonymous referees.