The study of hydraulic head changes over time is a common task for groundwater hydrologists. Groundwater signatures are numerical metrics, or statistical aggregates, that quantify the behavior observed in hydraulic head hydrographs. Signatures can be helpful in a number of classical hydrological tasks, such as hydrograph classification, clustering, change detection, and model evaluation, selection, and calibration. Despite the potential benefits of using signatures in groundwater studies, their application has not yet been thoroughly explored. To support research into the application of signatures in groundwater studies, we introduce the new groundwater signatures module from the Pastas software. The signatures module is written in Python, fully tested and documented, and available as open-source software under the MIT license. In this paper, it is shown how the signatures are tested and can be used in practical applications through two examples. In the first example, signatures are used to characterize and cluster monitoring wells in a nationwide monitoring network in Switzerland. In the second example, signatures are used to evaluate how well different groundwater model structures simulate the heads. Future research opportunities involving groundwater signatures are discussed.

The performance of time series models is assessed using synthetic head series simulated with a numerical model that solves Richards' equation for variably saturated flow. Heads were simulated in a homogeneous unconfined aquifer between two parallel canals; measured daily precipitation and potential evaporation are specified at the land surface and root water uptake is simulated. The head response to a precipitation event is nonlinear and depends on the saturation degree and rainfall before and after the precipitation event while evaporation reduction occurs during summers. Synthetic series were generated for 27 years and three different soil types; the unsaturated zone thickness varies between 0 and >5 m. The synthetic head series were simulated with a linear and nonlinear time series model. Performance of a linear time series model with four parameters, using a scaled Gamma response, gave R² values ranging from 0.67 to 0.96. The nonlinear time series model with five parameters simulates recharge using a root zone reservoir after which the head response to recharge is simulated with a scaled Gamma response function. The nonlinear time series model was able to simulate all synthetic head series very well with R² values above 0.9 for almost all models. The head response of the nonlinear model to a single precipitation event compares well to the response of the variably saturated groundwater model. The provided scripts may be used to simulate synthetic head series for other climates or for systems with additional complexity to assess the performance of other data-driven models.

In 2018–2020, meteorological droughts over Northwestern Europe caused severe declines in groundwater heads with significant damage to groundwater-dependent ecosystems and agriculture. The response of the groundwater system to different hydrological stresses is valuable information for decision-makers. In this paper, a reproducible, data-driven approach using open-source software is proposed to quantify the effects of different hydrological stresses on heads. A scripted workflow was developed using the open-source Pastas software for time series modeling of heads. For each head time series, the best model structure and relevant hydrological stresses (rainfall, evaporation, river stages, and pumping at one or more well fields) were selected iteratively. A new method was applied to model multiple well fields with a single response function, where the response was scaled by the distances between the pumping and observation wells. Selection of the best model structure was performed through reliability checking based on four criteria. The time series model of each observation well represents an independent estimate of the contribution of different hydrological stresses to the head and is based exclusively on observed data. The approach was applied to estimate the drawdown caused by nearby well fields to 250 observed head time series measured at 122 locations in the eastern part of the Netherlands, a country where summer droughts can cause problems, even though the country is better known for problems with too much water. Reliable models were obtained for 126 head time series of which 78 contain one or more well fields as a contributing stress. The spatial variation of the modeled responses to pumping at the well fields show the expected decline with distance from the well field, even though all responses were modeled independently. An example application at one well field showed how the head response to pumping varies per aquifer. Time series analysis was used to determine the feasibility of reducing pumping rates to mitigate large drawdowns during droughts, which depends on the magnitude and response time of the groundwater system to changes in pumping. This is salient information for decision-makers. This article is part of the special issue “Rapid, Reproducible, and Robust Environmental Modeling for Decision Support: Worked Examples and Open-Source Software Tools”.