Data-Driven Estimation of Groundwater Level Time-Series at Unmonitored Sites Using Comparative Regional Analysis

A new method is presented to efficiently estimate daily groundwater level time series at unmonitored sites by linking groundwater dynamics to local hydrogeological system controls. The proposed approach is based on the concept of comparative regional analysis, an approach widely used in surface water hydrology, but uncommon in hydrogeology. Using physiographic and climatic site descriptors, the method utilizes regression analysis to estimate cumulative frequency distributions of groundwater levels (groundwater head duration curves, HDC) at unmonitored locations. The HDC is then used to construct a groundwater hydrograph using time series from distance-weighted neighboring monitored (donor) locations. For estimating times series at unmonitored sites, in essence, spatio-temporal interpolation, stepwise multiple linear regression (MLR), extreme gradient boosting (XGB), and nearest neighbors are compared. The methods were applied to 10-year daily groundwater level time series at 157 sites in unconfined alluvial aquifers in Southern Germany. Models of HDCs were physically plausible and showed that physiographic and climatic controls on groundwater level fluctuations are nonlinear and dynamic, varying in significance from “wet” to “dry” aquifer conditions. XGB yielded a significantly higher predictive skill than nearest neighbor and MLR. However, donor site selection is of key importance. The study presents a novel approach for regionalization and infilling of groundwater level time series that also aids conceptual understanding of controls on groundwater dynamics, both central tasks for water resources managers

Assessing automated gap imputation of regional scale groundwater level data sets with typical gap patterns

Large groundwater level (GWL) data sets are often patchy with hydrographs containing continuous gaps and irregular measurement frequencies. However, most statistical time series analyses require regular observations, thus hydrographs with larger gaps are routinely excluded from further analysis despite the loss of coverage and representativity of an initially large data set. Missing values can be filled in with different imputation methods, yet the challenge is to assess the imputation performance of automated methods. Assessment of such methods tends to be carried out on randomly introduced missing values. However, large GWL data sets are commonly dominated by more complex patterns of missing values with longer contiguous gaps. This study presents a new artificial gap introduction approach (TGP- typical gap patterns) that improves our understanding of automated imputation performance by mimicking typical gap patterns found in regional scale groundwater hydrographs. Imputation performance of machine learning algorithm missForest and imputePCA is then compared with commonly applied linear interpolation to prepare a gapless daily GWL data set for the Baltic states (Estonia, Latvia, Lithuania). We observed that imputation performance varies among different gap patterns, and performance for all imputation algorithms declined when infilling previously unseen extremes and hydrographs influenced by groundwater abstraction. Further, missForest algorithm substantially outperformed other methods when infilling contiguous gaps (up to 2.5 years), while linear interpolation performs similarly for short random gaps. The TGP approach can be of use to assess the complexity of missing observation patterns in a data set and its value lies in assessing the performance of gap filling methods in a more realistic way. Thus the approach aids the appropriate selection of imputation methods, a task not limited to groundwater level time series alone. The study further provides insights into region-specific data peculiarities that can assist groundwater analysis and modelling

Systematic visual analysis of groundwater hydrographs: potential benefits and challenges

Visual analysis of time series in hydrology is frequently seen as a crucial step to becoming acquainted with the nature of the data, as well as detecting unexpected errors, biases, etc. Human eyes, in particular those of a trained expert, are well suited to recognize irregularities and distinct patterns. However, there are limits as to what the eye can resolve and process; moreover, visual analysis is by definition subjective and has low reproducibility. Visual inspection is frequently mentioned in publications, but rarely described in detail, even though it may have significantly affected decisions made in the process of performing the underlying study. This paper presents a visual analysis of groundwater hydrographs that has been performed in relation to attempts to classify groundwater time series as part of developing a new concept for prediction in data-scarce groundwater systems. Within this concept, determining the similarity of groundwater hydrographs is essential. As standard approaches for similarity analysis of groundwater hydrographs do not yet exist, different approaches were developed and tested. This provided the opportunity to carry out a comparison between visual analysis and formal, automated classification approaches. The presented visual classification was carried out on two sets of time series from central Europe and Fennoscandia. It is explained why and where visual classification can be beneficial but also where the limitations and challenges associated with the approach lie. It is concluded that systematic visual analysis of time series in hydrology, despite its subjectivity and low reproducibility, should receive much more attention

Physiographic and climatic controls on regional groundwater dynamics

The main goal of this study is to explore whether the ideas established by surface water hydrologists in the context of “PUB” (predictions in ungauged basins) can be useful in hydrogeology. The concrete question is whether it is possible to create predictive models for groundwater systems with no or few observations based on knowledge derived from similar groundwater systems which are well‐observed. To do so, this study analyses the relationship between temporal dynamics of groundwater levels and climatic and physiographic characteristics. The analysis is based on data from 341 wells in Southern Germany with ten‐year daily groundwater hydrographs. Observation wells are used in confined and unconfined sand and gravel aquifers from narrow mountainous valleys as well as more extensive lowland alluvial aquifers. Groundwater dynamics at each location are summarized with 46 indices describing features of groundwater hydrographs. Besides borehole log‐derived geologic information, local and regional morphologic characteristics as well as topography‐derived boundary and climatic descriptors were derived for each well. Regression relationships were established by mining the data for associations between dynamics and descriptors with forward stepwise regression at a confidence level >95%. The most important predictors are geology and boundary conditions and secondarily, climate, as well as some topographic features, such as regional convergence. The multiple regression models are in general agreement with process understanding linked to groundwater dynamics in unconfined aquifers. This systematic investigation suggests that statistical regionalization of groundwater dynamics in ungauged aquifers based on map‐derived physiographic and climatic controls may be feasible

Disentangling coastal groundwater level dynamics on a global data set

This study aims to identify common hydrogeological patterns and to gain a deeper understanding of the underlying similarities and their link to physiographic, climatic, and anthropogenic controls of coastal groundwater. The most striking aspects of GWL dynamics and their controls were identified through a combination of statistical metrics, calculated from about 8,000 groundwater hydrographs, and pattern recognition, classification, and explanation using machine learning techniques and SHapley Additive exPlanations (SHAP). Overall, four different GWL dynamics patterns emerge, independent of the different seasons, time series lengths, and periods. We show in this study that similar GWL dynamics can be observed around the world with different combinations of site characteristics, but also that the main factors differentiating these patterns can be identified. Three of the identified patterns exhibit high short-term and interannual variability and are most common in regions with low terrain elevation and shallow groundwater depth. Climate and soil characteristics are most important in differentiating these patterns. This study provides new insights into the hydrogeological behavior of groundwater in coastal regions and guides systematic and holistic groundwater monitoring and modelling, motivating to consider various aspects of GWL dynamics when, for example, estimating climate-driven GWL changes &ndash; especially when information on potential controls is limited.</p

Similarity-based approaches in hydrogeology: proposal of a new concept for data-scarce groundwater resource characterization and prediction

A new concept is proposed for describing, analysing and predicting the dynamic behaviour of groundwater resources based on classification and similarity. The concept makes use of the ideas put forward by the “PUB” (predictions in ungauged basins) initiative in surface-water hydrology. One of the approaches developed in PUB uses the principle that similar catchments, exposed to similar weather conditions, will generate a similar discharge response at the catchment outlet. This way, models developed for well-observed catchments can be used to make predictions for ungauged catchments with similar properties (topography, land use, etc.). The concept proposed here applies the same idea to groundwater systems, with the goal to make predictions of the dynamic behaviour of groundwater in poorly observed systems using similarities to well-observed and understood systems. This paper gives an overview of the main ideas, the methodological background, the progress so far, and the challenges that the authors regard as most crucial for further development. One of the main goals of this article is thus to raise interest for this new concept within the groundwater community. There are a multitude of highly interesting aspects to investigate, and a community effort, as with PUB, is required. A second goal is to foster and exchange ideas between the groundwater and surface water research communities who, while often working on similar problems, have often missed the opportunity to learn from each other

A probabilistic approach to soil layer and bedrock-level modelling for risk assessment of groundwater drawdown induced land subsidence

Sub-surface construction in urban areas generally involves drainage of groundwater, which can induce subsidence in soil deposits. Knowledge of where compressible sediments are located and how thick these are is essential for estimating subsidence risk. A probabilistic method for coupled bedrock-level and soil-layer modeling to detect compressible sediments is presented. The method is applied in an area in central Stockholm, where clay is the compressible sediment layer. First, a bedrock-level model was constructed from three sources of information: (a) geotechnical drillings reaching the bedrock; (b) drillings not reaching the bedrock; and (c) mapped bedrock outcrops. Input data for the probabilistic bedrock-level model was generated by a stepwise Kriging procedure. Second, a three layer soil model was constructed, including the following materials: (a) coarse grained post glacial and filling material below the ground surface; (b) glacial and post-glacial clays; and (c) coarse grained glaciofluvial and glacial till deposits above the bedrock. Layer thicknesses were transformed to proportions of the total soil thickness. Since Kriging requires data to be normally distributed, the proportions were transformed from proportions (P) to standard normal quantiles (z). In each iteration of a Monte-Carlo simulation, a spatial distribution of the bedrock level was simulated together with the transformed values for the soil-layer proportions. From the iterations, the probability density of the clay thickness (compressible sediments) at each grid cell was calculated. The results of the case study map the expected value (mean) and the 95th percentile of the probability of compressible sediments at specific locations. The resulting model is geologically realistic and validated through a cross-validation procedure in order to be in good agreement with a reference dataset. The case study showed that the method can efficiently handle large amounts of data and requires little manual adjustment. Moreover, the mapped results can provide useful decision support when planning risk-reducing measures and when communicating with stakeholders. Although this novel method is developed for risk assessment of groundwater drawdown induced subsidence, it is useful for other applications involving spatial soil strata modeling

Comprehensive risk assessment of groundwater drawdown induced subsidence

We present a method for risk assessment of groundwater drawdown induced land subsidence when planning for sub-surface infrastructure. Since groundwater drawdown and related subsidence can occur at large distances from the points of inflow, the large spatial extent often implies heterogeneous geological conditions that cannot be described in complete detail. This calls for estimation of uncertainties in all components of the cause-effect chain with probabilistic methods. In this study, we couple four probabilistic methods into a comprehensive model for economic risk quantification: a geostatistical soil-stratification model, an inverse calibrated groundwater model, an elasto-plastic subsidence model, and a model describing the resulting damages and costs on individual buildings and constructions. Groundwater head measurements, hydraulic tests, statistical analyses of stratification and soil properties and an inventory of buildings are inputs to the models. In the coupled method, different design alternatives for risk reduction measures are evaluated. Integration of probabilities and damage costs result in an economic risk estimate for each alternative. Compared with the risk for a reference alternative, the best prior alternative is identified as the alternative with the highest expected net benefit. The results include spatial probabilistic risk estimates for each alternative where areas with significant risk are distinguished from low-risk areas. The efficiency and usefulness of this modelling approach as a tool for communication to stakeholders, decision support for prioritization of risk reducing measures, and identification of the need for further investigations and monitoring are demonstrated with a case study of a planned railway tunnel in Varberg, Sweden

Economic valuation of hydrogeological information when managing groundwater drawdown

A procedure is presented for valuation of information analysis (VOIA) to determine the need for additional information when assessing the effect of several design alternatives to manage future disturbances in hydrogeological systems. When planning for groundwater extraction and drawdown in areas where risks—such as land subsidence, wells running dry and drainage of streams and wetlands—are present, the need for risk-reducing safety measures must be carefully evaluated and managed. The heterogeneity of the subsurface calls for an assessment of trade-offs between the benefits of additional information to reduce the risk of erroneous decisions and the cost of collecting this information. A method is suggested that combines existing procedures for inverse probabilistic groundwater modelling with a novel method for VOIA. The method results in (1) a prior analysis where uncertainties regarding the efficiency of safety measures are estimated, and (2) a pre-posterior analysis, where the benefits of expected uncertainty reduction deriving from additional information are compared with the costs for obtaining this information. In comparison with existing approaches for VOIA, the method can assess multiple design alternatives, use hydrogeological parameters as proxies for failure, and produce spatially distributed VOIA maps. The method is demonstrated for a case study of a planned tunnel in Stockholm, Sweden, where additional investigations produce a low number of benefits as a result of low failure rates for the studied alternatives and a cause-effect chain where the resulting failure probability is more dependent on interactions within the whole system rather than on specific features

A probabilistic approach to soil layer and bedrock-level modelling for risk assessment of groundwater drawdown induced land subsidence

Sub-surface construction in urban areas generally involves drainage of groundwater, which can induce subsidence in soil deposits. Knowledge of where compressible sediments are located and how thick these are is essential for estimating subsidence risk. A probabilistic method for coupled bedrock-level and soil-layer modeling to detect compressible sediments is presented. The method is applied in an area in central Stockholm, where clay is the compressible sediment layer. First, a bedrock-level model was constructed from three sources of information: (a) geotechnical drillings reaching the bedrock; (b) drillings not reaching the bedrock; and (c) mapped bedrock outcrops. Input data for the probabilistic bedrock-level model was generated by a stepwise Kriging procedure. Second, a three layer soil model was constructed, including the following materials: (a) coarse grained post glacial and filling material below the ground surface; (b) glacial and post-glacial clays; and (c) coarse grained glaciofluvial and glacial till deposits above the bedrock. Layer thicknesses were transformed to proportions of the total soil thickness. Since Kriging requires data to be normally distributed, the proportions were transformed from proportions (P) to standard normal quantiles (z). In each iteration of a Monte-Carlo simulation, a spatial distribution of the bedrock level was simulated together with the transformed values for the soil-layer proportions. From the iterations, the probability density of the clay thickness (compressible sediments) at each grid cell was calculated. The results of the case study map the expected value (mean) and the 95th percentile of the probability of compressible sediments at specific locations. The resulting model is geologically realistic and validated through a cross-validation procedure in order to be in good agreement with a reference dataset. The case study showed that the method can efficiently handle large amounts of data and requires little manual adjustment. Moreover, the mapped results can provide useful decision support when planning risk-reducing measures and when communicating with stakeholders. Although this novel method is developed for risk assessment of groundwater drawdown induced subsidence, it is useful for other applications involving spatial soil strata modeling