The soil water retention curve (SWRC) is essential for describing water and energy exchange processes at the interface between the solid earth and the atmosphere. Despite its importance, measuring the SWRC using standard laboratory methods is challenging and time-consuming. This paper presents a novel physics-informed neural network (PINN) approach for developing pedotransfer functions (PTFs) to predict continuous SWRCs based on soil texture, organic carbon content, and dry bulk density. In contrast to conventional parametric PTFs developed for specific SWRC models, the PINN learns a non-specific form of the SWRC by effectively integrating both measurements and physical constraints into the training process. This approach allows the estimated SWRC to maintain its physical integrity from saturation to oven-dry conditions, even in scenarios with sparse data. The new approach is particularly effective for tackling the challenges encountered in developing PTFs on large SWRC datasets, which often have an imbalance towards the wet-end and include numerous samples with limited and unevenly distributed measurements. We compared the performance of the PINN with that of a conventional physics-agnostic neural network using a dataset of 4200 soil samples. While both networks performed similarly at the wet-end where data are abundant, the PINN excelled at the dry-end where data are sparse and unevenly distributed, achieving a normalized RMSE of 0.172 compared to 0.522 for the conventional neural network. The SWRC derived from the PINN is differentiable with respect to the matric potential and can be seamlessly integrated into the governing equations of water flow in the unsaturated zone.

Electromagnetic induction (EMI) is used widely for environmental studies. The apparent electrical conductivity (ECa), which can be mapped efficiently with EMI, correlates with a variety of important soil attributes. EMI instruments exist with several configurations of coil spacing, position, and height. There are general, rule-of-thumb guides to choose an optimal instrument configuration for a specific survey. The goal of this study was to use machine learning to improve this design optimization task. In this investigation, we used machine learning as an efficient tool for interpolating among the results of many forward model runs. Specifically, we generated an ensemble of 100,000 EMI forward models representing the responses of many EMI configurations to a range of three-layer subsurface models. We split the results into training and testing subsets and trained a decision tree (DT) with gradient boosting (GB) to predict the subsurface properties (layer thicknesses and EC values). We further examined the value of prior knowledge that could limit the ranges of some of the soil model parameters. We made use of the intrinsic feature importance measures of machine learning algorithms to identify optimal EMI designs for specific targets. The optimal designs identified using this approach agreed with those that are generally recognized as optimal by informed experts for standard targets, giving confidence in the ML-based approach. The approach also offered insight that would be difficult if not impossible to offer based on rule-of-thumb optimization. We contend that such ML-informed design approaches could be applied broadly to other survey design challenges.

Groundwater-dependent terrestrial ecosystems (GWDTE) have been increasingly under threat due to groundwater depletion globally. Within the past 200 years, there has been severe artificial drainage of low-lying areas in Denmark, leading to a gradual loss of GWDTE nature habitat areas. This study explores the spatial-temporal loss of Danish GWDTE using historically vectorized topographical maps. We carry out geographic information systems (GIS) overlap analysis between different historical topographic maps with signatures of GWDTE starting from the 19 th century up to a current river valley bottom map as a reference period. This is because farmworkers and monks have practiced drainage by ditching since the early middle ages (1100-1200). We then examine the changes in two protected GWDTE habitat types in different periods and different hydrologic spatial locations. Results reveal a decrease in the area of GWDTE over the last 200 years. We attribute this to different human interventions that through e.g., drainage, have impacted the low-lying landscape throughout history. We further conclude that downstream parts of the river network have been exposed to less GWDTE habitat loss than upstream ones. This indicates that upstream river valleys are more vulnerable to GWDTE decline. Therefore, as a management measure, caution should be exercised when designing these areas for agriculture activities using artificial drainage and groundwater abstraction since this may lead to further decline. In contrast, there is a higher potential for establishing constructed wetlands or rewetting peatlands to restore balance.