Analytical investigation of the exact groundwater divide between rivers beyond the Dupuit–Forchheimer approximation

The groundwater divide is a key feature of river basins and significantly influenced by subsurface hydrological processes. For an unconfined aquifer between two parallel rivers or ditches, it has long been defined as the top of the water table based on the Dupuit–Forchheimer approximation. However, the exact groundwater divide is subject to the interface between two local flow systems transporting groundwater to rivers from the infiltration recharge. This study contributes a new analytical model for two-dimensional groundwater flow between rivers of different water levels. The flownet is delineated in the model to identify groundwater flow systems and the exact groundwater divide. Formulas with two dimensionless parameters are derived to determine the distributed hydraulic head, the top of the water table and the groundwater divide. The locations of the groundwater divide and the top of the water table are not the same. The distance between them in horizontal can reach up to 8.9% of the distance between rivers. Numerical verifications indicate that simplifications in the analytical model do not significantly cause misestimates in the location of the groundwater divide. In contrast, the Dupuit–Forchheimer approximation yields an incorrect water table shape. The new analytical model is applied to investigate groundwater divides in the Loess Plateau, China, with a Monte Carlo simulation process taking into account the uncertainties in the parameters.     

Hydrological trends and the evolution of catchment research in the Alptal valley,central Switzerland

When the observation of small headwater catchments in the pre-Alpine Alptal valley (central Switzerland) started in the late 1960s, the researchers were mainly interested in questions related to floods and forest management. Investigations of geomorphological processes in the steep torrent channels followed in the 1980s, along with detailed observations of biogeochemical and ecohydrological processes in individual forest stands. More recently, research in the Alptal has addressed the impacts of climate change on water supply and runoff generation. In this article, we describe, for the first time, the evolution of catchment research at Alptal, and present new analyses of long-term trends and short-term hydrologic behaviour. Hydrometeorological time series from the past 50 years show substantial interannual variability, but only minimal long-term trends, except for the ~2°C increase in mean annual air temperature over the 50-year period, and a corresponding shift towards earlier snowmelt. Similar to previous studies in larger Alpine catchments, the decadal variations in mean annual runoff in Alptal's small research catchments reflect the long-term variability in annual precipitation. In the Alptal valley, the most evident hydrological trends were observed in late spring and are related to the substantial change in the duration of the snow cover. Streamflow and water quality are highly variable within and between hydrological events, suggesting rapid shifts in flow pathways and mixing, as well as changing connectivity of runoff-generating areas. This overview illustrates how catchment research in the Alptal has evolved in response to changing societal concerns and emerging scientific questions.     

Modelling the effect of changing precipitation inputs on deep soil water utilization

Forests in the Southeastern United States are predicted to experience future changes in seasonal patterns of precipitation inputs as well as more variable precipitation events. These climate change‐induced alterations could increase drought and lower soil water availability. Drought could alter rooting patterns and increase the importance of deep roots that access subsurface water resources. To address plant response to drought in both deep rooting and soil water utilization as well as soil drainage, we utilize a throughfall reduction experiment in a loblolly pine plantation of the Southeastern United States to calibrate and validate a hydrological model. The model was accurately calibrated against field measured soil moisture data under ambient rainfall and validated using 30% throughfall reduction data. Using this model, we then tested these scenarios: (a) evenly reduced precipitation; (b) less precipitation in summer, more in winter; (c) same total amount of precipitation with less frequent but heavier storms; and (d) shallower rooting depth under the above 3 scenarios. When less precipitation was received, drainage decreased proportionally much faster than evapotranspiration implying plants will acquire water first to the detriment of drainage. When precipitation was reduced by more than 30%, plants relied on stored soil water to satisfy evapotranspiration suggesting 30% may be a threshold that if sustained over the long term would deplete plant available soil water. Under the third scenario, evapotranspiration and drainage decreased, whereas surface run‐off increased. Changes in root biomass measured before and 4 years after the throughfall reduction experiment were not detected among treatments. Model simulations, however, indicated gains in evapotranspiration with deeper roots under evenly reduced precipitation and seasonal precipitation redistribution scenarios but not when precipitation frequency was adjusted. Deep soil and deep rooting can provide an important buffer capacity when precipitation alone cannot satisfy the evapotranspirational demand of forests. How this buffering capacity will persist in the face of changing precipitation inputs, however, will depend less on seasonal redistribution than on the magnitude of reductions and changes in rainfall frequency.     

Three-dimensional finite element simulation of fracture propagation in rock specimens with pre-existing fissure(s) under compression and their strength analysis

A FORTRAN program, consistent with the commercially available finite element (FE) code ABAQUS, is developed based on a three-dimensional (3D) linear elastic brittle damage constitutive model with two damage criteria. To consider the heterogeneity of rock, the developed FORTRAN program is used to set the stiffness and strength properties of each element of the FE model following a Weibull distribution function. The reliability of the program is assessed against available experimental results for granite cylindrical specimens with a throughgoing, flat and inclined fissure. The calibration procedure of the material parameters is explained in detail, and it is shown that the compressive to tensile strength ratio can have a substantial influence on the failure response of the specimens. Numerical simulations are conducted for models with different levels of heterogeneity. The results show a smaller load bearing capacity for models with less homogeneity, representing gradual coalescence of fully damaged elements forming throughout the models during loading. The maximum load bearing capacity is studied for various combinations of inclination angles of two centrally aligned, throughgoing and flat fissures of equal length embedded in cylindrical models under uniaxial and multiaxial loading conditions. The key role of the compressive to tensile strength ratio is highlighted by repeating certain simulations with a lower compressive to tensile strength ratio. It is proven that the peak loads of the rock models with sufficiently small compressive to tensile strength ratios containing two throughgoing fissures of equal length are similar, provided that the minimum inclination angles of the models are the same. The results are presented and discussed with respect to the existing experimental findings in the literature, suggesting that the numerical model applied in this study can provide useful insight into the failure behaviour of rock-like materials.     

Hydrological management strategies for the control of algal blooms in regulated lowland rivers

Reservoirs of lowland floodplain rivers with eutrophic backgrounds cause variations in the hydrological and hydraulic conditions of estuaries and low-dam reservoir areas, which can promote planktonic algae to proliferate and algal bloom outbreaks. Understanding the ecological effects of variations in hydrological and hydraulic processes in lowland rivers is important for algal bloom control. In this study, the middle and lower reaches of the Han River, China, a typical regulated lowland river with a eutrophic background, are selected. Based on the effect of hydrological and hydraulic variability on algal blooms, a hydrological management strategy for river algal bloom control is proposed. The results showed that (a) differences in river morphology and background nutrient levels cause significant differences in the critical threshold flow velocities for algal bloom outbreaks between natural river and low-dam reservoir sections; there is no uniform threshold flow velocity for algal bloom control. (b) There are significant differences in the river hydrological/hydraulic conditions between years with and without algal blooms. The average river flow, water level and velocity in years with algal blooms are significantly lower than those in years without algal blooms. (c) For different river sections where algal blooms occur and to meet the threshold flow velocities, the joint operation of cascade reservoirs and diversion projects is an effective method to prevent and control algal blooms in regulated lowland rivers. This study is expected to deepen our understanding of the ecological significance of special hydrological processes and guide algal bloom management in regulated lowland rivers.     

Implementation of a coupled plastic damage distinct lattice spring model for dynamic crack propagation in geomaterials

This paper studies dynamic crack propagation by employing the distinct lattice spring model (DLSM) and 3‐dimensional (3D) printing technique. A damage‐plasticity model was developed and implemented in a 2D DLSM. Applicability of the damage‐plasticity DLSM was verified against analytical elastic solutions and experimental results for crack propagation. As a physical analogy, dynamic fracturing tests were conducted on 3D printed specimens using the split Hopkinson pressure bar. The dynamic stress intensity factors were recorded, and crack paths were captured by a high‐speed camera. A parametric study was conducted to find the influences of the parameters on cracking behaviors, including initial and peak fracture toughness, crack speed, and crack patterns. Finally, selection of parameters for the damage‐plasticity model was determined through the comparison of numerical predictions and the experimentally observed cracking features.     

Evaluation of the temporal variations of groundwater storage and its interactions with climatic variables using GRACE data and hydrological models: A study from Turkey

Monitoring of the fluctuations of groundwater storage is particularly important in arid and semi-arid regions where water scarcity brings about various challenges. Remote sensing data and techniques play a preponderant role in developing solutions to environmental problems. The launch of Gravity Recovery and Climate Experiment (GRACE) satellites has eased the remote monitoring and evaluation of groundwater resources with an unprecedented precision over large scales. Within the scope of the current study, the latest release (RL06) of GRACE mass concentrations (Mascons) from Jet Propulsion Laboratory (JPL) dataset as well as Global Land Data Assimilation System (GLDAS) models of Noah and Catchment Land Surface Model (CLSM) were used to provide Groundwater Storage Anomalies (GWSA) over Turkey. The temporal interactions of the estimated GWSA with the climatic variables of precipitation and temperature (derived from the reanalysis datasets of CHELSA [Climatologies at High resolution for the Earth's Land Surface Areas] and FLDAS [the Famine Early Warning Systems Network Land Data Assimilation System], respectively) were investigated statistically. The results suggest that there is a descending trend (from 2003 to 2016) for Terrestrial Water Storage Anomalies (TWSA) and GWSA over Turkey with a total loss of 11 and 6 cm of water, respectively. The statistical analysis results also indicate that the monthly variations of GWSA over Turkey are highly correlated with precipitation and temperature at 2-month lag. The analysis of the climatology (long-term) values of monthly GWSA, precipitation and temperature also revealed high agreement between the variables.     

Assessment of alternative adsorption models and global sensitivity analysis to characterize hexavalent chromium loss from soil to surface runoff

We investigate our ability to assess transfer of hexavalent chromium, Cr(VI), from the soil to surface runoff by considering the effect of coupling diverse adsorption models with a two‐layer solute transfer model. Our analyses are grounded on a set of two experiments associated with soils characterized by diverse particle size distributions. Our study is motivated by the observation that Cr(VI) is receiving much attention for the assessment of environmental risks due to its high solubility, mobility, and toxicological significance. Adsorption of Cr(VI) is considered to be at equilibrium in the mixing layer under our experimental conditions. Four adsorption models, that is, the Langmuir, Freundlich, Temkin, and linear models, constitute our set of alternative (competing) mathematical formulations. Experimental results reveal that the soil samples characterized by the finest grain sizes are associated with the highest release of Cr(VI) to runoff. We compare the relative abilities of the four models to interpret experimental results through maximum likelihood model calibration and four model identification criteria (i.e., the Akaike information criteria [AIC and AIC_C] and the Bayesian and Kashyap information criteria). Our study results enable us to rank the tested models on the basis of a set of posterior weights assigned to each of them. A classical variance‐based global sensitivity analysis is then performed to assess the relative importance of the uncertain parameters associated with each of the models considered, within subregions of the parameter space. In this context, the modelling strategy resulting from coupling the Langmuir isotherm with a two‐layer solute transfer model is then evaluated as the most skilful for the overall interpretation of both sets of experiments. Our results document that (a) the depth of the mixing layer is the most influential factor for all models tested, with the exception of the Freundlich isotherm, and (b) the total sensitivity of the adsorption parameters varies in time, with a trend to increase as time progresses for all of the models. These results suggest that adsorption has a significant effect on the uncertainty associated with the release of Cr(VI) from the soil to the surface runoff component.     

Predicting quantiles of water quality from catchment characteristics

Water quality is often highly variable both in space and time, which poses challenges for modelling the more extreme concentrations. This study developed an alternative approach to predicting water quality quantiles at individual locations. We focused on river water quality data that were collected over 25 years, at 102 catchments across the State of Victoria, Australia. We analysed and modelled spatial patterns of the 10th, 25th, 50th, 75th and 90th percentiles of the concentrations of sediments, nutrients and salt, with six common constituents: total suspended solids (TSS), total phosphorus (TP), filterable reactive phosphorus (FRP), total Kjeldahl nitrogen (TKN), nitrate-nitrite (NO_x), and electrical conductivity (EC). To predict the spatial variation of each quantile for each constituent, we developed statistical regression models and exhaustively searched through 50 catchment characteristics to identify the best set of predictors for that quantile. The models predict the spatial variation in individual quantiles of TSS, TKN and EC well (66%–96% spatial variation explained), while those for TP, FRP and NO_x have lower performance (37%–73% spatial variation explained). The most common factors that influence the spatial variations of the different constituents and quantiles are: annual temperature, percentage of cropping land area in catchment and channel slope. The statistical models developed can be used to predict how low- and high-concentration quantiles change with landscape characteristics, and thus provide a useful tool for catchment managers to inform planning and policy making with changing climate and land use conditions.     

Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock

The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution.