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Variably saturated subsurface flow models require knowledge of the soil hydraulic parameters. However, the determination of these parameters in heterogeneous soils is not easily feasible and subject to large uncertainties. As the modeled soil moisture is very sensitive to these parameters, especially the saturated hydraulic conductivity, porosity, and the parameters describing the retention and relative permeability functions, it is likewise highly uncertain. Data assimilation can be used to handle and reduce both the state and parameter uncertainty. In this work, we apply the ensemble Kalman filter (EnKF) to a three-dimensional heterogeneous hillslope model and investigate the influence of updating the different soil hydraulic parameters on the accuracy of the estimated soil moisture. We further examine the usage of a simplified layered soil structure instead of the fully resolved heterogeneous soil structure in the ensemble. It is shown that the best estimates are obtained when performing a joint update of porosity and the van Genuchten parameters and (optionally) the saturated hydraulic conductivity. The usage of a simplified soil structure gave decent estimates of spatially averaged soil moisture in combination with parameter updates but led to a failure of the EnKF and very poor soil moisture estimates at non-observed locations.

Models of variably saturated subsurface flow require knowledge of the soil hydraulic parameters. However, the determination of these parameters in heterogeneous soils is not easily feasible and subject to large uncertainties. As the modeled soil moisture is very sensitive to these parameters, especially the saturated hydraulic conductivity, porosity and the parameters describing the retention and relative permeability functions, it is likewise highly uncertain. Data assimilation can be used to handle and reduce both, state and parameter uncertainty. In this work, we apply the ensemble Kalman filter (EnKF) to a three-dimensional heterogeneous hillslope model and investigate the influence of updating the different soil hydraulic parameters on the accuracy of the estimated soil moisture. We further examine the usage of a simplified layered soil structure instead of the fully resolved heterogeneous soil structure in the ensemble. It is shown that the best estimates are obtained when performing a joint update of porosity and van Genuchten parameters and optionally the saturated hydraulic conductivity. The usage of a simplified soil structure gave decent estimates of spatially averaged soil moisture in combination with parameter updates but led to a failure of the EnKF and very poor soil moisture estimates at non-observed locations.

Soil hydrological processes (SHP) support ecosystems, modulate the impact of climate change on terrestrial systems and control feedback mechanisms between water, energy and biogeochemical cycles. However, land-use changes and extreme events are increasingly impacting these processes. In this Review, we describe SHP across scales and examine their links with soil properties, ecosystem processes and climate. Soil structure influences SHP such as infiltration, soil water redistribution and root water uptake on small scales. On local scales, SHP are driven by root water uptake, vegetation and groundwater dynamics. Regionally, SHP are impacted by extreme events such as droughts, floods, heatwaves and land-use change; however, antecedent and current SHP partially determine the broader effects of extreme events. Emerging technologies such as wireless and automated sensing, soil moisture observation through novel synthetic aperture radars satellites, big data analysis and machine learning approaches offer unique opportunities to advance soil hydrology. These advances, in tandem with the inclusion of more key soil types and properties in models, will be pivotal in predicting the role of SHP during global change.

We study the mechanisms of advective trapping in composite porousmedia that consist of circular inclusions of distributed hydraulic con-ductivity embedded in a high conductivity matrix. Advective trappingoccurs when solute enters low velocity regions in the media.Transportis analyzed in terms of breakthrough curves measured at the outlet ofthe system. The curve’s peak behavior depends on the volume frac-tion occupied by the inclusions, while the tail behavior depends onthe distribution of hydraulic conductivity values. In order to quantifythe observed behaviors we derive two equivalent upscaled transportmodels. First, we derive a Lagrangian trapping model using the con-tinuous time random walk framework that is parameterized intermsof volume fraction and the distribution of conductivites in the inclu-sions. Second, we establish a non-local partial differential equation forthe mobile solute concentration by volume averaging of the microscaletransport equation. We show the equivalence between the two modelsas well as (first-order) multirate mass transfer models. Theupscaledapproach, parameterized by medium and flow properties captures allfeatures of the observed solute breakthrough curves, and sheds newlight on the modeling of advective trapping in heterogeneous media.

The vadose zone is subject to dynamic boundary conditions in the form of infiltration and evaporation. A better understanding of implications for flow and solute transport, arising from these dynamic boundary conditions in combination with heterogeneous structure, will help to improve the prediction of the fate of solutes. We present laboratory experiments and numerical simulations of heterogeneous porous media under unsaturated conditions where controlled, temporally varying precipitation and evaporation are applied to study the effect of dynamic boundary conditions on solute transport in the presence of material interfaces. Dye tracers Eosine Y and Brilliant Blue FCF are utilized to visualize solute transport and analyze redistribution processes in a flow cell. Water and solute fluxes in and out of the flow cell are quantified. While in dynamic experiments application of small infiltration rates (significantly below the saturated hydraulic conductivities of the materials) led to a reversal of transport paths between infiltration and succeeding evaporation, larger infiltration rates altered downward transport such that flow and transport paths differed from those observed during evaporation. Differences in transport paths ultimately led to a redistribution and trapping of solute in one material which manifested as pronounced tailing in breakthrough curves. Trapping was induced not by the formation of a stagnant zone as result of large parameter contrast but by an interplay of dynamic boundary conditions and material heterogeneity. This study thereby highlights the importance to consider dynamic boundary conditions in predictions of solute leaching. © 2019. The Authors.

We present a multi-dimensional continuum mathematical model for modeling the growth of a symbiotic biofilm system. We take a dual-species namely, the Streptococcus - Veillonella sp. biofilm system as an example for numerical investigations. The presented model describes both the cooperation and competition between these species of bacteria. The coupled partial differential equations are solved by using an integrative finite element numerical strategy. Numerical examples are carried out for studying the evolution and distribution of the bio-components. The results demonstrate that the presented model is capable of describing the symbiotic behavior of the biofilm system. However, homogenized numerical solutions are observed locally. To study the homogenization behavior of the model, numerical investigations regarding on how random initial biomass distribution influences the homogenization process are carried out. We found that a smaller correlation length of the initial biomass distribution leads to faster homogenization of the solution globally, however, shows more fluctuated biomass profiles along the biofilm thickness direction. More realistic scenarios with bacteria in patches are also investigated numerically in this study.

Pluvial floods in urban areas are caused by local, fast storm events with very high rainfall rates, which lead to inundation of streets and buildings before the storm water reaches a watercourse. An increase in frequency and intensity of heavy rainfall events and an ongoing urbanization may further increase the risk of pluvial flooding in many urban areas. Currently, warnings for pluvial floods are mostly limited to information on rainfall intensities and durations over larger areas, which is often not detailed enough to effectively protect people and goods. We present a proof‐of‐concept for an impact‐based forecasting system for pluvial floods. Using a model chain consisting of a rainfall forecast, an inundation, a contaminant transport and a damage model, we are able to provide predictions for the expected rainfall, the inundated areas, spreading of potential contamination and the expected damage to residential buildings. We use a neural network‐based inundation model, which significantly reduces the computation time of the model chain. To demonstrate the feasibility, we perform a hindcast of a recent pluvial flood event in an urban area in Germany. The required spatio‐temporal accuracy of rainfall forecasts is still a major challenge, but our results show that reliable impact‐based warnings can be forecasts are available up to 5 min before the peak of an extreme rainfall event. Based on our results, we discuss how the outputs of the impact‐based forecast could be used to disseminate impact‐based early warnings., Plain Language Summary: Pluvial floods are caused by local rain storms with extreme rainfall rates, which leads to immediate flooding of streets and buildings in urban areas. These events are expected to increase in the future due to climate change and growing urban areas. Pluvial floods are directly caused by a rainstorm, which gives citizens and emergency responders usually only a few minutes to act. Existing forecasting systems for pluvial floods are limited to rainfall forecasts that neither provide information about where a flood might occur nor how severe the impacts will be. Here, the main challenge is that current computer models that predict inundation take too long to run to release flood forecasts early enough. We present a new inundation model that can predict inundation for an upcoming flood event in a fraction of the time of existing models. We combine this model with models that predict the spreading of contamination (e.g., from a car accident) and the damage to residential buildings. For a real flood event we can show that this information can be released up to 5 min before the rainfall peak, which gives citizens and emergency responders the opportunities to safe lives and protect important valuables., Key Points: First impact‐based forecasting for pluvial foods. Artificial neural network inundation model significantly cuts calculation time to 0.1% of a physically based model with comparable accuracy. Forecast with estimates for inundated areas, spreading of contaminants and expected damage could be released 5 min before peak rainfall., Bundesministerium für Bildung und Forschung (BMBF), Z Zurich Foundation, Grantham Foundation for the Protection of the Environment, ESRC Centre for Climate Change Economics and Policy: ES/R009708/1

Fully integrated three-dimensional (3D) physically based hydrologic models usually require many computational resources. For many applications, simplified models can be a cost-effective alternative. The 3D models of subsurface flow are often simplified by coupling a 2D groundwater model with multiple 1D models for the unsaturated zone. The crucial part of such models is the coupling between the two model compartments. In this work we compare two approaches for the coupling. One is iterative where the 1D unsaturated zone models go down to the impervious bottom of the aquifer, and the other one is non-iterative and uses a moving lower boundary for the unsaturated zone. In this context we also propose a new way of treating the specific yield, which plays a crucial role in linking the unsaturated and the groundwater model. Both models are applied to three test cases with increasing complexity and analyzed in terms of accuracy and speed compared to fully integrated model runs. The non-iterative approach is faster but does not yield a good accuracy for the model parameters in all applied test cases, whereas the iterative one gives good results in all cases. Which strategy is applied depends on the requirements: computational speed vs. model accuracy.

Advective trapping occurs when solute enters low velocity zones in heterogeneous porous media. Classical local modelling approaches combine the impact of slow advection and diffusion into a hydrodynamic dispersion coefficient and many temporally non-local approaches lump these mechanisms into a single memory function. This joint treatment makes parameterization difficult and thus prediction of large-scale transport a challenge. Here, we investigate the mechanisms of advective trapping and their impact on transport in media composed of a high conductivity background and isolated low permeability inclusions. Breakthrough curves show that effective transport changes from a streamtube-like behaviour to genuine random trapping as the degree of disorder of the inclusion arrangement increases. We upscale this behaviour using a Lagrangian view point, in which idealized solute particles transition over a fixed distance at random advection times combined with Poissonian advective trapping events. We discuss the mathematical formulation of the upscaled model in the continuous time random walk and mobile–immobile mass transfer frameworks, and derive a model for large-scale solute non-Fickian dispersion. These findings give new insight into transport in highly heterogeneous media., Data used for producing the figures can be downloaded from digital.csic.es (https://digital.csic.es/handle/10261/216991) and by solving the respective equations. The authors thank Professor T.R. Ginn and two anonymous reviewers for their comments on the paper. J.J.H. and M.D. acknowledge the support of the Spanish Ministry of Science and Innovation (project CEX2018-000794-S and project HydroPore PID2019-106887GB-C31). J.J.H. acknowledges the support of the European Social Fund and Spanish Ministry of Ministry of Science, Innovation and Universities through the ‘Ramón y Cajal’ fellowship (RYC-2017-22300). The authors thank P. Uszes for providing the code to measure the average distance between inclusions.

The DLVO (Derjaguin-Landau-Verwey-Overbeek) approach to predict colloid mobility in porous media is centered on solution ionic strength and physicochemical surface properties of colloids and solid matrix. However, several colloid retention mechanisms are not related to such interfacial properties, but instead to hydraulic features like flow regime and pore structure. We aimed to determine the relative importance of DLVO-related and non-DLVO-related retention mechanisms, which remains poorly understood. For that, we developed a conceptual approach based on previous research on organic matter-coated goethite (OMCG) colloid mobility in quartz sand. OMCG colloid retention by DLVO mechanisms was negligible at 0.0 mM ionic strength. Therefore, any retention at 0.0 mM can be assigned to non-DLVO retention. At increasing ionic strength, the amount of DLVO retention is rising, while the amount of non-DLVO retention is independent from ionic strength and thus remains constant. This allows for a differentiation between the two types of retention mechanisms. To test this conceptual approach, we conducted OMCG colloid breakthrough experiments at varying interfacial conditions (ionic strength: 0.0–5.53 mM) and hydraulic conditions (flow rate: 0.11 – 5.02 cm min−1). From sessile drop contact angles and zeta potentials, DLVO and extended DLVO (XDLVO) interactions including Lewis acid-base interactions were approximated. The results show that colloid retention was almost exclusively related to DLVO retention mechanisms, while retention by hydraulic factors was practically irrelevant. We conclude that our conceptual approach can be applied to determine the relative importance of colloid retention caused by DLVO and non-DLVO mechanisms for further colloid-solid matrix systems.

Due to the complexity of flow conditions as well as solid matrix and colloid surface properties, solid knowledge about the transport of iron oxide colloids in soils remains scarce. In order to analyze the influence of flow conditions on iron oxide colloid transport and retention, breakthrough behavior of negatively charged, organic matter-coated goethite (OMCG) colloids in saturated quartz sand columns was investigated under continuous and stagnant flow conditions. Classic DLVO and extended DLVO (XDLVO) interaction energies including Lewis acid/base parameters were evaluated using measurements of sessile drop contact angles and zeta potentials of OMCG colloids and quartz. Results elucidated that under continuous flow conditions, OMCG colloids were highly mobile, which was in agreement with calculated unfavorable attachment conditions revealed by predictions of both DLVO approaches. In contrast, during intervals of flow interruption, significant amounts of OMCG colloids were retained in the solid matrix and could not be remobilized via re-establishment of flow. The magnitude of colloid retention increased with the duration of flow interruption; OMCG colloids were almost completely immobilized after 112 h. Further experiments were conducted in order to determine possible colloid retention mechanisms. Results indicated that the major cause for retention during flow stagnation was OMCG colloid capture at locations with attractive DLVO/XDLVO interactions, promoted by fast gravitational settling of colloids onto the solid matrix. We compared breakthrough curves to model predictions, where we demonstrated that an attachment term with a stagnant fluid switch was required in the mass balance in order to reproduce the measurements. We conclude that high mobility of OMCG colloids and prediction of that transport behavior with the applied DLVO approaches were only valid under continuous flow conditions. Under more discontinuous hydraulic conditions relevant in natural soils, such as flow interruption, OMCG colloid transport behavior was modified significantly.

Models for flow in environmental systems are subject to uncertainty. Models can thus be interpreted as hypotheses on the validity of the underlying model assumptions. One important source of uncertainty in models for flow and transport processes in the subsurface is the model concept. While uncertain model parameters or forcing terms can be captured as random processes and random fields, this type of uncertainty cannot be included into a model in a straightforward manner. This is particularly true if established model descriptions of a given process are not known or are still being debated. In this contribution, we outline several examples of subsurface flow and transport modeling where uncertainty of the model concept plays an important role. We discuss the need for the development of methods and standards to deal with this type of uncertainty in model hypothesis testing. This article is protected by copyright. All rights reserved.

The paper presents a 2D upward infiltration experiment performed on a model porous medium consisting of fine sand background with two inclusions made of coarser sands. The purpose of the experiment was to investigate the effects of structural air trapping, which occurs during infiltration as a result of heterogeneous material structure. The experiment shows that a significant amount of air becomes trapped in each of the inclusions. Numerical simulations were carried out using the two-phase water-air flow model and the Richards equation. The experimental results can be reproduced with good accuracy only using a two-phase flow model, which accounts for both structural and pore-scale trapping. On the other hand, the Richards equation was not able to represent the structural trapping caused by material heterogeneity.

Editors of several journals in the field of hydrology met during the Assembly of the International Association of Hydrological Sciences - IAHS (within the Assembly of the International Union of Geodesy and Geophysics - IUGG) in Prague in June 2015. This event was a follow-up of a similar meeting held in July 2013 in Gothenburg (as reported by Bloschl et al. [2014]). These meetings enable the group of editors to review the current status of the journals and the publication process, and share thoughts on future strategies. Journals were represented in the 2015 meeting through their editors, as shown in the list of authors. The main points on fostering innovation and improving impact assessment in journal publications in hydrology are communicated in this joint editorial published in the above journals.

International audience; Editors of several journals in the field of hydrology met during the Assembly of the International Association of Hydrological Sciences—IAHS (within the Assembly of the International Union of Geodesy and Geophysics—IUGG) in Prague in June 2015. This event was a follow-up of a similar meeting held in July 2013 in Gothenburg (as reported by Blöschl et al. 2014). These meetings enable the group of editors to review the current status of the journals and the publication process, and share thoughts on future strategies. Journals were represented in the 2015 meeting through their editors, as shown in the list of authors. The main points on fostering innovation and improving impact assessment in journal publications in hydrology are communicated in this joint editorial published in the above journals.

The real-time forecasting of urban flooding is a challenging task for the following two reasons: (1) urban flooding is often characterized by short lead times, (2) the uncertainty in precipitation forecasting is usually high. Standard physically based numerical models are often too slow for the use in real-time forecasting systems. Data driven models have small computational costs and fast computation times and may be useful to overcome this problem. The present study presents an artificial neural network based model for the prediction of maximum water levels during a flash flood event. The challenge of finding a suitable structure for the neural network was solved with a new growing algorithm. The model is successfully tested for spatially uniformly distributed synthetic rain events in two real but slightly modified urban catchments with different surface slopes. The computation time of the model in the order of seconds and the accuracy of the results are convincing, which suggest that the method may be useful for real-time forecasts. Bundesministerium für Bildung und Forschung/Sonderprogramm GEOTECHNOLOGIEN/03G0846A/EU

International audience; We develop an efficient computational model for simulating fluid invasion patterns emerging in variable aperture fractures. This two-dimensional model takes into account the effect of capillary force on the fluid-fluid interfaces and viscous pressure drop in both fluid phases. The pressure distribution is solved at each time step based on mass balance and local cubic law, considering an imposed pressure jump condition at the fluid-fluid interface. This pressure jump corresponds to the Laplace pressure which includes both terms related to the out-of-plane (aperture-spanning) curvature and to the in-plane curvature. Simulating a configuration that emulates viscous fingering in two-dimensional random porous media confirms that the model accounts properly for the role of viscous forces. Furthermore, direct comparison with previously obtained experimental results shows that the model reproduces the observed drainage patterns in a rough fracture reasonably well. The evolutions of tip location, the inlet pressures, and the invading phase fractal dimensions are analyzed to characterize the transition from capillary fingering to viscous fingering regimes. A radial injection scenario of immiscible invasion is also studied with varying modified capillary number and viscosity ratio, showing displacement patterns ranging from capillary fingering to viscous fingering to stable displacement. Such simulations using two contact angles show that the invading phase becomes more compact when the wetting condition changes from strong to weak drainage, as already observed in 2-D porous media. The model can be used to bridge the gap in spatial scales of two-phase flow between pore-scale modeling approaches and the continuum Darcy-scale models.

Porous transport layers (PTL) are key components of proton exchange membrane water electrolysis (PEMWE) cells controlling species transport. Further optimization requires better understanding of how PTLs influence overpotentials. In this work, the data from an electrochemical overpotential breakdown is compared to a state-of-the-art model, which includes a Nernstian overpotential description, two-phase Darcian flow and advective-diffusive mass transport. Model parameters are derived from X-ray tomographic measurements, pore-scale calculations, standard models for porous materials and by transferring ex situ measurements from other materials. If the parameter set is available, model results and experimental data match well concerning PTL-related overpotentials at different current densities and operating pressures. Both experimental and modeling results suggest that mass transport through PTLs does not affect a considerable, pressure-independent share of mass transport overpotentials. Both model results and experimental findings conclude that mass transport through the cathode PTL causes overpotentials more than twice as high as through its anode counterpart. Further research opportunities regarding the relationship between PTL bulk properties and experimentally determined mass transport overpotentials are identified. © 2020 The Author(s). Published on behalf of The Electrochemical Society by IOP Publishing Limited.

In this paper, we present an upscaled model for horizontal immiscible displacement in highly heterogeneous media. This type of heterogeneity can be found, for instance, in fractured rock, which consists of two flow domains, a mobile fracture and a virtually immobile matrix. We derive an upscaled double-continuum model capable of predicting flow in mobile-immobile domains using homogenization theory. The model consists of a flow equation for the saturation of displacing fluid in the fracture domain, and a capillary flow equation for saturation in the matrix, which are coupled via a source term. By linearizing capillary counter current flow in the matrix domain, we combine this system of equations into a non-local single-equation model for the fracture saturation, which can be interpreted as a multi-rate mass-transfer (MRMT) model for immiscible displacement. We discuss this simplification and the parametrization of the upscaled model equation from local hydraulic parameters obtained from rock samples and from knowledge of the average flow properties of the fracture network. We demonstrate its performance for predicting two-phase flow by considering a single fracture with imbibition into a rectangular matrix domain. The upscaled model is parameterized directly from geometry and hydraulic parameters of matrix and fracture of the reference model, which means that no parameters need to be fitted. We compare the detailed and upscaled models in terms of breakthrough curves for the displaced fluid at a control plane within the medium. Both the detailed numerical simulations and the upscaled model show a preasymptotic t - 1 / 2 scaling and a breakoff at the characteristic time scale for filling the matrix by counter current flow. © 2013 Elsevier Ltd., M. D. and J. C. acknowledge the support of the FP7 EU project PANACEA (Grant No. 282900), and the Spanish Ministry of Economy and Competitivity through the project HEART (CGL2010-18450).

We consider a model for biofilm growth in the continuum mechanics framework, where the growth of different components of biomass is governed by a time dependent advection–reaction equation. The recently developed time-discontinuous Galerkin (TDG) method combined with two different stabilization techniques, namely the Streamline Upwind Petrov Galerkin (SUPG) method and the finite increment calculus (FIC) method, are discussed as solution strategies for a multi-dimensional multi-species biofilm growth model. The biofilm interface in the model is described by a convective movement following a potential flow coupled to the reaction inside of the biofilm. Growth limiting substrates diffuse through a boundary layer on top of the biofilm interface. A rolling ball method is applied to obtain a boundary layer of constant height. We compare different measures of the numerical dissipation and dispersion of the simulation results in particular for those with non-trivial patterns. By using these measures, a comparative study of the TDG–SUPG and TDG–FIC schemes as well as sensitivity studies on the time step size, the spatial element size and temporal accuracy are presented. The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-017-1388-1 State of Lower Saxony

We study modeling of two-phase flow in highly heterogeneous fractured and porous media. The flow behaviour is strongly influenced by mass transfer between a highly permeable (mobile) fracture domain and less permeable (immobile) matrix blocks. We quantify the effective two-phase flow behavior using a multirate rate mass transfer (MRMT) approach. We discuss the range of applicability of the MRMT approach in terms of the pertinent viscous and capillary diffusion time scales. We scrutinize the linearization of capillary diffusion in the immobile regions, which allows for the formulation of MRMT in the form of a non-local single equation model. The global memory function, which encodes mass transfer between the mobile and the immobile regions, is at the center of this method. We propose two methods to estimate the global memory function for a fracture network with given fracture and matrix geometry. Both employ a scaling approach based on the known local memory function for a given immobile region. With the first method, the local memory function is calculated numerically, while the second one employs a parametric memory function in form of truncated power-law. The developed concepts are applied and tested for fracture networks of different complexity. We find that both physically based parameter estimation methods for the global memory function provide predictive MRMT approaches for the description of multiphase flow in highly heterogeneous porous media. © 2016 Elsevier Ltd., This work was supported by the compute cluster, which is funded by the Leibniz University Hanover, the Lower Saxony Ministry of Science and Culture (MWK) and by the German Research Association (DFG) under the grant NE 34 824 10-1. We gratefully acknowledge the help of Bernd Flemisch from the Uni- versity of Stuttgart with the Dumux model. M.D. acknowledges the funding from the European Research Council through the project MHetScale (Grant agreement no. 617511).

Combining numerical models, which simulate water and energy fluxes in the subsurface-land surface-atmosphere system in a physically consistent way, becomes increasingly important to understand and study fluxes at compartmental boundaries and interdependencies of states across these boundaries. Complete state evolutions generated by such models, when run at highest possible resolutions while incorporating as many processes as attainable, may be regarded as a proxy of the real world – a virtual reality – which can be used to test hypotheses on functioning of the coupled terrestrial system and may serve as source for virtual measurements to develop data-assimilation methods. Such simulation systems, however, face severe problems caused by the vastly different scales of the processes acting in the compartments of the terrestrial system. The present study is motivated by the development of cross-compartmental data-assimilation methods, which face the difficulty of data scarcity in the subsurface when applied to real data. With appropriate and realistic measurement operators, the virtual reality not only allows taking virtual observations in any part of the terrestrial system at any density, thus overcoming data-scarcity problems of real-world applications, but also provides full information about true states and parameters aimed to be reconstructed from the measurements by data assimilation. In the present study, we have used the Terrestrial Systems Modeling Platform TerrSysMP, which couples the meteorological model COSMO, the land-surface model CLM, and the subsurface model ParFlow, to set up the virtual reality for a regional terrestrial system roughly oriented at the Neckar catchment in southwest Germany. We find that the virtual reality is in many aspects quite close to real observations of the catchment concerning, e.g., atmospheric boundary-layer height, precipitation, and runoff. But also discrepancies become apparent both in the ability of such models to correctly simulate some processes – which still need improvement – and the realism of the results of some observation operators like the SMOS and SMAP sensors, when faced with model states. In a succeeding step, we will use the virtual reality to generate observations in all compartments of the system for coupled data assimilation. The data assimilation will rely on a coarsened and simplified version of the model system.

For decades, extensive research efforts have been conducted to improve the functionality and stability of implants. Especially in dentistry, implant treatment has become a standard medical practice. The treatment restores full dental functionality, helping patients to maintain high quality of life. However, about 10% of the patients suffer from early and late device failure due to peri-implantitis, an inflammatory disease of the tissues surrounding the implant. Peri-implantitis is caused by progressive microbial colonization of the device surface and the formation of microbial communities, so-called biofilms. This infection can ultimately lead to implant failure. The causative agents for the inflammatory disease, periodontal pathogenic biofilms, have already been extensively studied, but are still not completely understood. As numerical simulations will have the potential to predict oral biofilm formation precisely in the future, for the first time, this study aimed to analyze Streptococcus gordonii biofilms by combining experimental studies and numerical simulation. The study demonstrated that numerical simulation was able to precisely model the influence of different nutrient concentration and spatial distribution of active and inactive biomass of the biofilm in comparison with the experimental data. This model may provide a less time-consuming method for the future investigation of any bacterial biofilm.

The numerical simulation of contaminant spreading in the vadose zone as well as the modeling of remediation scenarios requires, in general, very sophisticated model concepts. Particularly, compositional and nonisothermal effects increase the complexity of a model significantly. This makes the solution of large systems computationally costly. To save computation time, it is reasonable to adjust the required model complexity to the complexity of the relevant physical processes. The relevant physical processes governing the system9s behavior can change for distinct time scales. This can be taken into account by models that are adapted to the respective processes, which can be coupled sequentially.

We study the macroscopic representation of noise-driven interfaces in stochastic interface growth models in (1+1) dimensions. The interface is characterized macroscopically by saturation, which represents the fluctuating sharp interface by a smoothly varying phase field with values between 0 and 1. We determine the one-point interface height statistics for the Edwards-Wilkinson (EW) and Kadar-Paris-Zhang (KPZ) models in order to determine explicit deterministic equations for the phase saturation for each of them. While we obtain exact results for the EW model, we develop a Gaussian closure approximation for the KPZ model. We identify an interface compression term, which is related to mass transfer perpendicular to the growth direction, and a diffusion term that tends to increase the interface width. The interface compression rate depends on the mesoscopic mass transfer process along the interface and in this sense provides a relation between meso- and macroscopic interface dynamics. These results shed light on the relation between mesoscale and macroscale interface models, and provide a systematic framework for the upscaling of stochastic interface dynamics., MD acknowledges the funding from the European Research Council through the project MHetScale (Grant agreement no. 617511). IN acknowledges funding from DFG (Ne824/6-2 under the research unit MUSIS FOR 1083). DMT was supported in part by Defense Advanced Research Projects Agency under the EQUiPS program, the Air Force Office of Scientific Research under grant FA9550-12-1-0185 and by the National Science Foundation under grant DMS-1522799.

We investigate the effect of dynamic boundary conditions on solute transport in unsaturated, heterogeneous, bimodal porous media. Solute transport is studied with two-dimensional numerical flow and transport models for scenarios where either (i) solely infiltration or (ii) more realistic dynamic (infiltration–evaporation) boundary conditions are imposed at the soil surface. Travel times of solute are affected by duration and intensity of infiltration and evaporation events even when cycle-averaged inflow rates of the scenarios are identical. Three main transport mechanisms could be identified based on a criterion for the infiltration rate that is related to the hydraulic conductivity curves of the media. If, based on this criterion, infiltration rates are low, the transport paths for upward and downward transport do not differ significantly, and the breakthrough curves of solute are similar to the one obtained under stationary infiltration. If infiltration rates are moderate, travel paths deviate between upward and downward flow, leading to a trapping of solute and strong tailing of the breakthrough curves. If infiltration and evaporation rates are very high, lateral advective–diffusive transport can lead to very efficient and fast downward transport. Thus, solute breakthrough depends strongly on lateral flow paths enforced by the boundary conditions at the soil surface. If heterogeneity of the materials is not strong and the structure is tortuous, dynamic boundary conditions mainly lead to increased macrodispersion. We test simplified upscaled transport models based on stationary flow rates to estimate breakthrough curves and demonstrate how the transport mechanisms are captured in the model parameters.

Editors of several journals in the field of hydrology met during the Assembly of the International Association of Hydrological Sciences—IAHS (within the Assembly of the International Union of Geodesy and Geophysics—IUGG) in Prague in June 2015. This event was a follow-up of a similar meeting held in July 2013 in Gothenburg (as reported by Blöschl et al., 2014). These meetings enable the group of editors to review the current status of the journals and the publication process, and share thoughts on future strategies. Journals were represented in the 2015 meeting through their editors, as shown in the list of authors. The main points on fostering innovation and improving impact assessment in journal publications in hydrology are communicated in this joint editorial published in the above journals.

International audience; The spatial distribution of fluid phases and the geometry of fluid-fluid interfaces resulting from immiscible displacement in fractures cast decisive influence on a range of macroscopic flow parameters. Most importantly, these are the relative permeabilities of the fluids as well as the macroscopic irreducible saturations. They also influence parameters for component (solute) transport, as it usually occurs through one of the fluid phase only. Here, we present a numerical investigation on the critical role of aperture variation and spatial correlation on fluid trapping and the morphology of fluid phase distributions in a geological fracture. We consider drainage in the capillary dominated regime. The correlation scale, that is, the scale over which the two facing fracture walls are matched, varies among the investigated geometries between L/256 and L (self-affine fields), L being the domain/fracture length. The aperture variability is quantified by the coefficient of variation (δ), ranging among the various geometries from 0.05 to 0.25. We use an invasion percolation based model which has been shown to properly reproduce displacement patterns observed in previous experiments. We present a quantitative analysis of the size distribution of trapped fluid clusters. We show that when the in-plane curvature is considered, the amount of trapped fluid mass first increases with increasing correlation scale Lc and then decreases as Lc further increases from some intermediate scale towards the domain length scale L. The in-plane curvature contributes to smoothening the invasion front and to dampening the entrapment of fluid clusters of a certain size range that depends on the combination of random aperture standard deviation and spatial correlation.

Upscaling of the Richards equation is important for large-scale modeling of water flow in the unsaturated zone. We derive an upscaled model for Richards' equation in a layered porous medium. Homogenization theory is applied to derive the upscaled equations for slow flow processes. Two flow regimes are compared. The first flow regime is quantified by small Bond numbers, meaning forces due to pressure gradients are dominant on the small scale. The second flow regime is quantified by large Bond numbers, meaning that forces due to pressure gradients and gravity contribute equally on the small scale, while the large scale is dominated by gravity forces. The case of intermediate Bond numbers is also addressed. We compare the effective relative permeability function and the effective capillary pressure head–saturation function for both flow regimes. In the case of small Bond numbers the effective curves can be derived based on capillary equilibrium. The procedure to calculate effective curves is then quite simple. In the case of large Bond numbers the procedure is more complex. However, comparing effective curves of different test cases showed that the difference between the effective curves for different Bond numbers is not that large for moderate parameter contrasts and when the gradients of the capillary–saturation curve do not become too small. The effective parameter functions calculated with a capillary equilibrium assumption are therefore often a good estimate.

The spatial correlation structure of heterogeneous parameters plays an important role in upscaling of many flow and transport processes in porous media and fractures. We analyze upscaling of a slow drainage process in a horizontal open rough walled fracture. The applicability of upscaled continuum models for this kind of flow process is discussed. We consider two different fracture aperture distributions with different spatial correlation properties. One is described by a slowly decaying, the other one by a Gaussian autocovariance. The flow process is modelled using an invasion percolation model, which takes the in plane curvature of the fluid cluster into account. Results are compared to laboratory experiments in artificial plexiglas fractures. Different averaging procedures are tested in order to assess the applicability of continuum models. Independently of the correlation structure of the fracture aperture field, spatial averages do not converge to a continuum formulation. Ensemble averages do converge, however, they only give probabilistic information and are not applicable to model drainage in a fracture.

Prediction of infiltration in porous media is challenged by finger formation and unstable displacement of the wetting front. We present a systematic experimental study on the effect of packings and infiltration rates on unstable flow into initially dry porous media. We conducted small two- and three-dimensional experiments where water contents were measured with neutron radiography and larger two-dimensional experiments, which we evaluated by obtaining commonly used finger properties such as width and velocity from image analysis. Our results from experiments in macroscopically homogeneous packings were tested for correspondence with theoretical finger property predictions and are in good agreement. For the smaller experiments, water content profiles including “overshoots” at the finger tips as well as finger properties depending on the packing matched well results reported in the literature. For all homogeneous experiments, we found a strong dependence of finger properties on porosity. Homogeneous experiments served as reference cases for comparison with larger two-dimensional experiments where heterogeneity was induced by block-shaped inclusions. Unstable flow propagation in heterogeneous experiments was documented by inclusion fill rates in addition to finger properties. We found a multifaceted finger propagation behavior that depends on the impingement position of instabilities on an inclusion. Thereby, we are able to show that the location of the impingement on an inclusion is crucial to the filling rate of the inclusion and the propagation velocity of the finger. Results from the conducted experiments present a data set for testing of extended Richards’ models.

The paper presents numerical simulations of water infiltration in unsaturated porous media containing coarse-textured inclusions embedded in fine-textured background material. The calculations are performed using the two-phase model for water and air flow and a simplified model known as the Richards equation. It is shown that the Richards equation cannot correctly describe flow in the presence of heterogeneities. However, its performance can be improved by introducing appropriately defined effective capillary and permeability functions, representing largescale behaviour of the heterogeneous medium.

We study the transport behavior of a tracer in a radially diverging heterogeneous velocity field. Making use of homogenization theory, we derive effective transport equations. These effective transport equations are very similar to those defined on the local scale. However, the local transport parameters such as local dispersion coefficients are replaced by effective dispersion coefficients. For smoothly varying heterogeneous media, explicit results for effective radial dispersion coefficients are derived. Starting with the purely advective transport behavior (infinite Peclet numbers), we extend our calculations to transport with finite Peclet numbers. We find that the impact of molecular diffusion on the effective dispersivity differs from the impact of local dispersion: Including local dispersion leads to effective dispersivities which are constant and equivalent to the effective dispersivities found in uniform flow configurations. In contrast, effective dispersivities including diffusion are not constant but depend on the radial distance. We compare the results found by homogenization theory with those derived by Neuweiler et al. (this issue) by standard method of moments.

[1] Estimates of effective parameters for unsaturated flow models are typically based on observations taken on length scales smaller than the modeling scale. This complicates parameter estimation for heterogeneous soil structures. In this paper we attempt to account for soil structure not present in the flow model by using so-called external error models, which correct for bias in the likelihood function of a parameter estimation algorithm. The performance of external error models are investigated using data from three virtual reality experiments and one real world experiment. All experiments are multistep outflow and inflow experiments in columns packed with two sand types with different structures. First, effective parameters for equivalent homogeneous models for the different columns were estimated using soil moisture measurements taken at a few locations. This resulted in parameters that had a low predictive power for the averaged states of the soil moisture if the measurements did not adequately capture a representative elementary volume of the heterogeneous soil column. Second, parameter estimation was performed using error models that attempted to correct for bias introduced by soil structure not taken into account in the first estimation. Three different error models that required different amounts of prior knowledge about the heterogeneous structure were considered. The results showed that the introduction of an error model can help to obtain effective parameters with more predictive power with respect to the average soil water content in the system. This was especially true when the dynamic behavior of the flow process was analyzed.

[1] We consider flow in a porous medium containing coarse-textured inclusions with a low value of air entry pressure, embedded in a fine-textured background material having high entry pressure. During imbibition some air remains trapped in the inclusions, while during drainage the inclusions become drained only after the capillary entry pressure exceeds the pressure of the background material. These effects can only be reproduced by a two-phase flow model, and not by the Richards' equation. However, if an upscaled form of the Richards' equation with appropriately modified capillary and permeability functions is used, the results are in a reasonable agreement with the two-phase flow model.

[1] In this work, we studied the influence of heterogeneities, fluid properties, and infiltration rates on front morphology during two-phase flow. In our experiments, a sand box, 40 cm × 60 cm × 1.2 cm, was packed with two different structures (either random or periodic) composed of 25% coarse material and 75% fine material. The infiltration process was characterized by the capillary number, Ca, and the viscosity ratio, M, between the fluids. The displacing and the displaced fluid had the same densities, such that gravity effects could be neglected. Similar to the pore scale, the stability of the front depends on the relation between M and Ca. However, on the scale under study, depending on the structure, zones of immobilized wetting fluid developed during drainage. The lifetime of these zones depended on the flow regime. Here we show that immobilized zones have an influence on the length of the transition zone, which could lead to a different time behavior than for that of the front width.

5 [1] We study the influence of buoyancy and spatial heterogeneity on the spreading of the 6 saturation front of a displacing fluid during injection into a porous medium saturated 7 with another, immiscible fluid. To do so we use a stochastic modeling framework. We 8 derive an effective large‐scale flow equation for the saturation of the displacing fluid that 9 is characterized by six nonlocal flux terms, four that resemble dispersive type terms and 10 two that have the appearance of advection terms. From the effective large‐scale flow 11 equation we derive measures for the spreading of the saturation front. A series of 12 full two‐phase numerical solutions are conducted to complement the analytical 13 developments. We find that the interplay between density and heterogeneity leads to an 14 enhancement of the front spreading on one hand and to a renormalization of the evolution 15 of the mean front position compared with an equivalent homogeneous medium. The 16 quantification of these phenomena plays an important role in several applications, 17 including, for example, carbon sequestration and enhanced oil recovery.

[1] Many environmental systems are driven by complex gas-water processes in fractured aquifers. One example is degassing processes occurring in fractures in the vicinity of radioactive waste disposal sites. These fractures can represent a potential fast track for radioactive substances to reach the surface: due to buoyancy effects, the created gas phase can move relatively quickly to the surface. The aim of this paper is to investigate and model the involved processes. First, a model for a single fracture is developed. Based on statistical properties of real fractures, an aperture distribution (raster element model) is created. A percolation-renormalization model yields effective properties, such as relative permeabilities and capillary pressure, and provides the size of a representative elementary volume. These effective relationships represent the basis for modeling the migration of the created gas phase through the fractured aquifer of the subsurface. An example modeling degassing and flow in a single fracture is shown and compared to experimental data. The presented model represents a conceptual method for degassing processes and the subsequent migration of the gas phase in fracture-matrix systems, improving predictions on the fate of radioactive substances.

Infiltration and evaporation are governing processes for water exchange between soil and atmosphere. In addition to atmospheric supply or demand, infiltration and evaporation rates are controlled by the material properties of the subsurface and the interplay between capillary, viscous and gravitational forces. This is commonly modeled with semi-empirical approaches using continuum models, such as the Richards equation for unsaturated flow. However, preferential flow phenomena often occur, limiting or even entirely suspending the applicability of continuum-based models. During infiltration, unstable fingers may form in homogeneous or heterogeneous porous media. On the other hand, the evaporation process may be driven by the hydraulic coupling of materials with different hydraulic functions found in heterogeneous systems. To analyze such preferential flow processes, water distribution was monitored in infiltration and evaporation lab experiments using neutron transmission techniques. Measurements were performed in 2D and 3D, using homogeneous and heterogeneous setups. The experimental findings demonstrate the fingering effect in infiltration and how it is influenced by the presence of fine inclusions in coarse background material. During evaporation processes, the hydraulic coupling effect is found to control the evaporation rate, limiting the modeling of water balances between soil and surface based on surface information alone.

In this paper we discuss estimates of effective parameters for an upscaled model for buoyant counter flow of DNAPL and water in a closed box filled with heterogeneous porous material. The upscaling procedure is based on the assumption that the flow is dominated by capillary forces on the small scale and that the fluids are segregated. The upscaled model has the same form as the usual two-phase flow model with an effective capillary pressure function and an effective mobility function Λ. Effective parameters are then estimated in two different ways. Stochastic theory can be applied to calculate the effective parameters to first order in the parameter fluctuations. This approach does not take into account that different parameter ranges of the heterogeneous field may be connected or isolated, yielding very different macroscopic residual saturations. Therefore, the second estimate of effective parameters takes connectivity of parameter ranges into account. In this case, the univariate parameter distribution of the heterogeneous field and the values that mark connected materials are the only information about heterogeneity that is used. Effective parameters are then estimated using mean field theory (the Maxwell approach). The upscaled model and the estimation of effective parameters are applied to a numerical test case. Buoyant counter flow in heterogeneous parameter fields with different structures is simulated numerically and compared to the solutions of the quasi-1d upscaled model with differently estimated parameters. It is demonstrated that connectivity of the different parameter ranges is an important information that determines typical time scales for the flow process and the macroscopic residual saturation. Even simple estimates of effective parameters based on little information may capture the typical time scales, provided that information about connected parameter ranges is taken into account.

[1] In recent years, statistical theory has been used to compute the ensemble mean and variance of solute concentration in aquifer formations with second-order stationary velocity fields. The merit of accurately estimating the mean and variance of concentration, however, remains unclear without knowing the shape of the probability density function (pdf). In a setup where a conservative solute is continuously injected into a domain, the concentration is bounded between zero and the concentration value in the injected solution. At small travel distances close to the fringe of the plume, an observation point may fall into the plume or outside, so that the statistical concentration distribution clusters at the two limiting values. Obviously, this results in non-Gaussian pdf's of concentration. With increasing travel distance, the lateral plume boundaries are smoothed, resulting in increased probability of intermediate concentrations. Likewise, averaging the concentration in a larger sampling volume, as typically done in field measurements, leads to higher probabilities of intermediate concentrations. We present semianalytical results of concentration pdf's for measurements with point-like or larger support volumes based on stochastic theory applied to stationary media. To this end, we employ a reversed auxiliary transport problem, in which we use analytical expressions for first and second central spatial lateral moments with an assumed Gaussian pdf for the uncertainty of the first lateral moment and Gauss-like shapes in individual cross sections. The resulting concentration pdf can be reasonably fitted by beta distributions. The results are compared to Monte Carlo simulations of flow and steady state transport in 3-D heterogeneous domains. In both methods the shape of the concentration pdf changes with distance to the contaminant source: Near the source, the distribution is multimodal, whereas it becomes a unimodal beta distribution far away from the contaminant source. The semianalytical and empirical pdf's differ slightly, which we contribute to the numerical artifacts in the Monte Carlo simulations but also to hard assumptions made in the semianalytical approach. Our results imply that geostatistical techniques for interpolation and other statistical inferences based on Gaussian distributions, such as kriging and cokriging, may be feasible only far away from the contaminant source. For calculations near the source, the beta-like distribution of concentration should be accounted for.

[1] In this study, we assess probability density functions of hydraulic heads and specific discharges in three-dimensional bounded heterogeneous porous media by Monte Carlo (MC) simulation. We discuss their empirical shapes and demonstrate that the intuitive use of obvious information on boundedness leads to parametric distribution functions, which fit surprisingly well. On the basis of statistical moments of hydraulic heads and velocities up to fourth order, we discuss the spatial dependence of the empirical distributions and their dependence on the variance of log conductivity. Comparison of the first and second central moment to the results from classical numerical first-order second-moment (FOSM) analysis reveals that FOSM predicts these moments surprisingly close for hydraulic heads. On the basis of this fact, we demonstrate that fitting the chosen parametric distributions for hydraulic heads to FOSM moments is promising for the sake of estimating exceedance probabilities. Our MC scenarios vary in variance of log conductivity (0.125 to 5.0), in the type of multivariate dependence, in correlation scale and types of boundary conditions. Our study illustrates that in contrast to the common assumption, FOSM is a reasonable choice for evaluating multivariate and univariate moments for heads, if used in conjunction with additional information on distribution shapes. In the absence of utilizable additional information, we demonstrate that second-moment methods are mostly inadequate for assessing distributions accurately. Significant deviations from Gaussian distributions occurred for discharge components even at a variance of log conductivity as low as 0.125, and we found that the distributions of transverse discharge components are extremely fat-tailed. The observed non-Gaussianity questions the results of approximate approaches in solute flux and dispersion studies where velocity fields are assumed to be multi-Gaussian and then directly represented by or generated from their covariances. The main implication is to apply more accurate schemes such as exact non-local methods, extensive MC or higher-order stochastic Galerkin approaches, and to include higher-order moments, at least if no additional assumptions on the shape of distributions are available or justifiable.

[1] Large-scale models of transient flow processes in the unsaturated zone require, in general, upscaling of the flow problem in order to capture the impact of heterogeneities on a small scale, which cannot be resolved by the model. Effective parameters for the upscaled models are often derived from second-order stochastic properties of the parameter fields. Such properties are good quantifications for parameter fields, which are multi-Gaussian. However, the structure of soil does rarely resemble these kinds of fields. The non-multi-Gaussian field properties can lead to strong discrepancies between predictions of upscaled models and the averaged real flow process. In particular, the connected paths of parameter ranges of the medium are important features, which are usually not taken into account in stochastic approaches. They are determined here by the Euler number of one-cut indicator fields. Methods to predict effective parameters are needed that incorporate this type of information. We discuss different simple and fast approaches for estimating the effective parameter for upscaled models of slow transient flow processes in the unsaturated zone, where connected paths of the material may be taken into account. Upscaled models are derived with the assumption of capillary equilibrium. The effective parameters are calculated using effective media approaches. We also discuss the limits of the applicability of these methods.

[1] Large-scale modeling of transient flow in the unsaturated zone is important for the estimation of the water budget and solute transport in the vadose zone. Upscaled flow models need to capture the impact of small-scale heterogeneities, which are not resolved by the model, on large-scale flow. We perform upscaling of the Richards equation in heterogeneous porous media with continuous distributions of the soil hydraulic parameters using homogenization theory and stochastic averaging techniques. We restrict the analysis to flow regimes in which the capillary-equilibrium assumption holds on the small scale. In order to account for effects of capillary entry pressure we apply the Brooks-Corey model for the soil retention and relative permeability curves and consider Leverett scaling for the coupling of intrinsic permeability and entry pressure. For this model we derive and analyze the ensemble-averaged parameter functions for the macroscopic flow equations. The effects of a definite entry pressure vanish with increasing variance of the log intrinsic permeability. We compare the statistically averaged parameter functions to numerically calculated effective functions for parameter fields with different connectivity properties. These results illustrate that soils with well-connected coarse materials differ in the relative permeability from those with well-connected fine materials or those without particular connectedness.

Prediction of fluid phase dynamics in the vadose zone is hampered by the presence of different types of sharp interfaces, questioning the validity of standard theory that is based on assumption of continuity of air and water phases, uniform distribution of fluids in a control volume, local equilibrium of phase contents and pressures, and slow process velocities. Complexity of fluid front morphology and burst-like redistribution processes may be accentuated across material contrasts or at the interface between soil and atmosphere. This special section presents eleven contributions highlighting the role of interfaces on water and air distributions and outlining methods to improve prediction of interfacial displacement.