Land surface depressions play a central role in the transformation of rainfall to ponding, infiltration and runoff, yet digital elevation models (DEMs) used by spatially distributed hydrologic models that resolve land surface processes rarely capture land surface depressions at spatial scales relevant to this transformation. Methods to generate DEMs through processing of remote sensing data, such as optical and light detection and ranging (LiDAR) have favored surfaces without depressions to avoid adverse slopes that are problematic for many hydrologic routing methods. Here we present a new topographic conditioning workflow, Depression-Preserved DEM Processing (D2P) algorithm, which is designed to preserve physically meaningful surface depressions for depression-integrated and efficient hydrologic modeling. D2P includes several features: (1) an adaptive screening interval for delineation of depressions, (2) the ability to filter out anthropogenic land surface features (e.g., bridges), (3) the ability to blend river smoothing (e.g., a general downslope profile) and depression resolving functionality. From a case study in the Goodwin Creek Experimental Watershed, D2P successfully resolved 86% of the ponds at a DEM resolution of 10 m. Topographic conditioning was achieved with minimum impact as D2P reduced the number of modified cells from the original DEM by 51% compared to a conventional algorithm. Furthermore, hydrologic simulation using a D2P processed DEM resulted in a more robust characterization on surface water dynamics based on higher surface water storage as well as an attenuated and delayed peak streamflow.

This study presents a model-based methodology to characterize the surface roughness effect on immiscible fluids in porous media using the measurements obtained with the gas-phase interfacial partitioning tracer test (IPTT). The characterization approach captures how adsorbed wetting film configuration on grain surfaces influences fluid-fluid interfaces in unsaturated porous media. The method establishes a novel representation of surface and interface roughness that delineates the micro-scale fractal nature of grain surfaces and the fluid-surface interactions at these scales. The method was tested using reported experimental data for several soils. The results showed that the methodology was effective for natural porous media comprising a range of physical and geochemical properties. Comparisons between characterized parameters of different media revealed that micro-scale surface roughness was only partially correlated to soil texture properties. Images of the test media obtained with scanning electron microscopy (SEM) illustrates the complexity of micro-scale surface roughness, and its variability among different media. Tests with an organic liquid-water system validated the generalness of surface roughness properties generated by the model. The proposed methodology is anticipated to provide a means to characterize and quantify the effects of surface roughness on fluid-solid interaction and fluid-fluid interfacial area, which are critical to various environmental disciplines.

A tracer breakthrough curve (BTC) for each sampling station is the ultimate goal of every quantitative hydrologic tracing study, and dataset size can critically affect the BTC. Groundwater-tracing data obtained using automatic sampling or detection devices may result in very high-density data sets. Data-dense tracer BTCs obtained using devices and stored in dataloggers can result in visually cluttered overlapping data points. The relatively large amounts of data detected by high-frequency settings available on devices and stored in dataloggers ensure that important tracer BTC features, such as data peaks, are not missed. Alternatively, such dense datasets can also be difficult to interpret. Even more difficult, is the application of such dense data sets in solute-transport models that may not be able to adequately reproduce tracer BTC shapes due to the overwhelming mass of data. One solution to the difficulties associated with analyzing, interpreting, and modeling dense data sets is the selective removal of blocks of the data from the total dataset. Although it is possible to arrange to skip blocks of tracer BTC data in a periodic sense (data decimation) so as to lessen the size and density of the dataset, skipping or deleting blocks of data also may result in missing the important features that the high-frequency detection setting efforts were intended to detect. Rather than removing, reducing, or reformulating data overlap, signal filtering and smoothing may be utilized but smoothing errors (e.g., averaging errors, outliers, and potential time shifts) need to be considered. Appropriate probability distributions to tracer BTCs may be used to describe typical tracer BTC shapes, which usually include long tails. Recognizing appropriate probability distributions applicable to tracer BTCs can help in understanding some aspects of the tracer migration.

This paper assesses the sustainability of bioenergy production under a nexus perspective through a new efficiency type index. The index describes 1st generation biofuel production under the perspective of the implied consumption of natural resources. We consider the sustainability of energy production as a sequence of steps, each characterised by its efficiency, and propose an index which returns an overall efficiency value describing the adequacy or inadequacy of the considered processes under a nexus perspective. The direct application of the nexus index entails an indication of the possible improvements needed to move production towards most sustainable processes or places. Moreover, it allows evaluating the efficiency of the main crops currently used in biofuel production with respect to the water-food-energy nexus. The results depict countries presently capable of performing sustainable production of 1st generation biofuel from particular crops. Furthermore, the analysis of the single components of the nexus index allows understanding the effects of possible improvements (e.g. soil and water management, new generation biofuels) on the overall production efficiency under a nexus perspective.

Drywells are increasingly used for stormwater management and enhanced aquifer recharge, but only limited research has quantitatively determined the performance of drywells. Numerical and field scale experiments were, therefore, conducted to improve our understanding and ability to characterize the drywell behavior. In particular, HYDRUS (2D/3D) was modified to simulate transient head boundary conditions for the complex geometry of the Maxwell Type IV drywell; i.e., a sediment chamber, an overflow pipe, and the variable geometry and storage of the drywell system with depth. Falling-head infiltration experiments were conducted on drywells located at the National Training Center in Fort Irwin, California (CA) and a commercial complex in Torrance, CA to determine in situ soil hydraulic properties (the saturated hydraulic conductivity, , and the retention curve shape parameter, α) for an equivalent uniform soil profile by inverse parameter optimization. A good agreement between the observed and simulated water heights in wells was obtained for both sites as indicated by the coefficient of determination 0.95-0.99-%, unique parameter fits, and small standard errors. Fort Irwin and Torrance drywells had very distinctive soil hydraulic characteristics. The fitted value of =1.01 × 10 m min at the Torrance drywell was consistent with the sandy soil texture at this site and the default value for sand in the HYDRUS soil catalog. The drywell with this = 1.01 × 10 m min could easily infiltrate predicted surface runoff from a design rain event (∼51.3 m) within 5760 min (4 d). In contrast, the fitted value of 2.25 × 10 m min at Fort Irwin was very low compared to the Torrance drywell and more than an order of magnitude smaller than the default value reported in the HYDRUS soil catalog for sandy clay loam at this site, likely due to clogging. These experiments and simulations provide useful information to characterize effective soil hydraulic properties in situ, and to improve the design of drywells for enhanced recharge.

This paper draws together several lines of argument to suggest that an ecohydrological framework, i.e. laboratory, field and theoretical approaches focused on hydrologic controls on biota, has contributed substantially to our understanding of the function of river networks as ecological corridors. Such function proves relevant to: the spatial ecology of species; population dynamics and biological invasions; the spread of waterborne disease. As examples, we describe metacommunity predictions of fish diversity patterns in the Mississippi-Missouri basin, geomorphic controls imposed by the fluvial landscape on elevational gradients of species' richness, the zebra mussel invasion of the same Mississippi-Missouri river system, and the spread of proliferative kidney disease in salmonid fish. We conclude that spatial descriptions of ecological processes in the fluvial landscape, constrained by their specific hydrologic and ecological dynamics and by the ecosystem matrix for interactions, i.e. the directional dispersal embedded in fluvial and host/pathogen mobility networks, have already produced a remarkably broad range of significant results. Notable scientific and practical perspectives are thus open, in the authors' view, to future developments in ecohydrologic research.

Schistosomiasis is a parasitic, water-related disease that is prevalent in tropical and subtropical areas of the world, causing severe and chronic consequences especially among children. Here we study the spatial spread of this disease within a network of connected villages in the endemic region of the Lower Basin of the Senegal River, in Senegal. The analysis is performed by means of a spatially explicit metapopulation model that couples local-scale eco-epidemiological dynamics with spatial mechanisms related to human mobility (estimated from anonymized mobile phone records), snail dispersal and hydrological transport of schistosome larvae along the main water bodies of the region. Results show that the model produces epidemiological patterns consistent with field observations, and point out the key role of spatial connectivity on the spread of the disease. These findings underline the importance of considering different transport pathways in order to elaborate disease control strategies that can be effective within a network of connected populations.

Although a differential sensitivity of cholera dynamics to climate variability has been reported in the spatially heterogeneous megacity of Dhaka, Bangladesh, the specific patterns of spread of the resulting risk within the city remain unclear. We build on an established probabilistic spatial model to investigate the importance and role of human mobility in modulating spatial cholera transmission. Mobility fluxes were inferred using a straightforward and generalizable methodology that relies on mapping population density based on a high resolution urban footprint product, and a parameter-free human mobility model. In accordance with previous findings, we highlight the higher sensitivity to the El Niño Southern Oscillation (ENSO) in the highly populated urban center than in the more rural periphery. More significantly, our results show that cholera risk is largely transmitted from the climate-sensitive core to the periphery of the city, with implications for the planning of control efforts. In addition, including human mobility improves the outbreak prediction performance of the model with an 11 month lead. The interplay between climatic and human mobility factors in cholera transmission is discussed from the perspective of the rapid growth of megacities across the developing world.

Debris-covered glaciers are increasingly studied because it is assumed that debris cover extent and thickness could increase in a warming climate, with more regular rockfalls from the surrounding slopes and more englacial melt-out material. Debris energy-balance models have been developed to account for the melt rate enhancement/reduction due to a thin/thick debris layer, respectively. However, such models require a large amount of input data that are not often available, especially in remote mountain areas such as the Himalaya, and can be difficult to extrapolate. Due to their lower data requirements, empirical models have been used extensively in clean glacier melt modelling. For debris-covered glaciers, however, they generally simplify the debris effect by using a single melt-reduction factor which does not account for the influence of varying debris thickness on melt and prescribe a constant reduction for the entire melt across a glacier. In this paper, we present a new temperature-index model that accounts for debris thickness in the computation of melt rates at the debris-ice interface. The model empirical parameters are optimized at the point scale for varying debris thicknesses against melt rates simulated by a physically-based debris energy balance model. The latter is validated against ablation stake readings and surface temperature measurements. Each parameter is then related to a plausible set of debris thickness values to provide a general and transferable parameterization. We develop the model on Miage Glacier, Italy, and then test its transferability on Haut Glacier d'Arolla, Switzerland. The performance of the new debris temperature-index (DETI) model in simulating the glacier melt rate at the point scale is comparable to the one of the physically based approach, and the definition of model parameters as a function of debris thickness allows the simulation of the nonlinear relationship of melt rate to debris thickness, summarised by the Østrem curve. Its large number of parameters might be a limitation, but we show that the model is transferable in time and space to a second glacier with little loss of performance. We thus suggest that the new DETI model can be included in continuous mass balance models of debris-covered glaciers, because of its limited data requirements. As such, we expect its application to lead to an improvement in simulations of the debris-covered glacier response to climate in comparison with models that simply recalibrate empirical parameters to prescribe a constant across glacier reduction in melt.

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

Drinking water wells indiscriminatingly placed adjacent to fecal contaminated surface water represents a significant but difficult to quantify health risk. Here we seek to understand mechanisms that limit the contamination extent by scaling up bacterial transport results from the laboratory to the field in a well constrained setting. Three pulses of originating during the early monsoon from a freshly excavated pond receiving latrine effluent in Bangladesh were monitored in 6 wells and modeled with a two-dimensional (2-D) flow and transport model conditioned with measured hydraulic heads. The modeling was performed assuming three different modes of interaction of with aquifer sands: 1) irreversible attachment only (best-fit k=7.6 day); 2) reversible attachment only (k=10.5 and k=0.2 day); and 3) a combination of reversible and irreversible modes of attachment (k=60, k=7.6, k=5.2 day). Only the third approach adequately reproduced the observed temporal and spatial distribution of , including a 4-log lateral removal distance of ∼9 m. In saturated column experiments, carried out using aquifer sand from the field site, a combination of reversible and irreversible attachment was also required to reproduce the observed breakthrough curves and retention profiles within the laboratory columns. Applying the laboratory-measured kinetic parameters to the 2-D calibrated flow model of the field site underestimates the observed 4-log lateral removal distance by less than a factor of two. This is promising for predicting field scale transport from laboratory experiments.

Groundwater age distributions are used to estimate the parameters of Fickian, and non-Fickian, effective models of solute transport. Based on the similarities between the transport and age equations, we develop a deconvolution based approach that describes transport between two monitoring wells. We show that the proposed method gives exact estimates of the travel time distribution between two wells when the domain is stationary and that the method still provides useful information on transport when the domain is non-stationary. The method is demonstrated using idealized uniform and layered 2-D aquifers. Homogeneous transport is determined exactly and non-Fickian transport in a layered aquifer was also approximated very well, even though this example problem is shown to be scale-dependent. This work introduces a method that addresses a significant limitation of tracer tests and non-Fickian transport modeling which is the difficulty in determining the effective parameters of the transport model.

The traditional Richards' equation implies that the wetting front in unsaturated soil follows Boltzmann scaling, with travel distance growing as the square root of time. This study proposes a fractal Richards' equation (FRE), replacing the integer-order time derivative of water content by a fractal derivative, using a power law ruler in time. FRE solutions exhibit anomalous non-Boltzmann scaling, attributed to the fractal nature of heterogeneous media. Several applications are presented, fitting the FRE to water content curves from previous literature.

Advances in Water Resources has been a prime archival source for implementation of averaging theories in changing the scale at which processes of importance in environmental modeling are described. Thus in celebration of the 35th year of this journal, it seems appropriate to assess what has been learned about these theories and about their utility in describing systems of interest. We review advances in understanding and use of averaging theories to describe porous medium flow and transport at the macroscale, an averaged scale that models spatial variability, and at the megascale, an integral scale that only considers time variation of system properties. We detail physical insights gained from the development and application of averaging theory for flow through porous medium systems and for the behavior of solids at the macroscale. We show the relationship between standard models that are typically applied and more rigorous models that are derived using modern averaging theory. We discuss how the results derived from averaging theory that are available can be built upon and applied broadly within the community. We highlight opportunities and needs that exist for collaborations among theorists, numerical analysts, and experimentalists to advance the new classes of models that have been derived. Lastly, we comment on averaging developments for rivers, estuaries, and watersheds.

Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus.

Standard models of flow of two immiscible fluids in a porous medium make use of an expression for the dependence of capillary pressure on the saturation of a fluid phase. Data to support the mathematical expression is most often obtained through a sequence of equilibrium experiments. In addition to such expressions being hysteretic, recent experimental and theoretical studies have suggested that the equilibrium functional forms obtained may be inadequate for modeling dynamic systems. This situation has led to efforts to express relaxation of a system to an equilibrium capillary pressure in relation to the rate of change of saturation. Here, based on insights gained from the thermodynamically constrained averaging theory (TCAT) we propose that dynamic processes are related to changes in interfacial area between phases as well as saturation. A more complete formulation of capillary pressure dynamics is presented leading to an equation that is suitable for experimental study.

This work is the eighth in a series that develops the fundamental aspects of the thermodynamically constrained averaging theory (TCAT) that allows for a systematic increase in the scale at which multiphase transport phenomena is modeled in porous medium systems. In these systems, the explicit locations of interfaces between phases and common curves, where three or more interfaces meet, are not considered at scales above the microscale. Rather, the densities of these quantities arise as areas per volume or length per volume. Modeling of the dynamics of these measures is an important challenge for robust models of flow and transport phenomena in porous medium systems, as the extent of these regions can have important implications for mass, momentum, and energy transport between and among phases, and formulation of a capillary pressure relation with minimal hysteresis. These densities do not exist at the microscale, where the interfaces and common curves correspond to particular locations. Therefore, it is necessary for a well-developed macroscale theory to provide evolution equations that describe the dynamics of interface and common curve densities. Here we point out the challenges and pitfalls in producing such evolution equations, develop a set of such equations based on averaging theorems, and identify the terms that require particular attention in experimental and computational efforts to parameterize the equations. We use the evolution equations developed to specify a closed two-fluid-phase flow model.

This work is the seventh in a series that introduces and employs the thermodynamically constrained averaging theory (TCAT) for modeling flow and transport in multiscale porous medium systems. This paper expands the previous analyses in the series by developing models at a scale where spatial variations within the system are not considered. Thus the time variation of variables averaged over the entire system is modeled in relation to fluxes at the boundary of the system. This implementation of TCAT makes use of conservation equations for mass, momentum, and energy as well as an entropy balance. Additionally, classical irreversible thermodynamics is assumed to hold at the microscale and is averaged to the megascale, or system scale. The fact that the local equilibrium assumption does not apply at the megascale points to the importance of obtaining closure relations that account for the large-scale manifestation of small-scale variations. Example applications built on this foundation are suggested to stimulate future work.

This work is the fifth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are used to develop models that describe species transport and single-fluid-phase flow through a porous medium system in varying physical regimes. Classical irreversible thermodynamics formulations for species in fluids, solids, and interfaces are developed. Two different approaches are presented, one that makes use of a momentum equation for each entity along with constitutive relations for species diffusion and dispersion, and a second approach that makes use of a momentum equation for each species in an entity. The alternative models are developed by relying upon different approaches to constrain an entropy inequality using mass, momentum, and energy conservation equations. The resultant constrained entropy inequality is simplified and used to guide the development of closed models. Specific instances of dilute and non-dilute systems are examined and compared to alternative formulation approaches.

This work is the fourth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are built upon by formulating macroscale models for conservation of mass, momentum, and energy, and the balance of entropy for a species in a phase volume, interface, and common curve. In addition, classical irreversible thermodynamic relations for species in entities are averaged from the microscale to the macroscale. Finally, we comment on alternative approaches that can be used to connect species and entity conservation equations to a constrained system entropy inequality, which is a key component of the TCAT approach. The formulations detailed in this work can be built upon to develop models for species transport and reactions in a variety of multiphase systems.