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In recent years, higher-order geostatistical methods have been used for modeling of a wide variety of large-scale porous media, such as groundwater aquifers and oil reservoirs. Their popularity stems from their ability to account for qualitative data and the great flexibility that they offer for conditioning the models to hard (quantitative) data, which endow them with the capability for generating realistic realizations of porous formations with very complex channels, as well as features that are mainly a barrier to fluid flow. One group of such models consists of pattern-based methods that use a set of data points for generating stochastic realizations by which the large-scale structure and highly-connected features are reproduced accurately. The cross correlation-based simulation (CCSIM) algorithm, proposed previously by the authors, is a member of this group that has been shown to be capable of simulating multimillion cell models in a matter of a few CPU seconds. The method is, however, sensitive to pattern's specifications, such as boundaries and the number of replicates. In this paper the original CCSIM algorithm is reconsidered and two significant improvements are proposed for accurately reproducing large-scale patterns of heterogeneities in porous media. First, an effective boundary-correction method based on the graph theory is presented by which one identifies the optimal cutting path/surface for removing the patchiness and discontinuities in the realization of a porous medium. Next, a new pattern adjustment method is proposed that automatically transfers the features in a pattern to one that seamlessly matches the surrounding patterns. The original CCSIM algorithm is then combined with the two methods and is tested using various complex two- and three-dimensional examples. It should, however, be emphasized that the methods that we propose in this paper are applicable to other pattern-based geostatistical simulation methods. [ABSTRACT FROM AUTHOR]

Water‐rock interaction cannot be ignored for shale reservoirs with high‐salinity formation brine and complex rock composition, and stimulated by massive slick‐water fracturing treatment. However, there have been few studies on the flowback model fully coupled with different effects of water‐rock interaction. This paper presents the development of a coupled hydro‐chemical‐mechanical model for modeling water‐rock interaction in fractured shale during the post‐fracturing flowback period. The model considers distinguishing water‐rock interaction phenomena, that is, mineral dissolution, clay swelling and chemical osmosis, and accounts for multi‐phase flow in a fractured shale reservoir. The coupling and solution method and a numerical simulator were developed. Numerical simulation indicates that the swelling volume of clay minerals occupies the pores and leads to a decline in matrix porosity, while mineral dissolution increases both the matrix porosity and the solute concentration in the aqueous phase in matrix pores. Clay swelling mainly affects the shape of the porosity ratio profiles. The effect of mineral dissolution becomes increasingly stronger as flowback progresses. Mineral dissolution mainly affects the relative positions of the porosity ratio curves with the progress of flowback. The water‐rock interaction coupled flowback modeling and the numerical simulation results in this study quantify the effects of chemical osmosis, clay swelling and mineral dissolution. Results from this study provide new insights into the mechanisms of fracturing‐fluid flowback and value to flowback transient analysis. Key Points: A hydro‐chemical‐mechanical model involving mineral dissolution, clay swelling and osmosis to model water‐rock interaction is proposedMineral dissolution rates, clay swelling volumes, and the matrix porosity influenced by water‐rock interaction are studiedClay swelling and mineral dissolution mainly affect the shapes and relative positions of matrix porosity ratio curves, respectively [ABSTRACT FROM AUTHOR]

This work advances a unified approach to process-based hydrologic modeling, which we term the 'Structure for Unifying Multiple Modeling Alternatives (SUMMA).' The modeling framework, introduced in the companion paper, uses a general set of conservation equations with flexibility in the choice of process parameterizations (closure relationships) and spatial architecture. This second paper specifies the model equations and their spatial approximations, describes the hydrologic and biophysical process parameterizations currently supported within the framework, and illustrates how the framework can be used in conjunction with multivariate observations to identify model improvements and future research and data needs. The case studies illustrate the use of SUMMA to select among competing modeling approaches based on both observed data and theoretical considerations. Specific examples of preferable modeling approaches include the use of physiological methods to estimate stomatal resistance, careful specification of the shape of the within-canopy and below-canopy wind profile, explicitly accounting for dust concentrations within the snowpack, and explicitly representing distributed lateral flow processes. Results also demonstrate that changes in parameter values can make as much or more difference to the model predictions than changes in the process representation. This emphasizes that improvements in model fidelity require a sagacious choice of both process parameterizations and model parameters. In conclusion, we envisage that SUMMA can facilitate ongoing model development efforts, the diagnosis and correction of model structural errors, and improved characterization of model uncertainty. [ABSTRACT FROM AUTHOR]

This paper concerns a new modeling approach to multicomponent NAPL dissolution and transport, based on analytic solutions and Laguerre series. This approach allows virtually any of the numerous existing 1-D analytic transport solutions in the literature to be coupled with arbitrary boundary conditions stemming from nonlinear NAPL dissolution, as dictated by Raoult's Law. A computer implementation of this approach to coupled dissolution and transport in parallel fractures-which no other screening tool known to the authors covers-is presented. This is verified against an existing analytic transport solution that assumes a constant boundary condition. Subsequently, the model is demonstrated via a study of separation of PAH and phenolic plumes generated by dissolution of creosote, using the new computer implementation. The PAH and phenolic constituents of creosote strongly differ in both their dissolution and their transport behavior, and this is shown to necessitate the use of a tool that can account for both processes, such as the one developed here. We also find the possibility of PAH and phenolic plumes becoming entirely disjoint. [ABSTRACT FROM AUTHOR]

A seepage face is a nonlinear dynamic boundary that strongly affects pressure head distributions, water table fluctuations, and flow patterns. Its handling in hydrological models, especially under complex conditions such as heterogeneity and coupled surface/subsurface flow, has not been extensively studied. In this paper, we compare the treatment of the seepage face as a static (Dirichlet) versus dynamic boundary condition, we assess its resolution under conditions of layered heterogeneity, we examine its interaction with a catchment outlet boundary, and we investigate the effects of surface/subsurface exchanges on seepage faces forming at the land surface. The analyses are carried out with an integrated catchment hydrological model. Numerical simulations are performed for a synthetic rectangular sloping aquifer and for an experimental hillslope from the Landscape Evolution Observatory. The results show that the static boundary condition is not always an adequate stand-in for a dynamic seepage face boundary condition, especially under conditions of high rainfall, steep slope, or heterogeneity; that hillslopes with layered heterogeneity give rise to multiple seepage faces that can be highly dynamic; that seepage face and outlet boundaries can coexist in an integrated hydrological model and both play an important role; and that seepage faces at the land surface are not always controlled by subsurface flow. The paper also presents a generalized algorithm for resolving seepage face outflow that handles heterogeneity in a simple way, is applicable to unstructured grids, and is shown experimentally to be equivalent to the treatment of atmospheric boundary conditions in subsurface flow models. [ABSTRACT FROM AUTHOR]

Training image-based geostatistical methods are increasingly popular in groundwater hydrology even if existing algorithms present limitations that often make real-world applications difficult. These limitations include a computational cost that can be prohibitive for high-resolution 3-D applications, the presence of visual artifacts in the model realizations, and a low variability between model realizations due to the limited pool of patterns available in a finite-size training image. In this paper, we address these issues by proposing an iterative patch-based algorithm which adapts a graph cuts methodology that is widely used in computer graphics. Our adapted graph cuts method optimally cuts patches of pixel values borrowed from the training image and assembles them successively, each time accounting for the information of previously stitched patches. The initial simulation result might display artifacts, which are identified as regions of high cost. These artifacts are reduced by iteratively placing new patches in high-cost regions. In contrast to most patch-based algorithms, the proposed scheme can also efficiently address point conditioning. An advantage of the method is that the cut process results in the creation of new patterns that are not present in the training image, thereby increasing pattern variability. To quantify this effect, a new measure of variability is developed, the merging index, quantifies the pattern variability in the realizations with respect to the training image. A series of sensitivity analyses demonstrates the stability of the proposed graph cuts approach, which produces satisfying simulations for a wide range of parameters values. Applications to 2-D and 3-D cases are compared to state-of-the-art multiple-point methods. The results show that the proposed approach obtains significant speedups and increases variability between realizations. Connectivity functions applied to 2-D models transport simulations in 3-D models are used to demonstrate that pattern continuity is preserved. [ABSTRACT FROM AUTHOR]

This paper presents the fundamental theory and laboratory test results on a new device that is deployed in boreholes in fractured rock aquifers to characterize vertical distributions of water and contaminant fluxes, aquifer hydraulic properties, and fracture network properties (e.g., active fracture density and orientation). The device, a fractured rock passive flux meter (FRPFM), consists of an inflatable core assembled with upper and lower packers that isolate the zone of interest from vertical gradients within the borehole. The outer layer of the core consists of an elastic fabric mesh equilibrated with a visible dye which is used to provide visual indications of active fractures and measures of fracture location, orientation, groundwater flux, and the direction of that flux. Beneath the outer layer is a permeable sorbent that is preloaded with known amounts of water soluble tracers which are eluted at rates proportional to groundwater flow. This sorbent also captures target contaminants present in intercepted groundwater. The mass of contaminant sorbed is used to quantify cumulative contaminant flux; whereas, the mass fractions of resident tracers lost are used to provide measures of water flux. In this paper, the FRPFM is bench tested over a range of fracture velocities (2-20 m/day) using a single fracture flow apparatus (fracture aperture = 0.5 mm). Test results show a discoloration in visible dye corresponding to the location of the active fracture. The geometry of the discoloration can be used to discern fracture orientation as well as direction and magnitude of flow in the fracture. Average contaminant fluxes were measured within 16% and water fluxes within 25% of known imposed fluxes. [ABSTRACT FROM AUTHOR]

A major neglected weakness of many current hydrological models is the numerical method used to solve the governing model equations. This paper thoroughly evaluates several classes of time stepping schemes in terms of numerical reliability and computational efficiency in the context of conceptual hydrological modeling. Numerical experiments are carried out using 8 distinct time stepping algorithms and 6 different conceptual rainfall-runoff models, applied in a densely gauged experimental catchment, as well as in 12 basins with diverse physical and hydroclimatic characteristics. Results show that, over vast regions of the parameter space, the numerical errors of fixed-step explicit schemes commonly used in hydrology routinely dwarf the structural errors of the model conceptualization. This substantially degrades model predictions, but also, disturbingly, generates fortuitously adequate performance for parameter sets where numerical errors compensate for model structural errors. Simply running fixed-step explicit schemes with shorter time steps provides a poor balance between accuracy and efficiency: in some cases daily-step adaptive explicit schemes with moderate error tolerances achieved comparable or higher accuracy than 15 min fixed-step explicit approximations but were nearly 10 times more efficient. From the range of simple time stepping schemes investigated in this work, the fixed-step implicit Euler method and the adaptive explicit Heun method emerge as good practical choices for the majority of simulation scenarios. In combination with the companion paper, where impacts on model analysis, interpretation, and prediction are assessed, this two-part study vividly highlights the impact of numerical errors on critical performance aspects of conceptual hydrological models and provides practical guidelines for robust numerical implementation. [ABSTRACT FROM AUTHOR]

Parameter specification is an important source of uncertainty in large, complex geophysical models. These models generally have multiple model outputs that require multiobjective optimization algorithms. Although such algorithms have long been available, they usually require a large number of model runs and are therefore computationally expensive for large, complex dynamic models. In this paper, a multiobjective adaptive surrogate modeling-based optimization (MO-ASMO) algorithm is introduced that aims to reduce computational cost while maintaining optimization effectiveness. Geophysical dynamic models usually have a prior parameterization scheme derived from the physical processes involved, and our goal is to improve all of the objectives by parameter calibration. In this study, we developed a method for directing the search processes toward the region that can improve all of the objectives simultaneously. We tested the MO-ASMO algorithm against NSGA-II and SUMO with 13 test functions and a land surface model - the Common Land Model (CoLM). The results demonstrated the effectiveness and efficiency of MO-ASMO. [ABSTRACT FROM AUTHOR]

Based on the theoretical framework for sensitivity analysis called 'Variogram Analysis of Response Surfaces' (VARS), developed in the companion paper, we develop and implement a practical 'star-based' sampling strategy (called STAR-VARS), for the application of VARS to real-world problems. We also develop a bootstrap approach to provide confidence level estimates for the VARS sensitivity metrics and to evaluate the reliability of inferred factor rankings. The effectiveness, efficiency, and robustness of STAR-VARS are demonstrated via two real-data hydrological case studies (a 5-parameter conceptual rainfall-runoff model and a 45-parameter land surface scheme hydrology model), and a comparison with the 'derivative-based' Morris and 'variance-based' Sobol approaches are provided. Our results show that STAR-VARS provides reliable and stable assessments of 'global' sensitivity across the full range of scales in the factor space, while being 1-2 orders of magnitude more efficient than the Morris or Sobol approaches. [ABSTRACT FROM AUTHOR]

Computer simulation models are continually growing in complexity with increasingly more factors to be identified. Sensitivity Analysis (SA) provides an essential means for understanding the role and importance of these factors in producing model responses. However, conventional approaches to SA suffer from (1) an ambiguous characterization of sensitivity, and (2) poor computational efficiency, particularly as the problem dimension grows. Here, we present a new and general sensitivity analysis framework (called VARS), based on an analogy to 'variogram analysis,' that provides an intuitive and comprehensive characterization of sensitivity across the full spectrum of scales in the factor space. We prove, theoretically, that Morris (derivative-based) and Sobol (variance-based) methods and their extensions are special cases of VARS, and that their SA indices can be computed as by-products of the VARS framework. Synthetic functions that resemble actual model response surfaces are used to illustrate the concepts, and show VARS to be as much as two orders of magnitude more computationally efficient than the state-of-the-art Sobol approach. In a companion paper, we propose a practical implementation strategy, and demonstrate the effectiveness, efficiency, and reliability (robustness) of the VARS framework on real-data case studies. [ABSTRACT FROM AUTHOR]

Integrated, process-based numerical models in hydrology are rapidly evolving, spurred by novel theories in mathematical physics, advances in computational methods, insights from laboratory and field experiments, and the need to better understand and predict the potential impacts of population, land use, and climate change on our water resources. At the catchment scale, these simulation models are commonly based on conservation principles for surface and subsurface water flow and solute transport (e.g., the Richards, shallow water, and advection-dispersion equations), and they require robust numerical techniques for their resolution. Traditional (and still open) challenges in developing reliable and efficient models are associated with heterogeneity and variability in parameters and state variables; nonlinearities and scale effects in process dynamics; and complex or poorly known boundary conditions and initial system states. As catchment modeling enters a highly interdisciplinary era, new challenges arise from the need to maintain physical and numerical consistency in the description of multiple processes that interact over a range of scales and across different compartments of an overall system. This paper first gives an historical overview (past 50 years) of some of the key developments in physically based hydrological modeling, emphasizing how the interplay between theory, experiments, and modeling has contributed to advancing the state of the art. The second part of the paper examines some outstanding problems in integrated catchment modeling from the perspective of recent developments in mathematical and computational science. [ABSTRACT FROM AUTHOR]

Abstract: Hydraulic tomography (HT) is a recently developed technology for characterizing high‐resolution, site‐specific heterogeneity using hydraulic data (nd) from a series of cross‐hole pumping tests. To properly account for the subsurface heterogeneity and to flexibly incorporate additional information, geostatistical inverse models, which permit a large number of spatially correlated unknowns (ny), are frequently used to interpret the collected data. However, the memory storage requirements for the covariance of the unknowns (ny × ny) in these models are prodigious for large‐scale 3‐D problems. Moreover, the sensitivity evaluation is often computationally intensive using traditional difference method (ny forward runs). Although employment of the adjoint method can reduce the cost to nd forward runs, the adjoint model requires intrusive coding effort. In order to resolve these issues, this paper presents a Reduced‐Order Successive Linear Estimator (ROSLE) for analyzing HT data. This new estimator approximates the covariance of the unknowns using Karhunen‐Loeve Expansion (KLE) truncated to nkl order, and it calculates the directional sensitivities (in the directions of nkl eigenvectors) to form the covariance and cross‐covariance used in the Successive Linear Estimator (SLE). In addition, the covariance of unknowns is updated every iteration by updating the eigenvalues and eigenfunctions. The computational advantages of the proposed algorithm are demonstrated through numerical experiments and a 3‐D transient HT analysis of data from a highly heterogeneous field site. [ABSTRACT FROM AUTHOR]

Abstract: Relative permeability is a critical parameter characterizing multiphase flow in porous media and it is strongly dependent on the wettability. In many situations, the porous media are nonuniformly wet. To investigate the effect of wettability heterogeneity on relative permeability of two‐phase flow in porous media, a multi‐relaxation‐time color‐gradient lattice Boltzmann model is adopted to simulate oil/water two‐phase flow in porous media with different oil‐wet solid fractions. For the water phase, when the water saturation is high, the relative permeability of water increases with the increase of oil‐wet solid fraction under a constant water saturation. However, as the water saturation decreases to an intermediate value (about 0.4–0.7), the relative permeability of water in fractionally wet porous media could be lower than that in purely water‐wet porous media, meaning additional flow resistance exists in the fractionally wet porous media. For the oil phase, similar phenomenon is observed. This phenomenon is mainly caused by the wettability‐related microscale fluid distribution. According to both our simulation results and theoretical analysis, it is found that the relative permeability of two‐phase flow in porous media is strongly related to three parameters: the fluid saturation, the specific interfacial length of fluid, and the fluid tortuosity in the flow direction. The relationship between the relative permeability and these parameters under different capillary numbers is explored in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we present a hydrochemical model that can be used to generate plausible karstic conduit networks that honor what is known about geology, hydrology, and topography of a karst system. To make the model applicable to a range of natural karst systems, we introduce a flexible and physically realistic flow boundary condition along the land surface. Moreover, whereas comparable existing speleogenesis models use an explicit reactive-transport scheme, we propose an implicit reactive-transport scheme to permit a coarser spatial discretization of the conduit cells. An application to a real karst system illustrates that the model can generate a realistic karstic network that reproduces observed hydrologic behavior in terms of current spring flow rates, regional hydraulic head field as well as average groundwater residence times. Our model provides a useful tool to generate ensembles of possible karstic conduit networks that may be used within a stochastic framework to analyze flow and transport prediction uncertainty associated with a lack of knowledge about network geometry. [ABSTRACT FROM AUTHOR]

Climate impact analyses are usually based on driving hydrological models by future climate scenarios, assuming that the model parameters calibrated to past runoff are representative of the future. In this paper we calibrate the parameters of a conceptual rainfall-runoff model to six consecutive 5 year periods between 1976 and 2006 for 273 catchments in Austria and analyze the temporal change of the calibrated parameters. The calibrated parameters representing snow and soil moisture processes show significant trends. For example, the parameter controlling runoff generation doubled, on average, in the 3 decades. Comparisons of different subregions, comparisons with independent data sets, and analyses of the spatial variability of the model parameters indicate that these trends represent hydrological changes rather than calibration artifacts. The trends can be related to changes in the climatic conditions of the catchments such as higher evapotranspiration and drier catchment conditions in the more recent years. The simulations suggest that the impact on simulated runoff of assuming time invariant parameters can be very significant. For example, if using the parameters calibrated to 1976-1981 for simulating runoff for the period 2001-2006, the biases of median flows are, on average, 15% and the biases of high flows are about 35%. The errors increase as the time lag between the simulation and calibration periods increases. The implications for hydrologic prediction in general and climate impact analyses in particular are discussed. [ABSTRACT FROM AUTHOR]

Hydrological forecasts strongly rely on predictions of precipitation amounts and temperature as meteorological forcings for hydrological models. Ensemble weather predictions provide a number of different scenarios that reflect the uncertainty about these meteorological inputs, but these are often biased and under-dispersive, and therefore require statistical postprocessing. In addition to correcting the marginal distributions of the two weather variables, postprocessing methods must reconstruct their spatial, temporal, and intervariable dependence in order to generate physically realistic forecast trajectories that can be used as forcings of hydrological streamflow forecast models. For many years, a sample reordering method referred to as 'Schaake shuffle' has been used successfully to address this multivariate aspect of forecast distributions by using historical observation trajectories as multivariate 'dependence templates.' This paper proposes a variant of the Schaake shuffle, in which the historical dates are selected such that the marginal distributions of the corresponding observation trajectories are similar to the forecast marginal distributions, thus making it more likely that spatial and temporal gradients are preserved during the reordering procedure. This new approach is demonstrated with temperature and precipitation forecasts over four river basins in California, and it is shown to improve upon the standard Schaake shuffle both with respect to verification metrics applied to the forcings, and verification metrics applied to the resulting streamflow predictions. [ABSTRACT FROM AUTHOR]

Regional extreme value models for estimation of extreme rainfall intensities are widely applied, but their underlying assumption of stationarity is challenged. Many recent studies show that the rainfall extremes worldwide exhibit a nonstationary behavior. This paper presents a spatiotemporal model of extreme rainfall. The framework is built on a partial duration series approach with a nonstationary, regional threshold value. The model is based on generalized linear regression solved by generalized estimation equations. It allows a spatial correlation between the stations in the network and accounts furthermore for variable observation periods at each station and in each year. Marginal regional and temporal regression models solved by generalized least squares are used to validate and discuss the results of the full spatiotemporal model. The model is applied on data from a large Danish rain gauge network for four durations ranging from 10 min to 24 h. The observation period differs between stations, and the number of stations with more than 10 years of observations has increased over the years. A spatiotemporal model for the threshold is suggested, applying the mean annual precipitation and time as the explanatory variables in the regional and temporal domain, respectively. Further analysis of partial duration series with nonstationary and regional thresholds shows that the mean exceedances also exhibit a significant variation in space and time for some rainfall durations, while the shape parameter is found to be constant. [ABSTRACT FROM AUTHOR]

Where high-resolution topographic data are available, modelers are faced with the decision of whether it is better to spend computational resource on resolving topography at finer resolutions or on running more simulations to account for various uncertain input factors (e.g., model parameters). In this paper we apply global sensitivity analysis to explore how influential the choice of spatial resolution is when compared to uncertainties in the Manning's friction coefficient parameters, the inflow hydrograph, and those stemming from the coarsening of topographic data used to produce Digital Elevation Models (DEMs). We apply the hydraulic model LISFLOOD-FP to produce several temporally and spatially variable model outputs that represent different aspects of flood inundation processes, including flood extent, water depth, and time of inundation. We find that the most influential input factor for flood extent predictions changes during the flood event, starting with the inflow hydrograph during the rising limb before switching to the channel friction parameter during peak flood inundation, and finally to the floodplain friction parameter during the drying phase of the flood event. Spatial resolution and uncertainty introduced by resampling topographic data to coarser resolutions are much more important for water depth predictions, which are also sensitive to different input factors spatially and temporally. Our findings indicate that the sensitivity of LISFLOOD-FP predictions is more complex than previously thought. Consequently, the input factors that modelers should prioritize will differ depending on the model output assessed, and the location and time of when and where this output is most relevant. [ABSTRACT FROM AUTHOR]

Estimation of base flow from streamflow hydrographs has been a major challenge in hydrology for decades, leading to developments of base flow separation filters. When without tracer or groundwater data to calibrate the filters, the standard approach to apply these filters in practice involves some degrees of subjectivity in choosing the filter parameters. This paper investigates the use of signature-based calibration in implementing base flow filtering by testing seven possible hydrological signatures of base flow against modeled daily base flow produced by Li et al. (2014) for a range of synthetic catchments simulated with HydroGeoSphere. Our evaluation demonstrates that such a calibration method with few selected signatures as objectives is capable of calibrating a filter- Eckhardt filter-to yield satisfactory base flow estimates at daily, monthly and long-term time scales, outperforming the standard approach. The best performing signatures can be readily derived from streamflow time series. While their performance depends on the catchment characteristics, the catchments where the signature method performs can be distinguished using commonly-used descriptors of flow dynamics. [ABSTRACT FROM AUTHOR]

The use of additional types of observational data has often been suggested to alleviate the ill-posedness inherent to parameter estimation of groundwater models and constrain model uncertainty. Disinformation in observational data caused by errors in either the observations or the chosen model structure may, however, confound the value of adding observational data in model conditioning. This paper uses the global generalized likelihood uncertainty estimation methodology to investigate the value of different observational data types (heads, fluxes, salinity, and temperature) in conditioning a groundwater flow and transport model of an extensively monitored field site in the Netherlands. We compared model conditioning using the real observations to a synthetic model experiment, to demonstrate the possible influence of disinformation in observational data in model conditioning. Results showed that the value of different conditioning targets was less evident when conditioning to real measurements than in a measurement error-only synthetic model experiment. While in the synthetic experiment, all conditioning targets clearly improved model outcomes, minor improvements or even worsening of model outcomes was observed for the real measurements. This result was caused by errors in both the model structure and the observations, resulting in disinformation in the observational data. The observed impact of disinformation in the observational data reiterates the necessity of thorough data validation and the need for accounting for both model structural and observational errors in model conditioning. It further suggests caution when translating results of synthetic modeling examples to real-world applications. Still, applying diverse conditioning data types was found to be essential to constrain uncertainty, especially in the transport of solutes in the model. [ABSTRACT FROM AUTHOR]

Shallow Water Equations (SWE) provide a fundamental component for the quantification and mapping of hydraulic hazard. In steep mountain valleys, the use of one-dimensional SWE (also known as St. Venant Equations, SVE) is often legitimate and computationally competitive against two-dimensional solvers. However, in the same environment, the solution of SVE is hindered by the need of an accurate bathymetric reconstruction, which implies a number of cross sections which cannot be readily acquired by conventional field surveys. On the other hand, Digital Elevation Models ( DEM) with resolution adequate for studies of flood propagation are available in many areas of the world. In this paper, I propose to compute cross sections automatically by operating along the channel network derived from a valley's raster DEM, on the basis of algorithms that hitherto have been used for geomorphological and hydrological purposes. The extraction process can be refined by varying cross section inter-distance and width, in order to prevent superimpositions that might occur due to the sinuosity of the thalweg and to better capture the valley's local topography. At the end of this process, the geometric functions needed by SVE solvers can be computed for each cross section. A software tool that implements the described algorithm is provided to the scientific community. [ABSTRACT FROM AUTHOR]

River deltas are intricate landscapes with complex channel networks that self-organize to deliver water, sediment, and nutrients from the apex to the delta top and eventually to the coastal zone. The natural balance of material and energy fluxes, which maintains a stable hydrologic, geomorphologic, and ecological state of a river delta, is often disrupted by external perturbations causing topological and dynamical changes in the delta structure and function. A formal quantitative framework for studying delta channel network connectivity and transport dynamics and their response to change is lacking. Here we present such a framework based on spectral graph theory and demonstrate its value in computing delta's steady state fluxes and identifying upstream (contributing) and downstream (nourishment) areas and fluxes from any point in the network. We use this framework to construct vulnerability maps that quantify the relative change of sediment and water delivery to the shoreline outlets in response to possible perturbations in hundreds of upstream links. The framework is applied to the Wax Lake delta in the Louisiana coast of the U.S. and the Niger delta in West Africa. In a companion paper, we present a comprehensive suite of metrics that quantify topologic and dynamic complexity of delta channel networks and, via application to seven deltas in diverse environments, demonstrate their potential to reveal delta morphodynamics and relate to notions of vulnerability and robustness. [ABSTRACT FROM AUTHOR]

The linearized hillslope Boussinesq equation, introduced by Brutsaert (1994), describes the dynamics of saturated, subsurface flow from hillslopes with shallow, unconfined aquifers. In this paper, we use a new analytical technique to solve the linearized hillslope Boussinesq equation to predict water table dynamics and hillslope discharge to channels. The new solutions extend previous analytical treatments of the linearized hillslope Boussinesq equation to account for the impact of spatiotemporal heterogeneity in water table recharge. The results indicate that the spatial character of recharge may significantly alter both steady state subsurface storage characteristics and the transient hillslope hydrologic response, depending strongly on similarity measures of controls on the subsurface flow dynamics. Additionally, we derive new analytical solutions for the linearized hillslope-storage Boussinesq equation and explore the interaction effects of recharge structure and hillslope morphology on water storage and base flow recession characteristics. A theoretical recession analysis, for example, demonstrates that decreasing the relative amount of downslope recharge has a similar effect as increasing hillslope convergence. In general, the theory suggests that recharge heterogeneity can serve to diminish or enhance the hydrologic impacts of hillslope morphology. [ABSTRACT FROM AUTHOR]

The spatial shape of a precipitation event has an important role in determining the catchment's hydrological response to a storm. To be able to generate stochastic design storms with a realistic spatial structure, the anisotropy of the storm has to be quantified. In this paper, a method is proposed to estimate the anisotropy of precipitation fields, using the concept of linear Generalized Scale Invariance (GSI). The proposed method is based on identifying the values of GSI parameters that best describe isolines of constant power on the two-dimensional power spectrum of the fields. The method is evaluated using two sets of simulated fields with known anisotropy and a measured precipitation event with an unknown anisotropy from Brisbane, Australia. It is capable of accurately estimating the anisotropy parameters of simulated nonzero fields, whereas introducing the rain-no rain intermittency alters the power spectra of the fields and slightly reduces the accuracy of the parameter estimates. The parameters estimated for the measured event correspond well with the visual observations on the spatial structure of the fields. The method requires minimum amount of decision making and user interaction, making it suitable for analyzing anisotropy of storm events consisting of long time series of fields with a changing spatial structure. [ABSTRACT FROM AUTHOR]

New survey techniques provide a large amount of high-resolution data, which can be extremely precious for flood inundation modeling. Such data availability raises the issue as to how to exploit their information content to effectively improve flood risk mapping and predictions. In this paper, we will discuss a number of important issues which should be taken into account in works related to flood modeling. These include the large number of uncertainty sources in model structure and available data; the difficult evaluation of model results, due to the scarcity of observed data; computational efficiency; false confidence that can be given by high-resolution outputs, as accuracy is not necessarily increased by higher precision. Finally, we briefly review and discuss a number of existing approaches, such as subgrid parameterization and roughness upscaling methods, which can be used to incorporate high detailed data into flood inundation models, balancing efficiency and reliability. [ABSTRACT FROM AUTHOR]

Based on a literature overview, this paper summarizes the impact and legacy of the contributions of Wilfried Brutsaert and Jean-Yves Parlange (Cornell University) with respect to the current state-of-the-art understanding in hydraulic groundwater theory. Forming the basis of many applications in catchment hydrology, ranging from drought flow analysis to surface water-groundwater interactions, hydraulic groundwater theory simplifies the description of water flow in unconfined riparian and perched aquifers through assumptions attributed to Dupuit and Forchheimer. Boussinesq (1877) derived a general equation to study flow dynamics of unconfined aquifers in uniformly sloping hillslopes, resulting in a remarkably accurate and applicable family of results, though often challenging to solve due to its nonlinear form. Under certain conditions, the Boussinesq equation can be solved analytically allowing compact representation of soil and geomorphological controls on unconfined aquifer storage and release dynamics. The Boussinesq equation has been extended to account for flow divergence/convergence as well as for nonuniform bedrock slope (concave/convex). The extended Boussinesq equation has been favorably compared to numerical solutions of the three-dimensional Richards equation, confirming its validity under certain geometric conditions. Analytical solutions of the linearized original and extended Boussinesq equations led to the formulation of similarity indices for baseflow recession analysis, including scaling rules, to predict the moments of baseflow response. Validation of theoretical recession parameters on real-world streamflow data is complicated due to limited measurement accuracy, changing boundary conditions, and the strong coupling between the saturated aquifer with the overlying unsaturated zone. However, recent advances are shown to have mitigated several of these issues. The extended Boussinesq equation has been successfully applied to represent baseflow dynamics in catchment-scale hydrological models, and it is currently considered to represent lateral redistribution of groundwater in land surface schemes applied in global circulation models. From the review, it is clear that Wilfried Brutsaert and Jean-Yves Parlange stimulated a body of research that has led to several fundamental discoveries and practical applications with important contributions in hydrological modeling. [ABSTRACT FROM AUTHOR]

Component-based modeling is an approach for simulating water resource systems where a model is composed of a set of components, each with a defined modeling objective, interlinked through data exchanges. Component-based modeling frameworks are used within the hydrologic, atmospheric, and earth surface dynamics modeling communities. While these efforts have been advancing, it has become clear that the water resources modeling community in particular, and arguably the larger earth science modeling community as well, faces a challenge of fully and precisely defining the metadata for model components. The lack of a unified framework for model component metadata limits interoperability between modeling communities and the reuse of models across modeling frameworks due to ambiguity about the model and its capabilities. To address this need, we propose an ontology for water resources model components that describes core concepts and relationships using the Web Ontology Language (OWL). The ontology that we present, which is termed the Water Resources Component (WRC) ontology, is meant to serve as a starting point that can be refined over time through engagement by the larger community until a robust knowledge framework for water resource model components is achieved. This paper presents the methodology used to arrive at the WRC ontology, the WRC ontology itself, and examples of how the ontology can aid in component-based water resources modeling by (i) assisting in identifying relevant models, (ii) encouraging proper model coupling, and (iii) facilitating interoperability across earth science modeling frameworks. [ABSTRACT FROM AUTHOR]

Beneficiaries of common pool resources (CPRs) may select available noncooperative and regulatory exogenous institutions for managing the resource, as well as cooperative management institutions. All these institutions may increase the long-term gains, prolong the life of the resource, and help to escape the tragedy of the commons trap. Cooperative game theory approaches can serve as the backbone of cooperative CPR management institutions. This paper formulates and applies several commonly used cooperative game theoretic solution concepts, namely, the core, Nash-Harsanyi, Shapley, and nucleolus. Through a numerical groundwater example, we show how CPR users can share the gains obtained from cooperation in a fair and efficient manner based on these cooperative solution concepts (management institutions). Although, based on their fairness rationales, various cooperative management institutions may suggest different allocations that are potentially acceptable to the users, these allocation solutions may not be stable as some users may find them unfair. This paper discusses how different methods, such as application of the plurality rule and power index, stability index, and propensity to disrupt concepts, can help identify the most stable and likely solutions for enforcing cooperation among the CPR beneficiaries. Furthermore, how the noncooperative managerial characteristics of the CPR users can affect the stability and acceptability of the different cooperative CPR management institutions is discussed, providing valuable policy insights for cooperative CPR management at community levels. [ABSTRACT FROM AUTHOR]

Surrogate modeling, also called metamodeling, has evolved and been extensively used over the past decades. A wide variety of methods and tools have been introduced for surrogate modeling aiming to develop and utilize computationally more efficient surrogates of high-fidelity models mostly in optimization frameworks. This paper reviews, analyzes, and categorizes research efforts on surrogate modeling and applications with an emphasis on the research accomplished in the water resources field. The review analyzes 48 references on surrogate modeling arising from water resources and also screens out more than 100 references from the broader research community. Two broad families of surrogates namely response surface surrogates, which are statistical or empirical data-driven models emulating the high-fidelity model responses, and lower-fidelity physically based surrogates, which are simplified models of the original system, are detailed in this paper. Taxonomies on surrogate modeling frameworks, practical details, advances, challenges, and limitations are outlined. Important observations and some guidance for surrogate modeling decisions are provided along with a list of important future research directions that would benefit the common sampling and search (optimization) analyses found in water resources. [ABSTRACT FROM AUTHOR]

Many flood events involving water and sediments have been characterized using classic hydraulics principles, assuming the existence of critical flow and many other simplifications. In this paper, hyperconcentrated flow discharge was evaluated by using paleoflood reconstructions (based on paleostage indicators [PSI]) combined with a detailed hydraulic analysis of the critical flow assumption. The exact location where this condition occurred was established by iteratively determining the corresponding cross section, so that specific energy is at a minimum. In addition, all of the factors and parameters involved in the process were assessed, especially those related to the momentum equation, existing shear stresses in the wetted perimeter, and nonhydrostatic and hydrostatic pressure distributions. The superelevation of the hyperconcentrated flow, due to the flow elevation curvature, was also estimated and calibrated with the PSI. The estimated peak discharge was established once the iterative process was unable to improve the fit between the simulated depth and the depth observed from the PSI. The methodological approach proposed here can be applied to other higher-gradient mountainous torrents with a similar geomorphic configuration to the one studied in this paper. Likewise, results have been derived with fewer uncertainties than those obtained from standard hydraulic approaches, whose simplifying assumptions have not been considered. [ABSTRACT FROM AUTHOR]

Multivariate extreme value models are a fundamental tool in order to assess potentially dangerous events. The target of this paper is two-fold. On the one hand we outline how, exploiting recent theoretical developments in the theory of copulas, new multivariate extreme value distributions can be easily constructed; in particular, we show how a suitable number of parameters can be introduced, a feature not shared by traditional extreme value models. On the other hand, we introduce a proper new definition of multivariate return period and show the differences with (and the advantages over) the definition presently used in literature. An illustration involving flood data is presented and discussed, and a generalization of the well-known multivariate logistic Gumbel model is also given. [ABSTRACT FROM AUTHOR]

Abstract: The classical continuum modeling of evaporation in capillary porous media is revisited from pore network simulations of the evaporation process. The computed moisture diffusivity is characterized by a minimum corresponding to the transition between liquid and vapor transport mechanisms confirming previous interpretations. Also the study suggests an explanation for the scattering generally observed in the moisture diffusivity obtained from experimental data. The pore network simulations indicate a noticeable nonlocal equilibrium effect leading to a new interpretation of the vapor pressure‐saturation relationship classically introduced to obtain the one‐equation continuum model of evaporation. The latter should not be understood as a desorption isotherm as classically considered but rather as a signature of a nonlocal equilibrium effect. The main outcome of this study is therefore that nonlocal equilibrium two‐equation model must be considered for improving the continuum modeling of evaporation. [ABSTRACT FROM AUTHOR]

[1] This paper proposes a strategy for improving the computational efficiency of model inversion using the method of anchored distributions (MAD) by "bundling" similar model parametrizations in the likelihood function. Inferring the likelihood function typically requires a large number of forward model (FM) simulations for each possible model parametrization; as a result, the process is quite expensive. To ease this prohibitive cost, we present an approximation for the likelihood function called bundling that relaxes the requirement for high quantities of FM simulations. This approximation redefines the conditional statement of the likelihood function as the probability of a set of similar model parametrizations "bundle" replicating field measurements, which we show is neither a model reduction nor a sampling approach to improving the computational efficiency of model inversion. To evaluate the effectiveness of these modifications, we compare the quality of predictions and computational cost of bundling relative to a baseline MAD inversion of 3-D flow and transport model parameters. Additionally, to aid understanding of the implementation we provide a tutorial for bundling in the form of a sample data set and script for the R statistical computing language. For our synthetic experiment, bundling achieved a 35% reduction in overall computational cost and had a limited negative impact on predicted probability distributions of the model parameters. Strategies for minimizing error in the bundling approximation, for enforcing similarity among the sets of model parametrizations, and for identifying convergence of the likelihood function are also presented. [ABSTRACT FROM AUTHOR]

This study reports on two strategies for accelerating posterior inference of a highly parameterized and CPU-demanding groundwater flow model. Our method builds on previous stochastic collocation approaches, e.g., Marzouk and Xiu (2009) and Marzouk and Najm (2009), and uses generalized polynomial chaos (gPC) theory and dimensionality reduction to emulate the output of a large-scale groundwater flow model. The resulting surrogate model is CPU efficient and serves to explore the posterior distribution at a much lower computational cost using two-stage MCMC simulation. The case study reported in this paper demonstrates a two to five times speed-up in sampling efficiency. [ABSTRACT FROM AUTHOR]

There is widespread recognition that spatially distributed information on soil surface roughness (SSR) is required for hydrological and geomorphological applications. Such information is necessary to describe variability in soil structure, which is highly heterogeneous in time and space, to parameterize hydrology and erosion models and to understand the temporal evolution of the soil surface in response to rainfall. This paper demonstrates how results from semivariogram analysis can quantify key elements of SSR for such applications. Three soil types (silt, silt loam, and silty clay) were used to show how different types of structural variance in SSR evolve during simulated rainfall events. All three soil types were progressively degraded using artificial rainfall to produce a series of roughness states. A calibrated laser profiling instrument was used to measure SSR over a 10 cm x 10 cm spatial extent, at a 2 mm resolution. These data were geostatistically analyzed in the context of aggregate breakdown and soil crusting. The results show that such processes are represented by a quantifiable decrease in sill variance, from 7.81 (control) to 0.94 (after 60 min of rainfall). Soil surface features such as soil cracks, tillage lines and erosional areas were quantified by local maxima in semivariance at a given length scale. This research demonstrates that semivariogram analysis can retrieve spatiotemporal variations in soil surface condition; in order to provide information on hydrological pathways. Consequently, geostatistically derived SSR shows strong potential for inclusion as spatial information in hydrology and erosion models to represent complex surface processes at different soil structural scales. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a decomposition and multistage approach for optimizing the design of water distribution systems with multiple supply sources (WDS-MSS). An algorithm is first proposed to identify the optimal source partitioning cut-set for a WDS-MSS. A WDS with K supply sources is therefore decomposed to K disconnected subnetworks by the removal of the determined cut-set. Then, a total of K separate differential evolution (DE) algorithms are used to optimize the designs for the K subnetworks, respectively. This is the first optimization stage. The optimal solutions for the K subnetworks plus the optimal cut-set being the minimum allowable pipe sizes are used to create a tailored seeding table. This table is used to initialize a second-stage DE algorithm to optimize the whole of the original WDS, which is the second stage of the optimization process. Four WDS-MSS case studies are used to demonstrate the effectiveness of the proposed method. A standard DE algorithm seeded by the total choice table rather than the tailored seeding table is applied to the entire network for each case study, and the results are compared with those of the proposed method in terms of efficiency and solution quality. The comparison demonstrates that the proposed method (i.e., decomposition followed by multistage optimization) shows better performance than results from a whole of network optimization. In addition, the proposed method also exhibits significantly improved performance compared with the optimization techniques that have been previously used to optimize these case studies. [ABSTRACT FROM AUTHOR]

In analytical modeling of two-phase flow problems in porous media, the saturation profile for a fixed time can be obtained by using the method of characteristics (MOC). One of the basic assumptions in the application of the MOC is that the fractional flow is a function of saturation only. However, when gas is injected, it is often flowing under nonlinear flow conditions and inertial losses are significant in the near-well region. Therefore, in a radial displacement non-Darcy flow applies at the injection well, but as the saturation front gets further away, its velocity will decrease and the fractional flow curve will vary with the distance along the streamline. This paper presents the extension of the Buckley-Leverett analytical solution when the injected gas phase flow is governed by the two-phase extension to the Forchheimer equation and the fractional flow function depends both on the saturation and radial distance from the well. The behavior of a gas-liquid system under non-Darcy flow conditions is shown for carbon dioxide injection into saline aquifers. Finally, this analytical solution is tested against the corresponding finite difference numerical model and the limitations of the approach are discussed. [ABSTRACT FROM AUTHOR]

This paper develops a general mathematical model for describing head fluctuations in an aquifer of long but narrow islands subject to a dual tide effect. The upper boundary condition of the aquifer is represented by an equation combining the simplified free surface equation with a leakage term. Such an equation is considered as a general expression representing the upper boundary condition of a confined, unconfined, or leaky confined aquifer. The closed-form solution of the model represented by two series terms is developed by the direct Fourier method and finite Fourier sine transform. One of the series can reduce to a closed-form expression by means of contour integral and residue theorem. If the width of the island is very large, this solution gives the predicted head almost the same as that of the solution for an aquifer subject to a single tide effect. It is found that the presence of an upper aquitard produces significant vertical flow in the lower leaky confined aquifer even if the aquitard permeability is low. Neglecting such vertical flow may result in an overestimate of hydraulic head in the leaky confined aquifer. The attenuation factor and phase lag predicted from the present solution subject to the dual tide effect agree well with those estimated from 57 day head fluctuation data observed at Garden Island, Australia. [ABSTRACT FROM AUTHOR]

Domains composed of a porous part and an adjacent free-flow region are of special interest in many fields of application. So far, the coupling of free flow with porous-media flow has been considered only for single-phase systems. Here we extend this classical concept to two-component nonisothermal flow with two phases inside the porous medium and one phase in the free-flow region. The mathematical modeling of flow and transport phenomena in porous media is often based on Darcy's law, whereas in free-flow regions the (Navier-) -Stokes equations are used. In this paper, we give a detailed description of the employed subdomain models. The main contribution is the developed coupling concept, which is able to deal with compositional (miscible) flow and a two-phase system in the porous medium. It is based on the continuity of fluxes and the assumption of thermodynamic equilibrium, and uses the Beavers-Joseph-Saflhrnn condition. The phenomenological explanations leading to a simple, solvable model, which accounts for the physics at the interface, are laid out in detail. Our model can account for evaporation and condensation processes at the interface and is used to model evaporation from soil influenced by a wind field in a first numerical example. [ABSTRACT FROM AUTHOR]

Prediction of the physical transport and mixing of pollutants or other soluble material is crucial for effective river management. Although well established methods exist which describe mixing processes m open channel flow, the presence of vegetation has a significant impact on mixing and few existing techniques account for this. To date, existing models which predict longitudinal dispersion coefficients in vegetated open channel flow have been derived and verified based on experiments conducted in simulated vegetation. This paper presents observations of longitudinal dispersion coefficients in a channel featuring living vegetation and tests against both an existing and a newly proposed model for longitudinal dispersion coefficient in submerged vegetated open channel flow. A model based on a mathematical technique of predicting dispersion in plain shear flow is shown to be capable of predicting longitudinal dispersion coefficients to within 20%. [ABSTRACT FROM AUTHOR]

The quest for improved hydrological models is one of the big challenges in hydrology. When discrepancies are observed between simulated and measured discharge, it is essential to identify which algorithms may be responsible for poor model behavior. Particularly in complex hydrological models, different process representations may dominate at different moments and interact with each other, thus highly complicating this task. This paper investigates the analysis of the temporal dynamics of parameter sensitivity as a way to disentangle the simulation of a hydrological model and identify dominant parameterizations. Three existing methods (the Fourier amplitude sensitivity test, the extended Fourier amplitude sensitivity test, and Sobol's method) are compared by applying them to a TOPMODEL implementation in a small mountainous catchment in the tropics. For the major part of the simulation period, the three methods give comparable results, while the Fourier amplitude sensitivity test is much more computationally efficient. This method is also applied to the complex hydrological model WaSiM-ETH implemented in the Weisseritz catchment, Germany. A qualitative model validation was performed on the basis of the identification of relevant model components. The validation revealed that the saturation deficit parameterization of WaSiM-ETH is highly susceptible to parameter interaction and lack of identifiability. We conclude that temporal dynamics of model parameter sensitivity can be a powerful tool for hydrological model analysis, especially to identify parameter interaction as well as the dominant hydrological response modes. Finally, an open source implementation of the Fourier amplitude sensitivity test is provided. [ABSTRACT FROM AUTHOR]

In this paper we investigate the use of hydrological models as learning tools to help improve our understanding of the hydrological functioning of a catchment. With the model as a hypothetical conceptualization of how dominant hydrological processes contribute to catchment-scale response, we investigate three questions: (I) During which periods does the model (not) reproduce observed quantities and dynamics? (2) What is the nature of the error during times of bad model performance? (3) Which model components are responsible for this error? To investigate these questions, we combine a method for detecting repeating patterns of typical differences between model and observations (time series of grouped errors, TIGER) with a method for identifying the active model components during each simulation time step based on parameter sensitivity (temporal dynamics of parameter sensitivities, TEDPAS). The approach generates a time series of occurrence of dominant error types and time series of parameter sensitivities. A synoptic discussion of these time series highlights deficiencies in the assumptions about the functioning of the catchment. The approach is demonstrated for the Weisseritz headwater catchment in the eastern Ore Mountains. Our results indicate that the WaSiM-ETH complex grid-based model is not a sufficient working hypothesis for the functioning of the Weisseritz catchment and point toward future steps that can help improve our understanding of the catchment. [ABSTRACT FROM AUTHOR]

Flood estimation for ungauged catchments is a challenging task for hydrologists. A modem geographical mformation system is able to extract a large number of catchment characteristics as input variables for regionalization analysis. Effective and efficient selection of the best input variables is urgently needed in this field. This paper explores a new methodology for selecting the best input variable combination on the basis of the gamma test and leave-one-out cross validation (LOOCV) to estimate the median annual maximum flow (as an index flood). Since the gamma test is capable of efficiently calculating the output variance on the basis of the input without the need to select a model structure type, more effective regionalization models could be developed because there is no need to define an a priori model structure. A case study from 20 catchments in southwest England has been used to illustrate and validate the proposed scheme. It has been found that the gamma test is able to narrow down the search options to be further explored by the LOOCV. The best formula from this approach outperforms the conventional approaches based on cross validation, data filtering with Spearman's rank correlation matrix, and corrected Akaike information criterion. In addition, the developed formula is significantly more accurate than the existing equation used in the Flood Estimation Handbook. [ABSTRACT FROM AUTHOR]

We develop a novel method of parameterization for spatial hydraulic property characterization to mitigate the challenges associated with the nonlinear inverse problem of subsurface flow model calibration. The parameterization is performed by the projection of the estimable hydraulic property field onto an orthonormal basis derived from the grid connectivity structure. The basis functions represent the modal shapes or harmonics of the grid, are defined by a modal frequency, and converge to special cases of the discrete Fourier series under certain grid geometries and boundary assumptions; therefore, hydraulic property updates are performed in the spectral domain and merge with Fourier analysis in ideal cases. Dependence on the grid alone implies that the basis may characterize any grid geometry, including corner point and unstructured, is model independent, and is constructed off-line and only once prior to flow data assimilation. We apply the parameterization in an adaptive multiscale model calibration workflow for three subsurface flow models. Several different grid geometries are considered. In each case the prior hydraulic property model is updated using a parameterized multiplier field that is superimposed onto the grid and assigned an initial value of unity at each cell. The special case corresponding to a constant multiplier is always applied through the constant basis function. Higher modes are adaptively employed during minimization of data misfit to resolve multiscale heterogeneity in the geomodel. The parameterization demonstrates selective updating of heterogeneity at locations and spatial scales sensitive to the available data, otherwise leaving the prior model unchanged as desired. [ABSTRACT FROM AUTHOR]

Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage. [ABSTRACT FROM AUTHOR]

A 7-d, constant rate aquifer test conducted by University of Waterloo researchers at Canadian Forces Base Borden in Ontario, Canada, is useful for advancing understanding of fluid flow processes in response to pumping from an unconfined aquifer. Measured data include not only drawdown in the saturated zone but also volumetric soil moisture measured at various times and distances from the pumped well. Analytical analyses were conducted with the model published in 2001 by Moench and colleagues, which allows for gradual drainage but does not include unsaturated zone characteristics, and the model published in 2006 by Mathias and Butler, which assumes that moisture retention and relative hydraulic conductivity (RHC) in the unsaturated zone are exponential functions of pressure head. Parameters estimated with either model yield good matches between measured and simulated drawdowns in piezometers. Numerical analyses were conducted with two versions of VS2DT: one that uses traditional Brooks and Corey functional relations and one that uses a RHC function introduced in 2001 by Assouline that includes an additional parameter that accounts for soil structure and texture. The analytical model of Mathias and Butler and numerical model of VS2DT with the Assouline model both show that the RHC function must contain a fitting parameter that is different from that used in the moisture retention function. Results show the influence of field-scale heterogeneity and suggest that the RHC at the Borden site declines more rapidly with elevation above the top of the capillary fringe than would be expected if the parameters were to reflect local- or core-scale soil structure and texture. [ABSTRACT FROM AUTHOR]