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We address the problem of stochastic simulation of soil particle-size curves (PSCs) in heterogeneous aquifer systems. Unlike traditional approaches that focus solely on a few selected features of PSCs (e.g., selected quantiles), our approach considers the entire particle-size curves and can optionally include conditioning on available data. We rely on our prior work to model PSCs as cumulative distribution functions and interpret their density functions as functional compositions. We thus approximate the latter through an expansion over an appropriate basis of functions. This enables us to (a) effectively deal with the data dimensionality and constraints and (b) to develop a simulation method for PSCs based upon a suitable and well defined projection procedure. The new theoretical framework allows representing and reproducing the complete information content embedded in PSC data. As a first field application, we demonstrate the quality of unconditional and conditional simulations obtained with our methodology by considering a set of particle-size curves collected within a shallow alluvial aquifer in the Neckar river valley, Germany.

Improper storage and disposal of nonaqueous-phase liquids (NAPLs) has resulted in widespread contamination of the subsurface, threatening the quality of groundwater as a freshwater resource. The high frequency of contaminated sites and the difficulties of remediation efforts demand rational decisions based on a sound risk assessment. Due to sparse data and natural heterogeneities, this risk assessment needs to be supported by appropriate predictive models with quantified uncertainty. This study proposes a physically and stochastically coherent model concept to simulate and predict crucial impact metrics for DNAPL contaminated sites, such as contaminant mass discharge and DNAPL source longevity. To this end, aquifer parameters and the contaminant source architecture are conceptualized as random space functions. The governing processes are simulated in a three-dimensional, highly resolved, stochastic, and coupled model that can predict probability density functions of mass discharge and source depletion times. While it is not possible to determine whether the presented model framework is sufficiently complex or not, we can investigate whether and to which degree the desired model predictions are sensitive to simplifications often found in the literature. By testing four commonly made simplifications, we identified aquifer heterogeneity, groundwater flow irregularity, uncertain and physically based contaminant source zones, and their mutual interlinkages as indispensable components of a sound model framework.

A stochastic rainfall simulator based on the concept of “dry drift” is proposed. It is characterized by a new and nonstationary representation of rainfall in which the average rain rate (in log-space) depends on the distance to the closest surrounding dry areas. The result is a more realistic transition between dry and rainy areas and a better distribution of low and high rain rates inside the simulated rainy areas. The proposed approach is very general and can be used to simulate both unconditional and conditional rain rate time series, two-dimensional fields, and space-time fields. The parameterization is intuitive and can be done using time series and/or radar rain-rate maps. Several examples illustrating the simulator's capabilities are given. The results show that the simulated time series and rain rate fields look realistic and that they are difficult to distinguish from real observations.

A generalized framework for single-variate and multivariate simulation and forecasting problems in stochastic hydrology is proposed. It is appropriate for short-term or long-term memory processes and preserves the Hurst coefficient even in multivariate processes with a different Hurst coefficient in each location. Simultaneously, it explicitly preserves the coefficients of skewness of the processes. The proposed framework incorporates short-memory (autoregressive moving average) and long-memory (fractional Gaussian noise) models, considering them as special instances of a parametrically defined generalized autocovariance function, more comprehensive than those used in these classes of models. The generalized autocovariance function is then implemented in a generalized moving average generating scheme that yields a new time-symmetric (backward-forward) representation, whose advantages are studied. Fast algorithms for computation of internal parameters of the generating scheme are developed, appropriate for problems including even thousands of such parameters. The proposed generating scheme is also adapted through a generalized methodology to perform in forecast mode, in addition to simulation mode. Finally, a specific form of the model for problems where the autocorrelation function can be defined only for a certain finite number of lags is also studied. Several illustrations are included to clarify the features and the performance of the components of the proposed framework.

[1] Nonstationary oscillation (NSO) processes are observed in a number of hydroclimatic data series. Stochastic simulation models are useful to study the impacts of the climatic variations induced by NSO processes into hydroclimatic regimes. Reproducing NSO processes in a stochastic time series model is, however, a difficult task because of the complexity of the nonstationary behaviors. In the current study, a novel stochastic simulation technique that reproduces the NSO processes embedded in hydroclimatic data series is presented. The proposed model reproduces NSO processes by utilizing empirical mode decomposition (EMD) and nonparametric simulation techniques (i.e., k-nearest-neighbor resampling and block bootstrapping). The model was first tested with synthetic data sets from trigonometric functions and the Rossler system. The North Atlantic Oscillation (NAO) index was then examined as a real case study. This NAO index was then employed as an exogenous variable for the stochastic simulation of streamflows at the Romaine River in the province of Quebec, Canada. The results of the application to the synthetic data sets and the real-world case studies indicate that the proposed model preserves well the NSO processes along with the key statistical characteristics of the observations. It was concluded that the proposed model possesses a reasonable simulation capacity and a high potential as a stochastic model, especially for hydroclimatic data sets that embed NSO processes.

[1] A novel data-driven artificial neural network (ANN) that quantitatively combines large numbers of multiple types of soft data is presented for performing stochastic simulation and/or spatial estimation. A counterpropagation ANN is extended with a radial basis function to estimate parameter fields that reproduce the spatial structure exhibited in autocorrelated parameters. Applications involve using three geophysical properties measured on a slab of Berea sandstone and the delineation of landfill leachate at a site in the Netherlands using electrical formation conductivity as our primary variable and six types of secondary data (e.g., hydrochemistry, archaea, and bacteria). The ANN estimation fields are statistically similar to geostatistical methods (indicator simulation and cokriging) and reference fields (when available). The method is a nonparametric clustering/classification algorithm that can assimilate significant amounts of disparate data types with both continuous and categorical responses without the computational burden associated with the construction of positive definite covariance and cross-covariance matrices. The combination of simplicity and computational speed makes the method ideally suited for environmental subsurface characterization and other Earth science applications with spatially autocorrelated variables.

[1] A time series simulation scheme based on wavelet decomposition coupled to an autoregressive model is presented for hydroclimatic series that exhibit band-limited low-frequency variability. Many nonlinear dynamical systems generate time series that appear to have amplitude- and frequency-modulated oscillations that may correspond to the recurrence of different solution regimes. The use of wavelet decomposition followed by an autoregressive model of each leading component is explored as a model for such time series. The first example considered is the Lorenz-84 low-order model of extratropical circulation, which has been used to illustrate how chaos and intransitivity (multiple stable solutions) can lead to low-frequency variability. The central England temperature (CET) time series, the NINO3.4 series that is a surrogate for El Nino–Southern Oscillation, and seasonal rainfall from Everglades National Park, Florida, are then modeled with this approach. The proposed simulation model yields better results than a traditional linear autoregressive (AR) time series model in terms of reproducing the time-frequency properties of the observed rainfall, while preserving the statistics usually reproduced by the AR models.

We study the migration of sorbing tracers through crystalline rock by combining relatively simple transport measures with particle tracking in a discrete fracture network. The rock volume is on a 1 ...

Long samples of weather data are frequently needed to evaluate the long-term effects of proposed hydrologic changes. The evaluations are often undertaken using deterministic mathematical models that require daily weather data as input. Stochastic generation of the required weather data offers an attractive alternative to the use of observed weather records. This paper presents an approach that may be used to generate long samples of daily precipitation, maximum temperature, minimum temperature, and solar radiation. Precipitation is generated independently of the other variables by using a Markov chain-exponential model. The other three variables are generated by using a multivariate model with the means and standard deviations of the variables conditioned on the wet or dry status of the day as determined by the precipitation model. Daily weather samples that are generated with this approach preserve the seasonal and statistical characteristics of each variable and the interrelations among the four variables that exist in the observed data.

The objective of the current study is to build a stochastic model to simulate climate indices that are teleconnected with the hydrologic regimes of large‐scale water resources systems such as the Great Lakes system. Climate indices generally contain nonstationary oscillations (NSOs). We adopted a stochastic simulation model based on Empirical Mode Decomposition (EMD). The procedure for the model is to decompose the observed series and then to simulate the decomposed components with the NSO resampling (NSOR) technique. Because the model has only been previously applied to single variables, a multivariate version of NSOR (M‐NSOR) is developed to consider the links between the climate indices and to reproduce the NSO process. The proposed M‐NSOR model is tested in a simulation study on the Rossler system. The simulation results indicate that the M‐NSOR model reproduces the significant oscillatory behaviors of the system and the marginal statistical characteristics. Subsequently, the M‐NSOR model is applied to three climate indices (i.e., Arctic Oscillation, El Nino‐Southern Oscillation, and Pacific Decadal Oscillation) for the annual and winter data sets. The results of the proposed model are compared to those of the Contemporaneous Shifting Mean and Contemporaneous Autoregressive Moving Average model. The results indicate that the proposed M‐NSOR model is superior to the Contemporaneous Shifting Mean and Contemporaneous Autoregressive Moving Average model for reproducing the NSO process, while the other basic statistics are comparatively well preserved in both cases. The current study concludes that the proposed M‐NSOR model can be a good alternative to simulate NSO processes and their teleconnections with climate indices.

The quantification of spatial rainfall is critical for distributed hydrological modeling. Rainfall spatial patterns generated by similar weather conditions can be extremely diverse. This variability can have a significant impact on hydrological processes. Stochastic simulation allows generating multiple realizations of spatial rainfall or filling missing data. The simulated data can then be used as input for numerical models to study the uncertainty on hydrological forecasts. In this paper, we use the direct sampling technique to generate stochastic simulations of high-resolution (1-km) daily rainfall fields, conditioned by elevation and weather state. The technique associates historical radar estimates to variables describing the daily weather conditions, such as the rainfall type and mean intensity, and selects radar images accordingly to form a conditional training image set of each day. Rainfall fields are then generated by resampling pixels from these images. The simulation at each location is conditioned by neighbor patterns of rainfall amount and elevation. The technique is tested on the simulation of daily rainfall amount for the eastern Mediterranean. The results show that it can generate realistic rainfall fields for different weather types, preserving the temporal weather pattern, the spatial features, and the complex relation with elevation. The concept of conditional training image provides added value to multiple-point simulation techniques dealing with extremely non-stationary heterogeneities and extensive datasets.

A method for the stochastic design of groundwater quality observation well network is presented. The method uses calibration constrained Null-space Monte Carlo analysis for the stochastic simulation of the reduction ratio of peak concentration and the time corresponding to this in an injection well field. The numerical groundwater model simulations are constrained with a limited amount of field measurements. The objective of the monitoring network design is to identify optimal monitoring locations that allow for prediction of spatial fields from the data collected at limited number of points in the spatial domain. These locations need to be robust to different possible outcomes simulated using the stochastic model runs, and result in good spatial predictions, regardless of which one of the many possibilities turned out to be the true representation of nature. Multiple simulated fields of concentration and time are used to identify a small set of empirical orthogonal functions (spatial basis functions) for reduced-rank prediction of the spatial patterns in these two fields. The Differential Evolution algorithm was used to find the monitoring locations that allowed for optimal reconstruction of all the simulated fields (potential future states of reality) from the set of empirical orthogonal functions. The applicability is demonstrated for designing a monitoring network for an injection well field. Optimal locations of 10 monitoring wells were identified. The method has the capability to simultaneously identify the optimal locations and inform optimal times for monitoring reduction ratio of peak concentration. The method is flexible to iteratively combine stochastic modelling and monitoring for optimal groundwater management

Risk analysis plays an important role in decision making for real-time flood control operation of complex flood control systems. A typical flood control system consists of reservoirs, river channels, and downstream control points. The system generally is characterized by nonlinearity and large scale. Additionally, the input variables are mostly stochastic. Because of the dimensionality problem, generally, it would not be possible to carry out risk analysis without decomposition. In this paper, we propose a decomposition-integration approach whereby the original complex flood control system is decomposed into a number of independent subsystems. We conduct risk analysis for each subsystem and then integrate the results by means of combination theory of stochastic processes. We evaluate the propagation of uncertainties through the complex flood control system and calculate the risk of reservoir overtopping, as well as the risk of flooding at selected downstream control points. We apply the proposed methodology to a flood control system in the middle reaches of the Huaihe River basin in China. The results show that the proposed method is practical and provides a way to estimate the risks in real-time flood control operation of a complex flood control system. This article is protected by copyright. All rights reserved.

High-resolution space-time stochastic models for precipitation are crucial for hydrological applications related to flood risk and water resources management. In this study, we present a new stochastic space-time model, STREAP, which is capable of reproducing essential features of the statistical structure of precipitation in space and time for a wide range of scales, and at the same time can be used for continuous simulation. The model is based on a three-stage hierarchical structure that mimics the precipitation formation process. The stages describe the storm arrival process, the temporal evolution of areal mean precipitation intensity and wet area, and the evolution in time of the two-dimensional storm structure. Each stage of the model is based on appropriate stochastic modeling techniques spanning from point processes, multivariate stochastic simulation and random fields. Details of the calibration and simulation procedures in each stage are provided so that they can be easily reproduced. STREAP is applied to a case study in Switzerland using 7 years of high-resolution (2 × 2 km2; 5 min) data from weather radars. The model is also compared with a popular parsimonious space-time stochastic model based on point processes (space-time Neyman-Scott) which it outperforms mainly because of a better description of spatial precipitation. The model validation and comparison is based on an extensive evaluation of both areal and point scale statistics at hydrologically relevant temporal scales, focusing mainly on the reproduction of the probability distributions of rainfall intensities, correlation structure, and the reproduction of intermittency and wet spell duration statistics. The results shows that a more accurate description of the space-time structure of precipitation fields in stochastic models such as STREAP does indeed lead to a better performance for properties and at scales which are not used in model calibration.

[1] The paper introduces a logical extension to data-based mechanistic (DBM) modeling, which provides hypothetico-inductive (HI-DBM) bridge between conceptual models, derived in a hypothetico-deductive manner, and the DBM model identified inductively from the same time-series data. The approach is illustrated by a quite detailed example of HI-DBM analysis applied to the well-known Leaf River data set and the associated HyMOD conceptual model. The HI-DBM model significantly improves the explanation of the Leaf River data and enhances the performance of the original DBM model. However, on the basis of various diagnostic tests, including recursive time-variable and state-dependent parameter estimation, it is suggested that the model should be capable of further improvement, particularly as regards the conceptual effective rainfall mechanism, which is based on the probability distributed model hypothesis. In order to verify the efficacy of the HI-DBM analysis in a situation where the actual model generating the data is completely known, the analysis is also applied to a stochastic simulation model based on a modified HyMOD model.

We present a method for inverse modeling in hydrology that incorporates a physical understanding of the geological processes that form a hydrologic system. The method is based on constructing a stochastic model that is approximately representative of these geologic processes. This model provides a prior probability distribution for possible solutions to the inverse problem. The uncertainty in the inverse solution is characterized by a conditional (posterior) probability distribution. A new stochastic simulation method, called conditional coding, approximately samples from this posterior distribution and allows study of solution uncertainty through Monte Carlo techniques. We examine a fracture-dominated flow system, but the method can potentially be applied to any system where formation processes are modeled with a stochastic simulation algorithm.

This study evaluates commonly used geostatistical methods to assess reproduction of hydraulic conductivity (K) structure and sensitivity under limiting amounts of data. Extensive conductivity measurements from the Cape Cod sand and gravel aquifer are used to evaluate two geostatistical estimation methods, conditional mean as an estimate and ordinary kriging, and two stochastic simulation methods, simulated annealing and sequential Gaussian simulation. Our results indicate that for relatively homogeneous sand and gravel aquifers such as the Cape Cod aquifer, neither estimation methods nor stochastic simulation methods give highly accurate point predictions of hydraulic conductivity despite the high density of collected data. Although the stochastic simulation methods yielded higher errors than the estimation methods, the stochastic simulation methods yielded better reproduction of the measured In (K) distribution and better reproduction of local contrasts in In (K). The inability of kriging to reproduce high In (K) values, as reaffirmed by this study, provides a strong instigation for choosing stochastic simulation methods to generate conductivity fields when performing fine-scale contaminant transport modeling. Results also indicate that estimation error is relatively insensitive to the number of hydraulic conductivity measurements so long as more than a threshold number of data are used to condition the realizations. This threshold occurs for the Cape Cod site when there are approximately three conductivity measurements per integral volume. The lack of improvement with additional data suggests that although fine-scale hydraulic conductivity structure is evident in the variogram, it is not accurately reproduced by geostatistical estimation methods. If the Cape Cod aquifer spatial conductivity characteristics are indicative of other sand and gravel deposits, then the results on predictive error versus data collection obtained here have significant practical consequences for site characterization. Heavily sampled sand and gravel aquifers, such as Cape Cod and Borden, may have large amounts of redundant data, while in more common real world settings, our results suggest that denser data collection will likely improve understanding of permeability structure.

A new fractal scaling model is proposed for use in aquifer heterogeneity modeling and simulation. The new model, which is obtained by subordination of fractional Brownian motion, provides a unifying framework for scaling models of heterogeneity in that it includes previous scaling models as special cases and can also be tuned continuously between these models. Choosing the subordinator to be a lognormal distribution results in a non-Gaussian scaling model with a moderate degree of variability that matches data better than previous fractal scaling models, thus providing more accurate heterogeneity representations for use in stochastic flow and transport predictions. Two new stochastic simulation algorithms are constructed from the new models, one based on sequential simulation algorithms and the other based on probability field simulation. Both algorithms can be made conditional on available measurements.

[1] We propose a framework that combines simulation optimization with Bayesian decision analysis to evaluate the worth of hydraulic conductivity data for optimal groundwater resources management in ecologically sensitive areas. A stochastic simulation optimization management model is employed to plan regionally distributed groundwater pumping while preserving the hydroecological balance in wetland areas. Because predictions made by an aquifer model are uncertain, groundwater supply systems operate below maximum yield. Collecting data from the groundwater system can potentially reduce predictive uncertainty and increase safe water production. The price paid for improvement in water management is the cost of collecting the additional data. Efficient data collection using Bayesian decision analysis proceeds in three stages: (1) The prior analysis determines the optimal pumping scheme and profit from water sales on the basis of known information. (2) The preposterior analysis estimates the optimal measurement locations and evaluates whether each sequential measurement will be cost-effective before it is taken. (3) The posterior analysis then revises the prior optimal pumping scheme and consequent profit, given the new information. Stochastic simulation optimization employing a multiple-realization approach is used to determine the optimal pumping scheme in each of the three stages. The cost of new data must not exceed the expected increase in benefit obtained in optimal groundwater exploitation. An example based on groundwater management practices in Florida aimed at wetland protection showed that the cost of data collection more than paid for itself by enabling a safe and reliable increase in production.

A multivariate disaggregation method is developed for stochastic simulation of hydrologie series. The method is based on three simple ideas that have been proven effective. First, it starts using directly a typical PAR(1) model and keeps its formalism and parameter set, which is the most parsimonious among linear stochastic models. This model is run for the lower-level variables without any reference to the known higher-level variables. Second, it uses accurate adjusting procedures to allocate the error in the additive property, i.e., the departure of the sum of lower-level variables within a period from the corresponding higher-level variable. They are accurate in the sense that they preserve explicitly certain statistics or even the complete distribution of lower-level variables. Three such procedures have been developed and studied in this paper, both theoretically and empirically. Third, it uses repetitive sampling in order to improve the approximations of statistics that are not explicitly preserved by the adjusting procedures. The model, owing to the wide range of probability distributions it can handle (from bell-shaped to J-shaped) and to its multivariate framework, is useful for a plethora of hydrologic applications such as disaggregation of annual rainfall or runoff into monthly or weekly amounts, and disaggregation of event rainfall depths into partial amounts of hourly or even less duration. Such real-world hydrologic applications have been explored in this study to test the model performance, which has proven very satisfactory.

With the increased ability to model subsurface heterogeneity provided by stochastic simulation methods, there is a corresponding increase in the need for numerical flow models to accomodate the spatial variability of hydrodynamic parameters. These trends make it necessary to reexamine methods for calculating finite difference interblock conductivities originally developed for use in homogeneous media. This study describes a new method for calculating interblock conductivities better suited to the numerical modeling of unsaturated flow in heterogeneous media. An expression for interblock conductivity is derived by equating the finite difference flux between adjacent blocks with the exact analytical flux for one-dimensional steady unsaturated flow, assuming an exponential model for relative conductivity. This expression appears as a function of the saturated conductivities, alpha parameters, and matric potentials of the adjacent blocks and the potential at the interblock boundary. Since this last quantity is not directly featured in the discretized flow equation, it must be evaluated iteratively. The interblock conductivity calculation scheme is implemented within a block-centered seven-point finite difference model of steady unsaturated flow where nonlinearity is resolved using a Newton-Raphson iterative approach. In a series of numerical experiments this scheme is compared with the more familiar geometric averaging method. The proposed interblock conductivity scheme is shown to provide perfect agreement between numerical and analytical solutions for the one-dimensional case of steady infiltration into a perfectly layered medium. In problems of two-dimensional unsaturated flow in heterogeneous media, comparisons with the geometric averaging method show that the proposed scheme allows more rapid convergence of Newton-Raphson iterations and consideration of greater parameter spatial variability before the onset of divergence in these iterations.

[1] Quantile-quantile plots (QQ plots) are often applied to investigate tail behavior in extreme value analysis. When used for flood frequency analysis, based on river flow data, dependence in these data affects the extreme value distribution's tail behavior in the QQ plot. This problem is investigated on the basis of both synthetic and observed river flow series. The synthetic series are generated on the basis of a stochastic simulation procedure, which allows the real statistical flow properties to be known. Through simulation study, we demonstrate that serial dependence causes bending behavior in the QQ plot in the region of higher quantiles. This leads to the estimating error when the slope of the QQ plot is used as an estimator in the extreme value analysis. A correction method is proposed by modifying the plotting position using the extremal index.

[1] The effects of geological heterogeneity representation on the hydraulic properties of two-dimensional flow and transport simulations are studied using various stochastic simulation algorithms. An alternative multiple-point method (HOSIM) on the basis of high-order spatial cumulants and Legendre polynomials is used and compared to the multiple-point FilterSIM method, and the sequential Gaussian simulation (SGS) method. Conditional realizations of a fluvial reservoir system are generated by HOSIM, FilterSIM, and SGS methods. Then, the simulated hydraulic permeability fields (K) are used in a numerical groundwater flow and solute transport models. Numerical results showed that the HOSIM method created greater connectivity in the reservoir/aquifer (channel) network than FilterSIM and SGS realizations. The numerical simulations show that in a reservoir/aquifer system with a strongly connected network of high-K materials, the Gaussian and FilterSIM approaches are not as effective as HOSIM in reproducing this behavior. The simulations showed a good agreement between HOSIM realizations and the exhaustive reference image.

[1] The nonhomogeneous spatial activation of raincells (NSAR) model is presented which provides a continuous spatial-temporal stochastic simulation of rainfall exhibiting spatial nonstationarity in both amounts and occurrence. Spatial nonstationarity of simulated rainfall is important for hydrological modeling of mountainous catchments where orographic effects on precipitation are strong. Such simulated rainfall fields support the current trend toward distributed hydrological modeling. The NSAR model extends the Spatial Temporal Neyman-Scott Rectangular Pulses (STNSRP) model, which has a homogeneous occurrence process, by generating raincells with a spatially nonhomogeneous Poisson process. An algorithm to simulate nonhomogeneous raincell occurrence is devised. This utilizes a new efficient and accurate algorithm to simulate raincells from an infinite 2-D Poisson process, in which only raincells relevant to the application are simulated. A 4009 km2 Pyrenean catchment exhibiting extreme orographic effects provides a suitable case study comprising seven daily rain gauge records with hourly properties estimated using regional downscaling relationships. Both the NSAR and the STNSRP models are fitted to five calibration rain gauges. Simulated hourly fields are validated using the remaining two rain gauges providing the first validation of time series sampled from STNSRP or NSAR processes at locations not used in model fitting. The NSAR model exhibits considerable improvement over the STNSRP model particularly with respect to nonhomogeneous rainfall occurrence at both daily and hourly resolutions. Further, the NSAR simulation provides an excellent match to the spatially nonhomogeneous observed daily mean, proportion dry, variance, coefficient of variation, autocorrelation, skewness coefficient, cross correlation and extremes, and to the hourly proportion dry and variance properties.

[1] The integration of geophysical data into the subsurface characterization problem has been shown in many cases to significantly improve hydrological knowledge by providing information at spatial scales and locations that is unattainable using conventional hydrological measurement techniques. The investigation of exactly how much benefit can be brought by geophysical data in terms of its effect on hydrological predictions, however, has received considerably less attention in the literature. Here, we examine the potential hydrological benefits brought by a recently introduced simulated annealing (SA) conditional stochastic simulation method designed for the assimilation of diverse hydrogeophysical data sets. We consider the specific case of integrating crosshole ground-penetrating radar (GPR) and borehole porosity log data to characterize the porosity distribution in saturated heterogeneous aquifers. In many cases, porosity is linked to hydraulic conductivity and thus to flow and transport behavior. To perform our evaluation, we first generate a number of synthetic porosity fields exhibiting varying degrees of spatial continuity and structural complexity. Next, we simulate the collection of crosshole GPR data between several boreholes in these fields, and the collection of porosity log data at the borehole locations. The inverted GPR data, together with the porosity logs, are then used to reconstruct the porosity field using the SA-based method, along with a number of other more elementary approaches. Assuming that the grid-cell-scale relationship between porosity and hydraulic conductivity is unique and known, the porosity realizations are then used in groundwater flow and contaminant transport simulations to assess the benefits and limitations of the different approaches.

The large variability of the drop size distribution (DSD) in space and time must be taken into account to improve remote sensing of precipitation. The ability to simulate a large number of 2D fields of DSD sharing the same statistical properties provides a very useful simulation framework that nicely complements experimental approaches based on DSD ground measurements. These simulations can be used to investigate radar beam propagation through rain and to evaluate different radar retrieval techniques. The proposed approach uses geostatistics to provide structural analysis and stochastic simulation of DSD fields. First, the DSD is assumed to follow a Gamma distribution with three parameters. Therefore, 2D fields of DSDs can be described as a three-component multivariate random function. Such 2D fields are normalized using a Gaussian anamorphosis and simulated by taking advantage of fast multivariate Gaussian simulation algorithms. Variograms and cross-variograms are used to generate fields with identical spatial structure that are consistent with the observations. To assess the proposed approach, the method is applied to data collected during intense Mediterranean rainfall. Taylor’s hypothesis is assumed to convert time series into 1D range profiles. The anisotropy of the DSD fields is derived from radar reflectivity measurements collected over the same area during the same event. A large number of DSD fields are generated and the corresponding reflectivity fields are derived. The results of the simulations are in good agreement with respect to the mean, the standard deviation and the spatial structure, demonstrating the promising potential of the proposed stochastic model of DSD fields

[1] A method for optimal remediation of heterogeneous aquifers based on stochastic simulation with adaptive determination of critical realizations is developed. Multiple hydraulic conductivity realizations are generated using the turning bands method while Monte Carlo simulation is incorporated into a multiobjective genetic optimization algorithm. In order to reduce the computational burden of Monte Carlo simulations, an adaptive procedure is developed for identifying “critical realizations” which are the ones that have an effect on the optimal solution depending on desired reliability level. The adaptive procedure is embedded into the genetic optimization algorithm where noncritical realizations are eliminated step by step during the advancement of optimization. When the number of remaining realizations reaches a minimum, some new realizations are added. The specific realizations which are removed or added in the critical set are selected by an automatic procedure controlled by a similarity criterion based on rankings of realizations. This is a significant improvement over the nonadaptive methodology for identification of critical realizations and does not require using a number of initial designs and a safety threshold. The methodology is applied in a remediation problem with two objectives (reduction of contaminant mass and cleanup cost). The applications indicate significant savings in computer time without loss of performance.

[1] Because of the necessary simplification of the complex natural processes and the limited availability of observations, model simulations are always uncertain and this uncertainty should be quantified. In this contribution, the model error is quantified using a combined procedure. For the uncertainty of discharge due to meteorological input, a stochastic simulation method is used. To quantify the effect of process representation and parameterization, a sensitivity analysis is carried out. It is assumed that the model error due to process uncertainty is proportional to the sensitivity. The final model error variance can thus be calculated from the stochastic errors and the process sensitivities. The coefficients used for the quantification are estimated simultaneously with the model parameters. The methodology presented produces error series that are normally distributed and that represent the varying importance of different processes in time. This uncertainty time series can be used as a weighting factor to normalize the model residuals during calibration so that the assumptions of least squares optimization are fulfilled. Calibration and uncertainty estimation are demonstrated with an example application of a distributed Hydrological Bureau Waterbalance (HBV) model of three watersheds in the Neckar basin in southwest Germany. The model residual distributions are presented and compared to a standard calibration method. Further, it is shown that the new methodology leads to more realistic confidence intervals for model simulations. Although applied to the HBV model as an example, the method is general and can be applied to any model and also in conjunction with other uncertainty estimation techniques.

[1] The estimation of effective soil hydraulic parameters and their uncertainties is a critical step in all large-scale hydrologic and climatic model applications. Here a scale-dependent (top-down) parameter estimation (inverse modeling) scheme called the noisy Monte Carlo genetic algorithm (NMCGA) was developed and tested for estimating these effective soil hydraulic parameters and their uncertainties. We tested our method using three case studies involving a synthetic pixel (pure and mixed) where all modeling conditions are known, and with actual airborne remote sensing (RS) footprints and a satellite RS footprint. In the synthetic case studies under pure (one soil texture) and mixed-pixel (multiple soil textures) conditions, NMCGA performed well in estimating the effective soil hydraulic parameters even with pixel complexities contributed by various soil types and land management practices (rain-fed/irrigated). With the airborne and satellite remote sensing cases, NMCGA also performed well for estimating effective soil hydraulic properties so that when applied in forward stochastic simulation modeling it can mimic large-scale soil moisture dynamics. The results also suggest a possible scaling down of the effective soil water retention curve θ(h) at the larger satellite remote sensing pixel compared with the airborne remote sensing pixel. However, it did not generally imply that all effective soil hydraulic parameters should scale down like the soil water retention curve. The reduction of the soil hydraulic parameters was most profound in the saturated soil moisture content (θsat) as we relaxed progressively the soil hydraulic parameter search spaces in our satellite remote sensing studies. Overall, the NMCGA framework was found to be very promising in the inverse modeling of remotely sensed near-surface soil moisture for estimating the effective soil hydraulic parameters and their uncertainties at the remote sensing footprint/climate model grid.

[1] This paper reports on recent work on modeling the effect of spatial patterns in infiltration rate on the uncertainty in predicted runoff from two hypothetical catchments with distinct topographic characteristics. Specifically, in the first catchment the hillslopes are directly coupled to the channel, while in the second, the hillslopes are decoupled from the channel by floodplains. Spatial patterns of infiltration were generated as model inputs using the geostatistical method of stochastic simulation. Multiple infiltration scenarios were produced with spatial autocorrelation based on a spherical variogram model with a variable range and nugget and were used as inputs to the model COUP2D. Monte Carlo simulations were run for each condition. Results show that the uncertainty in modeled runoff due to spatially varying infiltration patterns varies with the magnitude of the runoff event through time and with different topography. Generally, increasing the range of spatial correlation of infiltration rates leads to increased connectivity in runoff pathways and an increased uncertainty in modeled runoff. Conversely, increasing the proportion of nonspatially correlated variation in infiltration decreased the uncertainty in modeled runoff to variable infiltration.

[1] Inverse solutions of the Richards equation, either for evaluating soil hydraulic parameters from experimental data or for optimizing irrigation parameters, require considerable numerical effort. We present an alternative methodology based on self-organizing maps (SOM) which was further developed in order to include multiple input-output (MIO) relationships. The resulting SOM-MIO network approximates the Richards equation and its inverse solution with an outstanding accuracy, and both tasks can be performed by the same network. No additional training is required for solving the different tasks, which represents a significant advantage over conventional networks. An application of the SOM-MIO simulating a laboratory irrigation experiment in a Monte Carlo–based framework shows a much improved computational efficiency compared to the used numerical simulation model. The high consistency of the results predicted by the artificial neural network and by the numerical model demonstrates the excellent suitability of the SOM-MIO for dealing with such kinds of stochastic simulation or for solving inverse problems.