Conditional Stochastic Simulation Research Articles

Reconstruction of High-Resolution 3D GPR Data from 2D Profiles: A Multiple-Point Statistical Approach

Ground-penetrating radar (GPR) is a popular geophysical tool for mapping the underground. High-resolution 3D GPR data carry a large amount of information and can greatly help to interpret complex subsurface geometries. However, such data require a dense collection along closely spaced parallel survey lines, which is time consuming and costly. In many cases, for the sake of efficiency, a choice is made during 3D acquisitions to use a larger spacing between the profile lines, resulting in a dense measurement spacing along the lines but a much coarser one in the across-line direction. Simple interpolation methods are then commonly used to increase the sampling before interpretation, which can work well when the subsurface structures are already well sampled in the across-line direction but can distort such structures when this is not the case. In this work, we address the latter problem using a novel multiple-point geostatistical (MPS) simulation methodology. For a considered 3D GPR dataset with reduced sampling in the across-line direction, we attempt to reconstruct a more densely spaced, high-resolution dataset using a series of 2D conditional stochastic simulations in both the along-line and across-line directions. For these simulations, the existing profile data serve as training images from which complex spatial patterns are quantified and reproduced. To reduce discontinuities in the generated 3D spatial structures caused by independent 2D simulations, the target profile being simulated is chosen randomly, and simulations in the along-line and across-line directions are performed alternately. We show the successful application of our approach to 100 MHz synthetic and 200 MHz field GPR data under multiple decimation scenarios where survey lines are regularly deleted from a dense 3D reference dataset, and the corresponding reconstructions are compared with the original data.

Conditional stochastic simulation of fluvial reservoirs using multi-scale concurrent generative adversarial networks

Conditional stochastic simulation of fluvial reservoirs using multi-scale concurrent generative adversarial networks

A Performance-Based Wind Engineering Framework for Engineered Building Systems Subject to Hurricanes

Over the past decade, significant research efforts have been dedicated to the development of performance-based wind engineering (PBWE). Notwithstanding these efforts, frameworks that integrate the damage assessment of the structural and envelope system are still lacking. In response to this need, the authors have recently proposed a PBWE framework that holistically treats envelope and structural damages through progressive multi-demand fragility models that capture the inherent coupling in the demands and damages. Similar to other PBWE methodologies, this framework is based on describing the hurricane hazard through a nominal straight and stationary wind event with constant rainfall and one-hour duration. This study aims to develop a PBWE framework based on a full description of the hurricane hazard in which the entire evolution of the storm track and time-dependent wind/rain fields is simulated. Hurricane-induced pressures impacting the building envelope are captured through the introduction of a non-stationary/-straight/-Gaussian wind pressure model. Time-dependent wind-driven rain is modeled through a computational fluid dynamics Eulerian multiphase framework with interpolation schemes for the rapid computation of wind-driven rain intensities over the building surface. Through the development of a conditional stochastic simulation algorithm, the envelope performance is efficiently characterized through probabilistic metrics associated with rare events of design interest. The framework is demonstrated through analyzing a 45-story archetype building located in Miami, FL, for which the envelope performance is estimated in terms of a suite of probabilistic damage and loss metrics. A comparative study is carried out in order to provide insights into the differences that can occur due to the use of nominal hurricane models.

A New Inference Algorithm of Dynamic Uncertain Causality Graph Based on Conditional Sampling Method for Complex Cases

Dynamic Uncertain Causality Graph(DUCG) is a recently proposed model for diagnoses of complex systems. It performs well for industry system such as nuclear power plants, chemical system and spacecrafts. However, the variable state combination explosion in some cases is still a problem that may result in inefficiency or even disability in DUCG inference. In the situation of clinical diagnoses, when a lot of intermediate causes are unknown while the downstream results are known in a DUCG graph, the combination explosion may appear during the inference computation. Monte Carlo sampling is a typical algorithm to solve this problem. However, we are facing the case that the occurrence rate of the case is very small, e.g. $10^{-20}$, which means a huge number of samplings are needed. This paper proposes a new scheme based on conditional stochastic simulation which obtains the final result from the expectation of the conditional probability in sampling loops instead of counting the sampling frequency, and thus overcomes the problem. As a result, the proposed algorithm requires much less time than the DUCG recursive inference algorithm presented earlier. Moreover, a simple analysis of convergence rate based on a designed example is given to show the advantage of the proposed method. % In addition, supports for logic gate, logic cycles, and parallelization, which exist in DUCG, are also addressed in this paper. The new algorithm reduces the time consumption a lot and performs 3 times faster than old one with 2.7% error ratio in a practical graph for Viral Hepatitis B.

A New Type of Conditioning of Stationary Fields and Its Application to the Spectral Simulation Approach in Geostatistics

This paper considers the problem of conditional stochastic simulation in geostatistics. A new type of conditioning method that generalizes the well-known two-step conditioning approach is introduced. The distinctive feature of the new method is that it solves the modeling problem for multiple stochastic fields in a general setup. A generalized kriging procedure is developed in the paper, using linear combinations of the simulated fields as input data instead of the commonly used separate fields’ values. Although the new conditioning method was developed initially in the framework of a particular approach to geostatistical simulation (the spectral method), it can be applied in many more general settings of conditional simulation of stationary stochastic fields of arbitrary dimension. The workings of the method and its applicability are illustrated with the results of several numerical experiments, including simulation on real oil field data.

Topographic uncertainty quantification for flow-like landslide models via stochastic simulations

Abstract. Digital elevation models (DEMs) representing topography are an essential input for computational models capable of simulating the run-out of flow-like landslides. Yet, DEMs are often subject to error, a fact that is mostly overlooked in landslide modeling. We address this research gap and investigate the impact of topographic uncertainty on landslide run-out models. In particular, we will describe two different approaches to account for DEM uncertainty, namely unconditional and conditional stochastic simulation methods. We investigate and discuss their feasibility, as well as whether DEM uncertainty represented by stochastic simulations critically affects landslide run-out simulations. Based upon a historic flow-like landslide event in Hong Kong, we present a series of computational scenarios to compare both methods using our modular Python-based workflow. Our results show that DEM uncertainty can significantly affect simulation-based landslide run-out analyses, depending on how well the underlying flow path is captured by the DEM, as well as on further topographic characteristics and the DEM error's variability. We further find that, in the absence of systematic bias in the DEM, a performant root-mean-square-error-based unconditional stochastic simulation yields similar results to a computationally intensive conditional stochastic simulation that takes actual DEM error values at reference locations into account. In all other cases the unconditional stochastic simulation overestimates the variability in the DEM error, which leads to an increase in the potential hazard area as well as extreme values of dynamic flow properties.

Post-processing Multiensemble Temperature and Precipitation Forecasts Through an Exchangeable Normal-Gamma Model and Its Tobit Extension

Meteorological ensembles are a collection of scenarios for future weather delivered by a meteorological center. Such ensembles form the main source of valuable information for probabilistic forecasting which aims at producing a predictive probability distribution of the quantity of interest instead of a single best guess estimate. Unfortunately, ensembles cannot generally be considered as a sample from such a predictive probability distribution without a preliminary post-processing treatment to calibrate the ensemble. Two main families of post-processing methods, either competing such as BMA or collaborative such as EMOS, can be found in the literature. This paper proposes a mixed effect model belonging to the collaborative family. The structure of the model is based on the hypothesis of invariance under the relabelling of the ensemble members. Its interesting specificities are as follows: 1) exchangeability, which contributes to parsimony, with a latent pivot variable synthesizing the essential meteorological features of the ensembles, 2) a multi-ensemble implementation, allowing to take advantage of various information so as to increase the sharpness of the forecasting procedure. Focus is cast onto Normal statistical structures, first with a direct application for temperatures, then with its Tobit extension for precipitation. Inference is performed by EM algorithms with recourse made to stochastic conditional simulations in the precipitation case. After checking its good behavior on artificial data, the proposed post-processing technique is applied to temperature and precipitation ensemble forecasts produced over five river basins managed by Hydro-Qu$\'e$bec. These ensemble forecasts were extracted from the THORPEX Interactive Grand Global Ensemble (TIGGE) database. The results indicate that post-processed ensemble are calibrated and generally sharper than the raw ensembles.

Conditional stochastic simulation model for spatial downscaling for assessing the effects of climate change on hydro-meteorological variables

The current study examines the recently proposed “bias correction and stochastic analogues” (BCSA) statistical spatial downscaling technique and attempts to improve it by conditioning coarse resolution data when generating replicates. While the BCSA method reproduces the statistical features of the observed fine data, this existing model does not replicate the observed coarse spatial pattern, and subsequently, the cross-correlation between the observed coarse data and downscaled fine data with the model cannot be preserved. To address the dissimilarity between the BCSA downscaled data and observed fine data, a new statistical spatial downscaling method, “conditional stochastic simulation with bias correction” (BCCS), which employs the conditional multivariate distribution and principal component analysis, is proposed. Gridded observed climate data of mean daily precipitation (mm/day) covering a month at 1/8° for a fine resolution and at 1° for a coarse resolution over Florida for the current and future periods were used to verify and cross-validate the proposed technique. The observed coarse and fine data cover the 50-year period from 1950 to1999, and the future RCP4.5 and RCP8.5 climate scenarios cover the 100-year period from 2000 to 2099. The verification and cross-validation results show that the proposed BCCS downscaling method serves as an effective alternative means of downscaling monthly precipitation levels to assess climate change effects on hydrological variables. The RCP4.5 and RCP8.5 GCM scenarios are successfully downscaled.

Stochastic Simulation and Management of an Over-Exploited Aquifer Using an Integrated Modeling System

A modeling system for the stochastic simulation and management of the overexploited groundwater resources of Lake Karla Basin in Central Greece is presented. The uncertainty of the hydrogeological environment which arises from the lack of the hydraulic conductivity data and aquifer’s heterogeneity necessitates the stochastic simulation of the underlying aquifer. For the conditional stochastic simulation of hydraulic conductivity, the geostatistical approach was used generating Monte-Carlo realizations. The impact of Lake Karla (or reservoir) restoration and the accompanying projects on the aquifer, is examined through various management scenarios taking into consideration this parameter uncertainty. The target of the restoration plan is to rehabilitate aquifer’s water table. This will be achieved through shutting down a great number of irrigation wells, as the irrigation needs of cultivations will be covered by the reservoir. The project with the highest environmental impact on the aquifer is the construction of 50 water supply wells at the lakeside zone of Lake Karla. Nowadays, due to the intense agricultural cultivation, the study area faces a serious water deficit problem, which has led to the over-exploitation of non-renewable groundwater and to a dramatic drawdown of aquifer’s water table. The results of the stochastic simulation and management indicates that the operation of the new water supply wells will lead, despite the operation of the new reservoir, to a further drawdown of aquifer’s water table, and will increase the effect of parameter uncertainty on hydraulic heads estimation by groundwater model.

Improved hydrograph prediction through subsurface characterization: conditional stochastic hillslope simulations

Subsurface heterogeneity is one of the largest sources of uncertainty associated with saturated hydraulic conductivity. Recent work has demonstrated that uncertainty in hydraulic conductivity can impart significant uncertainty in runoff generation processes and surface-water flow. Here, the role of site characterization in reducing hydrograph prediction bias and uncertainty is demonstrated. A fully integrated hydrologic model is used to conduct two sets of stochastic, transient simulation experiments comprising different overland flow mechanisms: Dunne and Hortonian. Conditioning hydraulic conductivity fields using values drawn from a simulated synthetic control case are shown to reduce both mean bias and variance in an ensemble of conditional hydrograph predictions when compared with the control case. The ensemble simulations show a greater reduction in uncertainty in the hydrographs for Hortonian flow. The conditional simulations predict surface ponding and surface pressure distributions with reduced mean error and reduced root mean square error compared with unconditional simulations. Uncertainty reduction in Hortonian and Dunne flow cases demonstrates different temporal signals, with more substantial reduction achieved for Hortonian flow.

Soil texture distribution simulation and risk assessment using transition probability-based geostatistics

A b s t r a c t. Three dimensional soil textural structure in a township was conditionally simulated using a transition probability-based indicator geostatistical method based on 270 soil texture samples from 27 profiles. Additionally the distribution of soil profiles lacking clay interlayers (indicating high irriga tion water and nutrient leaching risk) was analyzed using 500 realizations from the simulation. The results indicated that the simulation could predict the soil texture distribution with low uncertainties using the existing data, and the predicted soil map (0-10 cm) formed by the maximum probable soil textures also exhibited a good agreement with the legacy soil survey map. For water and nutrient leaching risk analysis, the areas lacking clay interlayer could be located; however, their distribution was still highly uncertain if based only on the existing sampling data. That means supplementary sampling in future is required for the risk assessment, and the existing study can help to optimise the sampling points and their distribution. Generally, the transition probability-based geostatistical simulation, as a stochastic conditional simulation method, exhibited its potential in soil texture spatial reproduction and related risk assessment. K e y w o r d s: soil texture, transition probability, geostatistics, conditional simulation, risk assessment

Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation

We derive a new method of conditional Karhunen-Loève (KL) expansions for stochastic coefficients in models of flow and transport in the subsurface, and in particular for the heterogeneous random permeability field. Exact values of this field are never known, and thus one must evaluate uncertainty of solutions to the flow and transport models. This is typically done by constructing independent realizations of the permeability field followed by numerical simulations of flow and transport for each realization and assembling statistical estimates of moments of desired quantities of interest. We follow the well-known framework of KL expansions and derive a new method that incorporates known values of the permeability at given locations so that the realizations of the permeability field honor this data exactly. Our method relies on projections to an appropriate subspace of random weights applied to the eigenfunctions of the covariance operator. We use the permeability realizations constructed with our stochastic simulation method in simulations of flow and transport and compare the results to those obtained when realizations are constructed with sequential Gaussian simulation (SGS). We also compare efficiency and stochastic convergence with that of stochastic collocation.

Alternative geostatistics tools applied to Morroa aquifer modeling (Sucre-Colombia)

In this paper, stochastic simulations and some multiple-point geostatistical principles are developed using a comparative methodology consisting of two phases. First, a traditional methodology based on variogram concepts called Conditional Stochastic Simulation (CSS) and more specifically the Sequential Indicator Simulation (SISIM) is applied to the aquifer modeling. Secondly, modern algorithm based on multiple-point geostatistics called SNESIM [1] and ζ Model [4] are implemented to integrate information available in the definition of Morroa aquifer facies. The simulations are realized by using algorithms constructed in references [1, 2] and S-Gems software prepared at Stanford University[3]. Results show the convenience of employing training images with soft and hard data conditioning integrated by ζ Model, and CSS for configuring hydrogeological models when barely deficient information is available.

Simulação geoestatística na caracterização espacial de óxidos de ferro em diferentes pedoformas

Os minerais da fração argila, goethita e hematita, são óxidos de ferro (Fe) indicadores pedoambientais com grande influência nos atributos físicos e químicos do solo. O conhecimento dos padrões espaciais desses óxidos auxilia a compreensão das interrelações de causa e efeito com os atributos do solo. Nesse sentido, a qualidade das estimativas espaciais produzidas pode alterar os resultados obtidos e, por consequência, as interpretações dos padrões espaciais obtidos. O presente estudo teve o objetivo de avaliar o desempenho dos métodos geoestatísticos de estimativas (KO) e simulações sequenciais gaussianas (SSG) na caracterização espacial de teores de óxidos de Fe, goethita (Gt) e hematita (Hm), em uma pedoforma côncava e outra convexa. Foram coletadas 121 amostras de solos em cada pedoforma de um Argissolo em pontos com espaçamentos regulares de 10 m. Os teores de óxidos de Fe foram obtidos por meio de difração de raios-X. Os dados foram submetidos a análises geoestatísticas por meio da modelagem do variograma e posterior interpolação por KO e SSG. A KO não refletiu a verdadeira variabilidade dos óxidos de Fe, hematita e goethita, demonstrando ser inapropriada para a caracterização espacial dos teores dos óxidos de Fe. Assim, o uso da SSG é preferível à krigagem quando a manutenção dos altos e baixos valores nas estimativas espaciais é necessária. O desempenho dos métodos geoestatísticos foi influenciado pelas pedoformas. Os mapas E-type devem ser recomendados em vez de mapas de KO para os óxidos de Fe, por serem ricos em detalhes e práticos na definição de zonas homogêneas para o manejo localizado em frente de KO, sobretudo em pedoforma côncava.

Comparison of geostatistical approaches dealing with the distribution of snow

Abstract This paper deals with a stochastic simulation. Snow cover, representing a regionalized variable, was studied and used as an input parameter for a stochastic simulation. The first step included basic statistical analysis of individual parameters of snow, e.g. snow height. In the next step, an analysis of relationships between the snow and the geomorphological parameters (altitude, slope and aspect) was conducted. The most current methods of spatial interpolation and multifactor evaluation are based on weighted regression relationships. Primarily, the use of conditional stochastic simulation was tested in a variety of software. The main aim of this investigation is to compare selected interpolation methods with stochastic simulation, based on the development of the values and on the evaluation of the incidence of extreme events. The study shall provide users with recommendations for selecting the optimal interpolation method and its application to real data.

Detecting, correcting and interpreting the biases of measured soil profile data: A case study in the Cap Bon Region (Tunisia)

The spatial sets of soil profiles that have been collected for these past 70years over the world constitute a major source of soil information that are indispensable for operational applications of Digital Soil Mapping. However, significant biases between soil profile datasets issued from different soil surveys could occur because of differences in survey methods (field data collection, laboratory analysis, etc.) or in sampling dates. A pre-processing is therefore needed to detect and remove these biases and then obtain adequate inputs for digital soil-mapping models. Such a pre-processing of legacy soil profile datasets is proposed in this study. The procedure is applied to different sets of geo-referenced legacy soil profiles available in the Cap Bon Region (Northern Tunisia) and use a “reference” spatial sampling of soil surface data that fits with modern standards of soil analysis and was recently collected.The general approach includes three steps: i) define the comparison area (i.e. the intersection of the spatial samplings), ii) compare the distributions of soil profiles properties with the references using a conditional stochastic simulation algorithm and decide whether they are different iii) if needed, apply a correction algorithm to remove the detected biases. Various implementations of this approach were undertaken and tested on theoretical and real soil sampling.

Contaminant discharge and uncertainty estimates from passive flux meter measurements

The passive flux meter (PFM) measures local cumulative water and contaminant fluxes at an observation well. Conditional stochastic simulation accounting for both spatial correlation and data skewness is introduced to interpret passive flux meter observations in terms of probability distributions of discharges across control planes (transects) of wells. An estimator of the effective number of independent data is defined and applied in the development of two significantly simpler approximate methods for estimating discharge distributions. One method uses a transformation of the t statistic to account for data skewness and the other method is closely related to the classic bootstrap. The approaches are demonstrated with passive flux meter data from two field sites (a trichloroethylene [TCE] plume at Ft. Lewis, WA, and a uranium plume at Rifle, CO). All methods require that the flux heterogeneity is sufficiently represented by the data and maximum differences in discharge quantile estimates between methods are ∼7%.

A geostatistical approach to the field-scale pattern of heterotrophic soil CO2 emission using covariates

Soil heterotrophic respiration fluxes at field scale may exhibit a substantial spatial variability. The aim of this study was (1) to elucidate the role of soil temperature and different carbon fractions on heterotrophic soil respiration and (2) to test by which of three different statistical approaches (multiple regression, external drift kriging and simulated annealing) such influences may be best represented. Chamber-based measurements of respiration fluxes were carried out within a 180 × 40 m bare soil plot. Soil temperature was measured simultaneously to the flux measurements. Further, we recorded total soil organic carbon content, apparent electrical conductivity as well as mid-infrared spectroscopy-based carbon fractions as co-variates in addition to basic soil properties like stone content and texture. A stepwise multiple linear regression procedure was used to spatially predict bare soil respiration from the co-variates. The results showed that the particulate organic matter (POM) fraction and terrain elevation were able to explain the spatial pattern of heterotrophic soil respiration (R2 = 0.45). In a second step we applied external drift kriging to determine the improvement of using co-variates in an estimation procedure in comparison to ordinary kriging. The maximum relative improvement using the co-variates in terms of the root mean square error was 16%. In a third step we applied simulated annealing to perform stochastic simulations conditioned with external drift kriging to generate more realistic spatial patterns of heterotrophic respiration at plot scale. The conditional stochastic simulations revealed a significantly improved reproduction of the probability density function, the G-statistics value increased from 0.36 to 0.92. Further, the error in the reproduction of the semivariogram of the original point data decreased by more than one order of magnitude. All this confirmed that the mapping of soil respiration patterns may be significantly improved when considering terrain elevation and spatial heterogeneity of POM in combination with a conditional stochastic simulation.

A constrained approach to multiscale stochastic simulation of chemically reacting systems

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems.

CSimMDMV: A parallel program for stochastic characterization of multi-dimensional, multi-variant, and multi-scale distribution of heterogeneous reservoir rock properties from well log data

We present CSimMDMV, a software package to simulate two- and three-dimensional, multi-variant heterogeneous reservoir models from well logs at different characteristic scales. Based on multi-variant conditional stochastic simulation, this software is able to parameterize multi-dimensional heterogeneities and to construct heterogeneous reservoir models with multiple rock properties. The models match the well logs at borehole locations, simulate heterogeneities at the level of detail provided by well logging data elsewhere in the model space, and simultaneously honor the correlations present in various rock properties. It provides a versatile environment in which a variety of geophysical experiments can be performed. This includes the estimation of petrophysical properties and the study of geophysical response to the heterogeneities. This paper describes the theoretical basis of the approach and provides the details of the parallel implementation on a Linux cluster. A case study on the assessment of natural gas hydrate amount in Northwest Territories, Canada is provided. We show that the combination of rock physics theory with multiple realizations of three-dimensional and three-variant (3D–3V) gas hydrate reservoir petrophysical models enable us to estimate the average amount of gas hydrate and associated uncertainties using Monte Carlo method.