Ensemble Smoother Research Articles

A One-Step-Ahead Ensemble Kalman Smoothing Approach Toward Estimating the Tropical Cyclone Surface-Exchange Coefficients

Abstract In this study, a one-step-ahead ensemble Kalman smoother (EnKS) is introduced for the purposes of parameter estimation. The potential for this system to provide new constraints on the surface-exchange coefficients of momentum (Cd) and enthalpy (Ck) is then explored using a series of observing system simulation experiments (OSSEs). The surface-exchange coefficients to be estimated within the data assimilation system are highly uncertain, especially at high wind speeds, and are well known to be important model parameters influencing the intensity and structure of tropical cyclones in numerical simulations. One major benefit of the developed one-step-ahead EnKS is that it allows for simultaneous updates of the rapidly evolving model state variables found in tropical cyclones using a short assimilation window and a long smoother window for the parameter updates, granting sufficient time for sensitivity to the parameters to develop. Overall, OSSEs demonstrate potential for this approach to accurately constrain parameters controlling the amplitudes of Cd and Ck, but the degree of success in recovering the truth model parameters varies throughout the tropical cyclone life cycle. During the rapid intensification phase, rapidly growing errors in the model state project onto the parameter updates and result in an overcorrection of the parameters. After the rapid intensification phase, however, the parameters are correctly adjusted back toward the truth values. Last, the relative success of parameter estimation in recovering the truth model parameter values also has sensitivity to the ensemble size and smoothing forecast length, each of which are explored. Significance Statement Large uncertainty in the surface-exchange coefficients of momentum and heat/moisture exists for hurricane conditions. This is a problem because the numerical weather model predictions of hurricane intensity and storm structure are sensitive to the surface-exchange coefficient values used. In this study we use data assimilation, or the relationships estimated between the surface-exchange coefficients and forecasted observations, to constrain uncertainty in the model’s surface-exchange coefficient values. More specifically, an approach to limit both the rapidly growing errors associated with the hurricane itself and the hurricane’s accumulated response to the surface-exchange coefficient values is presented. Overall, this approach has potential to accurately estimate the surface-exchange coefficients, but the success depends on the number of forecast realizations used and how rapidly the hurricane is changing.

Data-Driven Inversion-Free Workflow of Well Performance Forecast Under Uncertainty for Fractured Shale Gas Reservoirs

Abstract Well performance prediction and uncertainty quantification of fractured shale reservoir are crucial aspects of efficient development and economic management of unconventional oil and gas resources. The uncertainty related to the characterization of fracture topology is highly difficult to be quantified by the conventional model-based history matching procedure in practical applications. Data-space inversion (DSI) is a recently developed inversion-free and rapid forecast approach that directly samples the posterior distribution of quantities of interest using only prior model simulation results and historical data. This paper presents some comparative studies between a recent DSI implementation based on iterative ensemble smoother (DSI-IES), model-based history matching, and conventional decline curve analysis (DCA) for shale gas rate forecast. The DSI-IES method treats the shale gas production rate as target variables, which are directly predicted via conditioning to historical data. Dimensionality reduction is also used to regularize the time-series production data by low-order representation. This approach is tested on two examples with increasing complexity, e.g., a fractured vertical well and a multistage fractured horizontal well in the actual fractured Barnett shale reservoir. The results indicate that compared with the traditional history matching and DCA methods, the DSI-IES obtains high robustness with a high computational efficiency. The application of data-space inversion-free method can effectively tap the potential value directly from historical data, which provides theoretical guidance and technical support for rapid decision-making and risk assessment.

Using the (Iterative) Ensemble Kalman Smoother to Estimate the Time Correlation in Model Error

Numerical weather prediction systems contain model errors related to missing and simplified physical processes, and limited model resolution. While it has been widely recognized that these model errors need to be included in the data assimilation formulation, providing prior estimates of their spatio-temporal characteristics is a hard problem. We follow a systematic path to estimate parameters in the model error formulation, specifically related to time-correlated model errors. This problem is more difficult than the standard parameter estimation problem because the model error parameters are only visible through the random model error realisations. By concentrating on linear and nonlinear low-dimensional systems, we are able to highlight the many aspects of this problem, using state augmentation in an ensemble Kalman smoother (EnKS) and its iterative variant (IEnKS). It is not possible to estimate the model error parameters in one assimilation window because enough information has to be gathered to see the parameters through the random errors, even when every time step is observed. If only one parameter is estimated in a linear one-dimensional system the EnKS works well, but when we try to estimate two parameters the method fails. An IEnKS is able to find the correct parameter values for the linear system. For the highly nonlinear logistic map the IEnKS can get stuck in local minima, but with careful tuning of the step length in the iterations and careful transformation of the solution space the correct parameter values can be found. The main conclusion is that estimating model error parameters –even in low-dimensional systems– is a difficult problem, but via careful reformulation of the problem practical solutions can be found.

Identification of the inflow source in a foul sewer system through techniques of inverse modelling

Infiltration and illegal inflow into foul sewer systems can cause different problems such as a decrease in the performance of treatment plants, the surcharge of pipelines and more frequent overflows, which cause negative impacts on the environment. Water companies are increasingly been driven to address these problems by reducing infiltrations and identifying the sources of illegal inflows. Overall, the traditional techniques applied in these cases are expensive and time consuming and many times only partially efficient. Examples are the use of CCTV inspections, smoke tests and the installation of a large set of sensors to collect continuous data such as flow rates, water levels, temperature or concentrations of pollutants. The aim of this study is to apply two types of inverse numerical techniques to identify the source location of illegal inflows into wastewater systems based on information collected at the outlet of the drained basin and a calibrated numerical model of the sewer network. In this work, the numerical model is developed using the Storm Water Management Model (SWMM) software distributed by the Environmental Protection Agency (USA). We considered a realistic foul sewer system with known dimensional and hydrological characteristics. Synthetic case studies are set up to test the inverse approaches. Assuming a hypothetical rainfall event and an illegal inflow released at a certain location in the sewer system, the numerical model is run forward to obtain the flow hydrograph at the network outlet. This information is then used as available observations to perform the inverse modelling. The first investigated technique is an artificial neural network (ANN) of the feed-forward type. It will be trained to recover the inflow source using the simulation results of SWMM driven by a large set of rainfall events and inflows located at different positions in the sewer network. Once trained, the ANN will be used to identify the location of the inflow based the observed flood wave. The second procedure derives from Kalman filter techniques: the Ensemble Smoother with Multiple Data Assimilation (ES-MDA). Also in this case, the method, starting from the known rainfall event and the observed flow hydrograph, is used to locate the inflow source. In addition to the results of the synthetic case obtained by means of the two procedures, the field applicability to real case studies will be discussed.

Reservoir Modeling, History Matching, and Characterization with a Reservoir Graph Network Model

Summary Efficient reservoir models are more desirable for fast-paced reservoir management. Moreover, due to the complexity of flow underground, it is also essential to capture the fundamental physics for model reliability. Although they are fast, pure data-driven models frequently have issues associated with interpretability, physical consistency, and ability to forecast. On the other hand, we have used full-physics simulation models to mimic and investigate hydrocarbon systems for over several decades. However, considering its infrequent model updates related to high model complexity, it is a big challenge to manage reservoirs using full-physics models in short cycles. The objective here is to propose an approach that blends reservoir physics with data-driven models to fit in the framework of dynamic reservoir management. We propose to use a reservoir graph network (RGNet) modeling approach based on a diffusive time-of-flight (DTOF) concept to simulate reservoir behaviors. By assimilating field observation data (such as pressure and rates), an RGNet model can be used for future predictions, scenario studies, and well-control optimizations. By discretizing DTOF of a 3D system with multiple wells, RGNet simplifies the system into a graph network represented by a set of 1D grid blocks that significantly reduces the system complexity and run time. RGNet can also handle multiple flow problems with various types of physics. In this work, we propose to use two methods to develop reliable and parsimonious models scalable to large-scale systems. In addition, we propose a more robust method to assimilate pressure data. We applied the proposed approach to a synthetic and a field example. Two different history-matching algorithms, the ensemble smoother with multiple data assimilation (ES-MDA) and an adjoint-based method, are compared. While ES-MDA provides the capability for uncertainty analysis, an adjoint-based method generally requires fewer simulation runs to generate a posterior model. With the proposed methods for generating interwell connections, RGNet model calibration can be achieved without system redundancy and spurious long-distance well connectivity. Also, by using a more stable pressure-matching technique, we show that pressure data are better matched and reservoir volume is accurately characterized. RGNet provides a novel hybrid physics and data-driven reservoir modeling method to fit in closed-loop reservoir management (CLRM). As RGNet models are combined with fundamental flowing physics, the calibrated model parameters are easy to interpret and understand. An RGNet model runs with far less computational cost than required by a full-physics model, which allows it to be a more practical solution to history match, predict, and optimize real assets.

Reducing uncertainty on land subsidence modeling prediction by a sequential data-integration approach. Application to the Arlua off-shore reservoir in Italy

In recent years, the awareness about the critical importance of correctly dealing with uncertainty in numerical models is spreading over an increasing number of application fields, including geomechanics for energy resources. Sources of uncertainty are related for instance to the mathematical constitutive law that describes the deep rock behavior, the geomechanical parameters and the geological nature of the investigated field. Data assimilation techniques take advantage of the increasing availability of in-situ measurements in order to account for and reduce uncertainties in modeling outcomes. Recently, a comprehensive workflow for a stochastic analysis of land subsidence has been proposed. It combines a geomechanical model with successive steps of model diagnostic and data assimilation techniques, like χ2-test, Red Flag and Ensemble Smoother. Successive steps require increasing computational effort, but provide more accurate outcomes. The application of the workflow is repeated in time when new measurements become available so that the model is dynamically updated and the uncertainties are reduced. The objective of this study is to apply and validate the workflow on the Arlua reservoir. The outcome is the development and experimentation of a comprehensive geomechanical model that automatically integrates real measurements and progressively reduces the prediction uncertainties by a continuous training in time. The application confirms the effectiveness of the proposed integrated approach and proves its robustness and quality in a complex off-shore reservoir in Italy.

Data assimilation, sensitivity analysis and uncertainty quantification in semi-arid terminal catchments subject to long-term rainfall decline

Quantification of long-term hydrologic change in groundwater often requires the comparison of states pre- and post-change. The assessment of these changes in ungauged catchments using numerical models and other quantitative methods is particularly difficult from a conceptual point of view and due to parameter non-uniqueness and associated uncertainty of quantitative frameworks. In these contexts, the use of data assimilation, sensitivity analysis and uncertainty quantification techniques are critical to maximize the use of available data both in terms of conceptualization and quantification. This paper summarizes findings of a study undertaken in the Lake Muir-Unicup Natural Diversity Recovery Catchment (MUNDRC), a small-scale endorheic basin located in southwestern Australia that has been subject to a systematic decline in rainfall rates since 1970s. A combination of data assimilation techniques was applied to conceptual and numerical frameworks in order to understand and quantify impacts of rainfall decline on the catchment using a variety of metrics involving groundwater and lake levels, as well as fluxes between these compartments and mass balance components. Conceptualization was facilitated with the use of a novel data-driven method relating rainfall and groundwater responses running backwards in time, allowing the establishment of the likely baseline conditions prior to rainfall decline, estimation of net recharge rates and providing initial heads for the forward numerical modelling. Numerical model parameter and predictive uncertainties associated with data gaps were then minimized and quantified utilizing an Iterative Ensemble Smoother algorithm, while further refinement of conceptual model was made possible following results from sensitivity analysis, where major parameter controls on groundwater levels and other predictions of interest were quantified. The combination of methods can be considered as a template for other long-term catchment modelling studies that seek to constrain uncertainty in situations with sparse data availability.

Joint Estimation of Adsorptive Contaminant Source and Hydraulic Conductivity Using an Iterative Local Updating Ensemble Smoother with Geometric Inflation Selection

The joint estimation of groundwater contaminant source characteristics and hydraulic conductivity is of great significance for reactive contaminant transport models in heterogeneous subsurface media. The accurate determination of the sorption parameters of such contaminants is also a key prerequisite for estimating the parameters of the groundwater system. In this study, to investigate the impact of the sorption parameter field on the accuracy of hydraulic conductivity and source characteristics estimation, numerical experiments were conducted in a synthetic aquifer considering the contaminant sorption process in groundwater models with varying sorption parameter settings. Iterative local updating ensemble smoother with geometric inflation selection (ILUES-GEO) was employed to assimilate hydraulic head and contaminant concentration data to jointly estimate the contaminant source information and hydraulic conductivity in a heterogeneous aquifer. The results indicated that the ILUES-GEO successfully recovers contaminant source information simultaneously with hydraulic conductivity, and its performance improves as more accurate sorption parameters are introduced. Furthermore, the influence of the ILUES algorithm parameters and ensemble size is investigated to improve the estimation accuracy. Additionally, the characterization of contaminant sources and hydraulic conductivity fields is influenced by the number and locations of measurements. This study can help to understand the significance of sorption parameter setting for the joint estimation of reactive contaminant source and hydraulic parameters.

Estimation of hydraulic parameters in a heterogeneous low‐lying farmland near Venice

AbstractEstimating the hydraulic properties of the vadose zone is essential to understand soil‐water dynamics and achieving appropriate water management in agricultural lands. Inverse modelling methods are commonly used to estimate hydraulic properties from field observations. Unlike the extensively applied local search methodologies, data assimilation techniques can fully account for multiple uncertainties and are becoming a widely used tool for estimating hydraulic parameters. However, only few applications on real field tests are available. The main objective of this study was to estimate the van Genuchten‐Mualem (VGM) parameters and the saturated hydraulic conductivity () of a heterogeneous low‐lying farmland at the margin of the Venice Lagoon, Italy, characterized by high peat content, sandy drifts, and a very shallow water table. To this end, two methods were tested, that is, the Ensemble Smoother (ES) and the Levenberg–Marquardt (LM) algorithm associated with hydrological modelling performed with Hydrus‐1D. Volumetric water content (VWC) observations were collected at three monitoring sites from May to September 2011. Results on parameters highlighted that the ES technique effectively reduced the uncertainty of and , but it was less effective on and . The results on VWC showed that the ES efficiency decreased with the increasing non‐linearity of the system (e.g., higher sand content) and when the variability of the experimental data was lower (e.g., deepest soil layers where saturation remained permanently close to 1). Both LM and ES allowed to reproduce the VWC observations in the calibration and validation phases, with the former and the latter performing better in the case of sandy and peat soils, respectively. As concerns the method applicability, the ES was less time‐demanding as it efficiently updated all the parameters at once and was less dependent on the user choices. Finally, the paper points out the importance of previous knowledge of the VGM parameters (e.g., from lab hydraulic analyses) in defining the constraints for the optimization.

Comparison of simulation-based algorithms for parameter estimation and state reconstruction in nonlinear state-space models

<p style='text-indent:20px;'>This study aims at comparing simulation-based approaches for estimating both the state and unknown parameters in nonlinear state-space models. Numerical results on different toy models show that the combination of a Conditional Particle Filter (CPF) with Backward Simulation (BS) smoother and a Stochastic Expectation-Maximization (SEM) algorithm is a promising approach. The CPFBS smoother run with a small number of particles allows to explore efficiently the state-space and simulate relevant trajectories of the state conditionally to the observations. When combined with the SEM algorithm, this algorithm provides accurate estimates of the state and the parameters in nonlinear models, where the application of EM algorithms combined with a standard particle smoother or an ensemble Kalman smoother is limited.</p>

Inverse estimation of multiple contaminant sources in three-dimensional heterogeneous aquifers with variable-density flows

Groundwater contamination is an exacerbating global issue that severely threatens human health. Subsurface remediation thus has gained increased interest in recent years. To effectively remediate subsurface contaminated sites, one needs to identify the locations of contaminant sources and characterize contaminant spreading. Groundwater contamination is often driven by multiple contaminant sources, making source identification problems challenging. Further, when the densities of dissolved contaminants and ambient groundwater differ, the resultant variable-density flows add complexity to the task of source identification. However, most previous studies are limited to a single source identification in a two-dimensional aquifer. This study presents a novel inversion method based on ensemble smoothing that identifies the locations of multiple contaminant sources in three-dimensional heterogeneous aquifer systems. A new covariance localization algorithm based on a clustering method is integrated into the inversion method, which improves the accuracy of multi-source identification. Using the proposed inversion framework, we successfully estimate the locations of multiple contaminant sources and three-dimensional permeability fields utilizing pressure and concentration data from monitoring wells. Further, we investigate and elucidate the effects of aquifer heterogeneity and variable-density flows on multiple source identification. We find that variable-density flow increases the data information contents and thus improves the inversion accuracy. This is the first-time demonstration of the effects of variable-density flow on the inversion accuracy of multi-source identification in three-dimensional heterogeneous aquifer systems.

Groundwater contamination source identification and high-dimensional parameter inversion using residual dense convolutional neural network

Data assimilation for high-dimensional parameter joint inversion of multiple time-varying source strength and hydraulic conductivity fields can be computationally intensive as a large number of forward model runs are usually required. In this study, a deep neural network-based surrogate is proposed to replace the forward model in the data assimilation process to efficiently achieve high-dimensional parameter inversion. The deep convolutional encoding-decoding network architecture is used to leverage the advantages of the convolutional network in processing image-like data, where the high-dimensional input and output fields of the forward model are expressed as images. The encoding network extracts the main features of the multiple time-varying source input image and high-dimensional hydraulic conductivity fields, and the decoding network refines the extracted features to generate the output hydraulic head and contaminant concentration fields. The Residual Dense Convolutional Neural Network (RDCNN) is proposed by combining residual learning with a densely-connected convolutional neural network to solve the image regression problem for surrogate construction. Iterative local updating ensemble smoother (ILUES) is utilized to assimilate hydraulic head and contaminant concentration data to inverse high-dimensional parameters. The proposed method is evaluated by jointly inversing the high-dimensional hydraulic conductivity and source parameters for a synthetic multiple-source contaminated aquifer. The results indicate that compared to the surrogate constructed by Dense Convolutional Neural Network (DCNN) without addressing residual learning, the RDCNN surrogate captures the model input-output relationship better with relatively high training efficiency. The RDCNN surrogate-coupled ILUES achieves state-of-the-art performance in terms of inversion accuracy of 9 pollution source parameters and 255 hydraulic conductivity field parameters and computational efficiency in comparison to the ILUES based on the forward model.

The Multiple Snow Data Assimilation System (MuSA v1.0)

Abstract. Accurate knowledge of the seasonal snow distribution is vital in several domains including ecology, water resources management, and tourism. Current spaceborne sensors provide a useful but incomplete description of the snowpack. Many studies suggest that the assimilation of remotely sensed products in physically based snowpack models is a promising path forward to estimate the spatial distribution of snow water equivalent (SWE). However, to date there is no standalone, open-source, community-driven project dedicated to snow data assimilation, which makes it difficult to compare existing algorithms and fragments development efforts. Here we introduce a new data assimilation toolbox, the Multiple Snow Data Assimilation System (MuSA), to help fill this gap. MuSA was developed to fuse remotely sensed information that is available at different timescales with the energy and mass balance Flexible Snow Model (FSM2). MuSA was designed to be user-friendly and scalable. It enables assimilation of different state variables such as the snow depth, SWE, snow surface temperature, binary or fractional snow-covered area, and snow albedo and could be easily upgraded to assimilate other variables such as liquid water content or snow density in the future. MuSA allows the joint assimilation of an arbitrary number of these variables, through the generation of an ensemble of FSM2 simulations. The characteristics of the ensemble (i.e., the number of particles and their prior covariance) may be controlled by the user, and it is generated by perturbing the meteorological forcing of FSM2. The observational variables may be assimilated using different algorithms including particle filters and smoothers as well as ensemble Kalman filters and smoothers along with their iterative variants. We demonstrate the wide capabilities of MuSA through two snow data assimilation experiments. First, 5 m resolution snow depth maps derived from drone surveys are assimilated in a distributed fashion in the Izas catchment (central Pyrenees). Furthermore, we conducted a joint-assimilation experiment, fusing MODIS land surface temperature and fractional snow-covered area with FSM2 in a single-cell experiment. In light of these experiments, we discuss the pros and cons of the assimilation algorithms, including their computational cost.

Inferring surface energy fluxes using drone data assimilation in large eddy simulations

Abstract. Spatially representative estimates of surface energy exchange from field measurements are required for improving and validating Earth system models and satellite remote sensing algorithms. The scarcity of flux measurements can limit understanding of ecohydrological responses to climate warming, especially in remote regions with limited infrastructure. Direct field measurements often apply the eddy covariance method on stationary towers, but recently, drone-based measurements of temperature, humidity, and wind speed have been suggested as a viable alternative to quantify the turbulent fluxes of sensible (H) and latent heat (LE). A data assimilation framework to infer uncertainty-aware surface flux estimates from sparse and noisy drone-based observations is developed and tested using a turbulence-resolving large eddy simulation (LES) as a forward model to connect surface fluxes to drone observations. The proposed framework explicitly represents the sequential collection of drone data, accounts for sensor noise, includes uncertainty in boundary and initial conditions, and jointly estimates the posterior distribution of a multivariate parameter space. Assuming typical flight times and observational errors of light-weight, multi-rotor drone systems, we first evaluate the information gain and performance of different ensemble-based data assimilation schemes in experiments with synthetically generated observations. It is shown that an iterative ensemble smoother outperforms both the non-iterative ensemble smoother and the particle batch smoother in the given problem, yielding well-calibrated posterior uncertainty with continuous ranked probability scores of 12 W m−2 for both H and LE, with standard deviations of 37 W m−2 (H) and 46 W m−2 (LE) for a 12 min vertical step profile by a single drone. Increasing flight times, using observations from multiple drones, and further narrowing the prior distributions of the initial conditions are viable for reducing the posterior spread. Sampling strategies prioritizing space–time exploration without temporal averaging, instead of hovering at fixed locations while averaging, enhance the non-linearities in the forward model and can lead to biased flux results with ensemble-based assimilation schemes. In a set of 18 real-world field experiments at two wetland sites in Norway, drone data assimilation estimates agree with independent eddy covariance estimates, with root mean square error values of 37 W m−2 (H), 52 W m−2 (LE), and 58 W m−2 (H+LE) and correlation coefficients of 0.90 (H), 0.40 (LE), and 0.83 (H+LE). While this comparison uses the simplifying assumptions of flux homogeneity, stationarity, and flat terrain, it is emphasized that the drone data assimilation framework is not confined to these assumptions and can thus readily be extended to more complex cases and other scalar fluxes, such as for trace gases in future studies.

Model structure and ensemble size: Implications for predictions of groundwater age

This paper examines the influence of simplified vertical discretization using 50- to four- layer models and ensemble size on history matching and predictions of groundwater age for a national scale model of New Zealand (approximately 265,000 km2). A reproducible workflow using a combination of opensource tools and custom python scripts is used to generate three models that use the same model domain and underlying data with only the vertical discretization changing between the models. The iterative ensemble smoother approach is used for history matching each model to the same synthetic dataset. The results show that: 1) the ensemble based mean objective function is not a good indicator of model predictive ability, 2) predictive failure from model structural errors in the simplified models are compounded by history matching, especially when small (<100 member) ensembles are used, 3) predictive failure rates increase with iteration, 4) predictive failure rates for the simplified model reach 30–65% using 50-member ensembles, but stabilize at relatively low values (<10%) using the 300 member ensemble, 5) small (50 member) ensembles contribute to predictive failure of 22–30% after six iterations even in structurally “perfect” models, 6) correlation-based localization methods can help reduce prediction failure associated with small ensembles by up to 45%, 7) the deleterious effects of model simplification and ensemble size are problem specific. Systematic investigation of these issues is an important part of the model design, and this investigation process benefits greatly from a scripted, reproducible workflow using flexible, opensource tools.

Degeneracy-Free Particle Filter: Ensemble Kalman Smoother Multiple Distribution Estimation Filter

We propose the ensemble Kalman smoother multiple distribution estimation filter (EnKS-MDEF) for nonlinear state estimation problems. The EnKS-MDEF is an example of the multiple distribution estimation filter (MDEF), which is a particle filter (PF) that estimates the filtered state probability density function (pdf) using multiple conditional state pdfs. The one step behind (OSB) smoothed state pdf used for calculating the filtered state pdf of the MDEF is approximated by the ensemble Kalman smoother (EnKS). Then, the particle weights for the EnKS-MDEF remain equal during the filter execution, which indicates that the EnKS-MDEF is a degeneracy-free PF. Since, the MDEF and the EnKS-MDEF, both estimate the OSB smoothed state pdf prior to calculating the filtered state pdf, these filters provide a simultaneous estimation of filtered and OSB smoothed states. The examples of the EnKS-MDEF are the EnKS-extended and unscented Kalman multiple distribution estimation filters, and their filtering and OSB smoothing performances are evaluated and compared with those for the representative filters and smoothers using a benchmark simulation problems.

Groundwater contaminant source identification based on an ensemble learning search framework associated with an auto xgboost surrogate

Groundwater contaminant source identification (GCSI) is commonly accompanied by search process which tweaks the unknown contaminant source information to match the simulation model outputs with the measurements. When solving identification task, search accuracy and time cost have always been challenges that must be tackled. In the present study, a novel ensemble learning search framework associated with auto extreme gradient boosting tree (xgboost) was proposed to solve GCSI. In particular, auto xgboost was employed to reduce the calculation burden caused by repeatedly running simulation model. To promote search efficiency, boosting strategy (BOS) was employed to sequentially concatenate iterative ensemble smoother, differential evolution particle filter (DEPF), and swarm evolution algorithm. The identification results indicated that: 1. Auto xgboost could substitute a numerical simulation model with desired accuracy and expeditious running speed. 2. BOS could achieve better search accuracy, but with the sacrifice of infinitesimal calculated time cost, when compared with bagging strategy.

Reconstructing the release history of a contaminant source with different precision via the ensemble smoother with multiple data assimilation

Identifying a contaminant time-varying release history is an ill-posed problem but crucial for groundwater contamination issues. A precise inversed release history offers a promising estimation of contaminant movement and is of great importance for environmental monitoring and further management. In this paper, a recent emerging data assimilation method, the ensemble smoother with multiple data assimilation (ES-MDA) is employed to handle this conundrum. The study starts with some synthetic cases in which several factors are analyzed, such as the observation data frequency, covariance inflation schemes, iteration numbers used in the ES-MDA for the purpose of identifying a time-varying contaminant injection event with different precision. The results show that the ES-MDA performs well in recovering the release history when the injection is discretized into 50 or 100-time steps but encounters fluctuation problems in the cases with 300-time steps. Further comparison reveals that the observation data frequency is a very influential factor, while the number of iterations or the kind of covariance inflation used has a lesser effect. Nevertheless, this is a first test in a non-synthetic environment, in which the ES-MDA has proven its ability to recover the release history in two close-to-reality sandbox experiments. The outcome shows that the ES-MDA with Rafiee’s inflation scheme has the ability to capture the main pattern of the release history. But in order to move one more step to field cases, a more detailed description of uncertainties or elaborated parameterization of the time functions is paramount.

History matching of petroleum reservoirs using deep neural networks

• This paper proposes an approach based on ES-MDA coupled with ConvBiGRU-VAE. • ConvBiGRU-VAE is used to generate uncertain parameters. • The proposed approach is validated on PUNQ-S3 and Volve reservoir models. • ConvBiGRU-VAE gave overall enhanced performance in terms of production prediction. This paper proposes a novel approach based on deep learning to improve oil reservoirs' history matching problem. Deep autoencoders are widely used to solve the oil industry problems. However, as the input data increases, the autoencoder parameters increase exponentially. Our model is based on a convolutional variational autoencoder using AlexNet and bi-directional gated recurrent units. It parameterizes large-scale oilfield reservoirs. The proposed model is integrated into an ensemble smoother with multiple data assimilation to perform history matching. The proposed approach is validated on two reservoir models: PUNQ-S3 and Volve field. The root mean squared error, R 2 , and mean absolute error are calculated to verify the effectiveness of the proposed approach. The results show that the proposed model can effectively study the complex geological features of oil fields and be used in expert systems for reservoir modeling.

Identification of hydraulic conductivity field of a karst aquifer by using transition probability geostatistics and discrete cosine transform with an ensemble method

AbstractKnowledge of the spatial distribution characteristics of hydraulic parameters is essential for the management and protection of karst groundwater resources. In this study, we propose a workflow integrating the transition probability geostatistics (T‐PROGS) and the discrete cosine transform (DCT) with the ensemble smoother with multiple data assimilation (ES‐MDA) method to map the hydraulic conductivity of karst aquifers that usually follow a multimodal distribution. The priori parameter ensemble is constructed from the T‐PROGS and transformed into an approximately Gaussian distributed coefficient field containing critical spatial structural features about the aquifer using DCT. The ES‐MDA method is employed to update the DCT coefficients by assimilating the measurements. In addition, a postprocessing process based on cumulative distribution function (CDF) mapping is used to address the problem of parameters gradually tending to a Gaussian distribution after updating using the ES‐MDA and the inappropriate selection of initial parameter values. In practice, the limited amount of available data makes it difficult to fully capture the spatial distribution of the parameters in the initial ensemble of a single realization. Therefore, we suggest a new strategy for structuring the initial ensemble by mixing samples from multiple realizations. We then apply the proposed approach to four single realization models and a combined multiple realizations model in a field hydraulic tomography investigation of a real karst aquifer. The computed results show that this method can effectively identify the characteristics of the spatial distribution of hydraulic conductivity in karst aquifers. Compared with an individual realization model, the uncertainty of the hydraulic conductivity estimated by the combined multiple realizations model is significantly reduced. Therefore, including more uncertainty of the aquifer in the initial ensemble is beneficial to improve the accuracy of the parameter estimation.