Local spatial regression models: a comparative analysis on soil contamination

Spatial data analysis focuses on both attribute and locational information. Local analyses deal with differences across space whereas global analyses deal with similarities across space. This paper addresses an experimental comparative study to analyse the spatial data by some weighted local regression models. Five local regression models have been developed and their estimation capacities have been evaluated. The experimental studies showed that integration of objective function based fuzzy clustering to geostatistics provides some accurate and general models structures. In particular, the estimation performance of the model established by combining the extended fuzzy clustering algorithm and standard regional dependence function is higher than that of the other regression models. Finally, it could be suggested that the hybrid regression models developed by combining soft computing and geostatistics could be used in spatial data analysis.     

地震动强度参数估计的可解释性与不确定度机器学习模型

准确预测地震动强度参数(峰值加速度PGA、峰值速度PGV等)对于震后应急和地震危险性概率分析至关重要.作为地震动强度参数预测的新手段, 机器学习算法具有优势, 但也存在可解释性差和难给出预测结果不确定度的问题.本文提出采用自然梯度提升(NGBoost)算法在预测结果的同时提供其不确定度, 并结合SHAP值解释机器学习模型.基于NGA-WEST2强震动数据库, 本文训练出了适合预测活跃构造区地壳地震的PGA和PGV概率密度分布的机器学习模型.测试集数据PGA和PGV的预测值与真实值的相关系数可达0.972和0.984, 并可给出预测结果的合理概率密度分布.通过SHAP值, 我们从数据角度弄清了各输入特征(矩震级M_W、Joyner-Boore断层距R_jb、地下30 m平均S波速度V_S30、滑动角Rake、断层倾角Dip、断层顶部深度Z_TOR和V_S达到2.5 km·s^-1时的深度Z_2.5)对机器学习模型预测结果的影响机理.SHAP值显示, 基于NGBoost算法的机器学习模型的预测方式基本与物理原理相符, 说明了机器学习模型的合理性.SHAP值还揭示出一些以往研究忽视的现象: (1)对于活跃构造区地壳地震, 破裂深度较浅(Z_TOR＜~5 km)时, Z_TOR的SHAP值低于破裂深度较深(Z_TOR＞~5 km)时的值, 表明浅部破裂可能主要受速度强化控制, 地震动强度较弱.并且Z_TOR的SHAP值随Z_TOR值增大而减小, 表明地震动强度可能还受破裂深度变化引起的几何衰减变化影响; (2)破裂深度较深时, Z_TOR的SHAP值随Z_TOR值增大而增大, 表明深部破裂的地震动强度可能受和破裂深度变化相关的应力降或品质因子Q的变化影响; (3)Z_2.5较小(Z_2.5＜~1 km)时, Z_2.5的SHAP值的变化规律对于PGA和PGV预测是相反的, 表明加速度和速度频率不同, 受浅层沉积物厚度变化引起的共振频率变化影响不同.

     

Non-linear fuzzy-set based uncertainty propagation for improved DO prediction using multiple-linear regression

In this paper, a new non-linear fuzzy-set based methodology is proposed to characterize and propagate uncertainty through a multiple linear regression (MLR) model to predict DO using flow and water temperature as the regressors. The output is depicted as probabilistic rather than deterministic and is used to calculate the risk of low DO concentration. To demonstrate the new method, data from the Bow River in Calgary, Alberta from 2006 to 2008 are used. Low DO concentration has been occasionally observed in the river and correctly predicting, and quantifying the associated uncertainty and variability of DO is of interest to the City of Calgary. Flow, temperature and DO data were used to construct five MLR models, using different combinations of linear and non-linear fuzzy membership functions. The results show that non-linear representation of variance is superior to the linear approach based on model performance. Normal and Gumbel based membership functions produced the best results. The outputs from two non-linear fuzzy membership models were used to calculate risk of low DO. The predicted risk was between 3.9 and 4.9 %. This is an improvement over the traditional method, which can not indicate a risk of low DO for the same time period. This study demonstrates that water resource managers can adequately use MLR models to predict the risk of low DO using abiotic factors.     

Simultaneous quantification of epistemic and aleatory uncertainty in GMPEs using Gaussian process regression

This paper presents a Bayesian non-parametric method based on Gaussian Process (GP) regression to derive ground-motion models for peak-ground parameters and response spectral ordinates. Due to its non-parametric nature there is no need to specify any fixed functional form as in parametric regression models. A GP defines a distribution over functions, which implicitly expresses the uncertainty over the underlying data generating process. An advantage of GP regression is that it is possible to capture the whole uncertainty involved in ground-motion modeling, both in terms of aleatory variability as well as epistemic uncertainty associated with the underlying functional form and data coverage. The distribution over functions is updated in a Bayesian way by computing the posterior distribution of the GP after observing ground-motion data, which in turn can be used to make predictions. The proposed GP regression models is evaluated on a subset of the RESORCE data base for the SIGMA project. The experiments show that GP models have a better generalization error than a simple parametric regression model. A visual assessment of different scenarios demonstrates that the inferred GP models are physically plausible.     

Multiscale structure of UXO site characterization: spatial estimation and uncertainty quantification

Unexploded ordnance (UXO) site characterization must consider both how the contamination is generated and how we observe that contamination. Within the generation and observation processes, dependence structures can be exploited at multiple scales. We describe a conceptual site characterization process, the dependence structures available at several scales, and consider their statistical estimation aspects. It is evident that most of the statistical methods that are needed to address the estimation problems are known but their application-specific implementation may not be available. We demonstrate estimation at one scale and propose a representation for site contamination intensity that takes full account of uncertainty, is flexible enough to answer regulatory requirements, and is a practical tool for managing detailed spatial site characterization and remediation. The representation is based on point process spatial estimation methods that require modern computational resources for practical application. These methods have provisions for including prior and covariate information.     

Probabilistic and ensemble simulation approaches for input uncertainty quantification of artificial neural network hydrological models

Artificial neural network (ANN) has been demonstrated to be a promising modelling tool for the improved prediction/forecasting of hydrological variables. However, the quantification of uncertainty in ANN is a major issue, as high uncertainty would hinder the reliable application of these models. While several sources have been ascribed, the quantification of input uncertainty in ANN has received little attention. The reason is that each measured input quantity is likely to vary uniquely, which prevents quantification of a reliable prediction uncertainty. In this paper, an optimization method, which integrates probabilistic and ensemble simulation approaches, is proposed for the quantification of input uncertainty of ANN models. The proposed approach is demonstrated through rainfall-runoff modelling for the Leaf River watershed, USA. The results suggest that ignoring explicit quantification of input uncertainty leads to under/over estimation of model prediction uncertainty. It also facilitates identification of appropriate model parameters for better characterizing the hydrological processes.     

Quantifying the epistemic uncertainty in ground motion models and prediction

The aim of this paper is to compute the ground-motion prediction equation (GMPE)-specific components of epistemic uncertainty, so that they may be better understood and the model standard deviation potentially reduced. The reduced estimate of the model standard deviation may also be more representative of the true aleatory uncertainty in the ground-motion predictions.The epistemic uncertainty due to input variable uncertainty and uncertainty in the estimation of the GMPE coefficients are examined. An enhanced methodology is presented that may be used to analyse their impacts on GMPEs and GMPE predictions. The impacts of accounting for the input variable uncertainty in GMPEs are demonstrated using example values from the literature and by applying the methodology to the GMPE for Arias Intensity. This uncertainty is found to have a significant effect on the estimated coefficients of the model and a small effect on the value of the model standard deviation.The impacts of uncertainty in the GMPE coefficients are demonstrated by quantifying the uncertainty in hazard maps. This paper provides a consistent approach to quantifying the epistemic uncertainty in hazard maps using Monte Carlo simulations and a logic tree framework. The ability to quantify this component of epistemic uncertainty offers significant enhancements over methods currently used in the creation of hazard maps as it is both theoretically consistent and can be used for any magnitude–distance scenario.     

Efficient uncertainty quantification techniques in inverse problems for Richards’ equation using coarse-scale simulation models

This paper concerns efficient uncertainty quantification techniques in inverse problems for Richards’ equation which use coarse-scale simulation models. We consider the problem of determining saturated hydraulic conductivity fields conditioned to some integrated response. We use a stochastic parameterization of the saturated hydraulic conductivity and sample using Markov chain Monte Carlo methods (MCMC). The main advantage of the method presented in this paper is the use of multiscale methods within an MCMC method based on Langevin diffusion. Additionally, we discuss techniques to combine multiscale methods with stochastic solution techniques, specifically sparse grid collocation methods. We show that the proposed algorithms dramatically reduce the computational cost associated with traditional Langevin MCMC methods while providing similar sampling performance.     

基于数据分布域变换与贝叶斯神经网络的渗透率预测及不确定性估计

渗透率是储层评价和油气藏开发的关键参数.传统测井方法与常规机器学习方法估算的渗透率都是固定值.但由于测井数据本身存在噪声, 渗透率的预测结果可能受到噪声的影响出现测量性的随机误差(即任意不确定性); 同时, 当测试数据与训练数据存在差异时, 机器学习模型在预测渗透率时可能出现模型参数的不确定性(即认知不确定性).为实现渗透率的准确预测并量化两种不确定性对结果的影响, 本文提出基于数据分布域变换和贝叶斯神经网络同时实现渗透率预测及其不确定性的估计.提出方法主要包括两个部分: 一部分是不同域数据分布的相互转换, 另一部分是基于贝叶斯理论的神经网络渗透率建模预测和不确定性估计.由于贝叶斯神经网络存在数据分布的假设, 当标签的概率分布与网络的分布保持一致时, 贝叶斯神经网络可以更好的学习到数据之间的关系.因此通过寻找一个函数将一个原始域的渗透率标签转换为目标域的与渗透率有关的变量(我们称为目标域渗透率), 使得该变量符合贝叶斯神经网络的分布假设.我们使用贝叶斯神经网络预测目标域渗透率以及任意不确定性和认知不确定性.随后, 通过分布域的逆变换, 我们将目标域渗透率还原回原始域渗透率.应用本文方法到某油田的18口井的测井数据中, 使用16口井的数据进行训练, 2口井进行测试.测试井的预测渗透率与真实渗透率基本一致.同时, 任意不确定性的预测结果提供了渗透率预测值受到的测井数据噪声影响的位置.认知不确定的预测结果说明数据量少的位置具有更高的认知不确定性.我们提出的这一流程不仅显示了在储层表征方面的巨大潜力, 同时可以降低测井解释时的风险.

     

Methods used for quantifying the prediction uncertainty of artificial neural network based hydrologic models

Application of artificial neural network (ANN) models has been reported to solve variety of water resources and environmental related problems including prediction, forecasting and classification, over the last two decades. Though numerous research studies have witnessed the improved estimate of ANN models, the practical applications are sometimes limited. The black box nature of ANN models and their parameters hardly convey the physical meaning of catchment characteristics, which result in lack of transparency. In addition, it is perceived that the point prediction provided by ANN models does not explain any information about the prediction uncertainty, which reduce the reliability. Thus, there is an increasing consensus among researchers for developing methods to quantify the uncertainty of ANN models, and a comprehensive evaluation of uncertainty methods applied in ANN models is an emerging field that calls for further improvements. In this paper, methods used for quantifying the prediction uncertainty of ANN based hydrologic models are reviewed based on the research articles published from the year 2002 to 2015, which focused on modeling streamflow forecast/prediction. While the flood forecasting along with uncertainty quantification has been frequently reported in applications other than ANN in the literature, the uncertainty quantification in ANN model is a recent progress in the field, emerged from the year 2002. Based on the review, it is found that methods for best way of incorporating various aspects of uncertainty in ANN modeling require further investigation. Though model inputs, parameters and structure uncertainty are mainly considered as the source of uncertainty, information of their mutual interaction is still lacking while estimating the total prediction uncertainty. The network topology including number of layers, nodes, activation function and training algorithm has often been optimized for the model accuracy, however not in terms of model uncertainty. Finally, the effective use of various uncertainty evaluation indices should be encouraged for the meaningful quantification of uncertainty. This review article also discusses the effectiveness and drawbacks of each method and suggests recommendations for further improvement.     

Accounting for the uncertainty in the local mean in spatial prediction by Bayesian Maximum Entropy

Bayesian Maximum Entropy (BME) has been successfully used in geostatistics to calculate predictions of spatial variables given some general knowledge base and sets of hard (precise) and soft (imprecise) data. This general knowledge base commonly consists of the means at each of the locations considered in the analysis, and the covariances between these locations. When the means are not known, the standard practice is to estimate them from the data; this is done by either generalized least squares or maximum likelihood. The BME prediction then treats these estimates as the general knowledge means, and ignores their uncertainty. In this paper we develop a prediction that is based on the BME method that can be used when the general knowledge consists of the covariance model only. This prediction incorporates the uncertainty in the estimated local mean. We show that in some special cases our prediction is equal to results from classical geostatistics. We investigate the differences between our approach and the standard approach for predicting in this common practical situation.     

Improving reservoir thickness prediction using seismic attributes and attributes fusion

Usage of any single attribute would introduce unacceptable uncertainty due to limited reservoir thickness and distribution, and strong lateral variations in lithological traps. In this paper, a wide range of prestack and post-stack seismic attributes is utilized to identify a range of properties of turbidity channel sandstone reservoir in Block L118 of J Oilfield, China. In order to better characterize the turbidity channel and lower the uncertainty, we applied multi-attribute fusion to weight a variety of seismic attributes in terms of their relevance to the identification of turbidity channel reservoir. Turbidity channel boundary is clearly present in the new attribute and the reservoir thickness prediction is improved. Additionally, fluid potential of reservoir was predicted using this fused attribute with a high value anomaly indicating high fluid potential. The multi-attribute fusion is a valid approach for the fine prediction of lithologic reservoirs, reducing the risks typically associated with exploration.     

Parametric uncertainty assessment of hydrological models: coupling UNEEC-P and a fuzzy general regression neural network

Due to the complicated nature of environmental processes, consideration of uncertainty is an important part of environmental modelling. In this paper, a new variant of the machine learning-based method for residual estimation and parametric model uncertainty is presented. This method is based on the UNEEC-P (UNcertainty Estimation based on local Errors and Clustering – Parameter) method, but instead of multilayer perceptron uses a “fuzzified” version of the general regression neural network (GRNN). Two hydrological models are chosen and the proposed method is used to evaluate their parametric uncertainty. The approach can be classified as a hybrid uncertainty estimation method, and is compared to the group method of data handling (GMDH) and ordinary kriging with linear external drift (OKLED) methods. It is shown that, in terms of inherent complexity, measured by Akaike information criterion (AIC), the proposed fuzzy GRNN method has advantages over other techniques, while its accuracy is comparable. Statistical metrics on verification datasets demonstrate the capability and appropriate efficiency of the proposed method to estimate the uncertainty of environmental models.     

Application of newly developed ensemble machine learning models for daily suspended sediment load prediction and related uncertainty analysis

ABSTRACT

Ensemble machine learning models have been widely used in hydro-systems modeling as robust prediction tools that combine multiple decision trees. In this study, three newly developed ensemble machine learning models, namely gradient boost regression (GBR), AdaBoost regression (ABR) and random forest regression (RFR) are proposed for prediction of suspended sediment load (SSL), and their prediction performance and related uncertainty are assessed. The SSL of the Mississippi River, which is one of the major world rivers and is significantly affected by sedimentation, is predicted based on daily values of river discharge (Q) and suspended sediment concentration (SSC). Based on performance metrics and visualization, the RFR model shows a slight lead in prediction performance. The uncertainty analysis also indicates that the input variable combination has more impact on the obtained predictions than the model structure selection.     

Addressing snow model uncertainty for hydrologic prediction

Streamflow forecasting methods are moving towards probabilistic approaches that quantify the uncertainty associated with the various sources of error in the forecasting process. Multi-model averaging methods which try to address modeling deficiencies by considering multiple models are gaining much popularity. We have applied the Bayesian Model Averaging method to an ensemble of twelve snow models that vary in their heat and melt algorithms, parameterization, and/or albedo estimation method. Three of the models use the temperature-based heat and melt routines of the SNOW17 snow accumulation and ablation model. Nine models use heat and melt routines that are based on a simplified energy balance approach, and are varied by using three different albedo estimation schemes. Finally, different parameter sets were identified through automatic calibration with three objective functions. All models use the snow accumulation, liquid water transport, and ground surface heat exchange processes of the SNOW17. The resulting twelve snow models were combined using Bayesian Model Averaging (BMA). The individual models, BMA predictive mean, and BMA predictive variance were evaluated for six SNOTEL sites in the western U.S. The models performed best and the BMA variance was lowest at the colder sites with high winter precipitation and little mid-winter melting. An individual snow model would often outperform the BMA predictive mean. However, observed snow water equivalent (SWE) was captured within the 95% confidence intervals of the BMA variance on average 80% of the time at all sites. Results are promising that consideration of multiple snow structures would provide useful uncertainty information for probabilistic hydrologic prediction.     

Development of spatial regression models for predicting summer river temperatures from landscape characteristics: Implications for land and fisheries management

There is increasing demand for models that can accurately predict river temperature at the large spatial scales appropriate to river management. This paper combined summer water temperature data from a strategically designed, quality controlled network of 25 sites, with recently developed flexible spatial regression models, to understand and predict river temperature across a 3,000 km² river catchment. Minimum, mean and maximum temperatures were modelled as a function of nine potential landscape covariates that represented proxies for heat and water exchange processes. Generalised additive models were used to allow for flexible responses. Spatial structure in the river network data (local spatial variation) was accounted for by including river network smoothers. Minimum and mean temperatures decreased with increasing elevation, riparian woodland and channel gradient. Maximum temperatures increased with channel width. There was greater between‐river and between‐reach variability in all temperature metrics in lower‐order rivers indicating that increased monitoring effort should be focussed at these smaller scales. The combination of strategic network design and recently developed spatial statistical approaches employed in this study have not been used in previous studies of river temperature. The resulting catchment scale temperature models provide a valuable quantitative tool for understanding and predicting river temperature variability at the catchment scales relevant to land use planning and fisheries management and provide a template for future studies.     

地震属性优化及其在储层预测中的应用

利用地震资料属性信息预测油气储层已越来越受到石油地球物理工作者的广泛重视。但如何优化地震属性,从而更加精确地预测薄砂岩储层特征,提高其描述精度,更是地质及地球物理勘探家们始终不懈的追求。本文在借鉴主成分分析思想的基础上,提出一种新的地震属性优化方法-约束主成分分析。经理论模型的计算及油田区的实际应用表明:该方法不仅能提高储层预测的精度,而且具有更好的适用性。     

Estimation and prediction of the spatial occurrence of fish species using Bayesian latent Gaussian models

A methodological approach for modelling the occurrence patterns of species for the purpose of fisheries management is proposed here. The presence/absence of the species is modelled with a hierarchical Bayesian spatial model using the geographical and environmental characteristics of each fishing location. Maps of predicted probabilities of presence are generated using Bayesian kriging. Bayesian inference on the parameters and prediction of presence/absence in new locations (Bayesian kriging) are made by considering the model as a latent Gaussian model, which allows the use of the integrated nested Laplace approximation ( INLA ) software (which has been seen to be quite a bit faster than the well-known MCMC methods). In particular, the spatial effect has been implemented with the stochastic partial differential equation (SPDE) approach. The methodology is evaluated on Mediterranean horse mackerel (Trachurus mediterraneus) in the Western Mediterranean. The analysis shows that environmental and geographical factors can play an important role in directing local distribution and variability in the occurrence of species. Although this approach is used to recognize the habitat of mackerel, it could also be for other different species and life stages in order to improve knowledge of fish populations and communities.