Semiparametric regression models for spatial prediction and uncertainty quantification of soil attributes

In many studies, the distribution of soil attributes depends on both spatial location and environmental factors, and prediction and process identification are performed using existing methods such as kriging. However, it is often too restrictive to model soil attributes as dependent on a known, parametric function of environmental factors, which kriging typically assumes. This paper investigates a semiparametric approach for identifying and modeling the nonlinear relationships of spatially dependent soil constituent levels with environmental variables and obtaining point and interval predictions over a spatial region. Frequentist and Bayesian versions of the proposed method are applied to measured soil nitrogen levels throughout Florida, USA and are compared to competing models, including frequentist and Bayesian kriging, based an array of point and interval measures of out-of-sample forecast quality. The semiparametric models outperformed competing models in all cases. Bayesian semiparametric models yielded the best predictive results and provided empirical coverage probability nearly equal to nominal.     

基于标签传播的岩性预测半监督学习算法研究

低渗透油气藏、致密油气藏、页岩油气藏等非常规油气藏的开发已成为全球油气开发的热点,也为测井解释带来新的挑战.为了提高测井解释精度,本文研究了岩性预测的半监督学习问题,提出了"聚类—人工标注—伪标注—分类"的岩性预测框架.首先,利用聚类算法选取待标注样本;然后,基于数据在特征空间和地理空间的相似性,利用图半监督学习方法实...     

Critical uncertainty parameters influencing seismic performance of bridges using Lasso regression

Recent efforts of regional risk assessment of structures often pose a challenge in dealing with the potentially variable uncertain input parameters. The source of uncertainties can be either epistemic or aleatoric. This article identifies uncertain variables exhibiting strongest influences on the seismic demand of bridge components through various regression techniques such as linear, stepwise, Ridge, Lasso, and elastic net regressions. The statistical results indicate that Lasso regression is the most effective one in predicting the demand model as it has the lowest mean square error and absolute error. As the sensitivity study identifies more than 1 significant variable, a multiparameter fragility model using Lasso regression is suggested in this paper. The proposed fragility methodology is able to identify the relative impact of each uncertain input variable and level of treatment needed for these variables in the estimation of seismic demand models and fragility curves. Thus, the proposed approach helps bridge owners to spend their resources judiciously (e.g., data collection, field investigations, and censoring) in the generation of a more reliable database for regional risk assessment. This proposed approach can be applicable to other structures.     

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.     

Potential of support vector regression for prediction of monthly streamflow using endogenous property

In the recent past, a variety of statistical and other modelling approaches have been developed to capture the properties of hydrological time series for their reliable prediction. However, the extent of complexity hinders the applicability of such traditional models in many cases. Kernel‐based machine learning approaches have been found to be more popular due to their inherent advantages over traditional modelling techniques including artificial neural networks(ANNs ). In this paper, a kernel‐based learning approach is investigated for its suitability to capture the monthly variation of streamflow time series. Its performance is compared with that of the traditional approaches. Support vector machines (SVMs) are one such kernel‐based algorithm that has given promising results in hydrology and associated areas. In this paper, the application of SVMs to regression problems, known as support vector regression (SVR), is presented to predict the monthly streamflow of the Mahanadi River in the state of Orissa, India. The results obtained are compared against the results derived from the traditional Box–Jenkins approach. While the correlation coefficient between the observed and predicted streamflows was found to be 0·77 in case of SVR, the same for different auto‐regressive integrated moving average (ARIMA) models ranges between 0·67 and 0·69. The superiority of SVR as compared to traditional Box‐Jenkins approach is also explained through the feature space representation. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

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.     

基于传播矩阵法改进的SS及其前驱波合成算法

410 km和660 km地幔间断面在地球内部动力学研究中具有重要意义. 在研究地幔间断面的方法中, SS前驱波由于具有全球采样优势得以广泛应用. SS及其前驱波模拟可利用有限差分和谱元法等数值模拟方法, 它们在模拟全球尺度地震波传播时具有高精度的特点, 但往往计算量很大. 因此, 该类方法难以应用于反射点广泛分布的情形. 而基于传播矩阵发展的SS及其前驱波模拟方法在保持高精度计算的同时, 可大幅提高计算效率. 本文针对SS及其前驱波的传播特征, 改进了基于传播矩阵方法的波形合成算法FASHSHWF. 通过简单层状模型对该算法进行了测试, 验证了算法及相应程序的正确性. 计算效率测试表明改进算法相较常规传播矩阵算法可节约50%以上的计算时间. 通过与AxiSEM计算的波形对比, 验证了FASHSHWF用于SS及其前驱波模拟的有效性. 在上述工作的基础上, 本文进一步探讨了新算法在研究全球近地表结构对地幔间断面复杂性探测影响中的应用.

     

Sampling efficiency in Monte Carlo based uncertainty propagation strategies: Application in seawater intrusion simulations

The implementation of Monte Carlo simulations (MCSs) for the propagation of uncertainty in real-world seawater intrusion (SWI) numerical models often becomes computationally prohibitive due to the large number of deterministic solves needed to achieve an acceptable level of accuracy. Previous studies have mostly relied on parallelization and grid computing to decrease the computational time of MCSs. However, another approach which has received less attention in the literature is to decrease the number of deterministic simulations by using more efficient sampling strategies. Sampling efficiency is a measure of the optimality of a sampling strategy. A more efficient sampling strategy requires fewer simulations and less computational time to reach a certain level of accuracy. The efficiency of a sampling strategy is highly related to its space-filling characteristics.This paper illustrates that the use of optimized Latin hypercube sampling (OLHS) strategies instead of the widely employed simple random sampling (SRS) and Latin hypercube sampling (LHS) strategies, can significantly improve sampling efficiency and hence decrease the simulation time of MCSs. Nine OLHS strategies are evaluated including: improved Latin hypercube sampling (IHS); optimum Latin hypercube (OLH) sampling; genetic optimum Latin hypercube (GOLH) sampling; three sampling strategies based on the enhanced stochastic evolutionary (ESE) algorithm namely φ_p-ESE which employs the φ_p space-filling criterion, CLD-ESE which utilizes the centered L₂-discrepancy (CLD) space-filling criterion, and SLD-ESE which uses the star L₂-discrepancy (SLD) space-filling criterion; and three sampling strategies based on the simulated annealing (SA) algorithm namely φ_p-SA which employs the φ_p criterion, CLD-SA which uses the CLD criterion, and SLD-SA which utilizes the SLD criterion. The study applies SRS, LHS and the nine OLHS strategies to MCSs of two synthetic test cases of SWI. The two test cases are the Henry problem and a two-dimensional radial representation of SWI in a circular island. The comparison demonstrates that the CLD-ESE strategy is the most efficient among the evaluated strategies. This paper also demonstrates how the space-filling characteristics of different OLHS designs change with variations in the input arguments of their optimization algorithms.     

A new fuzzy linear regression approach for dissolved oxygen prediction

Abstract

A new method for fuzzy linear regression is proposed to predict dissolved oxygen using abiotic factors in a riverine environment, in Calgary, Canada. The proposed method is designed to accommodate fuzzy regressors, regressand and coefficients, i.e. representing full system uncertainty. The regression equation is built to minimize the distance between fuzzy numbers, and generalizes to crisp regression when crisp parameters are used. The method is compared to two existing fuzzy linear regression techniques: the Tanaka method and the Diamond method. The proposed new method outperforms the existing methods with higher Nash-Sutcliffe efficiency, and lower RMSE, AIC and total fuzzy distance. The new method demonstrates that nonlinear membership functions are more suitable for representing uncertain environmental data than the typical triangular representations. A result of this research is that low DO prediction is improved and consequently the approach can be used for risk analysis by water resource managers.

Editor D. Koutsoyiannis; Associate editor T. Okruszko     

基于粒子群优化算法与厄米多项式构建地震综合预测投影寻踪回归模型

在地震综合预测投影寻踪研究工作中,投影寻踪回归算法是其中应用最多的一种方法．但一般投影寻踪回归算法构造技术较为复杂,采用多次局部光滑回归,计算量较大,外推较为繁杂,容易陷于局部解．在综合考虑传统投影寻踪回归算法特点的基础上,针对投影寻踪回归计算中存在的一些不利因素,给出了一定的解决思路:采用粒子群优化算法代替高斯 牛顿算法优化投影方向;采用厄米多项式代替分段线性光滑回归来拟合岭函数,以简化优化过程;参数优化无需分组,获得全局优化的岭函数．利用数值仿真技术进行基于粒子群优化算法与厄米多项式构建的投影寻踪回归模型建模能力与计算精度的检验,再将其应用于多维地震时间序列和一般多维无序地震样本回归综合建模预测中．通过计算和分析表明,基于粒子群优化算法与厄米多项式构建的投影寻踪回归模型具有简单、快速、有效的特点,在实际地震综合预测建模中取得了满意的效果,可作为地震预测的一种综合分析方法．      

Estimation of uncertainty propagation in flood inundation mapping using a 1‐D hydraulic model

A need for more accurate flood inundation maps has recently arisen because of the increasing frequency and extremity of flood events. The accuracy of flood inundation maps is determined by the uncertainty propagated from all of the variables involved in the overall process of flood inundation modelling. Despite our advanced understanding of flood progression, it is impossible to eliminate the uncertainty because of the constraints involving cost, time, knowledge, and technology. Nevertheless, uncertainty analysis in flood inundation mapping can provide useful information for flood risk management. The twin objectives of this study were firstly to estimate the propagated uncertainty rates of key variables in flood inundation mapping by using the first‐order approximation method and secondly to evaluate the relative sensitivities of the model variables by using the Hornberger–Spear–Young (HSY) method. Monte Carlo simulations using the Hydrologic Engineering Center's River Analysis System and triangle‐based interpolation were performed to investigate the uncertainty arising from discharge, topography, and Manning's n in the East Fork of the White River near Seymour, Indiana, and in Strouds Creek in Orange County, North Carolina. We found that the uncertainty of a single variable is propagated differently to the flood inundation area depending on the effects of other variables in the overall process. The uncertainty was linearly/nonlinearly propagated corresponding to valley shapes of the reaches. In addition, the HSY sensitivity analysis revealed the topography of Seymour reach and the discharge of Strouds Creek to be major contributors to the change of flood inundation area. Copyright © 2014 John Wiley & Sons, Ltd.     

Combining the SWAT model with sequential uncertainty fitting algorithm for streamflow prediction and uncertainty analysis for the Lake Dianchi Basin,China

Streams play an important role in linking the land with lakes. Nutrients released from agricultural or urban sources flow via streams to lakes, causing water quality deterioration and eutrophication. Therefore, accurate simulation of streamflow is helpful for water quality improvement in lake basins. Lake Dianchi has been listed in the ‘Three Important Lakes Restoration Act’ in China, and the degradation of its water quality has been of great concern since the 1980s. To assist environmental decision making, it is important to assess and predict hydrological processes at the basin scale. This study evaluated the performance of the soil and water assessment tool (SWAT) and the feasibility of using this model as a decision support tool for predicting streamflow in the Lake Dianchi Basin. The model was calibrated and validated using monthly observed streamflow values at three flow stations within the Lake Dianchi Basin through application of the sequential uncertainty fitting algorithm (SUFI‐2). The results of the autocalibration method for calibrating and the prediction uncertainty from different sources were also examined. Together, the p‐factor (the percentage of measured data bracketed by 95% prediction of uncertainty, or 95PPU) and the r‐factor (the average thickness of the 95PPU band divided by the standard deviation of the measured data) indicated the strength of the calibration and uncertainty analysis. The results showed that the SUFI‐2 algorithm performed better than the autocalibration method. Comparison of the SUFI‐2 algorithm and autocalibration results showed that some snowmelt factors were sensitive to model output upstream at the Panlongjiang flow station. The 95PPU captured more than 70% of the observed streamflow at the three flow stations. The corresponding p‐factors and r‐factors suggested that some flow stations had relatively large uncertainty, especially in the prediction of some peak flows. Although uncertainty existed, statistical criteria including R² and Nash–Sutcliffe efficiency were reasonably determined. The model produced a useful result and can be used for further applications. Copyright © 2012 John Wiley & Sons, Ltd.     

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.

     

Conditional bias-penalized Kalman filter for improved estimation and prediction of extremes

Kalman filter (KF) and its variants are widely used for real-time state updating and prediction in environmental science and engineering. Whereas in many applications the most important performance criterion may be the fraction of the times when the filter performs satisfactorily under different conditions, in many other applications estimation and prediction specifically of extremes, such as floods, droughts, algal blooms, etc., may be of primary importance. Because KF is essentially a least squares solution, it is subject to conditional biases (CB) which arise from the error-in-variable, or attenuation, effects when the model dynamics are highly uncertain, the observations have large errors and/or the system being modeled is not very predictable. In this work, we describe conditional bias-penalized KF, or CBPKF, based on CB-penalized linear estimation which minimizes a weighted sum of error variance and expectation of Type-II CB squared and comparatively evaluate with KF through a set of synthetic experiments for one-dimensional state estimation under the idealized conditions of normality and linearity. The results show that CBPKF reduces root mean square error (RMSE) over KF by 10–20% or more over the tails of the distribution of the true state. In the unconditional sense CBPKF performs comparably to KF for nonstationary cases in that CBPKF increases RMSE over all ranges of the true state only up to 3%. With the ability to reduce CB explicitly, CBPKF provides a significant new addition to the existing suite of filtering techniques for improved analysis and prediction of extreme states of uncertain environmental systems.     

On the propagation characteristics of tunnel surface‐waves for seismic prediction

To increase the safety and efficiency of tunnel constructions, online seismic exploration ahead of a tunnel has become a valuable tool. One recent successful forward looking approach is based on the excitation and registration of tunnel surface‐waves. For further development and for finding optimal acquisition geometries it is important to study the propagation characteristics of tunnel surface‐waves. 3D seismic finite difference modelling and analytic solutions of the wave equation in cylindrical coordinates reveal that at higher frequencies, i.e., if the tunnel‐diameter is significantly larger than the wavelength of surface‐waves, these surface‐waves can be regarded as Rayleigh‐waves confined to the tunnel wall and following helical paths along the tunnel axis. For lower frequencies, i.e., when the tunnel surface‐wavelength approaches the tunnel‐diameter, the propagation characteristics of these surface‐waves are similar to S‐waves. We define the surface‐wave wavelength‐to‐tunnel diameter ratio w to be a gauge for separating Rayleigh‐ from S‐wave excitation. For w > 1.2 tunnel surface‐waves behave like S‐waves, i.e. their velocity approaches the S‐wave velocity and the particle motion is linear and perpendicular to the ray direction. For w < 0.6 they behave like Rayleigh‐waves, i.e., their velocity approaches the Rayleigh‐wave velocity and they exhibit elliptical particle motion. For 0.6 < w < 1.2 a mixture of both types is observed. Field data from the Gotthard Base Tunnel (Switzerland) show both types of tunnel surface‐waves and S‐waves propagating along the tunnel.     

Parameter and rating curve uncertainty propagation analysis of the SWAT model for two small Mediterranean catchments

Abstract

The SWAT model was tested to simulate the streamflow of two small Mediterranean catchments (the Vène and the Pallas) in southern France. Model calibration and prediction uncertainty were assessed simultaneously by using three different techniques (SUFI-2, GLUE and ParaSol). Initially, a sensitivity analysis was conducted using the LH-OAT method. Subsequent sensitive parameter calibration and SWAT prediction uncertainty were analysed by considering, firstly, deterministic discharge data (assuming no uncertainty in discharge data) and secondly, uncertainty in discharge data through the development of a methodology that accounts explicitly for error in the rating curve (the stage?discharge relationship). To efficiently compare the different uncertainty methods and the effect of the uncertainty of the rating curve on model prediction uncertainty, common criteria were set for the likelihood function, the threshold value and the number of simulations. The results show that model prediction uncertainty is not only case-study specific, but also depends on the selected uncertainty analysis technique. It was also found that the 95% model prediction uncertainty interval is wider and more successful at encompassing the observations when uncertainty in the discharge data is considered explicitly. The latter source of uncertainty adds additional uncertainty to the total model prediction uncertainty.

Editor D. Koutsoyiannis; Associate editor D. Gerten

Citation Sellami, H., La Jeunesse, I., Benabdallah, S., and Vanclooster, M., 2013. Parameter and rating curve uncertainty propagation analysis of the SWAT model for two small Mediterranean watersheds. Hydrological Sciences Journal, 58 (8), 1635?1657.     

Testing new sources of topographic data for flood propagation modelling under structural,parameter and observation uncertainty

ABSTRACT

This study assessed the utility of EUDEM, a recently released digital elevation model, to support flood inundation modelling. To this end, a comparison with other topographic data sources was performed (i.e. LIDAR, light detection and ranging; SRTM, Shuttle Radar Topographic Mission) on a 98-km reach of the River Po, between Cremona and Borgoforte (Italy). This comparison was implemented using different model structures while explicitly accounting for uncertainty in model parameters and upstream boundary conditions. This approach facilitated a comprehensive assessment of the uncertainty associated with hydraulic modelling of floods. For this test site, our results showed that the flood inundation models built on coarse resolutions data (EUDEM and SRTM) and simple one-dimensional model structure performed well during model evaluation.

Editor Z.W. Kundzewicz; Associate editor S. Weijs