Statistical downscaling of GCM simulations to streamflow using relevance vector machine

General circulation models (GCMs), the climate models often used in assessing the impact of climate change, operate on a coarse scale and thus the simulation results obtained from GCMs are not particularly useful in a comparatively smaller river basin scale hydrology. The article presents a methodology of statistical downscaling based on sparse Bayesian learning and Relevance Vector Machine (RVM) to model streamflow at river basin scale for monsoon period (June, July, August, September) using GCM simulated climatic variables. NCEP/NCAR reanalysis data have been used for training the model to establish a statistical relationship between streamflow and climatic variables. The relationship thus obtained is used to project the future streamflow from GCM simulations. The statistical methodology involves principal component analysis, fuzzy clustering and RVM. Different kernel functions are used for comparison purpose. The model is applied to Mahanadi river basin in India. The results obtained using RVM are compared with those of state-of-the-art Support Vector Machine (SVM) to present the advantages of RVMs over SVMs. A decreasing trend is observed for monsoon streamflow of Mahanadi due to high surface warming in future, with the CCSR/NIES GCM and B2 scenario.     

Estimation of monthly evaporative loss using relevance vector machine,extreme learning machine and multivariate adaptive regression spline models

The forecasting of evaporative loss (E) is vital for water resource management and understanding of hydrological process for farming practices, ecosystem management and hydrologic engineering. This study has developed three machine learning algorithms, namely the relevance vector machine (RVM), extreme learning machine (ELM) and multivariate adaptive regression spline (MARS) for the prediction of E using five predictor variables, incident solar radiation (S), maximum temperature (T _max), minimum temperature (T _min), atmospheric vapor pressure (VP) and precipitation (P). The RVM model is based on the Bayesian formulation of a linear model with appropriate prior that results in sparse representations. The ELM model is computationally efficient algorithm based on Single Layer Feedforward Neural Network with hidden neurons that randomly choose input weights and the MARS model is built on flexible regression algorithm that generally divides solution space into intervals of predictor variables and fits splines (basis functions) to each interval. By utilizing random sampling process, the predictor data were partitioned into the training phase (70 % of data) and testing phase (remainder 30 %). The equations for the prediction of monthly E were formulated. The RVM model was devised using the radial basis function, while the ELM model comprised of 5 inputs and 10 hidden neurons and used the radial basis activation function, and the MARS model utilized 15 basis functions. The decomposition of variance among the predictor dataset of the MARS model yielded the largest magnitude of the Generalized Cross Validation statistic (≈0.03) when the T _max was used as an input, followed by the relatively lower value (≈0.028, 0.019) for inputs defined by the S and VP. This confirmed that the prediction of E utilized the largest contributions of the predictive features from the T _max, verified emphatically by sensitivity analysis test. The model performance statistics yielded correlation coefficients of 0.979 (RVM), 0.977 (ELM) and 0.974 (MARS), Root-Mean-Square-Errors of 9.306, 9.714 and 10.457 and Mean-Absolute-Error of 0.034, 0.035 and 0.038. Despite the small differences in the overall prediction skill, the RVM model appeared to be more accurate in prediction of E. It is therefore advocated that the RVM model can be employed as a promising machine learning tool for the prediction of evaporative loss.     

Determination of reservoir induced earthquake using support vector machine and gaussian process regression

The prediction of magnitude (M) of reservoir induced earthquake is an important task in earthquake engineering. In this article, we employ a Support Vector Machine (SVM) and Gaussian Process Regression (GPR) for prediction of reservoir induced earthquake M based on reservoir parameters. Comprehensive parameter (E) and maximum reservoir depth (H) are considered as inputs to the SVM and GPR. We give an equation for determination of reservoir induced earthquake M. The developed SVM and GPR have been compared with the Artificial Neural Network (ANN) method. The results show that the developed SVM and GPR are efficient tools for prediction of reservoir induced earthquake M.     

SVM方法在扇体砂岩厚度预测中的应用

基于小样本学习理论的支持向量机(SVM)方法可用于建立非线性函数预测模型。利用支持向量机方法,根据样本数据采用自动拟合的方法构造核函数,使得建立的关系不仅具有较高的拟合精度,而且具有较好的推广性。地震波的频谱与其波形的关系是互为正、反傅立叶变换的关系,所以地震波的波形及其频谱是同一物理现象的两种不同的表达形式。波形特征沿纵横方向上的变化反映了地层介质在纵横方向上的差异;反射波频谱上的差异则反映了岩性和流体成分的不同以及地层厚度的变化等。直接由地震波波形预测扇体砂岩厚度,不仅充分利用了地震波信息,而且极大地提高了预测模型的准确性。模型及实例验证了该方法的适用性。     

Applicability of artificial intelligence to reservoir induced earthquakes

This paper proposes to use least square support vector machine (LSSVM) and relevance vector machine (RVM) for prediction of the magnitude (M) of induced earthquakes based on reservoir parameters. Comprehensive parameter (E) and maximum reservoir depth (H) are used as input variables of the LSSVM and RVM. The output of the LSSVM and RVM is M. Equations have been presented based on the developed LSSVM and RVM. The developed RVM also gives variance of the predicted M. A comparative study has been carried out between the developed LSSVM, RVM, artificial neural network (ANN), and linear regression models. Finally, the results demonstrate the effectiveness and efficiency of the LSSVM and RVM models.     

Urmia lake water level fluctuation hydro informatics modeling using support vector machine and conjunction of wavelet and neural network

In this research, the simulation of Urmia Lake water level fluctuation by means of two models was applied. For this, Support Vector Machines (SVM), and Neural Wavelet Network (NWN) models that conjugated both the wavelet function and ANN, developed for simulating the Urmia Lake water level fluctuation. The yearly data of rainfall, temperature and discharge to the Urmia Lake and water level fluctuation were used. Urmia Lake is the biggest and the hyper saline lake in Iran. The outcome of the SVM based models are compared with the NWN. The results of SVM model performs better than NWN and offered a practical solution to the problem of water level fluctuation predictions. Analysis results showed that the optimal situation occurred with use of precipitation, temperature and discharge for all station and water level fluctuations at the lag time of one year (RMSEs) of 0.23, 0.41 m obtained by SVM, NWN, respectively, and SSEs of 0.43, 1.33 and R ² of 0.97, 0 obtained by SVM, NWN, respectively. The results of SVM model show better accuracy in comparison with the NWN model.     

Estimating soil moisture using remote sensing data: A machine learning approach

Soil moisture is an integral quantity in hydrology that represents the average conditions in a finite volume of soil. In this paper, a novel regression technique called Support Vector Machine (SVM) is presented and applied to soil moisture estimation using remote sensing data. SVM is based on statistical learning theory that uses a hypothesis space of linear functions based on Kernel approach. SVM has been used to predict a quantity forward in time based on training from past data. The strength of SVM lies in minimizing the empirical classification error and maximizing the geometric margin by solving inverse problem. SVM model is applied to 10 sites for soil moisture estimation in the Lower Colorado River Basin (LCRB) in the western United States. The sites comprise low to dense vegetation. Remote sensing data that includes backscatter and incidence angle from Tropical Rainfall Measuring Mission (TRMM), and Normalized Difference Vegetation Index (NDVI) from Advanced Very High Resolution Radiometer (AVHRR) are used to estimate soil water content (SM). Simulated SM (%) time series for the study sites are available from the Variable Infiltration Capacity Three Layer (VIC) model for top 10 cm layer of soil for the years 1998–2005. SVM model is trained on 5 years of data, i.e. 1998–2002 and tested on 3 years of data, i.e. 2003–2005. Two models are developed to evaluate the strength of SVM modeling in estimating soil moisture. In model I, training and testing are done on six sites, this results in six separate SVM models – one for each site. Model II comprises of two subparts: (a) data from all six sites used in model I is combined and a single SVM model is developed and tested on same sites and (b) a single model is developed using data from six sites (same as model II-A) but this model is tested on four separate sites not used to train the model. Model I shows satisfactory results, and the SM estimates are in good agreement with the estimates from VIC model. The SM estimate correlation coefficients range from 0.34 to 0.77 with RMSE less than 2% at all the selected sites. A probabilistic absolute error between the VIC SM and modeled SM is computed for all models. For model I, the results indicate that 80% of the SM estimates have an absolute error of less than 5%, whereas for model II-A and II-B, 80% and 60% of the SM estimates have an error less than 10% and 15%, respectively. SVM model is also trained and tested for measured soil moisture in the LCRB. Results with RMSE, MAE and R of 2.01, 1.97, and 0.57, respectively show that the SVM model is able to capture the variability in measured soil moisture. Results from the SVM modeling are compared with the estimates obtained from feed forward-back propagation Artificial Neural Network model (ANN) and Multivariate Linear Regression model (MLR); and show that SVM model performs better for soil moisture estimation than ANN and MLR models.     

地震震级预测的相关向量机模型

为了借助容易获取的地震相关因素间接预测地震震级,提出基于相关向量机（Relevance Vector Machine,RVM）方法的地震震级预测模型。通过样本学习建立地震震级与地震累积频度、累积释放能量、平均震级、b值、η值和相关区震级等6个主要影响因素之间的非线性映射关系,利用已知影响因素预测地震震级。结果表明:RVM模型预测结果均优于BP神经网络及SOM-BP神经网络预测结果;通过敏感因子分析比较各因素的敏感程度,b值和η值最为突出,在震级研究中应重点分析。综合分析,RVM模型具有精度高和离散性小等优点,对地震震级预测有较好的推广价值。     

Data-based modelling approach for variable density flow and solute transport simulation in a coastal aquifer

Data-based models, namely artificial neural network (ANN), support vector machine (SVM), genetic programming (GP) and extreme learning machine (ELM), were developed to approximate three-dimensional, density-dependent flow and transport processes in a coastal aquifer. A simulation model, SEAWAT, was used to generate data required for the training and testing of the data-based models. Statistical analysis of the simulation results obtained by the four models show that the data-based models could simulate the complex salt water intrusion process successfully. The selected models were also compared based on their computational ability, and the results show that the ELM is the fastest technique, taking just 0.5 s to simulate the dataset; however, the SVM is the most accurate, with a Nash-Sutcliffe efficiency (NSE) ≥ 0.95 and correlation coefficient R ≥ 0.92 for all the wells. The root mean square error (RMSE) for the SVM is also significantly less, ranging from 12.28 to 77.61 mg/L.     

A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series

Developing a hydrological forecasting model based on past records is crucial to effective hydropower reservoir management and scheduling. Traditionally, time series analysis and modeling is used for building mathematical models to generate hydrologic records in hydrology and water resources. Artificial intelligence (AI), as a branch of computer science, is capable of analyzing long-series and large-scale hydrological data. In recent years, it is one of front issues to apply AI technology to the hydrological forecasting modeling. In this paper, autoregressive moving-average (ARMA) models, artificial neural networks (ANNs) approaches, adaptive neural-based fuzzy inference system (ANFIS) techniques, genetic programming (GP) models and support vector machine (SVM) method are examined using the long-term observations of monthly river flow discharges. The four quantitative standard statistical performance evaluation measures, the coefficient of correlation (R), Nash–Sutcliffe efficiency coefficient (E), root mean squared error (RMSE), mean absolute percentage error (MAPE), are employed to evaluate the performances of various models developed. Two case study river sites are also provided to illustrate their respective performances. The results indicate that the best performance can be obtained by ANFIS, GP and SVM, in terms of different evaluation criteria during the training and validation phases.     

Performance assessment of genetic programming (GP) and minimax probability machine regression (MPMR) for prediction of seismic ultrasonic attenuation

The determination of seismic attenuation (s) (dB/cm) is a challenging task in earthquake science. This article employs genetic programming (GP) and minimax probability machine regression (MPMR) for prediction of s. GP is developed based on genetic algorithm. MPMR maximizes the minimum probability of future predictions being within some bound of the true regression function. Porosity (n) (%), permeability (k) (millidarcy), grain size (d) (μm), and clay content (c) (%) have been considered as inputs of GP and MPMR. The output of GP and MPMR is s. The developed GP gives an equation for prediction of s. The results of GP and MPMR have been compared with the artificial neural network. This article gives robust models based on GP and MPMR for prediction of s.     

Evaluation of burst liability in kimberlite using support vector machine

Due to the complex mechanisms of rockburst, there is no current effective method to reliably predict these events. A statistical learning method, support vector machine (SVM), is employed in this paper for kimberlite burst prediction. Four indicators \(\sigma_{\theta } ,\sigma_{c} ,\sigma_{t} ,W_{\text{ET}}\) are chosen as input indices for the SVM, which is trained using 108 groups of rockburst cases from around the world. Data uniformization is used to avoid negative impact of differing dimensions across the original data. Parameter optimization is embedded in the training process of the SVM to achieve optimized predictive ability. After training and optimization, the SVM reaches an accuracy of 95% in rock burst prediction for validation samples. The constructed SVM is then employed in kimberlite burst liability evaluation. The model indicated a moderate burst risk, which matches observed instances of rockburst at a diamond mine in north Canada. The SVM method ignores the focus on rockburst mechanisms, instead relying on representative indicators to develop a predictive model through self-learning. The prediction results show an excellent accuracy, which means this method has a potential application in rockburst prediction.     

地震前兆综合预测支持向量机模型研究

该文介绍了支持向量机算法的原理与回归方法。 采用支持向量机中的非线性回归算法与理论公式产生的多维样本, 对其进行了数值仿真实验。 利用该方法和地震前兆异常建立了最佳地震综合预测模型, 对获得的最佳模型进行了内符检验, 得出最佳模型的预测结果与实际震例的地震震级基本一致。 综合分析认为, 支持向量机无论在学习或者预测精度方面不但具有很大的优越性和具有较强的外推泛化能力, 而且基于支持向量机回归算法建立的地震前兆综合预测模型是可行的, 其获得的知识可较为准确地实现对主震震级的综合预测。     

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.     

联合DBSCAN聚类采样和SVM分类的滑坡易发性评价

针对基于机器学习的滑坡易发性评价中非滑坡样本选取不规范导致的分类精度较低问题,本文提出联合基于密度的噪声应用空间聚类(Density-Based Spatial Clustering of Applications with Noise,DBSCAN)采样策略和支持向量机(Support Vector Machine,...     

基于支持向量机分类的嘉陵江草街水库甲藻水华预警

嘉陵江草街水库自建成后2011-2013年连续3年发生甲藻水华现象,给当地经济发展和生态安全带来影响.根据2011年5月至2013年7月草街水库大坝上、下游8个断面的逐月调查数据,利用支持向量机在处理小样本问题、非线性分类问题和泛化推广方面的优势,构建了基于支持向量机分类的草街水库甲藻水华预警模型.结果表明,利用本月理化数据和本月倪氏拟多甲藻(Peridiniopsis niei)密度数据建立的模型,对测试样本取得了80%以上的判别正确率,且对甲藻水华样本的判别正确率为100%.因此,支持向量机作为新兴的机器学习方法,可以为环境管理部门发布水华预警信息提供科学依据,并在环境保护领域具有广阔的应用前景.     

Analytical procedures for weekly hydrological droughts: a case of Canadian rivers

Abstract

Two entities of importance in hydrological droughts, viz. the longest duration, L_T , and the largest magnitude, M_T (in standardized terms) over a desired time period (which could also correspond to a specific return period) T, have been analysed for weekly flow sequences of Canadian rivers. Analysis has been carried out in terms of week-by-week standardized values of flow sequences, designated as SHI (standardized hydrological index). The SHI sequence is truncated at the median level for identification and evaluation of expected values of the above random variables, E(L_T ) and E(M_T ). SHI sequences tended to be strongly autocorrelated and are modelled as autoregressive order-1, order-2 or autoregressive moving average order-1,1. The drought model built on the theorem of extremes of random numbers of random variables was found to be less satisfactory for the prediction of E(L_T ) and E(M_T ) on a weekly basis. However, the model has worked well on a monthly (weakly Markovian) and an annual (random) basis. An alternative procedure based on a second-order Markov chain model provided satisfactory prediction of E(L_T ). Parameters such as the mean, standard deviation (or coefficient of variation), and lag-1 serial correlation of the original weekly flow sequences (obeying a gamma probability distribution function) were used to estimate the simple and first-order drought probabilities through closed-form equations. Second-order probabilities have been estimated based on the original flow sequences as well as SHI sequences, utilizing a counting method. The E(M_T ) can be predicted as a product of drought intensity (which obeys the truncated normal distribution) and E(L_T ) (which is based on a mixture of first- and second-order Markov chains).

Citation Sharma, T. C. & Panu, U. S. (2010) Analytical procedures for weekly hydrological droughts: a case of Canadian rivers. Hydrol. Sci. J. 55(1), 79–92.     

Comparison of machine learning models for predicting fluoride contamination in groundwater

Groundwater is an especially important freshwater source for water supplies in the Maku area of northwest Iran. The groundwater of the area contains high concentrations of fluoride and is, therefore, important in predicting the fluoride contamination of the groundwater for the purpose of planning and management. The present study aims to evaluate the ability of the extreme learning machine (ELM) model to predict the level of fluoride contamination in the groundwater in comparison to multilayer perceptron (MLP) and support vector machine (SVM) models. For this purpose, 143 water samples were collected in a five-year period, 2004–2008. The samples were measured and analyzed for electrical conductivity, pH, major chemical ions and fluoride. To develop the models, the data set—including Na⁺, K⁺, Ca²⁺ and HCO₃ ^? concentrations as the inputs and fluoride concentration as the output—was divided into two subsets; training/validation (80% of data) and testing (20% of data), based on a cross-validation technique. The radial basis-based ELM model resulted in an R ² of 0.921, an NSC of 0.9071, an RMSE of 0.5638 (mg/L) and an MABE of 0.4635 (mg/L) for the testing data. The results showed that the ELM models performed better than MLP and SVM models for prediction of fluoride contamination. It was observed that ELM models learned faster than the other models during model development trials and the SVM models had the highest computation time.     

Seismic liquefaction potential assessment by using Relevance Vector Machine

Determining the liquefaction potential of soil is important in earthquake engineering. This study proposes the use of the Relevance Vector Machine (RVM) to determine the liquefaction potential of soil by using actual cone penetration test (CPT) data. RVM is based on a Bayesian formulation of a linear model with an appropriate prior that results in a sparse representation. The results are compared with a widely used artifi cial neural network (ANN) model. Overall, the RVM shows good performance and is proven to be more accurate than the ANN model. It also provides probabilistic output. The model provides a viable tool for earthquake engineers to assess seismic conditions for sites that are susceptible to liquefaction.     

A simple model to estimate monthly forest evapotranspiration in Japan from monthly temperature

The estimation of evapotranspiration (E) in forested areas is required for various practical purposes (e.g. evaluation of drought risks) in Japan. This study developed a model that estimates monthly forest E in Japan with the input of monthly temperature (T). The model is based on the assumptions that E equals the equilibrium evaporation rate (E_eq) and that E_eq is approximated by a function of T. The model formulates E as E (mm month⁻¹) = 3·48 T ( °C) + 32·3. The accuracy of the model was examined using monthly E data derived using short‐term water balance (WB) and micrometeorological (M) methods for 15 forest sites in Japan. The model estimated monthly E more accurately than did the Thornthwaite and Hamon equations according to regression analysis of the estimated E and E derived using the WB and M methods. Although the model tended to overestimate monthly E, the overestimation could be reduced by considering the effect of precipitation on E. As T data are commonly available all over Japan, the model would be a useful tool to estimate forest E in Japan. Copyright © 2010 John Wiley & Sons, Ltd.