Comparison of forecasting performance of nonlinear models of hydrological time series

Mean monthly flows of the Tatry alpine mountain region in Slovakia are predominantly fed by snowmelt in the spring and convective precipitation in the summer. Therefore their regime properties exhibit clear seasonal patterns. Positive deviations from these trends have substantially different features than the negative ones. This provides intuitive justification for the application of nonlinear two-regime models for modelling and forecasting of these time series. Nonlinear time series structures often have lead to good fitting performances, however these do not guarantee an equally good forecasting performance. In this paper therefore the forecasting performance of several nonlinear time series models is compared with respect to their capabilities of forecasting monthly and seasonal flows in the Tatry region. A new type of regime-switching models is also proposed and tested. The best predictive performance was achieved for a new model subclass involving aggregation operators.     

Rain-fall modeling: An Application of Bayesian forecasting

The rainfall-runoff modeling is very useful for forecasting purposes. A good methodology for forecasting the future stream flow is a key requirement for designers and operators of water resources systems. A compromise between conceptual and classical time series modeling is applied to model the relationship between rainfall and runoff. The dynamic nonlinear model is composed of a probability distribution describing the observation, a link function relating its mean to the so called state parameters and a system of equations defining the evolution of these parameters. Its Bayesian nature permits to take into account subjective information, making forward intervention, defining monitoring schemes and introducing smoothing facilities. An application using the data of Fartura river's basin is reported. The assessment of the prior distribution is discussed and the predictive performance of the linear and the non-linear models is reported.     

地震活动性研究中的非线性动力学模型

本文利用非线性动力学模型研究了断层带的地震活动特性.断层系由多个耦合非线性单元模拟,每个基本单元由Maxwell体和刚性滑块组成.滑块的运动满足静、动摩擦强度本构关系.理论模拟的地震活动在短时间内是随机的,但当时间尺度足够大时,断层带的总体活动表现出某种规律性.多数实际观测到的地震活动现象均在这些非线性动力学模型中出现. 本文提出转换概率的观点来度量断层间和孕震区间的地震转移.模拟中发现活动地震带中存在条件安全区,这可能对地震预报的实践有重要的意义.     

Applying wavelet transformation and artificial neural networks to develop forecasting-based reservoir operating rule curves

ABSTRACT

In order to provide more accurate reservoir-operating policies, this study attempts to implement effective monthly forecasting models. Seven inflow forecasting schemes, applying discrete wavelet transformation and artificial neural networks are proposed and provided to forecast the monthly inflow of Dez Reservoir. Based on some different performance indicators the best scheme is achieved comparing to the observed data. The best forecasting model is coupled with a simulation-optimization framework, in which the performance of five different reservoir rule curves can be compared. Three applied rules are based on conventional Standard operation policy, Regression rules, and Hedging rule, and two others are forecasting-based regression and hedging rules. The results indicate that forecasting-based operating rule curves are superior to the conventional rules if the forecasting scheme provides results accurately. Moreover, it can be concluded that the time series decomposition of the observed data enhances the accuracy of the forecasting results efficiently.     

Phase-space reconstruction and self-exciting threshold modeling approach to forecast lake water levels

Lake water level forecasting is very important for an accurate and reliable management of local and regional water resources. In the present study two nonlinear approaches, namely phase-space reconstruction and self-exciting threshold autoregressive model (SETAR) were compared for lake water level forecasting. The modeling approaches were applied to high-quality lake water level time series of the three largest lakes in Sweden; Vänern, Vättern, and Mälaren. Phase-space reconstruction was applied by the k-nearest neighbor (k-NN) model. The k-NN model parameters were determined using autocorrelation, mutual information functions, and correlation integral. Jointly, these methods indicated chaotic behavior for all lake water levels. The correlation dimension found for the three lakes was 3.37, 3.97, and 4.44 for Vänern, Vättern, and Mälaren, respectively. As a comparison, the best SETAR models were selected using the Akaike Information Criterion. The best SETAR models in this respect were (10,4), (5,8), and (7,9) for Vänern, Vättern, and Mälaren, respectively. Both model approaches were evaluated with various performance criteria. Results showed that both modeling approaches are efficient in predicting lake water levels but the phase-space reconstruction (k-NN) is superior to the SETAR model.     

The implementation of Bayesian structural additive regression models in multi-city time series air pollution and human health studies

In this study, a novel Bayesian semiparametric structural additive regression (STAR) model is introduced in multi-city time series air pollution and human health studies. This modeling approach can simultaneously take into account the fixed effects, random effects, nonlinear smoothing functions and spatial functions in an integrated model framework. This study focuses on examining the powerful functionalities of this approach in modeling air pollution and mortality data of 100 U.S. cities from 1987 to 2000. Compared with previous studies, the modeling approach used in this study yields consistent findings of nation-level and city-level PM₁₀ (particulate matter less than 10?μm) effects on mortality. Notably, cities with significantly elevated mortality rates were concentrated in the Northeastern U.S. This modeling approach also emphasizes the important functionality of the spatial function in visualizing disease mapping. Model diagnostics were performed to confirm the availability of the STAR model. We also found consistent findings by using different hyperparameters in the sensitivity analysis. To sum up, the implementation of this modeling approach has achieved the goals of applying a spatial function and obtaining robust results in the multi-city time series air pollution and human health study.     

Multi-step SETARMA predictors in the analysis of hydrological time series

The performance of the self-exciting threshold autoregressive moving average model in forecasting river flow data is investigated. Multi-step forecasts of two daily time series are generated through three different nonlinear predictors. The model adequacy to capture the main features of the data under study and its forecasting performance are analysed and discussed.     

Regional scale rainfall–runoff modeling using VARX–MGARCH approach

Multivariate time series modeling approaches are known as useful tools for describing, simulating, and forecasting hydrologic variables as well as their changes over the time. These approaches also have temporal and cross-sectional spatial dependence in multiple measurements. Although the application of multivariate linear and nonlinear time series approaches such as vector autoregressive with eXogenous variables (VARX) and multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) models are commonly used in financial and economic sciences, these approaches have not been extensively used in hydrology and water resources engineering. This study employed VARX and VARX–MGARCH approaches in modeling mean and conditional heteroscedasticity of daily rainfall and runoff records in the basin of Zarrineh Rood Dam, Iran. Bivariate diagonal VECH (DVECH) model, as a main type of MGARCH, shows how the conditional variance–covariance and conditional correlation structure vary over the time between residuals series of the fitted VARX. For this purpose, five model fits, which consider different combinations of twofold rainfall and runoff, including both upstream and downstream stations, have been investigated in the present study. The VARX model, with different orders, was applied to the daily rainfall–runoff process of the study area in each of these model fits. The Portmanteau test revealed the existence of conditional heteroscedasticity in the twofold residuals of fitted VARX models. Therefore, the VARX–DVECH model is proposed to capture the heteroscedasticity existing in the daily rainfall–runoff process. The bivariate DVECH model indicated both short-run and long-run persistency in the conditional variance–covariance matrix related to the twofold innovations of rainfall–runoff processes. Furthermore, the evaluation criteria for the VARX–DVECH model revealed the improvement of VARX model performance.     

Groundwater Depth Forecasting Using Configurational Entropy Spectral Analyses with the Optimal Input

Accurate groundwater depth forecasting is particularly important for human life and sustainable groundwater management in arid and semi-arid areas. To improve the groundwater forecasting accuracy, in this paper, a hybrid groundwater depth forecasting model using configurational entropy spectral analyses (CESA) with the optimal input is constructed. An original groundwater depth series is decomposed into subseries of different frequencies using the variational mode decomposition (VMD) method. Cross-correlation analysis and Shannon entropy methods are applied to select the optimal input series for the model. The ultimate forecasted values of the groundwater depth can be obtained from the various forecasted values of the selected series with the CESA model. The applicability of the hybrid model is verified using the groundwater depth data from four monitoring wells in the Xi'an of Northwest China. The forecasting accuracy of the models was evaluated based on the average relative error (RE), root mean square error (RMSE), correlation coefficient (R) and Nash-Sutcliffe coefficient (NSE). The results indicated that comparing with the CESA and autoregressive model, the hybrid model has higher prediction performance.     

A nonlinear time series analysis using two‐stage genetic algorithms for streamflow forecasting

Streamflow forecasting is very important for the management of water resources: high accuracy in flow prediction can lead to more effective use of water resources. Hydrological data can be classified as non‐steady and nonlinear, thus this study applied nonlinear time series models to model the changing characteristics of streamflows. Two‐stage genetic algorithms were used to construct nonlinear time series models of 10‐day streamflows of the Wu‐Shi River in Taiwan. Analysis verified that nonlinear time series are superior to traditional linear time series. It is hoped that these results will be useful for further applications. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting monthly inflow with extreme seasonal variation using the hybrid SARIMA-ANN model

The optimal operation of dam reservoirs can be programmed and managed by predicting the inflow to these structures more accurately. To this end, there are various linear and nonlinear models. However, some hydrological problems like inflow with extreme seasonal variation are not purely linear or nonlinear. To improve the forecasting accuracy of this phenomenon, a linear Seasonal Auto Regressive Integrated Moving Average (SARIMA) model is combined with a nonlinear Artificial Neural Network (ANN) model. This new model is used to predict the monthly inflow to the Jamishan dam reservoir in West Iran. A comparison of the SARIMA and ANN models with the proposed hybrid model’s results is provided accordingly. More specifically, the models’ performance in forecasting base and flood flows is evaluated. The effect of changing the forecasting period length on the models’ accuracy is studied. The results of increasing the number of SARIMA model parameters up to five are investigated to achieve more accurate forecasting. The hybrid model predicts peak flood flows much better than the individual models, but SARIMA outperforms the other models in predicting base flow. The obtained results indicate that the hybrid model reduces the overall forecast error more than the ANN and SARIMA models. The coefficient of determination of the hybrid, ANN and SARIMA models were 0.72, 0.64 and 0.58, and the root mean squared error values were 1.02, 1.16 and 1.27 respectively, during the forecast period. Changing the forecasting length also indicated that these models can be used in the long term without increasing the forecast error.     

Tree-based threshold modeling for short-term forecast of daily maximum ozone level

This paper proposes a simple class of threshold autoregressive model for purpose of forecasting daily maximum ozone concentrations in Southern California. Linear time series model has been widely considered in environmental modeling. However, this class of models fails to capture the nonlinearity in ozone process and the complexity of meteorological interactions with ozone. In this article, we used the threshold autoregressive models with two classes of regimes; periodic and meteorological regimes. Days in week were used for the periodic regimes and the regression tree method was used to define the regimes as a function of meteorological variables. As the reference model we used the autoregressive model with lagged ozone and various lagged meteorological variables as the covariates. The proposed models were applied to a 3-year dataset of daily maximum ozone concentrations obtained from five monitoring stations in San Bernardino County, CA and their forecast performances were evaluated using an independent year-long dataset from the same stations. The results showed that the threshold models well capture the nonlinearity in ozone process and remove the nonstationarity in model residuals. The threshold models outperformed the non-threshold autoregressive models in day-ahead forecasts. The tree-based model showed slightly better performance than the periodic threshold model.     

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.     

Long-range forecasting of suspended sediment

This study examines the employment of two methods, multiple linear regression (MLR) and an artificial neural network (ANN), for multistep ahead forecasting of suspended sediment. The autoregressive integrated moving average (ARIMA) model is considered for one-step ahead forecasting of sediment series in order to provide a comparison with the MLR and ANN methods. For one- and two-step ahead forecasting, the ANN model performance is superior to that of the MLR model. For longer ranges, MLR models provide better accuracy, but there is an important assumption violation. The Durbin-Watson statistics of the MLR models show a noticeable decrease from 1.3 to 0.5, indicating that the residuals are not dependent over time. The scatterplots of the three methods (MLR, ARIMA and ANN) for one-step ahead forecasting for the validation period illustrate close fits with the regression line, with the ANN configuration having a slightly higher R² value.     

Prophet时序预测模型在电离层TEC异常探测中的应用

提出一种基于Facebook 开源的Prophet预测模型进行电离层TEC异常识别的新方法。 首先, 对比分析了该方法与传统时间序列预测方法(ARIMA模型等)预测电离层TEC建模背景值的精度, 以及与经典电离层TEC异常识别方法(滑动四分位法)提取前面对应一致的电离层TEC背景值的精度。 结果表明, Prophet预测模型预测建模背景值的精度要明显优于其他方法, 且预测的建模精度比ARIMA模型等方法高2.55倍左右, 比滑动四分位法高10.74倍左右。 同时, 在最佳预测建模区间时, 其精度值大小比较依次为RMSE_IQR=10.5841>RMSE_ARIMA=3.2780>RMSE_Prophet=0.8469, 说明传统探测法预测建模背景值时具有较大的不足。 随后, 以2017年8月8日九寨沟7.0级地震为例, 利用该方法分析了电离层TEC异常扰动情况, 并对比验证了该方法的有效性和准确性。 实验结果表明: 在震前第10 d和第2 d电离层TEC发生较为明显的负异常, 第7 d电离层TEC发生较为明显的正异常。 对比实验表明, Prophet预测模型的有效性和准确性明显优于滑动四分位法。     

Univariate streamflow forecasting using commonly used data-driven models: literature review and case study

Eight data-driven models and five data pre-processing methods were summarized; the multiple linear regression (MLR), artificial neural network (ANN) and wavelet decomposition (WD) models were then used in short-term streamflow forecasting at four stations in the East River basin, China. The wavelet–artificial neural network (W-ANN) method was used to predict 1-month-ahead monthly streamflow at Longchuan station (LS). The results indicate better performance of MLR and wavelet–multiple linear regression (W-MLR) in analysing the stationary trained dataset. Four models showed similar performance in 1-day-ahead streamflow forecasting, while W-MLR and W-ANN performed better in 5-day-ahead forecasting. Three reservoirs were shown to have more influence on downstream than upstream streamflow and models had the worst performance at Boluo station. Furthermore, the W-ANN model performed well for 1-month-ahead streamflow forecasting at LS with consideration of a deterministic component.     

Direct and Inverse Problems in a Variational Concept of Environmental Modeling

A concept of environmental forecasting based on a variational approach is discussed. The basic idea is to augment the existing technology of modeling by a combination of direct and inverse methods. By this means, the scope of environmental studies can be substantially enlarged. In the concept, mathematical models of processes and observation data subject to some uncertainties are considered. The modeling system is derived from a specially formulated weak-constraint variational principle. A set of algorithms for implementing the concept is presented. These are: algorithms for the solution of direct, adjoint, and inverse problems; adjoint sensitivity algorithms; data assimilation procedures; etc. Methods of quantitative estimations of uncertainty are of particular interest since uncertainty functions play a fundamental role for data assimilation, assessment of model quality, and inverse problem solving. A scenario approach is an essential part of the concept. Some methods of orthogonal decomposition of multi-dimensional phase spaces are used to reconstruct the hydrodynamic background fields from available data and to include climatic data into long-term prognostic scenarios. Subspaces with informative bases are constructed to use in deterministic or stochastic-deterministic scenarios for forecasting air quality and risk assessment. The results of implementing example scenarios for the Siberian regions are presented.     

A recurrent support vector regression model in rainfall forecasting

To minimize potential loss of life and property caused by rainfall during typhoon seasons, precise rainfall forecasts have been one of the key subjects in hydrological research. However, rainfall forecast is made difficult by some very complicated and unforeseen physical factors associated with rainfall. Recently, support vector regression (SVR) models and recurrent SVR (RSVR) models have been successfully employed to solve time‐series problems in some fields. Nevertheless, the use of RSVR models in rainfall forecasting has not been investigated widely. This study attempts to improve the forecasting accuracy of rainfall by taking advantage of the unique strength of the SVR model, genetic algorithms, and the recurrent network architecture. The performance of genetic algorithms with different mutation rates and crossover rates in SVR parameter selection is examined. Simulation results identify the RSVR with genetic algorithms model as being an effective means of forecasting rainfall amount. Copyright © 2006 John Wiley & Sons, Ltd.     

水文时间序列概率预报方法的通用架构

在准确揭示水文过程变化特性的基础上开展中长期(月尺度及以上)水文预报,是掌握未来水文情势和演变规律,以及研究解决实际水文水资源问题的重要基础.水文时间序列预报方法是揭示未来水文情势和演变规律的重要技术手段.本文首先梳理了目前常用的各类水文序列预报方法,分析讨论了各方法的基本原理和主要缺陷.然后,通过综合分析相关研究成果,总结得到关于水文序列预报方法的4点重要认识:序列预报前应进行序列分解;序列中确定成分和随机成分应分别建模预报;序列预报结果需要估计不确定性;模型集成效果常常优于单个模型效果.最后,提出一个水文时间序列概率预报方法的通用架构.利用该通用架构能够克服常规模型或方法的缺陷,进行物理成因分析的基础上,针对水文序列中不同特性的确定成分和随机成分别进行分析,既可得到准确的确定性预报结果,又可对预报结果的不确定性进行定量评估,并可提高最终预报结果的合理性和可靠性.     

时间域航空电磁2.5维非线性共轭梯度反演

对于时间域航空电磁法二维和三维反演来说,最大的困难在于有效的算法和大的计算量需求.本文利用非线性共轭梯度法实现了时间域航空电磁法2.5维反演方法,着重解决了迭代反演过程中灵敏度矩阵计算、最佳迭代步长计算、初始模型选取等问题.在正演计算中,我们采用有限元法求解拉式傅氏域中的电磁场偏微分方程,再通过逆拉氏和逆傅氏变换高精度数值算法得到时间域电磁响应.在灵敏度矩阵计算中,采用了基于拉式傅氏双变换的伴随方程法,时间消耗只需计算两次正演,从而节约了大量计算时间.对于最佳步长计算,二次插值向后追踪法能够保证反演迭代的稳定性.设计两个理论模型,检验反演算法的有效性,并讨论了选择不同初始模型对反演结果的影响.模型算例表明:非线性共轭梯度方法应用于时间域航空电磁2.5维反演中稳定可靠,反演结果能够有效地反映地下真实电性结构.当选择的初始模型电阻率值与真实背景电阻率值接近时,能得到较好的反演结果,当初始模型电阻率远大于或远小于真实背景电阻率值时反演效果就会变差.