A Comparative Study of Autoregressive,Autoregressive Moving Average,Gene Expression Programming and Bayesian Networks for Estimating Monthly Streamflow

In the recent years, artificial intelligence techniques have attracted much attention in hydrological studies, while time series models are rarely used in this field. The present study evaluates the performance of artificial intelligence techniques including gene expression programming (GEP), Bayesian networks (BN), as well as time series models, namely autoregressive (AR) and autoregressive moving average (ARMA) for estimation of monthly streamflow. In addition, simple multiple linear regression (MLR) was also used. To fulfill this objective, the monthly streamflow data of Ponel and Toolelat stations located on Shafarood and Polrood Rivers, respectively in Northern Iran were used for the period of October 1964 to September 2014. In order to investigate the models’ accuracy, root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R²) were employed as the error statistics. The obtained results demonstrated that the single AR and ARMA time series models had better performance in comparison with the single GEP, BN and MLR methods. Furthermore, in this study, six hybrid models known as GEP-AR, GEP-ARMA, BN-AR, BN-ARMA, MLR-AR and MLR-ARMA were developed to enhance the estimation accuracy of the monthly streamflow. It was concluded that the developed hybrid models were more accurate than the corresponding single artificial intelligence and time series models. The obtained results confirmed that the integration of time series models and artificial intelligence techniques could be of use to improve the accuracy of single models in modeling purposes related to the hydrological studies.     

基于人工神经网络的卡尔曼滤波实时校正技术

针对人工神经网络技术在实际应用中常出现的过拟合现象，设计了以人工神经网络模型做初级预报，用卡尔曼滤波技术对初级预报结果进行二次预报的方法。该方法用于淮河王家坝水文站最高洪水位的预报和岷江上游段紫坪埔水文站的流量预报，并与标准的BP网络模型以及卡尔曼滤波模型进行了比较。两个应用实例的计算结果表明，以上两种技术的结合，不仅有利于预防过拟合问题，还可提高预报精度。     

Streamflow and Hydrological Drought Trend Analysis and Forecasting in Cyprus

The persistent water shortage in Cyprus has been alleviated by importing freshwater from neighbouring countries, and severe droughts have been met with financial reimbursement from the EU at least twice. The goal of this research is to investigate and perform short-term forecasting of both streamflow and hydrological drought trends over the island. Eleven hydrometric stations with a 34-year common record length of the mean daily discharge from 10/1979 to 09/2013 are used for this purpose, with the relevant upstream catchments considered to represent pristine conditions. The Streamflow Drought Index (SDI) successfully captures the hydrological drought conditions over the island, and the performance of the index is validated based on both the historic drought archives and results from other drought indices for the island. The Mann–Kendall (M-K) test reveals that the annual and seasonal time series of the discharge volumes always illustrate a decreasing but insignificant trend at a significance level of a?=?0.05; additionally, the decrease per decade in the average annual streamflow volume based on Sen’s slope statistic is approximately ?9.4%. The M-K test on the SDI reveals that drought conditions intensified with time. Ten autoregressive integrated moving average (ARIMA) models are built and used to forecast the mean monthly streamflow values with moderate accuracy; the best ARIMA forecast model in each catchment is derived by comparing two model-performance statistical measures for the different (p,d,q) model parameters. The predicted discharge values are processed by the SDI-3 index, revealing that non-drought conditions are expected in most catchments in the upcoming three months, although mild-drought conditions are anticipated for catchments 7, 8 and 9.     

Reservoir Inflow Modeling Using Temporal Neural Networks with Forgetting Factor Approach

In this paper, a recursive training procedure with forgetting factor is proposed for on-line calibration of temporal neural networks. The forgetting factor discounts old measurements through an on-line model calibration. The forgetting factor approach enables the recursive algorithm to reduce the effect of the older error data by multiplying the error data by a discounting factor. The proposed procedure is used to calibrate a temporal neural network for reservoir inflow modeling. The mean monthly inflow of the Karoon-III reservoir dam in the south-western part of Iran is used to test the performance of the proposed approach. An autoregressive moving average (ARMA) model is also applied to the same data. The temporal neural network, which is trained with the proposed approach, has shown a significant improvement in the forecast accuracy in comparison with the network trained by the conventional method. It is also demonstrated that the neural network trained with forgetting factor results in better forecasts compared to the statistical ARMA model, which has been calibrated through this approach.     

改进BP神经网络集成模型在径流预测中的应用

为提高径流预测预报的精度和泛化能力,建立了基于3种基本改进算法的BP神经网络集成预测模型。利用ADF单位根检验方法、自相关分析方法确定径流时间序列的平稳性和模型的输入向量。针对BP神经网络标准算法收敛速度慢、易陷入局部极值的缺陷,采用自适应动量梯度法、共轭梯度法和Levenberg-Marquardt法分别改进BP神经网络标准算法,依次构建基于3种改进算法的BP神经网络模型对文山州南利河董湖水文站年径流进行预测,并构建GA-BP预测模型作为对比模型;采用加权平均方法对各单一模型预测结果进行综合集成。结果表明:集成模型对南利河2001-2005年径流预测平均相对误差绝对值为4.67%,最大相对误差绝对值为7.11%,精度和泛化能力均优于各单一模型和GA-BP模型。集成模型克服了单一模型预测精度不高和误差不稳定的缺点,具有较好的预测精度和泛化能力,是提高径流预测预报精度的有效方法。     

基于人工电场算法优化的大型灌区径流预测模型研究

针对水文预报中径流预测数据序列具有非线性和非平稳性等特点,将一种新型智能优化算法——人工电场算法AEFA与LSTM神经网络结合进行参数优化,建立AEFA-LSTM预测模型,并以赵口大型灌区涡河玄武水文站实测年径流量作为样本数据进行网络优化训练和预测分析,同时与传统优化算法（遗传算法GA和粒子群算法PSO）建立的GA-LSTM和PSO-LSTM预测模型进行对比。结果表明：AEFA-LSTM模型预测值的平均相对误差相较于GA-LSTM模型和PSO-LSTM模型分别降低了7.59%和5.22%,且平均绝对误差MAE、均方误差MSE、均方根误差RMSE均为3种模型中最小,说明所建立的AEFA-LSTM模型可以更高精度地预测径流量,为水文预报提供一种新型高精度径流预测方法。     

基于EEMD-LSTM-ARIMA的土石坝渗压预测模型研究

渗压监测是土石坝渗流安全评价的重要内容之一。由于渗压受到诸多外界因素的影响,测点的渗压值时间序列往往存在非平稳性、局部突变等特点,为此基于“分解-重构-组合”的思想构建了土石坝渗压预测的EEMD-LSTM-ARIMA模型。首先采用集合经验模态分解(EEMD)对时间序列特征进行提取,根据长短期记忆神经网络(LSTM)对提取出的特征分量进行预测,同时结合差分自回归移动平均方法(ARIMA)进行残差修正,组合LSTM和ARIMA的预测结果,重构得到改进预测模型。以某深厚覆盖层上的土石坝工程为例,选取主河床坝体防渗墙后2个典型测点的实测渗压值序列为研究对象进行应用验证。结果表明：相较于单一的LSTM模型和ARIMA模型,改进模型的平均绝对误差MAE、均方误差MSE、均方根误差RMSE均为3种模型中的最小值,预测精度明显优于另外2种模型,该模型为土石坝渗压的精确预测分析提供了新途径。     

Comparison of performance of statistical models in forecasting monthly streamflow of Kizil River,China

This paper presents the application of autoregressive integrated moving average(ARIMA),seasonal ARIMA(SARIMA),and Jordan-Elman artificial neural networks(ANN)models in forecasting the monthly streamflow of the Kizil River in Xinjiang,China.Two different types of monthly streamflow data(original and deseasonalized data)were used to develop time series and Jordan-Elman ANN models using previous flow conditions as predictors.The one-month-ahead forecasting performances of all models for the testing period(1998-2005)were compared using the average monthly flow data from the Kalabeili gaging station on the Kizil River.The Jordan-Elman ANN models,using previous flow conditions as inputs,resulted in no significant improvement over time series models in one-month-ahead forecasting.The results suggest that the simple time series models(ARIMA and SARIMA)can be used in one-month-ahead streamflow forecasting at the study site with a simple and explicit model structure and a model performance similar to the Jordan-Elman ANN models.     

An Integration of Stationary Wavelet Transform and Nonlinear Autoregressive Neural Network with Exogenous Input for Baseline and Future Forecasting of Reservoir Inflow

For effective water resources management and planning, an accurate reservoir inflow forecast is essential not only in training and testing phases but also in particular future periods. The objective of this study is to develop a reservoir inflow integrated forecasting model, relying on nonlinear autoregressive neural network with exogenous input (NARX) and stationary wavelet transform (SWT), namely SWT-NARX. Due to the elimination of down-sampling operation, SWT provides influential reinforcement of efficiently extracting the hidden significant, temporal features contained in the nonstationary inflow time series without information loss. The decomposed SWT sub-time series are determined as input-output for NARX forecaster; where a multi-model ensemble global mean (MMEGM) of downscaled precipitation based on nine global climate models (GCMs) represents as a climate-change exogenous input. Two major reservoirs in Thailand, Bhumibol and Sirikit ones are focused. Pearson’s correlation coefficient (r) and root mean square error (RMSE) are employed for performance evaluation. The achieved results indicate that the SWT-NARX explicitly outperforms the comparable forecasting approaches regarding a historical baseline period (1980–1999). Therefore, such SWT-NARX is further employed for future projection of the reservoir inflow over near (2010–2039) -, mid (2040–2069) - and far (2070–2099) - future periods against the inflow of the baseline one.     

ANN、ANFIS和AR模型在日径流时间序列预测中的应用比较

水文预测是水文学为经济和社会服务的重要方面。其预报结果不仅能为水库优化调度提供决策支持,而且对水电系统的经济运行、航运以及防洪等方面具有重大意义。自回归模型(AR模型)、人工神经网络(ANN)和自适应神经模糊推理系统(ANFIS)在日径流时间序列中应用广泛。将这三种模型应用于桐子林的日径流时间序列预测中,不仅采用纳什系数(NS系数)、均方根误差(RMSE)和平均相对误差(MARE)为评价指标,对三种模型的综合性能进行了比较。而且,在对三种模型预测结果的平均相对误差的阈值统计基础上,分析了三种模型的预测误差分布。同时,通过研究模型性能指标随预见期的变化过程评价了三种模型不同预见期下的预测能力。结果表明ANFIS相对于ANN和AR模型不仅具有更好的模拟能力、泛化能力,而且在相同的预见期下具有更优的模型性能,可以作为日径流时间序列预测的推荐模型。     

汤河水库实时洪水预报技术研究

汤河水库洪水预报对汤河水库及其下游的防洪安全极其重要,需要研究实时洪水预报技术,以提高洪水预报精度.根据汤河水库自然地理和水文特性,汤河水库实时洪水预报采用汤河水库洪水预报,考虑到各场次洪水预报误差之间存在一定的相依性,故采用人工神经网络方法构建实时校正系统,模型用实际洪水资料进行校准,并用2场较大洪水予以检验.2个场次的校验表明,实时校正能明显地提高洪水预报的精度     

Exploring the Regional Variance using ARMA-GARCH Models

Recently some generalized autoregressive conditional heteroskedasticity (GARCH) models are proposed and applied to various hydrologic variables to capture and remove the ARCH effect, which has been observed frequently in the residuals from linear autoregressive moving average (ARMA) models fitted to hydrologic time series. As a nonlinear phenomenon of variance behavior, the ARCH effect reveals partially nonstationarity and nonlinearity of hydrological processes. This paper deals with the variation of a river basin using the ARMA-GARCH error model, which combines an ARMA model for modelling the mean behavior and a GARCH model for modelling the variance behavior of the residuals from the ARMA model. Based on the heteroscedasticity of hydrological variable series, the time-varying regional variance is proposed to check the variation of a river basin for the first time. As a study case, the method is applied to four deseasonalized daily discharge series from the middle reach of Yangtze River, China. Through the analyses of the conditional variance in different streamflow series, it is concluded that: (1) The ARCH effect exists in all the studied series which means the stream processes is nonstationary in terms of the variance; (2) The variations of time-varying variances are similar for the series from adjacent hydrological stations, and the similarity degree increases from upstream to downstream; (3) The regional variance is time-varying and can be used for further regional research.     

Precipitation Estimation Using Support Vector Machine with Discrete Wavelet Transform

Precipitation prediction is of dispensable importance in many hydrological applications. In this study, monthly precipitation data sets from Serbia for the period 1946–2012 were used to estimate precipitation. To fulfil this objective, three mathematical techniques named artificial neural network (ANN), genetic programming (GP) and support vector machine with wavelet transform algorithm (WT-SVM) were applied. The mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), Pearson correlation coefficient (r) and coefficient of determination (R²) were used to evaluate the performance of the WT-SVM, GP and ANN models. The achieved results demonstrate that the WT-SVM outperforms the GP and ANN models for estimating monthly precipitation.     

基于神经网络理论的开河期冰坝预报研究

在北方高寒地区的天然河道,开河期冰坝形成和导致凌汛的机理复杂,目前的冰水动力学模型难以模拟和预报其发生、发展和溃决的过程,可用的冰坝预报多采用传统的统计学方法和经验判别式法,为应对严重的防凌形势,迫切需要找到冰坝预报的新方法。本文在对开河期冰坝成因及机理研究的基础上,建立了基于神经网络理论的冰坝预报模型,并将其应用到黑龙江上游凌汛灾害频发的漠河江段冰坝预报中。通过神经网络聚类法预报冰坝是否发生,神经网络聚类法预报精度为85%,高于传统统计学的几率分析法62%的预报精度。通过预报开河日期实现了对冰坝发生时间的预报,开河日期预报平均预见期为10天,最大误差2天,预报合格率100%。该模型提前准确预报2017年黑龙江漠河江段开河冰坝发生情况。及时、准确的冰坝预报能为提前制订主动防凌方案和采取必要防凌措施提供重要的依据。     

Bivariate Simulation of Potential Evapotranspiration Using Copula-GARCH Model

Developing statistical period and simulating the required values in case of data shortage increases certainty and reliability of simulations and statistical analyses, which is very important in studies on hydrology and water resources. Therefore, in this study, for simulating values of potential evapotranspiration at Birjand Station located in eastern Iran, contemporaneous autoregressive moving average (CARMA), CARMA-generalized autoregressive conditional heteroskedasticity (GARCH), and Copula-GARCH models were used in statistical period of 1984–2019. The potential evapotranspiration and relative humidity time series were simulated using these three models. CARMA model has acceptable accuracy for simulating potential evapotranspiration values due to the effect of the second parameter on simulations. Nash–Sutcliffe efficiency (NSE) coefficient of CARMA model for simulating potential evapotranspiration values was estimated as 0.85. NSE coefficient of CARMA-GARCH model was obtained as 0.87 through extracting residuals of CARMA model and simulating variance of data using GARCH model. Comparing the CARMA and CARMA-GARCH models with each other, it was concluded that a combination of two linear and non-linear time series models increases simulation accuracy to some extent. Using Clayton copula (the selected copula from the studied copulas), the mentioned values were simulated by Copula-GARCH model. The results showed that among the three models used, Copula-GARCH model reduced root mean square error of bivariate simulation compared to CARMA and CARMA-GARCH models by 15 and 13%, respectively. The results also showed that the proposed model simulates the average, first, and third quarters and range of changes in the data by 5 and 95% better than the two CARMA and CARMA-GARCH models.

     

WASMOD水文模拟残差统计特征检验

针对采用普通最小二乘法对水文模型进行参数估计时,模型残差需满足一定的内在统计假定的要求,分别选用Levene检验、Kolmogorov-Smirnov检验和残差自相关系数图等方法对水量平衡模型WASMOD的模型残差的同方差性、正态性以及相互独立性等统计假定进行了检验。结果表明:当对原始数据未经变换而直接采用普通最小二乘法进行参数估计时,得到的模型残差满足相互独立假定,但并不满足同方差性和正态性假定;对原始流量数据进行开根号变换,可以很好地解决模型残差的异方差性和非正态性问题。在模型残差统计假定得以满足的条件下,在月时间尺度上WASMOD模型可以为莺落峡流域的流量模拟与预报提供良好的工具。     

New Approaches for Estimation of Monthly Rainfall Based on GEP-ARCH and ANN-ARCH Hybrid Models

Accurate estimation of rainfall has an important role in the optimal water resources management, as well as hydrological and climatological studies. In the present study, two novel types of hybrid models, namely gene expression programming-autoregressive conditional heteroscedasticity (GEP-ARCH) and artificial neural networks-autoregressive conditional heteroscedasticity (ANN-ARCH) are introduced to estimate monthly rainfall time series. To fulfill this purpose, five stations with various climatic conditions were selected in Iran. The lagged monthly rainfall data was utilized to develop the different GEP and ANN scenarios. The performance of proposed hybrid models was compared to the GEP and ANN models using root mean square error (RMSE) and coefficient of determination (R²). The results show that the proposed GEP-ARCH and ANN-ARCH models give a much better performance than the GEP and ANN in all of the studied stations with various climates. Furthermore, the ANN-ARCH model generally presents better performance in comparison with the GEP-ARCH model.     

Deep Feature Learning Architectures for Daily Reservoir Inflow Forecasting

Inflow forecasting applies data supports for the operations and managements of reservoirs. To better accommodate the sophisticated characteristics of the daily reservoir inflow, two deep feature learning architectures, i.e., deep restricted Boltzmann machine (DRBM) and stack Autoencoder (SAE), respectively, are introduced in this paper. This study sheds light on the application of deep learning architectures for daily reservoir inflow forecasting, which has been attracting much attention in various areas for its ability to extract and learn useful features from a large number of data. Evaluations are made comparing the basic feed forward neural network (FFNN), the autoregressive integrated moving average (ARIMA), and two categories deep neural networks (DNNs) constructed by the integrations the FFNN with two deep feature learning architectures, named DRBM-based NN and stack SAE-based NN, respectively. Two daily inflow series of the Three Gorges reservoir (1/1/2000–31/12/2014) and the Gezhouba reservoir (1/1/1992–31/12/2014), China, are applied for four modeling exercises, respectively. The results show that, the two DNN models overwhelm the FFNN and the ARIMA models in terms of mean absolute percentage error, normalized root-mean-square error, and threshold statistic criteria.     

Forecasting Surface Water Level Fluctuations of Lake Van by Artificial Neural Networks

Lake Van in eastern Turkey has been subject to water level rise during the last decade and, consequently, the low-lying areas along the shore are inundated, giving problems to local administrators, governmental officials, irrigation activities and to people's property. Therefore, forecasting water levels of the Lake has started to attract the attention of the researchers in the country. An attempt has been made to use artificial neural networks (ANN) for modeling the temporal change water levels of Lake Van. A back-propagation algorithm is used for training. The study indicated that neural networks can successfully model the complex relationship between the rainfall and consecutive water levels. Three different cases were considered with the network trained for different arrangements of input nodes, such as current and antecedent lake levels, rainfall amounts. All of the three models yields relatively close results to each other. The neural network model is simpler and more reliable than the conventional methods such as autoregressive (AR), moving average (MA), and autoregressive moving average with exogenous input (ARMAX) models. It is shown that the relative errors for these two different models, are below 10% which is acceptable for engineering studies. In this study, dynamic changes of the lake level are evaluated. In contrast to classical methods, ANNs do not require strict assumptions such as linearity, normality, homoscadacity etc.     

A Comparative Study of Linear Stochastic with Nonlinear Daily River Discharge Forecast Models

Accurate forecast of the magnitude and timing of the flood peak river discharge and the extent of inundated areas during major storm events are a vital component of early warning systems around the world that are responsible for saving countless lives every year. This study assesses the forecast accuracy of two different linear and non-linear approaches to predict the daily river discharge. A new linear stochastic method is produced by evaluating a detailed comparison between three pre-processing approaches, differencing, standardization, spectral analysis, and trend removal. Daily river discharge values of the Bow River with strong seasonal and non-seasonal correlations located in Alberta, Canada were utilized in this study. The stochastic term for this daily flow time series is calculated with an auto-regressive integrated moving average. We found that seasonal differencing is the best stationarization method for periodic effect elimination. Moreover, the proposed non-linear Group Method of Data Handling (GMDH) model could overcome the known accuracy limitations of the classical GMDH models that use only two inputs in each neuron from the adjacent layer. The proposed new non-linear GMDH-based method (named GS-GMDH) can improve the structure of the classical linear GMDH. The GS-GMDH model produced the most accurate forecasts in the Bow River case study with statistical indices such as the coefficient of determination and Nash-Sutcliffe for the daily discharge time series higher than 97% and relative error less than 6%. Finally, an explicit equation for estimation of the daily discharge of the Bow River is developed using the proposed GS-GMDH model to showcase the practical application of the new method in flood forecasting and management.