Rainfall-Runoff Modeling using Clustering and Regression Analysis for the River Brahmaputra Basin

In this research, k-means, agglomerative hierarchical clustering and regression analysis have been applied in hydrological real time series in the form of patterns and models, which gives the fruitful results of data analysis, pattern discovery and forecasting of hydrological runoff of the catchment. The present study compares with the actual field data, predicted value and validation of statistical yields obtained from cluster analysis, regression analysis with ARIMA model. The seasonal autoregressive integrated moving average (SARIMA) and autoregressive integrated moving average (ARIMA) models is investigated for monthly runoff forecasting. The different parameters have been analyzed for the validation of results with casual effects. The comparison of model results obtained by K-means & AHC have very close similarities. Result of models is compared with casual effects in the same scenario and it is found that the developed model is more suitable for the runoff forecasting. The average value of R² determined is 0.92 for eight ARIMA models. This shows more accuracy of developed ARIMA model under these processes. The developed rainfall runoff models are highly useful for water resources planning and development.     

三种地下水位动态预测模型在吉林西部的应用与对比

准确而可靠地预测地下水埋深对生态环境保护和水资源规划管理具有重要意义。针对吉林西部浅层地下水位动态变化的复杂性和非线性,提出了基于小波分析与人工神经网络相结合的预测方法小波神经网络(WA-ANN)模型。将研究区2002年1月2009年12月当月降水量、蒸发量、人工开采量和前月平均地下水埋深4个参数作为输入,当月平均地下水埋深作为输出,建立浅层地下水埋深预测模型,并与BP神经网络(BP-ANN)模型和自回归移动平均(ARIMA)模型进行比较,对比分析了三者的建模过程及其模拟精度。结果显示:相比两种ANN模型,ARIMA模型建模过程更为简单,计算效率更高;但WA-ANN模型的拟合精度高于BP-ANN和ARIMA模型,预测效果更好。总体来看,WA-ANN模型在浅层地下水埋深预测中具有一定的应用推广价值。     

Optimization of the Garzan Hydropower System operations

Through the rapid development of the watersheds in Turkey with projects developed by incorporated companies, a problem has arisen of how to operate a cascade reservoir system composed of state- and private sector-owned reservoirs in terms of the volume and timing of water releases to meet downstream water demands. This study presents a catchment-based optimization model based on inflow forecast with frequent updating for the integrated operation of hydropower plants under various sales methods. The model is formulated in terms of nonlinear programming (NLP) on a monthly basis for a 1-year period to assess the production strategies of the system reservoirs for that year. This model provides the basic constraints on the reservoir volume for daily and hourly optimization procedures. Forecasted flows are generated using seasonal autoregressive integrated moving average (ARIMA) models based on historical flow values. The proposed model is tested on the Garzan Hydropower System using historical, mean, and forecasted flow values. The results show that the integrated operation plan and improvement in the accuracy of inflow forecasts yield economic benefits as a consequence of optimal reservoir operation.     

Univariate modelling of summer-monsoon rainfall time series: Comparison between ARIMA and ARNN

The present article reports studies to develop a univariate model to forecast the summer monsoon (June–August) rainfall over India. Based on the data pertaining to the period 1871–1999, the trend and stationarity within the time series have been investigated. After revealing the randomness and non-stationarity within the time series, the autoregressive integrated moving average (ARIMA) models have been attempted and the ARIMA(0,1,1) has been identified as a suitable representative model. Consequently, an autoregressive neural network (ARNN) model has been attempted and the neural network has been trained as a multilayer perceptron with the extensive variable selection procedure. Sigmoid non-linearity has been used while training the network. Finally, a three-three-one architecture of the ARNN model has been obtained and after thorough statistical analysis the supremacy of ARNN has been established over ARIMA(0,1,1). The usefulness of ARIMA(0,1,1) has also been described.     

Combined gamma and M-test-based ANN and ARIMA models for groundwater fluctuation forecasting in semiarid regions

The shortage of surface water in arid and semiarid regions has led to the more use of the groundwater resources. In these areas, the groundwater is essential for activities such as water supply and irrigation. One of the most important stages in sustainable yield of groundwater resources is awareness of groundwater level. In this study, we have applied artificial neural networks (ANN) and autoregressive integrated moving average (ARIMA) models for groundwater level forecasting to 4 months ahead in Shiraz basin, southwestern Iran. Time series analysis was conducted according to the Box–Jenkins method. Meanwhile, gamma and M-test were considered for determining the optimal input combination and length of training and testing data in the ANN model. The results indicated that performance of multilayer perceptron neural network (4, 14, 1) and ARIMA (2, 1, 2) is satisfactory in the groundwater level forecasting for one month ahead. The performance comparison shows that the ARIMA model performs appreciably better than the ANN.     

基于ARIMA模型的补远江含沙量预测

流域输沙的估算是水资源管理中广泛面临的问题。基于时间序列自回归滑动平均(ARIMA)预测模型,分别对补远江曼安水文站1993～2008年雨季、旱季月平均含沙量资料进行建模拟合。综合AIC值、相对误差,确定模型的阶数,运用Marquardt非线性最小二乘法估计模型参数,建立ARIMA预测模型。经检验,雨季AIC=-61.046,旱季AIC=-131.785,相对误差低于20%的合格率分别为92.1%、76.9%,残差序列均为白噪声序列,表明旱季ARIMA(1,1,1)、雨季ARIMA(1,1,2)模型较为合理。应用模型对2009～2011年曼安水文站的雨季、旱季平均含沙量进行了预测,实现了河流输沙状况的短期预报。     

Monthly karstic spring flow forecasting using a sequential gaussian simulation technique

Analyzing groundwater hydrologic equations related to karstic aquifers and spring hydrograph simulation have become the focus of many researches. Having double or triple porosity structure, mixed flow nature, and varying conduit permeability have made these formations become complex heterogenic systems with great temporal and spatial hydrodynamic variability. In this paper, a conditional sequential gaussian simulation (SGS) is used to simulate monthly flow data of five karstic springs with different hydrogeological properties, located in Zagros Mountain Chain, in western Iran. To evaluate the performance of the SGS algorithm, the results are compared with those of an autoregressive integrated moving average (ARIMA) model. The results demonstrate the efficiency of the SGS model in simulation of monthly flows compared to the ARIMA model. They also show the suitability of this model for handling uncertainty associated with karstic spring flows through generation of several equally probable stochastic realizations.     

Assessment of prediction performances of stochastic models: Monthly groundwater level prediction in Southern Italy

Stochastic modelling of hydrological time series with insufficient length and data gaps is a serious challenge since these problems significantly affect the reliability of statistical models predicting and forecasting skills. In this paper, we proposed a method for searching the seasonal autoregressive integrated moving average(SARIMA) model parameters to predict the behavior of groundwater time series affected by the issues mentioned. Based on the analysis of statistical indices, 8 stations among 44 available within the Campania region(Italy) have been selected as the highest quality measurements. Different SARIMA models, with different autoregressive, moving average and differentiation orders had been used.By reviewing the criteria used to determine the consistency and goodness-of-fit of the model, it is revealed that the model with specific combination of parameters, SARIMA(0,1,3)(0,1,2) _(12), has a high R~2 value,larger than 92%, for each of the 8 selected stations. The same model has also good performances for what concern the forecasting skills, with an average NSE of about 96%. Therefore, this study has the potential to provide a new horizon for the simulation and reconstruction of groundwater time series within the investigated area.     

Analysis and prediction of Caspian Sea level pattern anomalies observed by satellite altimetry using autoregressive integrated moving average models

In this study, we successfully present the analysis and forecasting of Caspian Sea level pattern anomalies based on about 15 years of Topex/Poseidon and Jason-1 altimetry data covering 1993–2008, which are originally developed and optimized for open oceans but have the considerable capability to monitor inland water level changes. Since these altimetric measurements comprise of a large datasets and then are complicated to be used for our purposes, principal component analysis is adopted to reduce the complexity of large time series data analysis. Furthermore, autoregressive integrated moving average (ARIMA) model is applied for further analyzing and forecasting the time series. The ARIMA model is herein applied to the 1993–2006 time series of first principal component scores (sPC1). Subsequently, the remaining data acquired from sPC1 is used for verification of the model prediction results. According to our analysis, ARIMA (1,1,0)(0,1,1) model has been found as optimal representative model capable of predicting pattern of Caspian Sea level anomalies reasonably. The analysis of the time series derived by sPC1 reveals the evolution of Caspian Sea level pattern can be subdivided into five different phases with dissimilar rates of rise and fall for a 15-year time span.     

Intermittent reservoir daily-inflow prediction using lumped and distributed data multi-linear regression models

In this study, multi-linear regression (MLR) approach is used to construct intermittent reservoir daily inflow forecasting system. To illustrate the applicability and effect of using lumped and distributed input data in MLR approach, Koyna river watershed in Maharashtra, India is chosen as a case study. The results are also compared with autoregressive integrated moving average (ARIMA) models. MLR attempts to model the relationship between two or more independent variables over a dependent variable by fitting a linear regression equation. The main aim of the present study is to see the consequences of development and applicability of simple models, when sufficient data length is available. Out of 47 years of daily historical rainfall and reservoir inflow data, 33 years of data is used for building the model and 14 years of data is used for validating the model. Based on the observed daily rainfall and reservoir inflow, various types of time-series, cause-effect and combined models are developed using lumped and distributed input data. Model performance was evaluated using various performance criteria and it was found that as in the present case, of well correlated input data, both lumped and distributed MLR models perform equally well. For the present case study considered, both MLR and ARIMA models performed equally sound due to availability of large dataset.     

Monthly reservoir inflow forecasting using a new hybrid SARIMA genetic programming approach

Forecasting reservoir inflow is one of the most important components of water resources and hydroelectric systems operation management. Seasonal autoregressive integrated moving average (SARIMA) models have been frequently used for predicting river flow. SARIMA models are linear and do not consider the random component of statistical data. To overcome this shortcoming, monthly inflow is predicted in this study based on a combination of seasonal autoregressive integrated moving average (SARIMA) and gene expression programming (GEP) models, which is a new hybrid method (SARIMA–GEP). To this end, a four-step process is employed. First, the monthly inflow datasets are pre-processed. Second, the datasets are modelled linearly with SARIMA and in the third stage, the non-linearity of residual series caused by linear modelling is evaluated. After confirming the non-linearity, the residuals are modelled in the fourth step using a gene expression programming (GEP) method. The proposed hybrid model is employed to predict the monthly inflow to the Jamishan Dam in west Iran. Thirty years’ worth of site measurements of monthly reservoir dam inflow with extreme seasonal variations are used. The results of this hybrid model (SARIMA–GEP) are compared with SARIMA, GEP, artificial neural network (ANN) and SARIMA–ANN models. The results indicate that the SARIMA–GEP model (R ²=78.8, VAF =78.8, RMSE =0.89, MAPE =43.4, CRM =0.053) outperforms SARIMA and GEP and SARIMA–ANN (R ²=68.3, VAF =66.4, RMSE =1.12, MAPE =56.6, CRM =0.032) displays better performance than the SARIMA and ANN models. A comparison of the two hybrid models indicates the superiority of SARIMA–GEP over the SARIMA–ANN model.     

Stochastic modelling of mineral deposits

Mineral deposits are characterized by certain continuity of assay values, thickness and top and bottom surfaces of ore zones etc., which are amenable to stochastic modelling with respect to spatial coordinates. The French School (Matheron, 1963) introduced rather difficult terminology of semi-variogram, kriging etc. for quantitative assessment of reserves and average grade of mining property under the assumption of second-order stationarity of first differenced (d=1) data. A more general, powerful and well-known time-domain (spatial) stochastic models (ARIMA (p, d, q); based on Box and Jenkins, 1970, 1976; Anderson, 1976) are introduced herein which include Matheron Model (d=1) as a special case.     

Determination and prediction of standardized precipitation index (SPI) using TRMM data in arid ecosystems

Drought over a period threatens the water resources, agriculture, and socioeconomic activities. Therefore, it is crucial for decision makers to have a realistic anticipation of drought events to mitigate its impacts. Hence, this research aims at using the standardized precipitation index (SPI) to predict drought through time series analysis techniques. These adopted techniques are autoregressive integrating moving average (ARIMA) and feed-forward backpropagation neural network (FBNN) with different activation functions (sigmoid, bipolar sigmoid, and hyperbolic tangent). After that, the adequacy of these two techniques in predicting the drought conditions has been examined under arid ecosystems. The monthly precipitation data used in calculating the SPI time series (SPI 3, 6, 12, and 24 timescales) have been obtained from the tropical rainfall measuring mission (TRMM). The prediction of SPI was carried out and compared over six lead times from 1 to 6 using the model performance statistics (coefficient of correlation (R), mean absolute error (MAE), and root mean square error (RMSE)). The overall results prove an excellent performance of both predicting models for anticipating the drought conditions concerning model accuracy measures. Despite this, the FBNN models remain somewhat better than ARIMA models with R?≥?0.7865, MAE?≤?1.0637, and RMSE?≤?1.2466. Additionally, the FBNN based on hyperbolic tangent activation function demonstrated the best similarity between actual and predicted for SPI 24 by 98.44%. Eventually, all the activation function of FBNN models has good results respecting the SPI prediction with a small degree of variation among timescales. Therefore, any of these activation functions can be used equally even if the sigmoid and bipolar sigmoid functions are manifesting less adjusted R² and higher errors (MAE and RMSE). In conclusion, the FBNN can be considered a promising technique for predicting the SPI as a drought monitoring index under arid ecosystems.     

An analysis of Indian tide-gauge records

The paper presents an analysis of four Indian tide-gauge records. The stations were: Bombay, Madras, Cochin and Vishakhapatnam (Vizag). They were selected because of their reliability. There was no evidence of a monotonic rising trend at all four stations. The test by Mann and Kendall (loc. cit.) showed a rising trend at Bombay from 1940 to 1986 and at Madras from 1910 to 1933. The other records did not reveal a significant trend. The records reveal evidence of long-period cycles (50–60 year period), with shorter cycles (4.5 to 5.7-year period) riding on them. Spectral peaks corresponding to shorter cycles passed a false alarm probability test at 95% level of significance. The peaks were identified by computing periodograms and by maximizing the entropy of the time series. ARIMA models suggest a third order autoregressive model for Bombay and Madras (1953–1986). The remaining records only had a moving average component. Monthly tide-gauge data of Bombay reveal a 13.4-month cycle which was statistically significant. This was close to the 14.7-month Chandler wobble. But, an interaction between a 13.4-month and an annual cycle could not fully explain the observed short period cycles. Finally, the paper summarizes evidence to indicate that a pattern exists between fluctuations of monsoon rain and relative sea level at Bombay.     

Estimation of the transfer function by autoregressive deconvolution techniques—An application to time series analysis

The transfer function of time-dependent models is classically inferred by the ordinary least squares (OLS) techniques. This OLS technique assumes independence of the residuals with time. However, in practical cases, this hypothesis is often not justified producing inefficient estimation of the transfer function. When the residuals constitute an autoregressive process, we propose to apply the Box-Jenkins' method to model the residuals, and to modify in a simple manner the primary convolution equation. Then, a multivariate regression technique is used to infer the transfer function of the new equation producing time-independent residuals. This three-step autoregressive deconvolution technique is particularly efficient for time series analysis. The reconstitution and the forecasting of real data are improved efficiently. Theoretically, the proposed method can be extended to the convolution equations for which the residuals follow a moving average or an autoregressive-moving average process, but the mathematical formulation is no longer direct and explicit. For this general case, we propose to approximate the moving average or the autoregressive-moving average process by an autoregressive process of sufficient order, and then the transfer function. Two case studies in hydrogeology will be used to illustrate the procedure.     

Surface runoff prediction regarding LULC and climate dynamics using coupled LTM,optimized ARIMA,and GIS-based SCS-CN models in tropical region

The effects of climate and land use/land cover (LULC) dynamics have directly affected the surface runoff and flooding events. Hence, current study proposes a full-packaged model to monitor the changes in surface runoff in addition to forecast of the future surface runoff based on LULC and precipitation variations. On one hand, six different LULC classes were extracted from Spot-5 satellite image. Conjointly, land transformation model (LTM) was used to detect the LULC pixel changes from 2000 to 2010 as well as predict the 2020 ones. On the other hand, the time series-autoregressive integrated moving average (ARIMA) model was applied to forecast the amount of rainfall in 2020. The ARIMA parameters were calibrated and fitted by latest Taguchi method. To simulate the maximum probable surface runoff, distributed soil conservation service-curve number (SCS-CN) model was applied. The comparison results showed that firstly, deforestation and urbanization have been occurred upon the given time, and they are anticipated to increase as well. Secondly, the amount of rainfall has non-stationary declined since 2000 till 2015 and this trend is estimated to continue by 2020. Thirdly, due to damaging changes in LULC, the surface runoff has been also increased till 2010 and it is forecasted to gradually exceed by 2020. Generally, model calibrations and accuracy assessments have been indicated, using distributed-GIS-based SCS-CN model in combination with the LTM and ARIMA models are an efficient and reliable approach for detecting, monitoring, and forecasting surface runoff.     

Forecasting for flood warning

Advances in flood forecasting have been constrained by the difficulty of estimating rainfall continuously over space, for catchment-, national- and continental-scale areas. This has had a concomitant impact on the choice of appropriate model formulations for given flood-forecasting applications. Whilst weather radar used in combination with raingauges – and extended to utilise satellite remote-sensing and numerical weather prediction models – have offered the prospect of progress, there have been significant problems to be overcome. These problems have curtailed the development and adoption of more complete distributed model formulations that aim to increase forecast accuracy. Advanced systems for weather radar display and processing, and for flood forecast construction, are now available to ease the task of implementation. Applications requiring complex networks of models to make forecasts at many locations can be undertaken without new code development and be readily revised to take account of changing requirements. These systems make use of forecast-updating procedures that assimilate data from telemetry networks to improve flood forecast performance, at the same time coping with the possibility of data loss. Flood forecasting systems that integrate rainfall monitoring and forecasting with flood forecasting and warning are now operational in many areas. Present practice in flood modelling and forecast updating is outlined from a UK perspective. Challenges for improvement are identified, particularly against a background of greater access to spatial datasets on terrain, soils, geology, land-cover, and weather variables. Representing the effective runoff production and translation processes operating at a given grid or catchment scale may prove key to improved flood simulation, and robust application to ungauged basins through physics-based linkages with these spatial datasets. The need to embrace uncertainty in flood-warning decision-making is seen as a major challenge for the future. To cite this article: R.J. Moore et al., C. R. Geoscience 337 (2005).     

Meteotsunami forecasting: sensitivities demonstrated by the 2008 Boothbay,Maine, event

To support development of a meteotsunami forecasting capability for the USA, the National Oceanic and Atmospheric Administration funded a project in 2011 focused on meteotsunami forecasting for the US east coast. Meteotsunami forecasting shares many similarities with traditional tsunami forecasting, though the characterization and integration of the source with numerical forecast models is much different. Given meteotsunami source characterization through atmospheric observations and models, it is conceivable that meteotsunami alerts could be issued and their impact forecasted using existing tsunami forecast models with high-resolution coastal definition. To test this, the 2008 Boothbay, Maine, meteotsunami is simulated using an atmospheric source consisting of a moving pressure disturbance coupled with a tsunami forecast model. Sensitivities of the modeled impact to the source characteristics, such as speed, wavelength, and direction, are also tested. Results show that the observed impact can be re-created through numerical modeling when the pressure disturbance period is roughly matched with the harbor resonance and observed meteotsunami period.     

A model for solar quiet day variation at low latitude from past observations using singular spectrum analysis

Singular spectrum isolates significant principal components in a time series from the embedded noise. This tool-kit is used to reconstruct trend-free individual time series, formed by restricting the mean monthly hourly values of geomagnetic field to one hour at a time at a low latitude station Alibag (dipole latitude 9.5°N). Each reconstructed component is extrapolated over the next 12 values using an autoregressive model based on Burg’s maximum entropy algorithm. Details of a numerical approach to increase the reliability of extrapolation are highlighted. The extrapolated reconstructed components are then combined to generate predicted monthly values for each hour. The mean diurnal variation for any month obtained from the extrapolated individual hourly time series compares favorably with the observations. This approach to Sq(H) modelling incorporating both long and short term variations will be beneficial in the derivation of Dst index.     

基于时间序列分析改进法的地下水位动态预报——以吉林省桦甸市为例

采用逐步回归法替代传统时间序列分析模型中的多项式拟合法和自回归法,仅选用对因变量影响较大的自变量建立方程,提高了模型的精度。依据桦甸市26130018号观测井2000—2008年逐月的地下水位埋深资料,分别利用传统的、改进的时间序列分析法建立模型,以2009—2010年的观测数据进行精度检验,选择较优的改进模型预测了2011—2013年逐月的地下水位。结果表明:2个模型均满足精度要求,但经过改进后,随机方程和趋势方程的相关系数分别由0.830 7和0.803 9增至0.913 5和0.970 9,拟合结果明显提高。