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.     

A hidden Markov model segmentation procedure for hydrological and environmental time series

In this paper we present a procedure for the segmentation of hydrological and enviromental time series. We consider the segmentation problem from a purely computational point of view which involves the minimization of Huberts segmentation cost; in addition this least squares segmentation is equivalent to Maximum Likelihood segmentation. Our segmentation procedure maximizes Likelihood and minimizes Huberts least squares criterion using a hidden Markov model (HMM) segmentation algorithm. This algorithm is guaranteed to achieve a local maximum of the Likelihood. We evaluate the segmentation procedure with numerical experiments which involve artificial, temperature and river discharge time series. In all experiments, the procedure actually achieves the global minimum of the Likelihood; furthermore execution time is only a few seconds, even for time series with over a thousand terms.     

Singular spectrum analysis and forecasting of hydrological time series

The singular spectrum analysis (SSA) technique is applied to some hydrological univariate time series to assess its ability to uncover important information from those series, and also its forecast skill. The SSA is carried out on annual precipitation, monthly runoff, and hourly water temperature time series. Information is obtained by extracting important components or, when possible, the whole signal from the time series. The extracted components are then subject to forecast by the SSA algorithm. It is illustrated the SSA ability to extract a slowly varying component (i.e. the trend) from the precipitation time series, the trend and oscillatory components from the runoff time series, and the whole signal from the water temperature time series. The SSA was also able to accurately forecast the extracted components of these time series.     

GRACE月时变模型缺失值的填补方法与精度分析

长时间序列的GRACE时变重力场对研究全球地表质量变化具有重要的意义.部分月份的GRACE卫星观测数据质量不佳导致了相应月份的时变重力场模型缺失,为了保持时变重力场模型的连续性,可采用一定的插值方法填补.本文以ITSG-Grace2016时变重力场模型序列为研究对象,详细分析了三次样条插值、三次埃尔米特插值和三次多项式插值等3种方法用于填补GRACE时变模型序列的精度,实验结果表明:(1)利用3种插值方法获取空缺1个月或连续空缺2个月的时变重力场模型时,插值时变模型与实测时变模型比较,阶误差均较小,且三次埃尔米特插值的精度稍好;(2)利用插值时变模型分析区域质量变化时,在空缺1个月数据的情况下,插值时变模型与实测时变模型符合度较高,但在连续空缺2个月数据的情况下,插值时变模型与实测时变模型的计算结果差异较大,说明利用阶误差评定模型精度具有一定局限性;(3)对区域质量变化的趋势项进行分析时,区域质量变化的复杂程度决定了模型内插的精度,当时间序列的长度在3年或3年以上时,插值时变模型的精度对区域质量变化分析的影响较小.在分析区域质量变化时,三次样条插值方法的插值结果与实测结果更为接近,建议...     

Application of spatial EOF and multivariate time series model for evaluating agricultural drought vulnerability in Korea

This study proposed a methodology using the empirical orthogonal function (EOF) and multivariate time series model for the analysis of drought both in time and space. The methodology proposed was then applied to evaluate the vulnerability of agricultural drought of major river basins in Korea. First, the three-month SPI data from 59 rain gauge stations over the Korean Peninsula were analyzed by deriving and spatially characterizing the EOFs. The shapes of major estimated EOFs were found to well reflect the observed spatial pattern of droughts. Second, the coefficient time series of estimated EOFs were then fitted by a multivariate time series model to generate the SPI data for 10,000 years, which were used to derive the annual maxima series of areal average drought severity over the Korean Peninsula. These annual maxima series were then analyzed to determine the mean drought severity for given return periods. Four typical spatial patterns of drought severity could also be selected for those return periods considered. This result shows that the southern part of the Korean Peninsula is most vulnerable to drought than the other parts. Finally, the agricultural drought vulnerability was evaluated by considering the potential water supply from dams. In an ideal case, when all the maximum dam storage was assumed to be assigned to agriculture, all river basins in Korea were found to have the potential to overcome a 30-year drought. However, under more realistic conditions considering average dam storage and water allocation priorities, most of the river basins could not overcome a 30-year drought.     

Seemingly unrelated intervention time series models for effectiveness evaluation of large scale environmental remediation

Large scale environmental remediation projects applied to sea water always involve large amount of capital investments. Rigorous effectiveness evaluations of such projects are, therefore, necessary and essential for policy review and future planning. This study aims at investigating effectiveness of environmental remediation using three different Seemingly Unrelated Regression (SUR) time series models with intervention effects, including Model (1) assuming no correlation within and across variables, Model (2) assuming no correlation across variable but allowing correlations within variable across different sites, and Model (3) allowing all possible correlations among variables (i.e., an unrestricted model). The results suggested that the unrestricted SUR model is the most reliable one, consistently having smallest variations of the estimated model parameters. We discussed our results with reference to marine water quality management in Hong Kong while bringing managerial issues into consideration.     

Unsaturated flows in soils with self-similar hydraulic conductivity distribution

In this article, we are concerned with the statistics of steady unsaturated flow in soils with a fractal hydraulic conductivity distribution. It is assumed that the spatial distribution of log hydraulic conductivity can be described as an isotropic stochastic fractal process. The impact of the fractal dimension of this process, the soil pore-size distribution parameter, and the characteristic length scale on the variances of tension head and the effective conductivity is investigated. Results are obtained for one-dimensional and three-dimensional flows. Our results indicate that the tension head variance is scale-dependent for fractal distribution of hydraulic conductivity. Both tension head variance and effective hydraulic conductivity depend strongly on the fractal dimension. The soil pore-size distribution parameter is important in reducing the variability of the unsaturated hydraulic conductivity and of the fluxes.     

foF2月中值太阳循环变化及单站谱模型研究

利用我国9个电离层观测站第21和22太阳周大约20年的foF2月中值数据,分析太阳活动和地磁活动对电离层foF2的影响,结果显示白天和夏季夜间foF2和太阳黑子数R之间存在着明显非线性关系,并且随着纬度的降低逐渐增强.当回归分析加入地磁Ap指数时,多重回归模型与实测值误差进一步减小,说明同时考虑太阳活动和地磁活动的非线性影响能够更好地描述foF2的变化.基于foF2与太阳黑子数R及地磁指数Ap之间的非线性统计关系,利用Fourier级数建立9个单站谱模型,并与国际参考电离层IRI进行了比较,精度有一定提高.     

Short and long memory unobserved components in hydrological time series

In this paper a semiparametric approach is introduced to decompose an ARFIMA model in the long memory and short memory unobserved components. The procedure is based on the DECOMEL method which produces a statistical decomposition by minimizing the Euclidean distance between the spectrum of the aggregated series and the sum of the parametric spectra of the components. The extension to long memory stationary models is achieved defining an approximate model where the fractional operator is replaced by the ratio of two polynomials of order one. The feasibility and performance of the proposed procedure are discussed through a case study.     

Multisite generalization of a daily stochastic precipitation generation model

The familiar chain-dependent-process stochastic model of daily precipitation, consisting of a two-state, first-order Markov chain for occurrences and a mixed exponential distribution for nonzero amounts, is extended to simultaneous simulation at multiple locations by driving a collection of individual models with serially independent but spatially correlated random numbers. The procedure is illustrated for a network of 25 locations in New York state, with interstation separations ranging approximately from 10 to 500 km. The resulting process reasonably reproduces various aspects of the joint distribution of daily precipitation observations at the modeled locations. The mixed exponential distributions, in addition to providing substantially better fits than the more conventional gamma distributions, are convenient for representing the tendency for smaller amounts at locations near the edges of wet areas. Means, variances, and interstation correlations of monthly precipitation totals are also well reproduced. In addition, the use of mixed exponential rather than gamma distributions yields interannual variability in the synthetic series that is much closer to the observed.     

Bootstrap based artificial neural network (BANN) analysis for hierarchical prediction of monthly runoff in Upper Damodar Valley Catchment

Estimation of runoff is a prerequisite for many applications involving conservation and management of water resources. This study is undertaken in the Upper Damodar Valley Catchment (UDVC) having a drainage area of 17513.08 km² for prediction of monthly runoff. Thirty one microwatersheds and 15 sub-watersheds were selected from a total of 716 microwatersheds in the catchment area for this study. The feasibility of using different soil attributes (particle size distribution, organic matter content and apparent density), topographic attributes (primary, secondary and compound), geomorphologic attributes (basin, relief and network indices) and vegetation attribute as Normalized Difference Vegetation Index (NDVI), on prediction of monthly runoff were explored in this study. Principal Component Analysis (PCA) was applied to minimize the data redundancy of the input variables. Ten significant input variables namely; watershed length (km), elongation ratio, bifurcation ratio, area ratio, coarse sand (%), fine sand (%), elevation (m), slope (°), profile curvature (rad/m) and NDVI were selected. The selected input variables were added in hierarchy with monthly rainfall (mm) as inputs for prediction of monthly runoff (mm) using Bootstrap based artificial neural networks (BANN). The performance of the models was tested using Spearman’s correlation coefficient (r), coefficient of efficiency (COE), Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). Best performance was observed for model with monthly rainfall, slope, coarse sand, bifurcation ratio and Normalized Difference Vegetation Index (NDVI) as inputs (r = 0.925 and COE = 0.839). Increase in number of input variables did not necessarily yield better performances of the BANN models. Selection of relevant inputs and their combinations were found to be key elements in determining the performance of BANN models. Annual runoff map was generated for all the microwatersheds utilizing the weights of the best performing BANN model. This study reveals that the specific combinations of soil, topography, geomorphology and vegetation inputs can be utilized for better prediction of monthly runoff.     

Sampling strategy to describe the temporal hydrochemical characteristics of an alpine proglacial stream

A hierarchical sampling programme (including continuous monitoring, twice-daily sampling and sampling at hourly intervals over selected 24 hour periods) was devised to support hydrochemical and hydrological research programmes on an alpine proglacial stream. The rationale for the research and for the sampling programme are explained and the hydrochemical time series generated over an ablation season are analysed to assess the degree to which they support the study aims. It appears that there is no satisfactory substitute for the chemical analysis of at least two water samples taken at approximately maximum and minimum discharge every day, if seasonal variations in meltwater chemistry are to be effectively characterized. Such time series data can be used to estimate Box-Jenkins transfer function-noise models between particular solutes (SO²⁻₄, Ca²⁺, Mg²⁺, Na⁺ and possibly K⁺) and either discharge or electrical conductivity, which can then be used to fill any short gaps in the data. This approach is not satisfactory even for filling short gaps in the twice-daily determinations of pH, HCO⁻₃ and NO⁻₃. At the diurnal time-scale (based on hourly determinations over 24 hour periods) electrical conductivity seems to provide a good surrogate for most of the solutes studied. HCO⁻₃, SO²⁻₄, Ca²⁺ and Mg²⁺ were found to be particularly strongly related to electrical conductivity and there was little if any significant serial autocorrelation in the residuals from all of the simple linear regression relationships that were estimated between individual species and conductivity. It is concluded that the hierarchical sampling design was suitable for the purposes of the study, and that the continuous monitoring of electrical conductivity provides excellent supporting information to the chemical analysis of water samples if it is used carefully as a means of short term calibration and interpolation of the solute record.     

Kalman filter estimation for periodic autoregressive-moving average models

An exact maximum likelihood procedure is presented for estimating the parameters of a periodic autogressive-moving average (PARMA) model. To develop an estimator which is both statistically and computationally efficient, the PARMA class of models is written using a state-space representation and a Kalman filtering algorithm is used to estimate the parameters. In order to demonstrate how to fit PARMA models in practice, the most appropriate types of PARMA models are identified for fitting to two average monthly riverflow time series and the new estimator is employed for estimating the model parameters.     

Revisiting the Phasor-Walkout method for detailed investigation of harmonic signals in time series

A well-known but rarely used powerful method to investigate the presence of harmonic signals in time series is the Phasor Walkout method (other names are: Graphical Fourier Transform, Summation Dial, Complex Demodulation). At a given test frequency the complex contributions (phasors) to the Fourier Transform of each sample in an equidistantly sampled series are added vectorially in the complex plane. The resulting pattern, the walkout, reveals information about the properties of the signal which is not easy to obtain by other methods. Synthetic examples are used to demonstrate the resolving power of the method. The following geophysical examples for the application of this method are shown: determination of the frequency of the breathing mode₀ S ₀ of the earth after a large earthquake; the study of superconducting gravimeter records after a large deep earthquake used in the core mode interpretation of a spectral peak, the study of the residualS ₃ (8 h period) signal in a tidal record and the bichromatic Rayleigh-waves from Mount Pinatubo on June 15, 1991.     

Scenario analysis for assessing the impact of hydraulic fracturing on stream low flows using the SWAT model

Scientists and water users are concerned about the potential impact on water resources, particularly during low-flow periods, of freshwater withdrawals for hydraulic fracturing (fracking). Therefore, the objective of this paper is to assess the potential impact of hydraulic fracturing on water resources in the Muskingum watershed of Eastern Ohio, USA, especially due to the trend of increased withdrawals for hydraulic fracking during drought years. The Statistical Downscaling Model (SDSM) was used to generate 30 years of plausible future daily weather series in order to capture the possible dry periods. The data generated were incorporated in the Soil and Water Assessment Tool (SWAT) to examine the level of impact due to fracking at various scales. Analyses showed that water withdrawal due to hydraulic fracking had a noticeable impact, especially during low-flow periods. Clear changes in the 7-day minimum flows were detected among baseline, current and future scenarios when the worst-case scenario was implemented. The headwater streams in the sub-watersheds were highly affected, with significant decrease in 7-day low flows. The flow alteration in hydrologically-based (7Q10, i.e. 7-day 10-year low flow) or biologically-based (4B3 and 1B3) design flows due to hydraulic fracking increased with decrease in the drainage area, indicating that the relative impact may not be as great for higher order streams. Nevertheless, change in the annual mean flow was limited to 10%.     

基于AR模型模拟超高层建筑的脉动风速时程

风荷载是超高层建筑设计的主要荷载之一,而且通过风振时域分析可以更全面地了解超高层建筑风振响应特性,更直观地反映超高层建筑风致振动控制的有效性。因此,本文使用线性滤波法即白噪声滤波法(white noise filtration method,WNFM)中的自回归(auto-regressive,AR)模型模拟超高层建筑的风速时程。首先,考虑超高层建筑风速时程的时间和空间相关性,导出了四阶AR模型的参数表达式。接着,基于AR模型模拟了一幢高度为200 m超高层建筑的风速时程。最后,通过比较模拟风速功率谱、模拟自相关函数和互相关函数与目标风速功率谱、目标自相关函数和互相关函数的吻合程度,验证基于AR模型模拟超高层建筑风速时程的可行性。     

小波分析在GPS位移时间序列特征中的应用

使用福建GPS台网2004年3月—2008年10月的连续观测资料,对各基准地震站原始数据进行处理,得到位移时间序列,进行初步分析。在此基础上,采用小波分析方法提取时间序列的时频特征,从而得到非线性变化信息,为GPS在大地震前获取前兆资料提供探索方向,进而通过对位移时间序列异常变化与区域地壳运动关系的研究,探讨两者间的内在联系。     

An analytical approach to capture zone delineation for a well near a stream with a leaky layer

Abstract

An analytical solution is developed to delineate the capture zone of a pumping well in an aquifer with a regional flow perpendicular to a stream, assuming a leaky layer between the stream and the aquifer. Three different scenarios are considered for different pumping rates. At low pumping rates, the capture zone boundary will be completely contained in the aquifer. At medium pumping rates, the tip of the capture zone boundary will intrude into the leaky layer. Under these two scenarios, all the pumped water is supplied from the regional groundwater flow in the aquifer. At high pumping rates, however, the capture zone boundary intersects the stream and pumped water is supplied from both the aquifer and the stream. The two critical pumping rates which separate these three scenarios, as well as the proportion of pumped water from the stream and the aquifer, are determined for different hydraulic settings.

Editor D. Koutsoyiannis; Associate editor A. Koussis

Citation Asadi-Aghbolaghi, M., Rakhshandehroo, G.R., and Kompani-Zare, M., 2013. An analytical approach to capture zone delineation for a well near a stream with a leaky layer. Hydrological Sciences Journal, 58 (8), 1813–1823.     

Worldwide correlations for subaerial aqueous flows with exponential longitudinal profiles

It is shown that very strong, worldwide correlations exist between the bed concavity coefficients of a wide range of subaerial aqueous flows with exponential longitudinal profiles and both the corresponding stream segment lengths and exponential bed particle size diminution coefficients. The former correlation is complementary to an existing similar correlation for the exponential size diminution coefficients, while the latter is consistent with earlier theoretical correlations based on very limited data. The data supporting the correlations extend over virtually the whole range of stream lengths, solids concentrations, and bed sediment particle sizes found on Earth. This universality strongly suggests that there are underlying mechanisms common to all kinds of mobile bed subaerial aqueous flows. However, the scatter of the data for the correlations is significant and is mostly attributable to variations in hydraulic conditions and sediment properties rather than measurement errors. Some of the conditions and properties have been identified, but others remain obscure. Copyright © 1999 John Wiley & Sons, Ltd.