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.     

Similarity search and pattern discovery in hydrological time series data mining

The rapid development of data mining provides a new method for water resource management, hydrology and hydroinformatics research. In the paper, based on data mining theory and technology, we analyse hydrological daily discharge time series of the Shaligunlanke Station in the Tarim River Basin in China from the year 1961 to 2000. Firstly, according to the four monthly statistics, namely mean monthly discharge, monthly maximum discharge, monthly amplitude and monthly standard deviation, K‐mean clustering was used to segment the annual process of the daily discharge. The clustering result showed that the annual process of the daily discharge can be divided into five segments: snowmelt period I (April), snowmelt period II (May), rainfall period I (June–August), rainfall period II (September) and dry period (October–December and January–March). Secondly, dynamic time warping (DTW), which is a different distance metric method from the traditional Euclidian distance metric, was used to look for similarities in the discharge process. On the basis of the similarity matrix, the similar discharge processes can be mined in each period. Thirdly, agglomerative hierarchical clustering was used to cluster and discover the discharge patterns in terms of the autoregressive model. It was found that the discharge had a close relationship with the temperature and the precipitation, and the discharge processes were more similar under the same climatic condition. Our study shows that data mining is a feasible and efficient approach to discover the hidden information in the historical hydrological data and mining the implicative laws under the hydrological process. Copyright © 2010 John Wiley & Sons, Ltd.     

Detection of changes in precipitation and runoff over eastern Canada and U.S. using a Bayesian approach

Inference about the existence and characteristics of changes in mean level of hydrometeorological sequences that may be generated by climatic variability is an important step before developing management rules in water resources systems. This paper presents a Bayesian approach, based on a single shifting model, which can be used to study a change in the mean level of a set of independent normal random variables. Two different problems are considered: the first is the detection of a change, while the second is the estimation of the change-point and its amplitude under the assumption that a change has occurred. This method is applied to precipitation and runoff data series over eastern Canada and U.S. during the twentieth century. The main results show an increase in the late sixties in the Eastern North American precipitation. This supports conclusions drawn from a number of studies which identified the late sixties to early seventies as a period of possible change.     

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.     

Analysis and interpretation of patterns within and between hydroclimatological time series in an alpine glacier basin

This paper explores patterns within and between climatological and hydrological time series from an alpine glacier basin. Time series recorded in the basin of the Haut Glacier d'Arolla over the 1989 ablation season are subdivided into five subperiods. Box-Jenkins ARIMA (AutoRegressive Integrated Moving Average) and TFN (Transfer Function-Noise) models are estimated for each of the five subperiods and differences between the models are interpreted in the context of changing glacier hydrology, particularly the changing nature and extent of the glacier drainage network.     

Statistical characteristics of detectable inhomogeneities in observed meteorological time series

Statistical characteristics of detectable inhomogeneities [IHs] in more than 600 observed meteorological time series have been investigated using 16 objective homogenisation methods. Forty and 100 year long series of monthly or annual characteristics of surface air temperature, precipitation total and relative air humidity from the Czech Republic and Hungary were examined. The area of the part of the Czech observing network used here is smaller, and the density of sites is larger, than in the Hungarian network, resulting in higher spatial correlations among data in the Czech dataset relative to the Hungarian dataset. Time series with low number of gaps were supplied with interpolated data. Before homogenisation relative time series were created, using weighted averages of time series from the same geographical region as reference series. For ease of comparison, the magnitudes of the detected IHs are normalised with the standard deviation of the noise in the relative time series. Results show that observed meteorological time series usually contain large number of small IHs, and that the magnitude distribution of IHs from different data segments are surprisingly similar. Effects of different spatial coherences on the results are discussed.     

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.     

The influence of autocorrelation on the ability to detect trend in hydrological series

This study investigated using Monte Carlo simulation the interaction between a linear trend and a lag‐one autoregressive (AR(1)) process when both exist in a time series. Simulation experiments demonstrated that the existence of serial correlation alters the variance of the estimate of the Mann–Kendall (MK) statistic; and the presence of a trend alters the estimate of the magnitude of serial correlation. Furthermore, it was shown that removal of a positive serial correlation component from time series by pre‐whitening resulted in a reduction in the magnitude of the existing trend; and the removal of a trend component from a time series as a first step prior to pre‐whitening eliminates the influence of the trend on the serial correlation and does not seriously affect the estimate of the true AR(1). These results indicate that the commonly used pre‐whitening procedure for eliminating the effect of serial correlation on the MK test leads to potentially inaccurate assessments of the significance of a trend; and certain procedures will be more appropriate for eliminating the impact of serial correlation on the MK test. In essence, it was advocated that a trend first be removed in a series prior to ascertaining the magnitude of serial correlation. This alternative approach and the previously existing approaches were employed to assess the significance of a trend in serially correlated annual mean and annual minimum streamflow data of some pristine river basins in Ontario, Canada. Results indicate that, with the previously existing procedures, researchers and practitioners may have incorrectly identified the possibility of significant trends. Copyright © Environment Canada. Published by John Wiley & Sons, Ltd.     

利用PSInSAR时间序列研究拉奎拉地震位移场变化特征

对2009年4月6日意大利拉奎拉(LAquila)Mw6.3级地震9景ENVISAT重轨单视复数据采用双轨模式进行永久散射体(Persistent Scatterer,PS)处理,获得了此次地震时序位移场,结合PS位移场Delaunay算法数值分析,结果表明:1)Envisat干涉雷达完整而清晰地探测到了地震前后位移场变化过程及其在不同阶段与震源断裂相关的不同形变特征:震前蠕动位移-明显变形-震期快速突变-震后量级明显减缓的持续变形;2)在此次分析的约54×59km2区域内,震中以西为大面积上升区,视线向最大上升量为130mm;震中以东为下降区域,但下降集中在破裂区,主要在发震过程及震后形成,视线向最大下沉量为210mm,与GPS监测结果一致;3)地震产生的破裂主要分布在约22×14km2范围内,沿NW走向、SW倾斜的Paganica-S.Demetrio正断层展布,方向约135°;4)本文为探索利用PSInSAR时间序列进行地震趋势预测提供了一个较好的案例.     

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.     

Time series decomposition of groundwater level changes in wells due to the Chi‐Chi earthquake in Taiwan: a possible hydrological precursor to earthquakes

The largest and most disastrous earthquake in Taiwan (Mw: 7·3) in the 20th century, the Chi‐Chi earthquake, hit central Taiwan at 01:47 local time on September 21, 1999. The groundwater level changes were rapid at that time. Studies have found that the rapid change in groundwater levels was a co‐seismic phenomenon. This work analyzes the possibility that the abnormal change in groundwater levels may have occurred before the earthquake. Three well stations with a total of five wells are considered. They are all near the Che‐Lung‐Pu fault, which caused the Chi‐Chi earthquake. The time series decomposition method was applied to decompose the seasonal groundwater level, the trend in groundwater levels, and the period of the change in the groundwater level. Residual groundwater levels were found by subtracting the determined seasonal, trend and period data from corresponding data for the original groundwater level. The computed residual water levels in July, August and September of 1999, were transformed into a frequency spectrum by a Fourier method. Additionally, the effects of barometric pressures on the groundwater level changes were also evaluated. Analytical results show that the spectral density functions of the irregular groundwater level in the confined aquifer at the Chu‐Shan well in September behaved differently from those in July and August. We posit that a pre‐seismic hydrogeological anomaly may have existed before the Chi‐Chi earthquake, and can be considered in future studies of anomalies associated with earthquakes. Copyright © 2007 John Wiley & Sons, Ltd.     

Spatial disaggregation and intensity correction of TRMM-based rainfall time series for hydrological applications in dryland catchments

Abstract

A novel approach is presented for combining spatial and temporal detail from newly available TRMM-based data sets to derive hourly rainfall intensities at 1-km spatial resolution for hydrological modelling applications. Time series of rainfall intensities derived from 3-hourly 0.25° TRMM 3B42 data are merged with a 1-km gridded rainfall climatology based on TRMM 2B31 data to account for the sub-grid spatial distribution of rainfall intensities within coarse-scale 0.25° grid cells. The method is implemented for two dryland catchments in Tunisia and Senegal, and validated against gauge data. The outcomes of the validation show that the spatially disaggregated and intensity corrected TRMM time series more closely approximate ground-based measurements than non-corrected data. The method introduced here enables the generation of rainfall intensity time series with realistic temporal and spatial detail for dynamic modelling of runoff and infiltration processes that are especially important to water resource management in arid regions.

Editor D. Koutsoyiannis

Citation Tarnavsky, E., Mulligan, M. and Husak, G., 2012. Spatial disaggregation and intensity correction of TRMM-based rainfall time series for hydrological applications in dryland catchments. Hydrological Sciences Journal, 57 (2), 248–264.     

Exploratory spectral analysis of hydrological times series

Current methods of estimation of the univariate spectral density are reviewed and some improvements are made. It is suggested that spectral analysis may perhaps be best thought of as another exploratory data analysis (EDA) tool which complements, rather than competes with, the popular ARMA model building approach. A new diagnostic check for ARMA model adequacy based on the nonparametric spectral density is introduced. Additionally, two new algorithms for fast computation of the autoregressive spectral density function are presented. For improving interpretation of results, a new style of plotting the spectral density function is suggested. Exploratory spectral analyses of a number of hydrological time series are performed and some interesting periodicities are suggested for further investigation. The application of spectral analysis to determine the possible existence of long memory in natural time series is discussed with respect to long riverflow, treering and mud varve series. Moreover, a comparison of the estimated spectral densities suggests the ARMA models fitted previously to these datasets adequately describe the low frequency component. Finally, the software and data used in this paper are available by anonymous ftp from fisher.stats.uwo.ca.     

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.     

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.     

Complexity analysis of riverflow time series

I have used the Lempel–Ziv measure to assess the complexity in riverflow activity over England and Wales for the period 1867–2002. In particular, I have examined the reconstructed monthly riverflow time series from fifteen representative catchments in these regions and calculated the Lempel–Ziv Complexity (LZC) value for each time series. The results indicate that the LZC values in some catchments are close to each other while in others they differ significantly. In addition, I have divided the period 1867–2002 into four equal subintervals: (a) 1867–1900, (b) 1901–1934, (c) 1935–1968, (d) 1969–2002, and calculated the LZC values for the various time series in these subintervals. It is found that during the period 1969–2002, there is a decrease in complexity in most of the catchments in comparison to the subinterval 1935–1968. This complexity loss may be attributed to increased human intervention involving land and crop use, urbanization, commercial navigation and climatic changes due to human activity. Determining the complexity in the riverflow time series is important because an understanding of the extent of complexity may be useful in developing appropriate models of riverflow activity. The extent of complexity may also influence the predictability of the variability in riverflow dynamics.     

Time series analysis for evaluating hydrological responses of pore-water pressure to rainfall in a slope

Characterization of pore-water pressure at the soil–atmosphere interface is a major requirement in relation to slope instability. A rain-gauge and five piezometers (BH1–BH5) were installed on a slope located in a Korean military base. The upper slope (BH4, BH5) was covered with plastic sheets to prevent rainwater from percolating into the slope due to safety issues. Rainfall is matched by prompt changes in the pore-water pressure except at BH5. Due to the plastic cover, the pore water does not show any significant change in the early period by evapotranspiration. From correlation analysis, two wells (BH3, BH5) have longer memory effects due to matrix flow of past precipitation. Two principal components show hydrological responses of pore water to rainfall during intense rainfall, but PC2 does not indicate any important changes in low or no rainfall. This study suggests that correlation analysis with PCA can be a valuable tool for interpreting datasets consisting only of pore-water pressure.     

Gaussianity and linearity tests of hydrologic time series

Although the non-Gaussian nature of many hydrologic time series is well recognized and their nonlinearity is suspected, neither property is well tested. This situation has existed partly because of a lack of appropriate tests. Recently Hinich (1982) has developed a test to test the linearity of time series which is based on the bispectral characteristics of the series. This test is used in this study to investigate the linearity and non-Gaussian characteristics of annual and daily rainfall and runoff series. The annual series may be modeled by linear models with Gaussian inputs. The daily data, on the other hand, often demonstrate nonlinear characteristics and are non-Gaussian as well.     

Arctic Mackenzie Delta channel planform evolution during 1983–2013 utilising Landsat data and hydrological time series

Arctic deltas, such as the Mackenzie Delta, are expected to face major climate change and increased human influence in the near future. Deltas are characterised by highly dynamic fluvial processes, and changing climate will cause considerable evolution of the riverine environment. The changes are difficult to predict with existing knowledge and data. This study quantified channel planform change of the Mackenzie Delta (1983–2013), analysing its temporal and spatial patterns. We addressed the main obstacle of research on large remote areas, the lack of data, by developing a unique work flow that utilised Landsat satellite imagery, hydrological time series, remote sensing‐based change analysis, and automatic vectorisation of channels. Our results indicate that the Mackenzie Delta experienced constant evolution but at a highly varying rate over the 30 years. The study demonstrates that the magnitude and duration of flood peaks and the presence of spring ice breakup floods determine the rate of Arctic delta planform change. Changing winter conditions and spring flood magnitudes may therefore affect the stability of Arctic deltas. However, no clear trends towards decreased recurrence or magnitude of spring floods or increased instability of the delta plain have yet been observed in the Mackenzie Delta. The delta plain was most dynamic at the beginning and at the end of the examined period, corresponding to intense flooding, whereas the rates of change were subtle during the low‐flood period 1994–2007. The largest changes have occurred along the wide Middle Channel and in the outermost delta. Relative to their size, however, smaller meandering channels have been highly dynamic. Hotspots of change in the delta plain are located in anastomosing and braiding channel segments and, at the local scale, in point bars and cut‐banks along meandering channels. Our study describes how Landsat satellite data can be utilised for advancing fluvial geomorphological research in remote areas. However, cloudiness in the delta restricts production of dense time series with simultaneous coverage of the whole area and requires manual preprocessing.