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.     

Complexity measure of regional seasonal precipitation series based on wavelet entropy

The chaos characteristics for system complexity, e.g. randomness and fractality, are generally ignored when researchers study the complex behaviour of precipitation time series, which makes it difficult to elicit adequate information for such series. The main objective of this study was to diagnose the complexity of seasonal precipitation by using wavelet entropy and mean wavelet entropy, and to find the complex system of spatial variation in seasonal precipitation for the sub-areas of Jiansanjiang Administration in China as a case study. The results illustrate that the complexity characteristic of the seasonal precipitation series is greatest in the North sub-area, lowest in the Middle sub-area, and intermediate in the South sub-area; topography and agricultural development are the key driving factors of the complex dynamic variation in the local seasonal precipitation time series. This study provides a basis for analysing the trend in development of complex precipitation time series and realizing the sustainable use of regional water resources.     

Urban hydrologic trend analysis based on rainfall and runoff data analysis and conceptual model calibration

Urban stormwater is a major cause of urban flooding and natural water pollution. It is therefore important to assess any hydrologic trends in urban catchments for stormwater management and planning. This study addresses urban hydrological trend analysis by examining trends in variables that characterize hydrological processes. The original and modified Mann‐Kendall methods are applied to trend detection in two French catchments, that is, Chassieu and La Lechere, based on approximately 1 decade of data from local monitoring programs. In both catchments, no trend is found in the major hydrological process driver (i.e., rainfall variables), whereas increasing trends are detected in runoff flow rates. As a consequence, the runoff coefficients tend to increase during the study period, probably due to growing imperviousness with the local urbanization process. In addition, conceptual urban rainfall‐runoff model parameters, which are identified via model calibration with an event based approach, are examined. Trend detection results indicate that there is no trend in the time of concentration in Chassieu, whereas a decreasing trend is present in La Lechere, which, however, needs to be validated with additional data. Sensitivity analysis indicates that the original Mann‐Kendall method is not sensitive to a few noisy values in the data series.     

Separating the effects of climate change and human activities on runoff over different time scales in the Zhang River basin

Most studies on separating the effects of climate change and human activities on runoff are mainly conducted at an annual scale with few analyses over different time scales, which is especially essential for regional water resources management. This paper investigates the impacts of climate change and human activities on runoff changes at annual, seasonal and monthly time scales in the Zhang River basin in North China. Firstly, the changing trends and inflection point are analyzed for hydro-climatic series over different time scales. Then the hydrological modeling based method and sensitivity based method are used to separate the effects. The results show that the effect of climate change is stronger than that of human activities on annual runoff changes. However, the driving factors on runoff are different at seasonal scale. In the wet season, the effect of human activities on runoff, accounting for 57 %, is stronger than that of climate change, while in the dry season climate change is the dominant factor for runoff reduction and the contribution rate is 72 %. Furthermore, the effects of climate change and human activities on monthly runoff changes are various in different months. The separated effects over different time scales in this study may provide more scientific basis for the water resources adaptive management over different time scales in this basin.     

Characteristic scales, temporal variability modes and simulation of monthly Elbe River flow time series at ungauged locations

Spatial and temporal patterns of the long-range extreme monthly Elbe River flows across Germany are investigated, using various statistical methods, among others, principal component and wavelet analysis. Characteristic time scales are derived for various time series statistics. The wavelet analysis of the raw river discharge data as well as of the major principal component reveal the main oscillatory components and their temporal behavior, namely low frequency oscillations at interannual (6.9 yr) and interdecadal (13.9 yr) scales. The EOFs at ungauged stations are estimated from the principal components of the observed time series sampled over a limited time span whose length equals the major temporal variability scale (≈7 yr). The EOFs (empirical orthogonal functions) obtained in this way are subsequently used to simulate long-range flows at these locations. A comparison of this method with linear interpolation and ordinary kriging of the EOF shows the superiority of the former in representing the distributional properties of the observed time series. The simulated time series preserve also short and long-memory.     

Assessing and modelling changes in rainfall erosivity at different climate scales

An understanding of the weather drivers of soil erosion necessitates an extended instrumental meteorological series and knowledge of the processes linking climate and hydrology. The nature of such linkages remains poorly understood for the Mediterranean region. This gap is addressed through a composite analysis of long‐term climatic controls on rain erosivity in the Calore River Basin (southern Italy) for the period 1869–2006. Based on a parsimonious interpretation of rainstorm processes, a model (comparable with the Revised Universal Soil Loss Equation) was adapted to generate erosivity values on different time‐aggregation scales (yearly and seasonal). The evolution of the generated series of cumulated and extreme erosivity events was assessed by two return period (T) quantiles via a 22‐year moving window analysis (low return period, T = 2 years; high return period, T = 50 years). Erosivity extremes are shown to be characterized by increasing yearly trends (at a 100‐year rate of ～150 MJ mm ha^–1 h^–1 for T = 2 years and ～800 MJ mm ha^–1 h^–1 for T = 50 years), especially during the spring and autumn seasons. Quantile patterns on the extremes are also shown to be decoupled from trends in the cumulated values. The Buishand test was applied to detect the presence of temporal change points, and a wavelet spectrum analysis used for time‐frequency localization of climate signals. A change‐point in the evolution of climate is revealed over the 1970s in the spring series, which correlates to a distinct rain erosivity increase. The results indicate that soil erosion risk tends to rise as a consequence of an escalation of the climate erosive hazard, predominantly between April and November (associated with cultivation and tillage practices). Copyright © 2009 John Wiley & Sons, Ltd.     

Interactions and connectivity between runoff generation processes of different spatial scales

Monitoring runoff generation processes in the field is a prerequisite for developing conceptual hydrological models and theories. At the same time, our perception of hydrological processes strongly depends on the spatial and temporal scale of observation. Therefore, the aim of this study is to investigate interactions between runoff generation processes of different spatial scales (plot scale, hillslope scale, and headwater scale). Different runoff generation processes of three hillslopes with similar topography, geology and soil properties, but differences in vegetation cover (grassland, coniferous forest, and mixed forest) within a small v‐shaped headwater were measured: water table dynamics in wells with high spatial and temporal resolution, subsurface flow (SSF) of three 10 m wide trenches at the bottom of the hillslopes subdivided into two trench sections each, overland flow at the plot scale, and catchment runoff. Bachmair et al. ( 2012 ) found a high spatial variability of water table dynamics at the plot scale. In this study, we investigate the representativity of SSF observations at the plot scale versus the hillslope scale and vice versa, and the linkage between hillslope dynamics (SSF and overland flow) and streamflow. Distinct differences in total SSF within each 10 m wide trench confirm the high spatial variability of the water table dynamics. The representativity of plot scale observations for hillslope scale SSF strongly depends on whether or not wells capture spatially variable flowpaths. At the grassland hillslope, subsurface flowpaths are not captured by our relatively densely spaced wells (3 m), despite a similar trench flow response to the coniferous forest hillslope. Regarding the linkage between hillslope dynamics and catchment runoff, we found an intermediate to high correlation between streamflow and hillslope hydrological dynamics (trench flow and overland flow), which highlights the importance of hillslope processes in this small watershed. Although the total contribution of SSF to total event catchment runoff is rather small, the contribution during peak flow is moderate to substantial. Additionally, there is process synchronicity between spatially discontiguous measurement points across scales, potentially indicating subsurface flowpath connectivity. Our findings stress the need for (i) a combination of observations at different spatial scales, and (ii) a consideration of the high spatial variability of SSF at the plot and hillslope scale when designing monitoring networks and assessing hydrological connectivity. Copyright © 2013 John Wiley & Sons, Ltd.     

On the use of maximum entropy/autoregressive spectrum in harmonic analysis of time series

The maximum entropy (ME) spectrum, or its equivalent form of the autoregressive (AR) spectrum, has been used as a tool for harmonic analysis of time series in geophysics. This paper critically examines its usage in estimating the amplitude and the exponential decay rate of a harmonic function. The argument is based upon Prony's relation, which relates a complex-conjugate pair of poles for the AR model of the time series on one hand, to the complex frequency of one harmonic component in the time series on the other. It is found that: (i) the ME spectrum can be used as an estimator for the decay rate in a way similar to the Fourier spectral analysis; (ii) the ME spectrum contains no information whatsoever about the amplitude, contrary to what has been claimed and practiced in geophysical applications.     

Sensitivity analysis of the probability distribution of groundwater level series based on information entropy

Information entropy is an effective method to analyze uncertainty in various processes. The principle of maximum entropy (POME) provides a guide line for the parameter estimation of probability density function (PDF). Mutual entropy analysis is well qualified for delineating the nonlinear and complex multivariable relationship. The probability distribution of model output is the element of model uncertainty analysis. In this paper, a synthetic groundwater flow field is build to produce groundwater level series (GLS). The probability distribution of GLS is obtained by the frequency analysis method based on POME and Chi-Squared test. The important uncertainty factors that affect the parameters of PDF of GLS are assessed by the sensitivity analysis methods, which include stepwise regression analysis and mutual entropy analysis. Results of this analysis indicate that most of the GLS follow normal distribution (or log-normal distribution), while a few obey others. The mean and variance of normal GLS are affected differently by the input variables of groundwater model. Mutual entropy analysis is more competitive and appropriate for delineating the nonlinear and nonmonotonic multivariable relationship than stepwise regression analysis.     

首都圈地区地震时间序列的最大熵谱分析方法及地震危险性预测

利用最大熵谱分析方法和最大熵原理方法,对首都圈（北纬38°～42°,东经113°～120°）1484年以来发生5．0级以上地震的时间序列资料进行了分析,结果表明,首都圈地区历史上5．0级以上地震存在12．9年的卓越周期,并且在今后50年内,发生5．0≤Ms〈6．0和6．0≤Ms〈7．0地震的概率分别是0．9907和0．6916,发生7．0≤Ms〈8．0地震的概率较低,只有0．2564发生Ms≥8．0地震的概率最低。仅为0．0718。     

基于复杂度理论的地磁变化场时间序列特征分析

复杂度理论为研究地磁变化场提供了新思路和新途径.地磁变化场从物理起源上可以看作是一种复杂系统,因此,本文从军事工程应用需求出发,基于复杂度理论,提出运用样本熵、多尺度熵及滑动窗样本熵方法对不同磁扰程度下的地磁变化场时间序列进行复杂度特征分析,结果表明：（1）样本熵和多尺度熵能够很好地表征地磁扰动强度及演化特征,启发我们可设计一种新的“熵指数”来衡量地磁扰动大小;（2）滑动窗样本熵能够准确定位地磁扰动时间段,对于磁暴识别与预测、空间灾害性天气预警等有一定的参考价值;（3）Mackey-Glass时滞混沌方程随时间的演化呈现出与地磁场日变曲线非常相似的形态,因此,地磁变化场或许可用时滞混沌方程来表示,对于我们更好地认识地磁变化场物理机理、建模预测与地磁寻的等军事工程应用都有一定的意义.     

Hydrography and plankton temporal variabilities at different time scales in the southwest lagoon of New Caledonia: A review

The New Caledonia SW lagoon is wide (5–20 nautical miles) and semi-closed. It is influenced by both the open ocean and the high island within a meteorological context subject to seasonal, inter-annual and longer term variations. The short-term variability (>1 day) of meteorological, hydrographical and planktonic parameters is illustrated by a 5-month long time series and is linked to local or remote wind, and precipitation. Seasonal and inter-annual variabilities, inferred from a 10-year long station by spectral analysis, appear clearly for all parameters. Seasonality is the main scale of variability as the island lies near the tropic of Capricorn. Inter-annual variability of a 3–4 year periodicity is poorly related to the Southern oscillation index (an equatorial climatic index), stressing the need for a separate tropical index. Long term trends appear on several parameters but their reliability depends on the length of the records. Considering only the longest records (1958–2005), surface temperature appears to have increased since the end of the 1960s in Noumea area. Finally, as a result of greater terrestrial influence, shallower depths, and longer water turnover times close to shore, the temporal variability amplitude decreases from the shore to the barrier reef.     

The compatibility of erosion data at different temporal scales

Soil erosion processes have been studied intensively throughout the last decades and rates have been measured at the plot scale as well as at larger scales. However, the relevance of this knowledge for the modelling of long-term landscape evolution remains a topic of considerable debate. Some authors state that measurements of current rates are irrelevant to landscape evolution over a longer time span, as they are inconsistent with some fundamental characteristics of landscapes, such as the fact that the long-term sediment delivery ratio needs to be equal to 1 and that extrapolation of current rates would imply that all soils in Europe should have disappeared by now (e.g. Parsons, A.J., Wainwright, J., Brazier, R.E., Powell, D.M., 2006. Is sediment delivery a fallacy? Earth Surface Processes and Landforms 31, 1325–1328). In this study, we investigate if and to what extent estimates of long-term erosion rates are consistent with information obtained over much shorter time spans for the Loam Belt of Belgium.In a first step, observed short-term and long-term patterns in the Belgian loess area are compared statistically by classifying the study area into landscape element classes and comparing average erosion values per class. This analysis shows that the erosion intensities on the two temporal scales are of the same order of magnitude for each landscape element class. Next, the spatially distributed model WaTEM LT (Water and Tillage Erosion Model Long Term) is calibrated based on the available short-term data by optimising average erosion values for the same landscape element classes. Finally, the calibrated model is used to simulate long-term landform evolution, and is validated using long-term data based on soil profile truncation. We found that the model allows simulating landscape evolution on a millennial time scale using information derived from short-term erosion and deposition data. However, it is important that land use is taken into account for the calibration in order to obtain realistic patterns on a longer time scale. Our analysis shows that, at least for the study area considered, data obtained on erosion and deposition rates over various temporal scales have the same orders of magnitude, thereby demonstrating that measurements of current rates of processes can be highly relevant for interpreting long-term landscape evolution.     

Effect of the inter-annual variability of rainfall statistics on stochastically generated rainfall time series: part 1. Impact on peak and extreme rainfall values

A noble approach of stochastic rainfall generation that can account for inter-annual variability of the observed rainfall is proposed. Firstly, we show that the monthly rainfall statistics that is typically used as the basis of the calibration of the parameters of the Poisson cluster rainfall generators has significant inter-annual variability and that lumping them into a single value could be an oversimplification. Then, we propose a noble approach that incorporates the inter-annual variability to the traditional approach of Poisson cluster rainfall modeling by adding the process of simulating rainfall statistics of individual months. Among 132 gage-months used for the model verification, the proportion that the suggested approach successfully reproduces the observed design rainfall values within 20 % error varied between 0.67 and 0.83 while the same value corresponding to the traditional approach varied between 0.21 and 0.60. This result suggests that the performance of the rainfall generation models can be largely improved not only by refining the model structure but also by incorporating more information about the observed rainfall, especially the inter-annual variability of the rainfall statistics.     

Effects of rainfall patterns on runoff and rainfall-induced erosion

Rainfall-induced erosion involves the detachment of soil particles by raindrop impact and their transport by the combined action of the shallow surface runoff and raindrop impact.Although temporal variation in rainfall intensity(pattern)during natural rainstorms is a common phenomenon,the available information is inadequate to understand its effects on runoff and rainfall-induced erosion processes.To address this issue,four simulated rainfall patterns(constant,increasing,decreasing,and increasing-decreasing)with the same total kinetic energy were designed.Two soil types(sandy and sandy loam)were subjected to simulated rainfall using 15 cm×30 cm long detachment trays under infiltration conditions.For each simulation,runoff and sediment concentration were sampled at regular intervals.No obvious difference was observed in runoff across the two soil types,but there were significant differences in soil losses among the different rainfall patterns and stages.For varying-intensity rainfall patterns,the dominant sediment transport mechanism was not only influenced by raindrop detachment but also was affected by raindrop-induced shallow flow transport.Moreover,the efficiency of equations that predict the interrill erosion rate increased when the integrated raindrop impact and surface runoff rate were applied.Although the processes of interrill erosion are complex,the findings in this study may provide useful insight for developing models that predict the effects of rainfall pattern on runoff and erosion.     

Error analysis for the evaluation of model performance: rainfall–runoff event time series data

This paper provides a procedure for evaluating model performance where model predictions and observations are given as time series data. The procedure focuses on the analysis of error time series by graphing them, summarizing them, and predicting their variability through available information (recalibration). We analysed two rainfall–runoff events from the R‐5 data set, and evaluated 12 distinct model simulation scenarios for these events, of which 10 were conducted with the quasi‐physically‐based rainfall–runoff model (QPBRRM) and two with the integrated hydrology model (InHM). The QPBRRM simulation scenarios differ in their representation of saturated hydraulic conductivity. Two InHM simulation scenarios differ with respect to the inclusion of the roads at R‐5. The two models, QPBRRM and InHM, differ strongly in the complexity and number of processes included. For all model simulations we found that errors could be predicted fairly well to very well, based on model output, or based on smooth functions of lagged rainfall data. The errors remaining after recalibration are much more alike in terms of variability than those without recalibration. In this paper, recalibration is not meant to fix models, but merely as a diagnostic tool that exhibits the magnitude and direction of model errors and indicates whether these model errors are related to model inputs such as rainfall. Copyright © 2004 John Wiley & Sons, Ltd.     

Segmentation-based approach for trend analysis and structural breaks in rainfall time series (1851–2006) over India

ABSTRACT

This study analysed long-term rainfall data (1851–2006) over seven climatic zones of India at seasonal and annual scales based on three techniques: (i) linear regression, (ii) multifractal detrended fluctuation analysis (MFDFA) and (iii) Bayesian algorithm. The linear regression technique was used for trend analysis of short-term (30 years) and long-term (156 years) rainfall data. The MFDFA revealed small- and large-scale fluctuations, whereas the Bayesian algorithm helped in quantifying the uncertainty in break-point detection from the rainfall time series. Major break points years identified through Bayesian algorithm were 1888, 1904 and 1976. The MFDFA technique identified that high fluctuation years were between 1871–1890, 1891–1910 and 1951–1970. Linear regression-based analysis revealed 1881–1910 and 1971–2006 as break-point periods in the North Mountainous Indian region. A similar analysis was carried out for India as a whole, as well as its seven climatic zones.     

Investigating the time dynamics of monthly rainfall time series observed in northern Lebanon by means of the detrended fluctuation analysis and the Fisher-Shannon method

We investigate the time dynamics of monthly rainfall series intermittently recorded on seven climatic stations in northern Lebanon from 1939 to 2010 using the detrending fluctuation analysis (DFA) and the Fisher-Shannon (FS) method. The DFA is employed to study the scaling properties of the series, while the FS method to analyze their order/organization structure. The obtained results indicate that most all the stations show a significant persistent behavior, suggesting that the dynamics of the rainfall series is governed by positive feedback mechanisms. Furthermore, we found that the Fisher Information Measure (the Shannon entropy power) seems to decrease (increase) with the height of the rain gauge; this indicates that the rainfall series appear less organized and less regular for higher-located stations. Such findings could be useful for a better comprehension of the climatic regimes governing northern Lebanon.     

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。     

Effects of landuse change on surface runoff and sediment yield at different watershed scales on the Loess Plateau

Erosion and sediment yield from large and small watersheds exhibit different laws. Variations in surface runoff and sediment yield because of landuse change in four watersheds of different scales from 1 km2 to 73 km2 were analyzed. Due to reforestation and farmland terracing, surface runoff and sediment yield reduced by 20-100% and 10-100% respectively. Reductions in surface runoff were differed significantly under different precipitation regimes. For the large watershed (73 km2) landuse change had similar effects on surface runoff regardless of changing of precipitation. For the small watershed (1 km2) landuse change had fewer effects on surface runoff under high precipitation. The relative changes of sediment yield in the four watersheds under reforestation and farmland terracing decreased as precipitation increased from 350 mm to 650 mm, then increased as precipitation increased from 650 mm to 870 mm. Where initial forest coverage rate was below 45%, sediment yield decreased dramatically as forest coverage rate increased. Watershed management with aiming at reducing both surface runoff and sediment yield should be conducted both on sloping surfaces and in channels in large watersheds.