River flow regimes in a changing climate

Abstract

A river flow regime describes an average seasonal behaviour of flow and reflects the climatic and physiographic conditions in a basin. Differences in the regularity (stability) of the seasonal patterns reflect different dimensionality of the flow regimes, which can change subject to changes in climate conditions. The empirical orthogonal functions (EOF) approach can be used to describe the intrinsic dimension of river flow regimes and is also an adopted method for reducing the phase space in connection to climate change studies, especially in studies of nonlinear dynamic systems with preferred states. A large data set of monthly river flow for the Nordic countries has been investigated in the phase space reduced to the first few amplitude functions to trace a possible signature of climate change on the seasonal flow patterns. The probability density functions (PDF) of the weight coefficients and their possible change over time were used as an indicator of climate change. Two preferred states were identified connected to stable snowmelt-fed and rainfed flow regimes. The results indicate changes in the PDF patterns with time towards higher frequencies of rainfed regime types. The dynamics of seasonal patterns studied in terms of PDF renders it an adequate and convenient characterization, helping to avoid bias connected to flow regime classifications as well as uncertainties inferred by a modelling approach.     

Quantification of the stability of river flow regimes

Abstract

An important characteristic of a river flow regime type is the time of year when high and low flows are likely to occur. How likely is it, however, to observe an identified seasonal pattern each individual year? Stability is an often neglected property of a flow regime, though shifts in the seasonal behaviour of flows affect both environmental and economic activities. An approach to characterize objectively the stability of a flow regime type, based on the concept of entropy, is presented. The stabilities of river flow maxima and minima are studied separately to investigate their respective contributions to the stability character of a particular regime type. A quantitative “instability index” permits a study of the development of a flow regime's stability in time, especially important in the context of a possible climate change. The method is presented using the example of a quantitative flow regime classification developed for Scandinavia and western Europe.     

地震前兆吸引子的演化特征

用非线性动力学重建相空间的方法对唐山地震前后（１９７１～１９７８年）昌黎地电台和地应力台前兆观测资料分别进行了关联维的计算．结果表明，地电阻率和地应力前兆资料吸引子具有分数维结构，并且发现这两种不同前兆资料的吸引子具有相同的前兆动态变化特征．在计算中发现，地电阻率的分数维具有多层次性．对此还进行了简单的讨论     

Monte Carlo Studies of Relations between Fractal Dimensions in Monofractal Data Sets

—Within the fractal approach to studying the distribution of seismic event locations, different fractal dimension definitions and estimation algorithms are in use. Although one expects that for the same data set, values of different dimensions will be different, it is usually anticipated that the direction of fractal dimension changes among different data sets will be the same for every fractal dimension.¶Mutual relations between the three most popular fractal dimensions, namely the capacity, cluster and correlation dimensions, have been investigated in the present work. The studies were performed on the Monte Carlo generated data sets. The analysis has shown that dependence of the fractal dimensions on epicenter distribution, and relations among the fractal dimensions, are complex and variable. Neither values nor even inequalities among dimension estimates are preserved when different fractal dimensions are used. The correlation and the capacity dimensions seem to be good tools to trace collinear tendencies of eipicenters while the cluster dimension is more appropriate to studying uniform clustering of points.     

Techniques for assessing the climatic sensitivity of river flow regimes

Regimes are useful tools for characterizing the seasonal behaviour of river flow and other hydroclimatological variables over an annual cycle (hydrological year). This paper develops and tests: (i) a regime classification method to identify spatial and temporal patterns in intraannual hydroclimatological response; and (ii) a novel sensitivity index (SI) to assess river flow regimes' climatic sensitivity. The classification of regime shape (form) and magnitude considers the whole annual cycle rather than isolating a single month or season for analysis, which has been the common approach of previous studies. The classification method is particularly useful for identifying large‐scale patterns in regimes and their between‐year stability, thus providing a context for short‐term, small‐scale process‐based research. The SI provides a means of assessing the often‐complex linkages between climatic drivers and river flow, as it identifies the strength and direction of associations between classifications of climate and river flow regimes. The SI has the potential for application to other problems where relationships between nominal classifications require to be found. These techniques are evaluated by application to a test data set of river flow, air temperature and rainfall time‐series (1974–1999) for a sample of 35 UK river basins. The results support current knowledge about the hydroclimatology of the UK. Although this research does not seek to yield new, detailed physical process understanding, it provides perspective at large spatial and temporal scales upon climate and flow regime patterns and quantifies linkages. Having clearly demonstrated the regime classification and SI to be effective in an environment where the hydroclimatology is relatively well known, there appears to be much to gain from applying these techniques in parts of the world where patterns and associations between climate and hydrology are poorly understood. Copyright © 2004 John Wiley & Sons, Ltd.     

Sensitivity of the stability of river flow regimes to small fluctuations in temperature

Abstract

A river regime describes the average seasonal behaviour of flow. This seasonal pattern reflects climatic and physiographic conditions in the basin. An inherent characteristic of a flow regime is its stability, i.e. regularity or irregularity of the seasonal pattern. A temperature rise, as predicted by climatic models, might cause changes in the patterns and stability of river flow regimes. Sensitivity of the stability of flow regimes to small fluctuations in temperature (= ± 1°C) is investigated with the help of historical temperature and flow series for Scandinavia. The concept of entropy is utilized for quantification of the stability of the flow regimes conditioned on temperature which also allows forecasting of possible changes in this stability due to changes in temperature. The study shows that the stability of flow regime types with rain or mixed rain and snowmelt sources of flow formation is already sensitive to small changes in temperature, especially concerning flow minima.     

Fractal analysis of 2-D fracture networks of geothermal reservoirs in south-western Turkey

Natural fracture patterns of producing geothermal formations in south-western Turkey are mapped at different scales. The fractal dimensions of different fracture network properties, such as spatial distribution, density, connectivity, orientation, and length are measured by different methods. Analysis of the natural fracture patterns from giga to microscales identifies the descending behavior of box-counting fractal dimension with respect to the scale. It is observed that the fracture networks represent scale-invariant properties, but fractal dimensions might notably differ when the mass dimension is measured applying different methods. Anisotropic nature of fracture networks is also included in the fractal analysis.     

Fractal analysis of earthquake swarms of Vogtland/NW-Bohemia intraplate seismicity

The special type of intraplate microseismicity with swarm-like occurrence of earthquakes within the Vogtland/NW-Bohemian Region is analysed to reveal the nature and the origin of the seismogenic regime. The long-term data set of continuous seismic monitoring since 1962, including more than 26000 events within a range of about 5 units of local magnitude, provides an unique database for statistical investigations. Most earthquakes occur in narrow hypocentral volumes (clusters) within the lower part of the upper crust, but also single event occurrence outside of spatial clusters is observed. Temporal distribution of events is concentrated in clusters (swarms), which last some days until few month in dependence of intensity. Since 1962 three strong swarms occurred (1962, 1985/86, 2000), including two seismic cycles. Spatial clusters are distributed along a fault system of regional extension (Leipzig-Regensburger Störung), which is supposed to act as the joint tectonic fracture zone for the whole seismogenic region. Seismicity is analysed by fractal analysis, suggesting a unifractal behaviour of seismicity and uniform character of seismotectonic regime for the whole region. A tendency of decreasing fractal dimension values is observed for temporal distribution of earthquakes, indicating an increasing degree of temporal clustering from swarm to swarm. Following the idea of earthquake triggering by magma intrusions and related fluid and gas release into the tectonically pre-stressed parts of the crust, a steady increased intensity of intrusion and/or fluid and gas release might account for that observation. Additionally, seismic parameters for Vogtland/NW-Bohemia intraplate seismicity are compared with an adequate data set of mining-induced seismicity in a nearby mine of Lubin/Poland and with synthetic data sets to evaluate parameter estimation. Due to different seismogenic regime of tectonic and induced seismicity, significant differences between b-values and temporal dimension values are observed. Most significant for intraplate seismicity are relatively low fractal dimension values for temporal distribution. That observation reflects the strong degree of temporal earthquake clustering, which might explain the episodic character of earthquake swarms and support the idea of push-like triggering of earthquake avalanches by intruding magma.     

Developing environmental standards for abstractions from UK rivers to implement the EU Water Framework Directive / Développement de standards environnementaux sur les prélèvements d'eau en rivière au Royaume Uni pour la mise en œuvre de la directive cadre sur l'eau de l'Union Européenne

Abstract

Under the European Union Water Framework Directive, Member States must put in place a river basin planning framework to determine what measures are necessary to maintain and improve the ecological status for all surface water bodies. The governmental organisations legally responsible for implementing the Directive in the UK have recognised that an appropriate river flow regime is fundamental to maintain a healthy river and, as a result, they need to regulate abstractions and effluent discharges and ensure sufficient water is released from impoundments. This paper reports on the process of producing environmental standards that define the maximum abstraction allowable from UK rivers, to leave sufficient flow to maintain a healthy river ecosystem. As there are currently insufficient data available to determine the relationships between river flow and ecological status empirically, expert knowledge was captured through a series of workshops at which leading UK freshwater scientists defined maximum levels of river flow regime alteration that would achieve ecological objectives for different river water body types. For the least ecologically sensitive rivers, maximum abstractions in the range 15–35% of the natural flow were proposed, depending on the flow magnitude and time of year. For the most sensitive rivers, the maximum abstraction proposed was in the range 7.5–25%. The knowledge was used by the responsible UK authorities to develop environmental standards. The authorities subsequently used the environmental standards to determine regulatory standards that could be implemented within practical constraints and current licensing policies.     

Fractal analysis of flow of the river Warta

A long time series (170 years) of daily flows of the river Warta (Poland) are subject to fractal analysis. A binary variable (renewal stream) illustrating excursions of the process of flow is examined. The raw series is subject to de-seasonalization and normalization. Fractal dimensions of crossings of Warta flows are determined using a novel variant of the box-counting method. Temporal variability of the flow process is studied by determination of fractal dimensions for shifted horizons of 10 or 30 years length. Spectral properties are compared between the time series of flows, and the fractional Brownian motion which describes both the fractal structure of the process and the Hurst phenomenon. The approach may be useful in further studies of non-stationary of the process of flow, analysis of extreme hydrological events and synthetic flow generation.     

Changes in the long-term hydrological regimes and the impacts of human activities in the main Wei River,China

ABSTRACT

Under the combined influence of climate changes and human activities, the hydrological regime of the Wei River shows remarkable variations which have caused many issues in the Wei River in recent decades, such as a lack of freshwater, water pollution, disastrous flooding and channel sedimentation. Hence, hydrological regime changes and potential human-induced impacts have been drawing increasing attention from local government and hydrologists. This study investigates hydrological regime changes in the natural and measured runoff series at four hydrological stations on the main Wei River and quantifies features of their long-term change by analysing their historical annual and seasonal runoff data using several approaches, i.e., continuous wavelet transform, cross-wavelet, wavelet coherence, trend-free pre-whitening Mann-Kendall test and detrended fluctuation analysis. By contrasting two different analysis results between natural and measured river runoff series, the impacts of human activities on the long-term hydrological regime were investigated via the changes of spatio-temporal distribution in dominant periods, the trends and long-range memory of river runoff. The results show : (a) that periodic properties of the streamflow changes are the result of climate, referring to precipitation changes in particular, while human activities play a minor role; (b) a significant decreasing trend can be observed in the natural streamflow series along the entire main stream of the Wei River and the more serious decrease emerging in measured flow should result from human-induced influences in recent decades; and (c) continuous decreasing streamflow in the Wei River will trigger serious shortages of freshwater in the future, which may challenge the sustainability and safety of water resources development in the river basin, and should be paid great attention before 2020.

Editor Z.W. Kundzewicz; Associate editor K. Hamed     

分形几何的数学基础及其在地震预报中的应用

本文就地震预报中常用的分形几何中的几个数学概念做了简要的介绍，包括测度，豪斯道夫维数、计盒维数等，并介绍了有关维数的性质和估计方法。作者试图通过了这些数学概念的简要介绍，使读者对分维有更准确的理解。     

Investigation of the fractal dimension of rainfall occurrence in a semi-arid Mediterranean climate

Abstract

The scale invariance of rainfall series in the Tunis area, Tunisia (semi-arid Mediterranean climate) is studied in a mono-fractal framework by applying the box counting method to four series of observations, each about 2.5 years in length, based on a time resolution of 5 min. In addition, a single series of daily rainfall records for the period 1873–2009 was analysed. Three self-similar structures were identified: micro-scale (5 min to 2 d) with fractal dimension 0.44, meso-scale (2 d to one week) and synoptic-scale (one week to eight months) with fractal dimension 0.9. Interpretation of these findings suggests that only the micro-scale and transition to saturation are consistent, while the high fractal dimension relating to the synoptic scale might be affected by the tendency to saturation. A sensitivity analysis of the estimated fractal dimension was performed using daily rainfall data by varying the series length, as well as the intensity threshold for the detection of rain.

Editor Z.W. Kundzewicz; Associate editor S. Grimaldi

Citation Ghanmi, H., Bargaoui, Z., and Mallet, C., 2013. Investigation of the fractal dimension of rainfall occurrence in a semi-arid Mediterranean climate. Hydrological Sciences Journal, 58 (3), 483–497.     

水系分维的构造含义

本文运用分数维几何学,研究了河流水系分维与地壳里向运动、活动断裂格局及运动学特征的关联性。结果表明:1)地壳垂向运动控制大型河流主干的总体形态;2)活动断裂格局复杂、水平运动强烈的地区,水系分维值高;3)走滑断裂较斜滑断裂对水系发育的控制强烈,而后者主要起到对水系的分区作用。     

Identification and Explanation of a Change in the Groundwater Regime using Time Series Analysis

Time series analysis is applied to identify and analyze a transition in the groundwater regime in the aquifer below the sand ridge of Salland in the Netherlands, where groundwater regime refers to the range of head variations throughout the seasons. Standard time series analysis revealed a discrepancy between modeled and observed heads in several piezometers indicating a possible change in the groundwater regime. A new time series modeling approach is developed to simulate the transition from the initial regime to the altered regime. The transition is modeled as a weighted sum of two responses, one representing the initial state of the system, the other representing the altered state. The inferred timing and magnitude of the change provided strong evidence that the transition was the result of significant dredging works that increased the river bed conductance of the main river draining the aquifer. The plausibility of this explanation is corroborated by an analytical model. This case study and the developed approach to identify a change in the groundwater regime are meant to stimulate a more systematic application of time series analysis to detect and understand changes in groundwater systems which may easily go unnoticed in groundwater flow modeling.     

台湾地区地震的空间关联维特征与构造环境研究

采用关联维方法对台湾地区地震活动的空间特征进行了研究。先利用 10 0a来台湾的地震目录计算各个地震区、带的关联维数 ,将地震空间分布的分形特征定量表达出来 ,然后综合分析地震空间分布的关联维数和孕震构造环境之间的关系 ,得出了以下结论 :1)台湾东、西部地震区由于地震属于不同的大地构造单元 ,因此关联维数有较大的差异 ;2 )在各地震区内部的各个地震带由于板块构造、地壳结构、活断层分布上的差异 ,而具有与其构造特征相对应的关联维数 ;3)各地震带内部的各个不同的部位又由于不同的构造应力场 ,而导致地震分布上出现不同的丛集性 ,表现为不同的关联维数。这些结论充分说明通过关联维分析所得到的地震活动的空间图像与地震活动所代表的不同地质构造背景有着良好的对应关系     

Fractal analysis of long-range paleoclimatic data: Oxygen isotope record of pacific core V28-239

R/S analysis of the oxygen isotope curve of Pacific core V28-239 yields a fractal dimension of 1.22. This value is considered to characterize global climatic change over the last 2 million years as expressed by changing O¹⁸ ratios and confirms that climatic variations are characterized by long-term persistence. The fractal dimension of 1.22 compares favorably with the approximate fractal dimension of 1.26 for annual precipitation records for nine major cities in the United States. Although the precipitation and oxygen isotope data are measured in different physical units and recorded at different time scales, fractal analysis allows for a mathematical comparison of the two phenomena. Additionally, since the fractal dimensions of the oxygen isotope and precipitation records are similar, it is implied that such fractal dimensions are characteristic of climate change over the spectral range of 10 to 10⁶ years. Given this temperature curves based on fractal parameters of long-term O¹⁸ data could be constructed which would allow examination of characteristics of temperature variation over tens and hundreds of years. Such studies may allow the establishment of limits on natural temperature variation and document the persistence of temperature trends through time. If these trends and limits can be resolved, long-range climatic prediction is feasible.     

The fractal geometry of flow paths in natural fractures in rock and the approach to percolation

The distributions of contact areas in single, natural fractures in quartz monzonite (Stripa granite) are found to have fractal dimensions which decrease fromD=2.00 to values nearD=1.96 as stress normal to the fractures is increased from 3 MPa up to 85 MPa. The effect of stress on fluid flow is studied in the same samples. Fluid transport through a fracture depends on two properties of the fracture void space geometry. the void aperture; and the tortuosity of the flow paths, determined through the distribution of contact area. Each of these quantities change under stress and contribute to changes observed in the flow rate. A general flow law is presented which separates these different effects. The effects of tortuosity on flow are largely governed by the proximity of the flow path distribution to a percolation threshold. A fractal model of correlated continuum percolation is presented which quantitatively reproduces the flow path geometries. The fractal dimension in this model is fit to the measured fractal dimensions of the flow systems to determine how far the flow systems are above the percolation threshold.     

Trend detection in river flow series: 1. Annual maximum flow / Détection de tendance dans des séries de débit fluvial: 1. Débit maximum annuel

Abstract

Results of a study on change detection in hydrological time series of annual maximum river flow are presented. Out of more than a thousand long time series made available by the Global Runoff Data Centre (GRDC) in Koblenz, Germany, a worldwide data set consisting of 195 long series of daily mean flow records was selected, based on such criteria as length of series, currency, lack of gaps and missing values, adequate geographical distribution, and priority to smaller catchments. The analysis of annual maximum flows does not support the hypothesis of ubiquitous growth of high flows. Although 27 cases of strong, statistically significant increase were identified by the Mann-Kendall test, there are 31 decreases as well, and most (137) time series do not show any significant changes (at the 10% level). Caution is advised in interpreting these results as flooding is a complex phenomenon, caused by a number of factors that can be associated with local, regional, and hemispheric climatic processes. Moreover, river flow has strong natural variability and exhibits long-term persistence which can confound the results of trend and significance tests.     

THE FRACTAL DIMENSION OF GRAVITY DATA SETS AND ITS IMPLICATION FOR GRIDDING1

Gravity survey station locations are, in general, inhomogeneously distributed. This inevitably results in interpolation errors in the computation of a regular grid from the gravity data. The fractal dimension of the station distribution can be used to determine if an interpolated map is aliased at a specific wave-length and, moreover, it is often possible to determine an optimum gridding interval. Synthetic distributions of gravity station locations have been used for theoretical studies and it is found that for randomly distributed data there is a range of sizes for which the spatial data distribution has a fractal dimension of 2; that is, Euclidean. The minimum length scale at which the distribution ceases to be Euclidean is the optimum interpolation interval obeying Shannon's sampling theorem. For dimensions less than 2, the optimum interpolation interval is the shortest length at which the scaling regime is constant. In this case the gravity field cannot be interpolated without introducing some aliasing. As the fractal dimension characterizes the data distribution globally over the whole study area, the actual gridding interval, in some cases, will be smaller in order to represent short-wavelength features properly in the more densely sampled sub-areas, but this may generate spurious anomalies elsewhere. The proposed technique is applied to the station distribution of the Canadian national gravity data base and a series of sub-areas. A fractal dimension of 1.87 is maintained over a range of sizes from 15 km to over 1600 km. Although aliasing occurs, since the gravity field certainly contains much shorter wavelength anomalies, aliasing errors may be minimized by selecting the proper interpolation interval from the fractal analysis.