Hydrological effects of within-catchment heterogeneity of drainage density

Local drainage density (dd) has been traditionally defined as the inverse of twice the distance one has to walk before encountering a channel. This formalization easily allows to derive raster-based maps of dd extracted straight off from digital elevation model data. Maps of local dd, which are continuous in space, are able to reveal the appearance of strong heterogeneities in the geological and geomorphological properties of natural landscapes across different scales. In this work we employ the information provided by these spatial maps to study the potential effects of the within-catchment variability of dd on the hydrologic response. A simple power law relationship between runoff yield at the local scale and the value of dd has been adopted; the hypothesis is supported by a large number of past empirical observations and modeling. The novel framework proposed (ddRWF) embeds this spatially variable runoff weight in the well-known Rescaled Width Function (RWF) framework, based on the more general geomorphological theory of the hydrologic response. The model is applied to four sub-basins in the Cascade Range Region (Oregon, USA) where strong contrasts in dissection patterns due the underlain geology have been broadly addressed in previous literature. The ddRWF approach is compared with the classic RWF in terms of shape, moments and peak of the simulated hydrograph response. Results hint that the variability of runoff yield due to the heterogeneity of dd (i.e. of hillslope lengths) determines a more rapid concentration of runoff, which implies shorter lag times, larger skewness and higher peak floods, especially in the case hillslope velocity is much smaller than channel velocity. The potential of the proposed framework relies on accounting for spatially variable losses related to geomorphologic heterogeneity in lumped rainfall–runoff models, still keeping the simple and robust structure of the IUH approach.     

Modelling drainage headwater development

Processes operative in the divideward sections of streams and channels are reviewed, and the effects of their action over long periods of time are modelled for insight into long-term valley head development. Upper valley axis profiles eventually become concave upwards over time but may show earlier convexity and convexo-concavity. After any particular length of development different upper valley axis forms can exist in areas of different climate and hydrological response characteristics.     

Explorations into the formal structure of drainage basins

Every basin of higher than first order is drained by a channel network composed of two subnetworks. Their basins are separated by a drainage divide line, called the basin divider, which is the primary organizing feature of the main basin. Each basin of magnitude n contains n – 1 subnetworks of higher order, and is therefore organized by a set of n – 1 dividers. The dividers and the basin boundary are interconnected in a graph called the divider network of the basin; in graph-theoretic terms this network forms a tree and has the same magnitude and link numbers as the channel network draining the basin. While the subbasins and subnetworks of a drainage basin form a nesting hierarchy, the corresponding dividers do not; indeed, any two dividers share at most one node in common, and whether they do so is independent of whether the corresponding subbasins are nesting or disjoint. However, the dividers of nesting basins are linked by recursive relationships which permit the derivation of a set of algebraic equations; these equations relate the dividers of a basin to other basin components; for example, their combined length is equal to half the length of all first-order basin boundaries minus the length of the main basin boundary. The second part of the paper explores the dependence of the divider length on other basin parameters. The expected length, as predicted by the assumption of topological randomness, is clearly rejected by the data. An alternative approach (regression) is based on the observed magnitudes of the subbasins separated by each divider, and is reasonably successful in estimating divider length. The last section introduces the concept of the standardized basin defined by a boundary length of unity; the estimated lengths of the basin divider and the basin boundary permit an approximate reconstruction of the idealized basin shape and the location of the divider in it.     

Relative scales of time and effectiveness of climate in watershed geomorphology

Peak rainfalls and peak runoff rates per unit area are comparable over a worldwide spectrum of climates. However, while the magnitude of the external contribution of energy or force in diverse regions is similar, the impact on the landscape varies markedly between regions. Absolute magnitudes of climatic events and absolute time intervals between such events do not provide satisfactory measures of the geomorphic effectiveness of events of different magnitudes and recurrence intervals. Although geomorphic processes are driven by complex sets of interrelated climatic, topographic, lithologic, and biologic factors, the work done by individual extreme events can be scaled as a ratio to mean annual erosion and the effectiveness of such events in forming landscape features can be related to the rate of recovery of channel form or mass wasting scars following alteration by the extreme event. Thus, a time scale for effectiveness may relate the recurrence interval of an event to the time required for a landform to recover the form existing prior to the event. River channels in temperate regions widened by floods of recurrence intervals from 50 to more than 200 years may regain their original width in matters of months or years. In semi-arid regions, recovery of channel form depends not only upon flows but upon climatic determinants of the growth of bottomland vegetation resulting in variable rates of recovery, on the order of decades, depending upon coincidence of average flows and strengthened vegetation. In truly arid regions the absence of vegetation and flow precludes recovery and the width of channels increases in drainage areas up to 100 km² but remains relatively constant at larger drainage areas. Area as well as time controls the effectiveness of specific events inasmuch as the likelihood of simultaneous peak discharges or rainfalls and large areas is less, particularly in arid regions where events spanning areas of more than several thousand km² are extremely rare if experienced at all. To some extent a decrease in area in a humid region is comparable with a regional change from humid toward more arid climate reflected in the increase in importance of episodic as contrasted with more continuous processes. Exceedingly rare floods of extreme magnitudes, estimated recurrence intervals of 500 years or longer, may exceed thresholds of competence otherwise unattainable in the ‘normal’ record resulting in ‘irreparable’ transformations of valley landforms. Denudation of hillslopes by mass wasting during relatively rare events can also be related to mean rates of denudation and to recovery of hillslope surfaces after scarring by different kinds of landslides. Measured recovery times described in the literature vary from less than a decade for some tropical regions to decades or more in temperate regions. Recurrence intervals of high magnitude storms which trigger mass wasting range from 1 to 2 years in some tropical areas, to 3 or 4 per hundred years in some areas of seasonal rainfall and to 100 or more years in some temperate regions. The effectiveness of climatic events on both hillslopes and rivers is not separable from gradient, lithology or other variables which control both thresholds of activity and recovery rate.     

Drainage density changes during rainfall

Observations of stream behaviour during rainfall indicate that previous notions of a simple expanding and contracting network need review and refinement. In a small rural catchment near Armidale, N.S.W. changes in flowing stream length during rainfall have been depicted on flow length graphs which indicate a varied network response to similar rainfall amounts. Channel flow phenomena include discontinuous flow, the generation of flow points within the channel and movement of water downslope from saturated depression sources. Localized physical controls have a significant effect on stream growth which is a sensitive indicator of the catchment response to rainfall. During rapid changes in stream length total flowing length and discharge are highly correlated. A model of the pattern of network expansion and contraction involves several phases of flow contraction.     

Applications of the random model of drainage basin composition

The random model of drainage basin composition is founded on the assumptions that (a) natural channels are topologically random in the absence of geological controls and (b) for channel networks developed in similar environments, the exterior and interior link lengths are independent random variables with a common distribution for each type. The effectiveness of this model in estimating the values of geomorphic variables and in explaining and predicting geomorphic relationships is illustrated by several examples. The data required for these examples were obtained from map studies of 30 channel networks, comprising a total of about 8700 links, in eastern Kentucky. A common factor in the success of all three applications of the model is the way in which the planimetric features of drainage basins are determined by their underlying topologic structure.     

The analysis of drainage network composition

The Horton method of analyzing drainage network composition is reviewed, with the conclusion that it has not been very effective either in improving understanding or in developing useful methods of characterizing drainage basins. New methods which are based on the link rather than the Horton (or Strahler) stream are described. A number of detailed examples of the application of these new methods to the topologic and geometric properties of networks are provided. The results are compared with the predictions of the random model. Data used in the analysis were obtained from 1:24,000 U.S.G.S. topographic maps of eastern Kentucky. Thirty drainage basins were selected and their channel networks were outlined first by the contour-crenulation (CC) method and then by another, more objective, method (SC) in which stream sources were identified by a quantitative slope criterion. The CC and SC samples comprise about 8,700 and 1,700 links, respectively. The three most important results of the analysis are: (1) the channel networks are slightly but significantly more elongated than predicted by the random model, (2) there are fewer second magnitude links than predicted, and (3) the length distribution for interior links depends upon the kind of link (interior or exterior) joined downstream. These features are found in both CC and SC networks.     

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.     

Drainage area and the variation of channel geometry downstream

Recent geomorphological studies tend to deal with small basins. The understanding of small basin dynamics provides important information for the understanding of large basin dynamics assuming that the extrapolation of small basin data to larger basins is valid. This work tests the validity of this extrapolation of data with reference to channel geometry. An analysis of the variation of channel width downstream reveals that the value b =0.5 (W = aQ^b) is a ‘good’ average. However, the use of a one-line model consisting of a simple power function incurs a loss of a considerable amount of relevant information concerning the channel form and hence the channel processes. It has been shown that the –b– value for small basins and very big basins is lower than the one for the intermediate basins.     

Invariance and scaling properties in the distributions of contributing area and energy in drainage basins

The cumulative probability distributions for stream order, stream length, contributing area, and energy dissipation per unit length of channel are derived, for an ordered drainage system, from Horton's laws of network composition. It is shown how these distributions can be related to the fractal nature of single rivers and river networks. Finally, it is shown that the structure proposed here for these probability distributions is able to fit the observed frequency distributions, and their deviations from straight lines in a log-log plot.     

An experimental study of sapped drainage network development

In a basin developed on a stream table, effluent subsurface flow supported a channel network that evolved by a combination of headward growth, lateral widening and divide decay. The area occupied by the developing network increased with time. Circularity was used to characterize network evolution which occurred in three phases (initiation, extension and abstraction). Basin sediment discharge declined exponentially with time. Pronounced quasi-cyclic variability was superimposed upon this general trend. Some of the variability was directly linked to changes in the amount of sediment supplied to the channel. The variation of mean network sediment yield (mean sediment discharge scaled by network area) with time adequately described the general decline in sediment discharge as the network evolved.     

Theoretical and experimental study of time domain-induced polarization in water-saturated sands

A theoretical model of spectral-induced polarization (IP) of sand is presented. In the proposed model, contacts of sand grains and intergrain solution-filled space are considered as electrical current passages of varying thickness, which differ in values of ion transport number. Ion-selective narrow passages are considered as active zones, large passages as passive. The proposed model describes spectral IP characteristics for the medium where the length of passive zones is much greater than the length of active ones. The model is called short narrow pores (SNP) model. The SNP model predicts a growth of IP time constant with increase of length of ion-selective zone. Both the time domain and frequency domain parameters are described. The parameters of Cole–Cole model corresponding to the SNP model were also found.The behaviour of model parameters is compared with experimental data obtained on natural and sieved sands using time domain technique. The natural sand spectra correspond neither to the simple SNP model nor simple Cole–Cole model with single time constant because the lengths of ion-selective zones vary, reflecting the grain-size distribution.The spectra of sieved sand compared with the theoretical SNP spectra reveal close correspondence between experimental data and theoretical parameters. For four sieved sands, both the theoretical and experimental data show that the time constant of the IP is proportional to the square of the average grain size.     

地球主磁场的能量密度谱及其长期变化

根据BJ地磁场模型和第8代国际地磁参考场(IGRF)模型，计算并分折了1690～2000年期间地球表面主磁场和分量的能量密度谱及其长期变化。结果表明1690～2000年期间主磁场的能量密度谱一直在减小，其主要原因是由于偶板子磁场的衰减产生的，而非偶板子磁场的能量密度谱在1690～1780年期间减小，1780～1890年增大，1890年以后快速增大。在地磁场总能谱的变化中，Z分量的贡献起主要作用。能量密度随谐波阶数的变化在半对数坐标中近似线性，非偶板子场的等效磁源深度位于核幔边界附近，n＝1，2谐波项的等效磁源位于地球内核边缘，其位置随时间变化。1780和1890年前后是地磁场变化的转折时期。能量密度谱的长期变化存在大约60a的周期规律。     

太湖流域南河水系无尺度结构

基于图论和无尺度结构视角及节点度指标初步探讨太湖流域南河水系结构的数量特征和空间秩序,为辨识和模拟域水文情势提供重要参数.主要结论如下:太湖流域南河水系结构的数量节点度不符合幂次分布,而长度和等级节点度符台无尺度结构;南河水系结构符合Horton第一定律和第二定律,同时此类特征亦符合无尺度结构,但指数函数回归模拟的R<'2>相比乘幂函数回归模拟的R<'2>较低;由幂次定律所支配的这种水系网络特征状况是由地区地形、农业灌溉、圩区建设和城市化过程共同推动;从节点度角度看,南河下游圩区使得河网数量节点度增加,等级节点度和长度节点度降低.     

基于能量密度的自解耦互相关成像条件

基于能量密度构建的弹性波能量成像条件,可以准确提取弹性波场的能量信息,并可以有效压制背向散射.但是该成像条件得到的成像结果将所有弹性波场能量信息耦合在一起,难以区分纯波模式的能量信息.为此,我们从势能及动能两方面将能量场解耦,得到纯纵波（PP）、纯横波（SS）、转换波（C）能量场.根据能量守恒定律,基于Helmholtz原理对位移场的空间导数进行因式分解,将弹性势能自解耦得到纯纵波、纯横波及转换波势能;引入体应力构建得到P波及S波速度,将弹性动能分解为纯纵波、纯横波和转换波动能.从而,构建基于能量密度自解耦得到纯波能量互相关成像条件.数值实验表明自解耦成像条件可实现弹性波场能量的分解,并得到背向散射压制、振幅有效保持的PP波、SS波和C波成像结果.

     

Dynamic investigation on the coupled changing process of moisture and density fields in freezing soil

The data reflecting the change in density are obtained, with computer tomograph scanning through the sample of freezing soil section by section at intervals without destruction. Combined with the changing characteristics of water content along the sample during test, the dynamic coupled process of moisture and density fields under the effect of temperature gradient on the freezing soil in closed system is discussed. The result reflects the internal process of frost heave improvement resulting from the transfer of mass and heat. Project supported by the National Natural Science Foundation of China (Grant No. 49401003).     

基于局部倾斜叠加的快速射线束叠前时间偏移

宽方位高密度地震勘探可以有效的提高地震资料的空间分辨率和裂缝预测的精度,但地震道数的增加也大幅度提升了地震数据的处理成本.为提高海量地震数据偏移处理的计算效率,本文发展了一种快速射线束叠前时间偏移方法.该方法首先根据给定的射线束中心间隔将炮记录划分为一系列数据子集,然后利用倾斜叠加将数据子集分解为不同方向的平面波,最后根据射线束中心到地下成像点的双程走时和射线参数拾取相应的平面波振幅累加到成像点上.同Kirchhoff叠前时间偏移相比,本文方法不但保持了一致的成像精度,且由于仅需在稀疏的射线束中心位置进行成像累加运算,计算效率得到了大幅度的提升.文中所给出的模型和实际资料的测试结果验证了本文方法的正确性和有效性.

     

A note on topological matrices and characteristic polynomials of fourth-magnitude drainage net maps

I suggest that a connection matrix and a characteristic polynomial, which can be formed for any drainage net, using Shreve link magnitudes, may be used in studying drainage nets. I show how the matrix and the polynomial can be formed, using selected drainage nets as examples.     

计算结构首次穿越时间概率密度函数的新方法

本文在M adsen等提出的积分方程方法基础上,采用单点FORM方法计算结构首次穿越问题中的条件穿越率、联合穿越率及首次穿越时间概率密度。提出的新方法计算简单,结果精确,适于进行脆性结构的首次穿越破坏分析。     

基于COSMIC掩星数据分析中低纬度地区电子密度分布变化

利用COSMIC掩星2009年电子密度剖面数据,筛选数据进行网格划分,网格内数据统计平均,基于球谐函数计算模型值,分析电离层中低纬度地区最大电子密度的地磁季节变化、昼夜测分布相对变化,及地磁活动对电子密度的分布影响.结果表明,最大电子密度昼测值明显高于夜测值,在中纬度部分区域增大明显.电子密度昼测值在地磁活动期间高度150-550 km中低纬度范围为正相扰动,随纬度变化存在区域差异,随高度增加,扰动加强.