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1.
Abstract

One of the basic tasks in geomorphologic analysis is to know the probability distributions of the stream lengths of different orders. In practical applications, this information is useful for basin rainfall-runoff modelling. The objective of this study is to determine the length distributions of the Strahler streams. A Poisson process was used to derive the theoretical distributions. The result showed that the length distribution of the first-order stream is an exponential distribution and the second-order or higher order stream length is a gamma distribution. In order to verify the theoretical distributions, a digital elevation model (DEM) was adopted to calculate the stream lengths of four basins in Taiwan. Kolmogorov-Smirnov and chi-square tests were used to test the goodness-of-fit of the data. Results showed that the length distributions of the first- and second-order streams analysed by using DEM correspond with those from the derived distribution method.  相似文献   

2.
Stream flow predictions in ungauged basins are one of the most challenging tasks in surface water hydrology because of nonavailability of data and system heterogeneity. This study proposes a method to quantify stream flow predictive uncertainty of distributed hydrologic models for ungauged basins. The method is based on the concepts of deriving probability distribution of model's sensitive parameters by using measured data from a gauged basin and transferring the distribution to hydrologically similar ungauged basins for stream flow predictions. A Monte Carlo simulation of the hydrologic model using sampled parameter sets with assumed probability distribution is conducted. The posterior probability distributions of the sensitive parameters are then computed using a Bayesian approach. In addition, preselected threshold values of likelihood measure of simulations are employed for sizing the parameter range, which helps reduce the predictive uncertainty. The proposed method is illustrated through two case studies using two hydrologically independent sub‐basins in the Cedar Creek watershed located in Texas, USA, using the Soil and Water Assessment Tool (SWAT) model. The probability distribution of the SWAT parameters is derived from the data from one of the sub‐basins and is applied for simulation in the other sub‐basin considered as pseudo‐ungauged. In order to assess the robustness of the method, the numerical exercise is repeated by reversing the gauged and pseudo‐ungauged basins. The results are subsequently compared with the measured stream flow from the sub‐basins. It is observed that the measured stream flow in the pseudo‐ungauged basin lies well within the estimated confidence band of predicted stream flow. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

3.
Satya P. Ojha 《水文研究》2014,28(18):4829-4842
This study presents the analysis of the velocity fluctuations to describe the conditional statistics of Reynolds shear stress in flow over two‐dimensional dunes in the presence of surface waves of varying frequency. The flow velocity measurements over the dunes are made using a 16‐MHz 3D acoustic Doppler velocimeter. The joint probability distributions of the normalized stream‐wise and vertical velocity fluctuations at different vertical locations are calculated in the trough region of a selected dune in quasi‐steady region of the flow. Third‐order moments of the stream‐wise and vertical velocity components over one dune length are also calculated throughout the flow depth for understanding the effect of surface waves on relative contributions to the Reynolds shear stress due to the four quadrant events. The structure of instantaneous Reynolds stresses is analysed using quadrant analysis technique. It has been shown that the contributions of second and fourth quadrant events to the Reynolds shear stress increase with increase in the frequency of surface waves. In fact, the largest contribution to turbulent stresses comes from the second quadrant. The cumulant discard method is applied to describe the statistical properties of the covariance term u′w′. Conditional statistics and conditional sampling are used to compare the experimental and theoretical relative contributions to the Reynolds shear stress from the four quadrant events. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

4.
Probability distributions of water flow and its turbidity after passing through water intake structures are considered. Heavy tails with a power distribution are shown to exist. These distributions are used to find the dependence between water turbidity at the inlet to the water station and water flow in the river. Quantiles of these distributions are estimated to characterize the levels of water flow and turbidity with a given exceedance probability.Translated from Vodnye Resursy, Vol. 32, No. 2, 2005, pp. 196–204.Original Russian Text Copyright © 2005 by Dolgonosov, Korchagin.  相似文献   

5.
Random walk models of fluvial sediment transport recognize that grains move intermittently, with short duration steps separated by rests that are comparatively long. These models are built upon the probability distributions of the step length and the resting time. Motivated by these models, tracer experiments have attempted to measure directly the steps and rests of sediment grains in natural streams. This paper describes results from a large tracer experiment designed to test stochastic transport models. We used passive integrated transponder (PIT) tags to label 893 coarse gravel clasts and placed them in Halfmoon Creek, a small alpine stream near Leadville, Colorado, USA. The PIT tags allow us to locate and identify tracers without picking them up or digging them out of the streambed. They also enable us to find a very high percentage of our rocks, 98% after three years and 96% after the fourth year. We use the annual tracer displacement to test two stochastic transport models, the Einstein–Hubbell–Sayre (EHS) model and the Yang–Sayre gamma‐exponential model (GEM). We find that the GEM is a better fit to the observations, particularly for slower moving tracers and suggest that the strength of the GEM is that the gamma distribution of step lengths approximates a compound Poisson distribution. Published in 2012. This article is a US Government work and is in the public domain in the USA.  相似文献   

6.
This article has been retracted and replaced. See Retraction and Replacement Notice DOI: 10.1002/hyp.6350 Studies of hyporheic exchange flows have identified physical features of channels that control exchange flow at the channel unit scale, namely slope breaks in the longitudinal profile of streams that generate subsurface head distributions. We recently completed a field study that suggested channel unit spacing in stream longitudinal profiles can be used to predict the spacing between zones of upwelling (flux of hyporheic water into the stream) and downwelling (flux of stream water into the hyporheic zone) in the beds of mountain streams. Here, we use two‐dimensional groundwater flow and particle tracking models to simulate vertical and longitudinal hyporheic exchange along the longitudinal axis of stream flow in second‐, third‐, and fourth‐order mountain stream reaches. Modelling allowed us to (1) represent visually the effect that the shape of the longitudinal profile has on the flow net beneath streambeds; (2) isolate channel unit sequence and spacing as individual factors controlling the depth that stream water penetrates the hyporheic zone and the length of upwelling and downwelling zones; (3) evaluate the degree to which the effects of regular patterns in bedform size and sequence are masked by irregularities in real streams. We simulated hyporheic exchange in two sets of idealized stream reaches and one set of observed stream reaches. Idealized profiles were constructed using regression equations relating channel form to basin area. The size and length of channel units (step size, pool length, etc.) increased with increasing stream order. Simulations of hyporheic exchange flows in these reaches suggested that upwelling lengths increased (from 2·7 m to 7·6 m), and downwelling lengths increased (from 2·9 m to 6·0 m) with increase in stream order from second to fourth order. Step spacing in the idealized reaches increased from 5·3 m to 13·7 m as stream size increased from second to fourth order. Simulated upwelling lengths increased from 4·3 m in second‐order streams to 9·7 m in fourth‐order streams with a POOL–RIFFLE–STEP channel unit sequence, and increased from 2·5 m to 6·1 m from second‐ to fourth‐order streams with a POOL–STEP–RIFFLE channel unit sequence. Downwelling lengths also increased with stream order in these idealized channels. Our results suggest that channel unit spacing, size, and sequence are all important in determining hyporheic exchange patterns of upwelling and downwelling. Though irregularities in the size and spacing of bedforms caused flow nets to be much more complex in surveyed stream reaches than in idealized stream reaches, similar trends emerged relating the average geomorphic wavelength to the average hyporheic wavelength in both surveyed and idealized reaches. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

7.
Many civil infrastructures are located near the confluence of two streams, where they may be subject to inundation by high flows from either stream or both. These infrastructures, such as highway bridges, are designed to meet specified performance objectives for floods of a specified return period (e.g. the 100 year flood). Because the flooding of structures on one stream can be affected by high flows on the other stream, it is important to know the relationship between the coincident exceedence probabilities on the confluent stream pair in many hydrological engineering practices. Currently, the National Flood Frequency Program (NFF), which was developed by the US Geological Survey (USGS) and based on regional analysis, is probably the most popular model for ungauged site flood estimation and could be employed to estimate flood probabilities at the confluence points. The need for improved infrastructure design at such sites has motivated a renewed interest in the development of more rigorous joint probability distributions of the coincident flows. To accomplish this, a practical procedure is needed to determine the crucial bivariate distributions of design flows at stream confluences. In the past, the copula method provided a way to construct multivariate distribution functions. This paper aims to develop the Copula‐based Flood Frequency (COFF) method at the confluence points with any type of marginal distributions via the use of Archimedean copulas and dependent parameters. The practical implementation was assessed and tested against the standard NFF approach by a case study in Iowa's Des Moines River. Monte Carlo simulations proved the success of the generalized copula‐based joint distribution algorithm. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

8.
Studies of hyporheic exchange flows have identified physical features of channels that control exchange flow at the channel unit scale, namely slope breaks in the longitudinal profile of streams that generate subsurface head distributions. We recently completed a field study that suggested channel unit spacing in stream longitudinal profiles can be used to predict the spacing between zones of upwelling (flux of hyporheic water into the stream) and downwelling (flux of stream water into the hyporheic zone) in the beds of mountain streams. Here, we use two‐dimensional groundwater flow and particle tracking models to simulate vertical and longitudinal hyporheic exchange along the longitudinal axis of stream flow in second‐, third‐, and fourth‐order mountain stream reaches. Modelling allowed us to (1) represent visually the effect that the shape of the longitudinal profile has on the flow net beneath streambeds; (2) isolate channel unit sequence and spacing as individual factors controlling the depth that stream water penetrates the hyporheic zone and the length of upwelling and downwelling zones; (3) evaluate the degree to which the effects of regular patterns in bedform size and sequence are masked by irregularities in real streams. We simulated hyporheic exchange in two sets of idealized stream reaches and one set of observed stream reaches. Idealized profiles were constructed using regression equations relating channel form to basin area. The size and length of channel units (step size, pool length, etc.) increased with increasing stream order. Simulations of hyporheic exchange flows in these reaches suggested that upwelling lengths increased (from 2·7 m to 7·6 m), and downwelling lengths increased (from 2·9 m to 6·0 m) with increase in stream order from second to fourth order. Step spacing in the idealized reaches increased from 5·3 m to 13·7 m as stream size increased from second to fourth order. Simulated downwelling lengths increased from 4·3 m in second‐order streams to 9·7 m in fourth‐order streams with a POOL–RIFFLE–STEP channel unit sequence, and increased from 2·5 m to 6·1 m from second‐ to fourth‐order streams with a POOL–STEP–RIFFLE channel unit sequence. Upwelling lengths also increased with stream order in these idealized channels. Our results suggest that channel unit spacing, size, and sequence are all important in determining hyporheic exchange patterns of upwelling and downwelling. Though irregularities in the size and spacing of bedforms caused flow nets to be much more complex in surveyed stream reaches than in idealized stream reaches, similar trends emerged relating the average geomorphic wavelength to the average hyporheic wavelength in both surveyed and idealized reaches. This article replaces a previously published version (Hydrological Processes, 19 (17), 2915–2929 (2005) [ DOI:10.1002/hyp.5790 ]. See also retraction notice DOI:10.1002/hyp.6350 Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

9.
Abstract

Two probability density functions (pdf), popular in hydrological analyses, namely the log-Gumbel (LG) and log-logistic (LL), are discussed with respect to (a) their applicability to hydrological data and (b) the drawbacks resulting from their mathematical properties. This paper—the first in a two-part series—examines a classical problem in which the considered pdf is assumed to be the true distribution. The most significant drawback is the existence of the statistical moments of LG and LL for a very limited range of parameters. For these parameters, a very rapid increase of the skewness coefficient, as a function of the coefficient of variation, is observed (especially for the log-Gumbel distribution), which is seldom observed in the hydrological data. These probability distributions can be applied with confidence only to extreme situations. For other cases, there is an important disagreement between empirical data and theoretical distributions in their tails, which is very important for the characterization of the distribution asymmetry. The limited range of shape parameters in both distributions makes the analyses (such as the method of moments), that make use of the interpretation of moments, inconvenient. It is also shown that the often-used L-moments are not sufficient for the characterization of the location, scale and shape parameters of pdfs, particularly in the case where attention is paid to the tail part of probability distributions. The maximum likelihood method guarantees an asymptotic convergence of the estimators beyond the domain of the existence of the first two moments (or L-moments), but it is not sensitive enough to the upper tails shape.  相似文献   

10.
The objective of this paper is to present an analytical solution for describing the head distribution in an unconfined aquifer with a single pumping horizontal well parallel to a fully penetrating stream. The Laplace-domain solution is developed by applying Fourier sine, Fourier and Laplace transforms to the governing equation as well as the associated initial and boundary conditions. The time-domain solution is obtained after taking the inverse Laplace transform along with the Bromwich integral method and inverse Fourier and Fourier sine transforms. The upper boundary condition of the aquifer is represented by the free surface equation in which the second-order slope terms are neglected. Based on the solution and Darcy’s law, the equation representing the stream depletion rate is then derived. The solution can simulate head distributions in an aquifer infinitely extending in horizontal direction if the well is located far away from the stream. In addition, the solution can also simulate head distributions in confined aquifers if specific yield is set zero. It is shown that the solution can be applied practically to evaluate flow to a horizontal well.  相似文献   

11.
Tracer studies are a commonly used tool to develop and test Einstein-type stochastic bedload transport models. The movements of these tracers are controlled by many factors including grain characteristics, hydrologic forcing, and channel morphology. Although the influence of these sediment storage zones related to morphological features (e.g., bars, pools, riffles) have long been observed to “trap” bedload particles in transport, this influence has not been adequately quantified. In this paper we explore the influence of channel morphology on particle travel distances through the development of a Bayesian survival process model. This model simulates particle path length distributions using a location-specific “trapping probability” parameter (pi ), which is estimated using the starting and ending locations of bedload tracers. We test this model using a field tracer study from Halfmoon Creek, Colorado. We find that (1) the model is able to adequately recreate the observed multi-modal path length distributions, (2) particles tend to accumulate in trapping zones, especially during large floods, and (3) particles entrained near a trapping zone will travel a shorter distance than one that is further away. Particle starting positions can affect path lengths by as much as a factor of two, which we confirm by modelling “starting-location-specific” path length probability distributions. This study highlights the importance of considering both tracer locations and channel topography in examinations of field tracer studies. © 2020 John Wiley & Sons, Ltd.  相似文献   

12.
Stream network morphometrics have been used frequently in environmental applications and are embedded in several hydrological models. This is because channel network geometry partly controls the runoff response of a basin. Network indices are often measured from channels that are mapped from digital elevation models (DEMs) using automated procedures. Simulations were used in this paper to study the influence of elevation error on the reliability of estimates of several common morphometrics, including stream order, the bifurcation, length, area and slope ratios, stream magnitude, network diameter, the flood magnitude and timing parameters of the geomorphological instantaneous unit hydrograph (GIUH) and the network width function. DEMs of three UK basins, ranging from high to low relief, were used for the analyses. The findings showed that moderate elevation error (RMSE of 1·8 m) can result in significant uncertainty in DEM‐mapped network morphometrics and that this uncertainty can be expressed in complex ways. For example, estimates of the bifurcation, length and area ratios and the flood magnitude and timing parameters of the GIUH each displayed multimodal frequency distributions, i.e. two or more estimated values were highly likely. Furthermore, these preferential estimates were wide ranging relative to the ranges typically observed for these indices. The wide‐ranging estimates of the two GIUH parameters represented significant uncertainty in the shape of the unit hydrograph. Stream magnitude, network diameter and the network width function were found to be highly sensitive to elevation error because of the difficulty in mapping low‐magnitude links. Uncertainties in the width function were found to increase with distance from outlet, implying that hydrological models that use network width contain greater uncertainty in the shape of the falling limb of the hydrograph. In light of these findings, care should be exercised when interpreting the results of analyses based on DEM‐mapped stream networks. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

13.
The determination of the probability distribution of recurrence times is the most important problem in the calculation of long-term conditional probabilities for the recurrence of large and great earthquakes.The principle of maximum entropy in conjunction with a goodness-of-fit test (chi-square or Kolmogorov-Smirnov test) may be employed to obtain estimates of these densities using recurrence data for some seismic regions.Four different distributions are characterized by the property of maximum entropy, as possible laws for recurrence times of the largest earthquakes: uniform, exponential, Gaussian and log-normal. To discriminate among these different probability distributions we use the probability theory and the chi-square test to check the goodness-of-fit to the distribution of recurrence time of shocks of magnitude 6.5 and largest occurred in the west-northwestern zone of the Hellenic arc from 1791 to 1983.It is found that the recurrence times data for the west-northwestern zone of the Hellenic arc cannot be represented by the uniform and the Gaussian probability densities. The recurrence times data for the west-northwestern zone of the Hellenic arc can be described accurately by the exponential and log-normal probability densities, which were predicted from the principle of maximum entropy. In other words, the principle of maximum entropy does not necessarily lead to a unique solution. In turn, the mathematical properties of these distributions could be used to derive different physical properties of the earthquake process in the west-northwestern zone of the Hellenic arc.  相似文献   

14.
River networks have been shown to obey power scaling laws and to follow self‐organization principles. Their self‐similar (fractal) properties open a path to relate small scale and large scale hydrological processes, such as erosion, deposition or geological movements. However, the existence of a self‐similar dimension has only been checked using either the whole channel network or, on the contrary, a single channel link. No study has explicitly addressed the possible spatial variation of the self‐similar properties between these two extreme geomorphologic objects. Here, a new method based on self‐similarity maps (SSM) is proposed to spatially explore the stream length self‐similar dimension Dl within a river network. The mapping principle consists in computing local self‐similar dimensions deduced from a fit of stream length estimations using increasing divider sizes. A local uncertainty related to the fit quality is also computed and localized on every stream. To assess the efficiency of the approach, contrasted river networks are simulated using optimal channel networks (OCN), where each network is characterized by an exponent γ conditioning its overall topology. By building SSM of these networks, it is shown that deviations from uniform self‐similarity across space occur. Depending on the type of network (γ parameter), these deviations are or are not related to Strahler's order structure. Finally, it is found numerically that the structural averaged stream length self‐similar dimension Dl is closely related to the more functional γ parameter. Results form a bridge between the studies on river sinuosity (single channel) and growth of channel networks (watershed). As for every method providing spatial information where they were lacking before, the SSM may soon help to accurately interpret natural networks and help to simulate more realistic channel networks. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

15.
A recourse-based nonlinear programming (RBNP) method is developed for stream water quality management under uncertainty. It can not only reflect uncertainties expressed as interval values and probability distributions but also address nonlinearity in the objective function. A 0-1 piecewise linearization approach and an interactive algorithm are advanced for solving the RBNP model. The RBNP is applied to a case of planning stream water quality management. The RBNP modeling system can provide an effective linkage between environmental regulations and economic implications expressed as penalties or opportunity losses caused by improper policies. The solutions can be used for generating a variety of alternatives under different combinations of pre-regulated targets, which are also associated with different water-quality-violation risk levels and varied potential economic penalty or loss values.  相似文献   

16.
The rainfall–runoff relationship is not only nonlinear and complex but also difficult to model. Artificial neural network (ANN), as a data-driven technique, has gained significant attention in recent years and has been shown to be an efficient alternative to traditional methods for hydrological modeling. However, for different input combinations, ANN models can yield different results. Therefore, input variables and ANN types need to be carefully considered, when using an ANN model for stream flow forecasting. This study proposes the copula-entropy (CE) theory to identify the inputs of an ANN model. The CE theory permits to calculate mutual information (MI) and partial MI directly which avoids calculating the marginal and joint probability distributions. Three different ANN models, namely multi-layer feed (MLF) forward networks, radial basis function networks and general regression neural network, were applied to predict stream flow of Jinsha River, China. Results showed that the inputs selected by the CE method were better than those by the traditional linear correlation analysis, and the MLF ANN model with the inputs selected by CE method obtained the best predicted results for the Jinsha River at Pingshan gauging station.  相似文献   

17.
Watershed structure influences the timing, magnitude, and spatial location of water and solute entry to stream networks. In turn, stream reach transport velocities and stream network geometry (travel distances) further influence the timing of export from watersheds. Here, we examine how watershed and stream network organization can affect travel times of water from delivery to the stream network to arrival at the watershed outlet. We analysed watershed structure and network geometry and quantified the relationship between stream discharge and solute velocity across six study watersheds (11.4 to 62.8 km2) located in the Sawtooth Mountains of central Idaho, USA. Based on these analyses, we developed stream network travel time functions for each watershed. We found that watershed structure, stream network geometry, and the variable magnitude of inputs across the network can have a pronounced affect on water travel distances and velocities within a stream network. Accordingly, a sample taken at the watershed outlet is composed of water and solutes sourced from across the watershed that experienced a range of travel times in the stream network. We suggest that understanding and quantifying stream network travel time distributions are valuable for deconvolving signals observed at watershed outlets into their spatial and temporal sources, and separating terrestrial and in‐channel hydrological, biogeochemical, and ecological influences on in‐stream observations. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

18.
The objective of the paper is to show that the use of a discrimination procedure for selecting a flood frequency model without the knowledge of its performance for the considered underlying distributions may lead to erroneous conclusions. The problem considered is one of choosing between lognormal (LN) and convective diffusion (CD) distributions for a given random sample of flood observations. The probability density functions of these distributions are similarly shaped in the range of the main probability mass and the discrepancies grow with the increase in the value of the coefficient of variation (C V ). This problem was addressed using the likelihood ratio (LR) procedure. Simulation experiments were performed to determine the probability of correct selection (PCS) for the LR method. Pseudo-random samples were generated for several combinations of sample sizes and the coefficient of variation values from each of the two distributions. Surprisingly, the PCS of the LN model was twice smaller than that of the CD model, rarely exceeding 50%. The results obtained from simulation were analyzed and compared both with those obtained using real data and with the results obtained from another selection procedure known as the QK method. The results from the QK are just the opposite to that of the LR procedure.  相似文献   

19.
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20.
Matthias Brunke   《Limnologica》2004,34(4):460-478
The objective of this paper is twofold: 1) to validate the German stream typology for Schleswig-Holstein, and 2) to develop an assessment system for lake outlets. The German stream typology, based on a top-down analysis of geomorphological variables, was validated using biotic data of streams in Schleswig-Holstein, northern Germany. A null model analysis was conducted to test for differences between seven stream types (sand streams and rivers, gravel streams and rivers, partly-mineralic streams, limnic marsh streams, and lake outlets). The dataset compiled for the statistical analysis comprised 28 streams, 65 different sampling sites, 428 samples, and 296 taxa. The analysis confirmed all stream type except partly-mineralic streams, which showed faunal overlap with all types except gravel streams. Gravel streams were the most distinctive stream type. Lake outlets were shown to be a unique type, having a distinct macroinvertebrate fauna. Furthermore it was shown, that the species composition differed between lentic and lotic outlets. Canonical correspondence analysis of 19 investigated lake outlets revealed that characteristics of the lakes had only a minor effect on macroinvertebrate community structure.

The developed assessment system of lake outlets was based on the habitat association of 132 macroinvertebrate taxa. Taxa were allotted to five categories of lake outlet preferences depending on the results from ordinations, frequency tables and abundance distributions. A qualitative and a quantitative lake outlet index (LTI) were tested with independent data sets. The quantitative LTIquan proved to be more robust and only slightly affected by seasonal changes in the macroinvertebrate community composition. Assessments of lake outlets based on macroinvertebrates should be conducted in spring and autumn to reduce the risk of misclassifications, in particular, for boundary cases rated between good and moderate quality classes.  相似文献   


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