Three‐dimensional flow structure around small‐scale bedforms in a simulated gravel‐bed environment

Pebble clusters are common small‐scale morphological features in gravel‐bed rivers, occupying as much as 10 per cent of the bed surface. Important links exist between the presence of pebble clusters and the development of flow structures. These links are poorly understood at the three‐dimensional level. Particularly neglected has been the effect of clusters on the lateral flow characteristics. A laboratory study was conducted using a hydraulic flume, within which simulated pebble clusters were superimposed onto a plane bed of gravel material. High‐resolution three‐dimensional flow data were collected above the bed at two different flow depths using an acoustic Doppler velocimeter. The results present evidence of the importance of lateral flow in the development of turbulent flow structure. Narrow regions of high lateral and downstream turbulence intensity exist to both sides of clusters and in a three‐dimensional separation zone in their lee. This may indicate the presence of horseshoe‐type vortical structures analogous to those identified in less hydraulically rough environments. However, it is likely that these structures are more complicated given the mutual interference of the surrounding medium. The lateral flow was also identified as a key component in the upwelling identified by other authors in the lee of pebble clusters. The results of the vertical flow analysis confirm the hypothesis that six regions with distinct vertical flow characteristics exist above clusters: flow acceleration up the stoss‐side of the cluster; recirculation behind the cluster in the wake region; vortex shedding from the pebble crest and shear layer; flow reattachment downstream of the cluster; upwelling of flow downstream of the point of reattachment; and recovery of flow. Copyright © 2001 John Wiley & Sons, Ltd.     

模糊数学在地震活动性图象研究中的应用

本文应用模糊数学方法从给定地区的地震目录中识别出地震簇.这些地震簇由一系列时空相关的地震组成,每一次强震前都可能有其地震簇出现.两次地震的函数由以下公式来确定:eij=1e-1t+2e-2s计算出某一地区所有 MM0地震相互之间的联系强度,并取一个经验参数之后,就可以根据编网原则识别出地震簇.利用地震簇,可以把强震的地震活动性图象识别得更清楚,简单和定量化.此方法曾用于我国大华北及西南地区的地震簇识别与地震活动图象研究.清楚地识别出了13次大震(M6.5)的地震簇.研究了它们的时空特性.近似建立了 lg△t,lgL,lgS 与震级 M 间的线性经验关系,此处△t,L,S 分别表示地震簇的前兆时间(持续时间)及其震中分布的最大线度与面积.显然,这些关系式对地震预报研究可能有一定用途.      

K-means cluster analysis and seismicity partitioning for Pakistan

Pakistan and the western Himalaya is a region of high seismic activity located at the triple junction between the Arabian, Eurasian and Indian plates. Four devastating earthquakes have resulted in significant numbers of fatalities in Pakistan and the surrounding region in the past century (Quetta, 1935; Makran, 1945; Pattan, 1974 and the recent 2005 Kashmir earthquake). It is therefore necessary to develop an understanding of the spatial distribution of seismicity and the potential seismogenic sources across the region. This forms an important basis for the calculation of seismic hazard; a crucial input in seismic design codes needed to begin to effectively mitigate the high earthquake risk in Pakistan. The development of seismogenic source zones for seismic hazard analysis is driven by both geological and seismotectonic inputs. Despite the many developments in seismic hazard in recent decades, the manner in which seismotectonic information feeds the definition of the seismic source can, in many parts of the world including Pakistan and the surrounding regions, remain a subjective process driven primarily by expert judgment. Whilst much research is ongoing to map and characterise active faults in Pakistan, knowledge of the seismogenic properties of the active faults is still incomplete in much of the region. Consequently, seismicity, both historical and instrumental, remains a primary guide to the seismogenic sources of Pakistan. This study utilises a cluster analysis approach for the purposes of identifying spatial differences in seismicity, which can be utilised to form a basis for delineating seismogenic source regions. An effort is made to examine seismicity partitioning for Pakistan with respect to earthquake database, seismic cluster analysis and seismic partitions in a seismic hazard context. A magnitude homogenous earthquake catalogue has been compiled using various available earthquake data. The earthquake catalogue covers a time span from 1930 to 2007 and an area from 23.00° to 39.00°N and 59.00° to 80.00°E. A threshold magnitude of 5.2 is considered for K-means cluster analysis. The current study uses the traditional metrics of cluster quality, in addition to a seismic hazard contextual metric to attempt to constrain the preferred number of clusters found in the data. The spatial distribution of earthquakes from the catalogue was used to define the seismic clusters for Pakistan, which can be used further in the process of defining seismogenic sources and corresponding earthquake recurrence models for estimates of seismic hazard and risk in Pakistan. Consideration of the different approaches to cluster validation in a seismic hazard context suggests that Pakistan may be divided into K?=?19 seismic clusters, including some portions of the neighbouring countries of Afghanistan, Tajikistan and India.     

The role of sediment specific gravity and availability on cluster evolution

The objective of this experimental study was to account for the role of sediment availability and specific gravity on cluster formation and cluster geometric characteristics (spacing and size). To isolate the effects of sediment availability and specific gravity on cluster evolution, mono‐sized spheres were used to simulate the cluster evolutionary cycle. Overall, twelve experimental runs were carried out in the laboratory flume. Six of these tests were performed by using glass spheres (specific gravity, SG = 2·58) and the other six by employing an equal combination of glass and Teflon spheres (SG = 2·12) of the same diameter to evaluate the role of specific gravity on cluster evolution. The three sediment availability conditions that were investigated here simulated isolated gravel elements, pool–riffle sequences and densely packed gravel‐bed. An advanced image analysis technique was employed to track the evolution of cluster microforms and provide quantitative information about the size and shape of clusters and the number of clusters per unit area. The results of this study showed that: (1) sediment availability affects the architecture and size of cluster microforms; and (2) clusters consisting of mono‐sized sediments start disintegrating at twice the incipient conditions. By performing complementary tests for the isolated gravel elements case, it was found that the evolutionary cycle of individual clusters could be described as follows, in order of increasing stress: no cluster→two particle cluster→comet→triangle→rhomboid→break up. Copyright © 2003 John Wiley & Sons, Ltd.     

Sequential analysis of hydrochemical data for watershed characterization

A methodology for characterizing the hydrogeology of watersheds using hydrochemical data that combine statistical, geochemical, and spatial techniques is presented. Surface water and ground water base flow and spring runoff samples (180 total) from a single watershed are first classified using hierarchical cluster analysis. The statistical clusters are analyzed for spatial coherence confirming that the clusters have a geological basis corresponding to topographic flowpaths and showing that the fractured rock aquifer behaves as an equivalent porous medium on the watershed scale. Then principal component analysis (PCA) is used to determine the sources of variation between parameters. PCA analysis shows that the variations within the dataset are related to variations in calcium, magnesium, SO4, and HCO3, which are derived from natural weathering reactions, and pH, NO3, and chlorine, which indicate anthropogenic impact. PHREEQC modeling is used to quantitatively describe the natural hydrochemical evolution for the watershed and aid in discrimination of samples that have an anthropogenic component. Finally, the seasonal changes in the water chemistry of individual sites were analyzed to better characterize the spatial variability of vertical hydraulic conductivity. The integrated result provides a method to characterize the hydrogeology of the watershed that fully utilizes traditional data.     

Performing cluster analysis and discrimination analysis of hydrological factors in one step

Based on self-organizing map, a method that can perform cluster analysis and discrimination analysis in one step is proposed in this paper. Using the proposed method, one can view the relative topological relationships of input patterns, determine the proper number of clusters, and assign unknown patterns to known clusters without losing any information of input patterns. Regarding the capability of determining the proper number of clusters, the proposed method is superior to conventional cluster analysis. The discrimination results also show that the assignments of unknown patterns to known clusters are reasonable using the proposed method. The advantages of the proposed method are also demonstrated by an application to the hydrological factors affecting low-flow duration curves in southern Taiwan.     

Use of Statistical Models to Analyze Periodic Seismicity Observed for Clusters in the Kanto Region, Central Japan

—A periodic pattern of seismicity has been reported for the Kinugawa cluster in the Kanto region, where several earthquake clusters are observed at depths between 40 and 90 km. To analyze this periodicity, statistical studies are performed for the Kinugawa cluster together with eight other clusters. Hypocentral parameters of the earthquakes with magnitudes 4.5 and larger for the period between 1950 and 1995 are taken from the JMA catalogue. The simple sinusoidal function, the exponential of sinusoidal function and the stress release model are applied as the intensity function. Model parameters are determined by the maximum likelihood method and the best model for each cluster is selected by using the Akaike Information Criterion (AIC). In six cases the sinusoidal model or the exponential of the sinusoidal model is selected as the best option and achieves AIC reductions of values between 2.4 and 13.2 units from the simple Poisson model. The stress release model is selected for two clusters. The three clusters, the Kinugawa, Kasumigaura, and Choshi clusters, have a similar optimal period of about 10 years, and align in the northwest–southeast direction at a similar depth range of 40 to 70 km. A model modified from the stress release model is applied to the three clusters so to analyze the relationship among them. In the modified model, an earthquake occurrence in one zone increases the stress in the other zone, which is different from the original stress release model which assumes a linear increase with time. Applying the modified model to the Kinugawa cluster, an AIC reduction from the Poisson model is significantly larger than the value obtained with the sinusoidal model. This suggests that the periodic seismicity observed for the Kinugawa cluster can be explained with the more comprehensive model than the sinusoidal model.     

Clustering spatial–temporal precipitation data using wavelet transform and self-organizing map neural network

A data analysis method is proposed to cluster and explore spatio-temporal characteristics of the 22 years of precipitation data (1982–2003) for Taiwan. The wavelet transform self-organizing map (WTSOM) framework combines the wavelet transform (WT) and a self-organizing map (SOM) neural network. WT is used to extract dynamic and multiscale features of the non-stationary precipitation time-series, and SOM is applied to objectively identify spatially homogeneous clusters on the high-dimensional wavelet-transformed feature space. Haar and Morlet wavelets are applied in the data preprocessing stage to preserve the desired characteristics of the precipitation data. A two-level SOM neural network is applied to identify clusters in the wavelet space in the clustering stage. The performance of clustering is evaluated using silhouette coefficients. The results indicate that singularities or sharp transitions are more significant than changes in the periodicity or data structure in the spatial–temporal precipitation data. The WTSOM results show that six clusters are optimal for both Haar and Morlet wavelet functions, but their corresponding geographic locations are different. The geographic locations of clusters based on the Haar wavelet, which captures the occurrence of extreme hydrological events, appear in blocks while those classified by the Morlet wavelet, which indicates periodicity changes and describes fine structures, appear in strips that cross the island of Taiwan. Principal component analysis is applied to the precipitation data of each cluster. The first principal components explain 62–90% of the total variation of data. Characteristics of precipitation data for each cluster are explored using scalogram analysis. The results show that both extreme hydrological events and periodicity changes appear in the spatial and temporal precipitation data but with different characteristics for each cluster. Recognizing homogeneous hydrologic regions and identifying the associated precipitation characteristics improves the efficiency of water resources management in adapting to climate change, preventing the degradation of the water environment, and reducing the impact of climate-induced disasters. Measures for countering the stress of precipitation variation for water resources management are provided.     

七株眼虫基于微卫星DNA指纹图谱的区分和关系分析

研究了牛山湖小型鱼类的群落结构、种群密度和多样性．共捕获14种小型鱼类,以1龄鱼为主,其中红鳍原鲌、似鱎、麦穗鱼和鳑鲏是优势种群．小型鱼类的密度为5．9 ind／m2或14．0 g／m2．小型鱼类的群落多样性较低,以个体数为单位计算的Shannon-Wiener多样性指数为1．802,Simpson优势度指数为0．484, Pielou种类均匀度指数为0．503．水生植被是牛山湖小型鱼类群落分布的主要影响因子,水草生境中小型鱼类数量显著比无水草生境中多,水深和透明度对小型鱼类群落分布无显著性影响．通过合理调控湖泊鱼类群落结构和放养食鱼性鱼类来合理持续利用小型鱼类,有利于提高湖泊经济效益和生态效益．     

巢湖沉积植硅体组合及中全新世以来的环境演变

尽管以前对眼虫进行过大量的形态发育研究和基于核糖体RNA基因的系统发育分析,但对于株系之间的关系仍然知之甚少．因其形态特征有限并且易变,很难鉴定眼虫的相似种和同种内不同的株．作者利用微卫星DNA指纹图谱,在七株眼虫中扩增了七个微卫星DNA位点,成功扩增的六个微卫星引物都得到了四到八个条带．从微卫星DNA指纹图谱计算得到的相似性系数范围从0．000到0．957．根据相似性系数得到的树状结构,七株眼虫在距离为0．9346处分为三支:E．mutabilis,E．intermedia和E．gracilis．其中,五株E．gracilis分为两组:来自日本的和美国的．不同地区的株得到不同的基因型,并初步分析了它们之间的关系．研究表明七株眼虫根据微卫星DNA指纹图谱被明显区分开．微卫星DNA指纹图谱具有很高的分辨率,是鉴定和区分原生动物相似种和同种内不同株的一种有用的新方法．     

A Methodology for Clustering Lakes in Alberta on the basis of Water Quality Parameters

In this study, a methodology for clustering 18 lakes in Alberta, Canada using the data of 19 water quality parameters for a period of 11 years (1988–2002) is presented. The methods consist of (i) principal component analysis (PCA) to determine the dominant water quality parameters, (ii) cluster analysis techniques to develop the characteristics of the clusters, and (iii) pattern‐match lakes to determine the appropriate cluster for each of the lakes. The PCA revealed that three principal components (PCs) were able to explain ～88% of the variability and the dominant water quality parameters were total dissolved solids, total phosphorus, and chlorophyll‐a. We obtained five clusters for the period 1994–1997 by using the dominant parameters with water quality deteriorating as the cluster number increased from 1 to 5. Upon matching cluster patterns with the entire dataset, it was observed that some of the lakes belonged to the same cluster all the time (e.g., cluster 1 for lakes Elkwater, Gregg, and Jarvis; cluster 3 for Sturgeon; cluster 4 for Moonshine; and cluster 5 for Saskatoon), while others changed with time. This methodology could be applied in other regions of the world to identify the most suitable source waters and prioritize their management. It could be helpful to analyze the natural controlling processes, pollution types, impact of seasonal changes and overall quality of source waters. This methodology could be used for monitoring water bodies in a cost effective and efficient way by sampling only less number of dominant parameters instead of using a large set of parameters.     

A hybrid neural network model for typhoon-rainfall forecasting

A hybrid neural network model is proposed in this paper to forecast the typhoon rainfall. Two different types of artificial neural networks, the self-organizing map (SOM) and the multilayer perceptron network (MLPN), are combined to develop the proposed model. In the proposed model, a data analysis technique is developed based on the SOM, which can perform cluster analysis and discrimination analysis in one step. The MLPN is used as the nonlinear regression technique to construct the relationship between the input and output data. First, the input data are analyzed using a SOM-based data analysis technique. Through the SOM-based data analysis technique, input data with different properties are first divided into distinct clusters, which can help the multivariate nonlinear regression of each cluster. Additionally, the topological relationships among data are discovered from which more insight into the typhoon-rainfall process can be revealed. Then, for each cluster, the individual relationship between the input and output data is constructed by a specific MLPN. For evaluating the forecasting performance of the proposed model, an application is conducted. The proposed model is applied to the Tanshui River Basin to forecast the typhoon rainfall. The results show that the proposed model can forecast more precisely than the model developed by the conventional neural network approach.     

Groundwater Quality: Analysis of Its Temporal and Spatial Variability in a Karst Aquifer

This study develops an approach based on hierarchical cluster analysis for investigating the spatial and temporal variation of water quality governing processes. The water quality data used in this study were collected in the karst aquifer of Yucatan, Mexico, the only source of drinking water for a population of nearly two million people. Hierarchical cluster analysis was applied to the quality data of all the sampling periods lumped together. This was motivated by the observation that, if water quality does not vary significantly in time, two samples from the same sampling site will belong to the same cluster. The resulting distribution maps of clusters and box‐plots of the major chemical components reveal the spatial and temporal variability of groundwater quality. Principal component analysis was used to verify the results of cluster analysis and to derive the variables that explained most of the variation of the groundwater quality data. Results of this work increase the knowledge about how precipitation and human contamination impact groundwater quality in Yucatan. Spatial variability of groundwater quality in the study area is caused by: a) seawater intrusion and groundwater rich in sulfates at the west and in the coast, b) water rock interactions and the average annual precipitation at the middle and east zones respectively, and c) human contamination present in two localized zones. Changes in the amount and distribution of precipitation cause temporal variation by diluting groundwater in the aquifer. This approach allows to analyze the variation of groundwater quality controlling processes efficiently and simultaneously.     

Temporal Changes of Shallow Seismic Velocity Around the Karadere-Düzce Branch of the North Anatolian Fault and Strong Ground Motion

We analyze temporal variations of seismic velocity along the Karadere-Düzce branch of the north Anatolian fault using seismograms generated by repeating earthquake clusters in the aftershock zones of the 1999 M_w7.4 İzmit and M_w7.1 Düzce earthquakes. The analysis employs 36 sets of highly repeating earthquakes, each containing 4–18 events. The events in each cluster are relocated by detailed multi-step analysis and are likely to rupture approximately the same fault patch at different times. The decay rates of the repeating events in individual clusters are compatible with the Omori's law for the decay rate of regional aftershocks. A sliding window waveform cross-correlation technique is used to measure travel time differences and evolving decorrelation in waveforms generated by each set of the repeating events. We find clear step-like delays in the direct S and early S-coda waves (sharp seismic velocity reduction) immediately after the Düzce main shock, followed by gradual logarithmic-type recoveries. A gradual increase of seismic velocities is also observed before the Düzce main shock, probably reflecting post-seismic recovery from the earlier İzmit main shock. The temporal behavior is similar at each station for clusters at various source locations, indicating that the temporal changes of material properties occur in the top most portion of the crust. The effects are most prominent at stations situated in the immediate vicinity of the recently ruptured fault zones, and generally decrease with normal distance from the fault. A strong correlation between the co-seismic delays and intensities of the strong ground motion generated by the Düzce main shock implies that the radiated seismic waves produced the velocity reductions in the shallow material.     

Inspecting the Reliability of Geochemical Facies Identified for the Waterworks' Capture Zone in Germany

Little research attention has been given to validating clusters obtained from the groundwater geochemistry of the waterworks' capture zone with a prevailing lake-groundwater exchange. To address this knowledge gap, we proposed a new scheme whereby Gaussian finite mixture modeling (GFMM) and Spike-and-Slab Bayesian (SSB) algorithms were utilized to cluster the groundwater geochemistry while quantifying the probability of the resulting cluster membership against each other. We applied GFMM and SSB to 13 geochemical parameters collected during different sampling periods at 13 observation points across the Barnim Highlands plateau located in the northeast of Berlin, Germany; this included 10 observation wells, two lakes, and a gallery of drinking production wells. The cluster analysis of GFMM yielded nine clusters, either with a probability ≥0.8, while the SSB produced three hierarchical clusters with a probability of cluster membership varying from <0.2 to >0.8. The findings demonstrated that the clustering results of GFMM were in good agreement with the classification as per the principal component analysis and Piper diagram. By superimposing the parameter clustering onto the observation clustering, we could identify discrepancies that exist among the parameters of a certain cluster. This enables the identification of different factors that may control the geochemistry of a certain cluster, although parameters of that cluster share a strong similarity. The GFMM results have shown that from 2002, there has been active groundwater inflow from the lakes towards the capture zone. This means that it is necessary to adopt appropriate measures to reverse the inflow towards the lakes.     

Application of singular value decomposition (SVD) and semi-discrete decomposition (SDD) techniques in clustering of geochemical data: an environmental study in central Iran

Common multivariate clustering techniques are ineffective in identifying subtle patterns of correlation, and clustering of variables or samples within complex geochemical datasets. This study compares the combination of singular value decomposition (SVD) and semi discrete decomposition (SDD), with that of hierarchical cluster analysis (HCA), to examine patterns within a multielement soil geochemical dataset from an agricultural area in the vicinity of Pb–Zn mining operations in central Iran. SVD was used to both identify patterns of correlation between variables and samples and to “denoise” the data, and SDD to simultaneously cluster the samples and variables. The results reveal various spatial associations of mining waste-associated metals As, Ba, Pb and Zn, and within the remaining elements whose distribution is largely controlled by the major oxides. SVD–SDD was found to be superior to HCA, in its ability to detect subtle clusters in soil geochemistry indicative of mine-related contamination in the study area.     

Multi-resolution graph-based clustering analysis for lithofacies identification from well log data: Case study of intraplatform bank gas fields,Amu Darya Basin

In this study, we used the multi-resolution graph-based clustering (MRGC) method for determining the electrofacies (EF) and lithofacies (LF) from well log data obtained from the intraplatform bank gas fields located in the Amu Darya Basin. The MRGC could automatically determine the optimal number of clusters without prior knowledge about the structure or cluster numbers of the analyzed data set and allowed the users to control the level of detail actually needed to define the EF. Based on the LF identification and successful EF calibration using core data, an MRGC EF partition model including five clusters and a quantitative LF interpretation chart were constructed. The EF clusters 1 to 5 were interpreted as lagoon, anhydrite flat, interbank, low-energy bank, and high-energy bank, and the coincidence rate in the cored interval could reach 85%. We concluded that the MRGC could be accurately applied to predict the LF in non-cored but logged wells. Therefore, continuous EF clusters were partitioned and corresponding LF were interpreted, and the distribution and petrophysical characteristics of different LF were analyzed in the framework of sequence stratigraphy.     

Analysis of nonlinear associations between prenatal methylmercury exposure from fish consumption and neurodevelopmental outcomes in the Seychelles Main Cohort at 17 years

The Seychelles Child Development Study has been examining the relationship between prenatal methylmercury (MeHg) exposure from consuming fish during pregnancy and child development. This study re-analyzes seven outcomes in the 17 year Main Cohort data to determine if there are nonlinear or non-homogeneous (subgroup) associations that were not identified in the linear analysis. We adopted two statistical approaches. First, we carried out an additive nonlinear analysis assuming homogeneous prenatal MeHg-outcome relationships to explore overall associations. Second, we applied the regression tree to the Woodcock–Johnson Calculation subtest (it was significantly associated in earlier analyses) and identified 4 clusters based on covariates. Then we used additive models to assess the prenatal MeHg association in each of the four clusters for all seven outcomes. This approach assumes nonlinear associations in each cluster and non-homogeneous associations between clusters. The additive nonlinear analysis yielded prenatal MeHg curves similar to the linear analysis. For the regression tree analysis, the curves relating prenatal MeHg to outcomes between the 4 clusters differed and some crossed at higher prenatal MeHg levels, suggesting non-homogeneity in the upper range of exposure. Additionally, some of the curves suggested a possible non-linear relationship within the range of exposure we studied. This non-linear analysis supports the findings from the linear analysis. It shows little evidence to support an adverse association of prenatal MeHg exposure through maternal consumption of fish contaminated with natural background levels. However, the tree analysis suggests that the prenatal exposure/outcome relationship may not be homogeneous across all individuals and that some subpopulations may have an adverse association in the upper range of the exposures studied. More robust data in the higher levels of exposure in this cohort are needed to confirm this finding.     

Application of array-based waveform cross-correlation techniques to aftershock sequences: the 2003 Lefkada Island,Greece, case

Cross-correlation analysis was applied to events in the 2003 Lefkada Island, Greece, sequence in order to identify clusters of seismicity within the extensive aftershock sequence along a fault zone of approximately 100 km length. Data from the small-aperture TRISAR array, covering the first 2 days of aftershock activity, were used. Array-based waveform correlation has a great advantage over single channel correlation analysis in that the validity of waveform matches with relatively low correlation coefficients can be examined by checking the alignment of correlation traces on the different channels. The length of the fault zone leads inevitably to a great diversity in the waveforms, although a small number of clusters of very similar events emerge from the TRISAR data. Events which the correlation analysis had placed within the same cluster were listed in the ISC Bulletin with separations of up to tens of kilometres. This made it necessary to check the validity of the TRISAR clusters by applying the same procedure independently to the three-component stations of the National Seismographic Network of the National Observatory of Athens, located at local to regional distances from the aftershock area. Results suggest that array-based waveform correlation provides a robust tool both for identifying event clusters within large aftershock areas and for identifying situations in which bulletin event location estimates need re-evaluation.     

The influence of microform bed roughness elements on flow and sediment transport in gravel bed rivers

Pebble clusters are reported widely as characteristic of gravel river beds and are known to influence the initial entrainment of bedload. A field assessment suggests that their distribution is not ubiquitous, favouring channel bars, but also reveals a tendency towards a preferred stream wise spacing. A series of laboratory flume experiments shows that flow resistance rises to, and falls from, a peak value as the longitudinal spacing of pebble clusters decreases, in a manner similar to that shown by others for strip roughness, isolated blocks, and simulated ripples and dunes. The experiments also reveal a strong inverse relationship between bedload flux rates and the flow resistance induced by the concentration of pebble clusters. It is concluded that pebble cluster spacing tends towards an equilibrium that is regulated by a feedback process involving sediment transport rates and that the spatial concentration of these microforms will adjust to the point where they induce maximum flow resistance.