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Flow direction and branching geometry at junctions in dendritic river networks

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Abstract

Automatic determination of flow direction from a partial view of a drainage network is a problem, notably in remote sensing. The main approach to determining which river link is pointing downstream uses spatial reasoning based on local features at junctions. Theoretical and empirical works on junction angles suggest that the two consecutive links which bound the most acute angle are the upstream links. This rule was tested using 2279 river junctions digitized from 19 dendritic drainage networks and was correct in nearly 90% of the cases. This result is better than that obtained from the decision table designed by Haralick, Wang et al. (1985) for the same purpose.

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... The general principle of acute junction angles is well established, however. Empirical observations and theoretical models of branching flow networks indicate that the overwhelming prevalence of junction angles are acute (Roy, 1983;De Serres and Roy, 1990). Obtuse angles occur "only in extreme circumstances," regardless of the relative size of the mainstream and tributary channels (De Serres and Roy, 1990). ...
... Empirical observations and theoretical models of branching flow networks indicate that the overwhelming prevalence of junction angles are acute (Roy, 1983;De Serres and Roy, 1990). Obtuse angles occur "only in extreme circumstances," regardless of the relative size of the mainstream and tributary channels (De Serres and Roy, 1990). An analysis of 2279 confluences in 19 watersheds digitized from maps allowed unequivocal determination of angles for 1718 junctions (De Serres and Roy, 1990). ...
... Obtuse angles occur "only in extreme circumstances," regardless of the relative size of the mainstream and tributary channels (De Serres and Roy, 1990). An analysis of 2279 confluences in 19 watersheds digitized from maps allowed unequivocal determination of angles for 1718 junctions (De Serres and Roy, 1990). Of these, eight (0.4%) were straight (90 o angle), and none were obtuse. ...
Article
The ``perfect landscape'' concept is based on the notion that any specific geomorphic system represents the combined, interacting effects of a set of generally applicable global laws and a set of geographically and historically contingent local controls. Because the joint probability of any specific combination of local and global controls is low, and the local controls are inherently idiosyncratic, the probability of existence of any given landscape is vanishingly small. A perfect landscape approach to geomorphic complexity views landscapes as circumstantial, contingent outcomes of deterministic laws operating in a specific environmental and historical context. Thus, explaining evolution of complex landscapes requires the integration of global and local approaches. Because perfection in this sense is the most important and pervasive form of complexity, the study of geomorphic complexity is not restricted to nonlinear dynamics, self-organization, or any other aspects of complexity theory. Beyond what can be achieved via complexity theory, the details of historical and geographic contexts must be addressed. One way to approach this is via synoptic analyses, where the relevant global laws are applied in specific situational contexts. A study of non-acute tributary junctions in the lower Brazos River, Texas illustrates this strategy. The application of generalizations about tributary junction angles, and of relevant theories, does not explain the unexpectedly high occurrence or the specific instances of barbed or straight junctions in the study area. At least five different causes for the development of straight or obtuse junction angles are evident in the lower Brazos. The dominant mechanism, however, is associated with river bank erosion and lateral channel migration which encroaches on upstream-oriented reaches of meandering tributaries. Because the tributaries are generally strongly incised in response to Holocene incision of the Brazos, the junctions are not readily reoriented to the expected acute angle. The findings are interpreted in the context of nonlinear divergent evolution, geographical and historical contingency, synoptic frameworks for generalizing results, and applicability of the dominant processes concept in geomorphology.
... Schumm et al. (2000) outline eight varieties of drainage network patterns, ranging from dendritic and parallel to multi-basinal and contorted, a schema first described by Howard (1967). De Serres and Roy (1990) claim that in trellis drainage networks, angles approaching, and possibly exceeding, 90°may be found but in dendritic networks, acute angles ( Figure 1a) will prevail. Junction angles greater than 90˚are herein termed obtuse ( Figure 1b) and a special obtuse case, termed barbed is also considered (Figure 1c). ...
... This observation suggests that angles greater than 90°are rarely found in nature. However, they have been observed in situations where rapid changes in downstream channel slope and channel geometry occur (De Serres and Roy, 1990). ...
... were found to be normal (90°) and 75 (30%) were found to be obtuse. This is in distinct contrast to work by De Serres and Roy (1990) who, in a larger study of 2279 junctions from 12 catchments, found that only eight (0.4%) were normal and none were obtuse. Despite acute-angled junctions making up the majority of confluences along the course of the River Mekong (66.2%), there are a surprisingly high number of obtuse tributaries in contrast to previous studies (Browne, 1921;Lublowe, 1964;De Serres and Roy, 1990;Phillips, 2007). ...
Article
Classic descriptions of drainage patterns suggest that confluence angle is determined by the shape of the drainage basin unless constraining factors, such as the geological structure, affect stream flow. Downstream changes in channel width below tributary junctions have long been associated with tributary inputs of flow and sediment. Analysis of tributary junction geometry and channel width changes in large rivers and over large reaches is sparse. The Lower Mekong Basin exhibits a generally dendritic drainage network despite flowing through a diverse array of geological settings. Publicly available SPOT‐5 imagery from Google Earth was used to identify and catalogue junction geometries and downstream changes in channel width below tributary junctions along a ~2200 km reach of the Mekong River. Of the 284 junctions identified, the majority (66.2%) were acute. However 12 (4.8%) were found to be normal (90°) and 75 (30%) were found to be obtuse. This latter number is in contrast to previous studies over similar spatial scales which found little evidence of obtuse junctions. Meander extension of the incoming tributary and deflection of the tributary across bedrock shoulders were found to be the dominant geomorphological causes of obtuse tributary junctions. The relationship between the width of the tributary channels and the width of the mainstem upstream and downstream of the confluences was analysed. It was observed that, over the whole reach, a slight narrowing occurred immediately below tributary junctions. Although the changes themselves were small, the slight net narrowing is shown to be statistically significant. The observed relationship is shown to vary considerably with geology. The geological control suggests that complex factors play important roles in determining changes to channel width across large systems and that simple cause–effect relationships do not hold in such complicated geological settings.
... Schumm et al. (2000) outline eight varieties of drainage network patterns, ranging from dendritic and parallel to multi-basinal and contorted, a schema first described by Howard (1967). De Serres and Roy (1990) claim that in trellis drainage networks, angles approaching, and possibly exceeding, 90°may be found but in dendritic networks, acute angles ( Figure 1a) will prevail. Junction angles greater than 90˚are herein termed obtuse ( Figure 1b) and a special obtuse case, termed barbed is also considered (Figure 1c). ...
... This observation suggests that angles greater than 90°are rarely found in nature. However, they have been observed in situations where rapid changes in downstream channel slope and channel geometry occur (De Serres and Roy, 1990). ...
... were found to be normal (90°) and 75 (30%) were found to be obtuse. This is in distinct contrast to work by De Serres and Roy (1990) who, in a larger study of 2279 junctions from 12 catchments, found that only eight (0.4%) were normal and none were obtuse. Despite acute-angled junctions making up the majority of confluences along the course of the River Mekong (66.2%), there are a surprisingly high number of obtuse tributaries in contrast to previous studies (Browne, 1921;Lublowe, 1964;De Serres and Roy, 1990;Phillips, 2007). ...
Article
Full-text available
Classic descriptions of drainage network patterns suggest that confluence angle is largely determined by the shape of the drainage basin with tributaries usually joining the main stem at acute angles less than 90°, but the subject is little studied in recent years. In particular low-order channels joining high-order main stems do not seem to have been studied systematically. A series of low- and high-order tributaries with obtuse angles greater than 90° (barbed tributaries) were identified along the course of the main stem of the Lower Mekong using Google Earth. Aerial photography of the region was used to measure junction angles and channel widths above and below 248 confluences between the Chinese-Laos border and the Mekong delta. Geological and geomorphic controls promoting obtuse junctions angles were identified and classified from review of the literature and inspection of the Mekong imagery. For the Mekong, meander extension was found to be the prominent control of obtuse angle junctions, accounting for 31% of occurrences. Geological controls accounted for 28% within bedrock confined reaches with other processes explaining the remaining 41%. Clear relationships between the bed-rock types of the Lower Mekong Basin and the controls on junction angle are reported. However, structural controls dominate in the alluvial and mixed bedrock:alluvial sections of the channel. Tributary discharge (indexed by tributary width) and tributary angle impacts on main channel width were analysed and were found to be minimal. Downstream channel widths do not increase proportionately with increasing widths of tributary channels, and no relationship with junction angle was present. These analyses indicate that the river bed downstream of each junction must deepen to allow for continuity of cumulative discharge of mainstem and tributary. Analysis reveals that the bed-rock confined sections of the channel are more sensitive to tributary inputs, displaying greater percentage change than the alluvial sections.
... In Figure 1, Q t , Q m , and Q tot denote the discharges in the tributary, the main channel (before confluence), and the postconfluence channel, respectively. These zones are governed by many factors, including the intersection angle (De Serres and Roy, 1990;Hackney and Carling, 2011), bed discordance (Bradbrook et al., 2001), flow and momentum ratios (Constantinescu et al., 2011;Rhoads and Sukhodolov, 2008), and planform geometry (De Serres and Roy, 1990;Hodskinson and Ferguson, 1998;Rhoads and Kenworthy, 1995). Their spatial extent, kinetic activities, and synergies make them active agents for controlling the beneath-bed changes at a confluence and its connected watercourses. ...
... In Figure 1, Q t , Q m , and Q tot denote the discharges in the tributary, the main channel (before confluence), and the postconfluence channel, respectively. These zones are governed by many factors, including the intersection angle (De Serres and Roy, 1990;Hackney and Carling, 2011), bed discordance (Bradbrook et al., 2001), flow and momentum ratios (Constantinescu et al., 2011;Rhoads and Sukhodolov, 2008), and planform geometry (De Serres and Roy, 1990;Hodskinson and Ferguson, 1998;Rhoads and Kenworthy, 1995). Their spatial extent, kinetic activities, and synergies make them active agents for controlling the beneath-bed changes at a confluence and its connected watercourses. ...
Article
Because of the flow influx of tributaries, a confluence forms a unique environment carrying interesting hydrodynamic features and other attributes. The understanding of flow behavior here is important, particularly if it is on a tidally influenced channel in a harbor metropolitan. Because of communal requirements, there is a possibility of building wading structures, which may interplay with the flow in this zone. The knowledge of unidirectional river or flume confluences so far is not readily applicable for similar features in channels near coastal areas that have tidal flow in addition to river runoff. In this study, a tidal confluence that has a highly dynamic bidirectional flow is investigated. Near-surface flow patterns in a tidal cycle are simulated by using a numerical model. A field survey provides the bathymetry, time-series boundary conditions, and corresponding verification data. Good agreement is reached between calculated and measured results. Based on the condition of tidal current, four scenarios are selected for which confluence flow patterns are observed, both spatially and temporally. The results indicate that at least one recirculation is always in the tidal confluence for all flow conditions, which rotates counterclockwise for the ebb flow and clockwise for the flood flow. In addition, there is no absolute slack water condition at the tidal junction in the study area. The study also finds that the flows of all three connected channels at the confluence change in a looped pattern with respect to one another. Furthermore, the study reports unique relationships among the ratios of different flows.
... Angle is the intersect relation of two rivers, showing intersect features of different class river. Serres and Roy (1990) contend that the joint angles in river features of arborization forms are more than 88% acute angle. This rule presents an foundation to classify river forms. ...
Article
River structure is a direct concept for the distribution of rivers in nature. In spatial database, river structure is a type of spatial relations composed by river features. This paper proposes the characteristic properties and classification rules to classify the river forms based on spatial statistics. Also a method to discover the classification knowledge of river forms is presented based on the data processing and statistical analysis of river features in spatial databases.
... Looking at the angle of confluence between the branching channels, these are mostly around 40 e55 , 70 or 90 , which is to be expected for a dendritic river system (De Serres and Roy, 1990;Hackney and Carling, 2011), since the angle of confluence is controlled by the shape of the basin, in areas without significant geological structures constraining the water flow (Hackney and Carling, 2011). ...
Article
The Danish North Sea has been subject to extensive seismic surveying (both 2D and 3D) during the past four decades. The 3D seismic data from the area has mainly been used for hydrocarbon exploration, but in the last decade, it has also been utilized for investigating the Quaternary sediments and especially buried incised valleys. The erosional and depositional processes involved in forming such valleys are important in paleolandscape reconstruction, but are often difficult to determine, since sediment deposited by flowing water, displays ambiguous geometric structures. In this study, we combine the analysis of infill geometries, from high-resolution 2D seismic data, with plan-view morphology analysis, from 3D seismic data, and lithological data from borehole reports, in order to constrain the origin of buried channels in the Danish North Sea. This data integration makes differentiations of a subaerial vs. subglacial origin more robust. The study focusses on analyzing a proglacial to fluvial channel system, which was initiated as a subglacial tunnel valley system during the Last Glacial Maximum, and subsequently evolved as a fluvial system after deglaciation. The channel system was active in a marsh environment during a period of subaerial exposure in the late Weichselian to early Holocene. During the Holocene transgression, the system was gradually flooded leaving estuarine tidal deposits in the underfilled channels. Once the area was completely flooded, the channel system was buried under marine sands.
... Furthermore, with increasing stream order and flow discharge, in-stream fluvial processes may become increasingly important in shaping the branching structure. Several theories for the branching angles of river junctions have been suggested, such as the geometric model [Howard, 1971;Pieri, 1984], the minimum work model [Howard, 1971[Howard, , 1990Serres and Roy, 1990], or the momentum balance model [Mosley, 1976]. These models are based on geometric factors such as longitudinal profile concavity or slope and water discharge and aim to predict the local angles at which two river segments should meet rather than the branching angle of the two upstream tributary valleys (supporting information). ...
Article
Branching stream networks are a ubiquitous feature of the Earth's surface, but the processes that shape them, and their dependence on the climate in which they grow, remain poorly understood. Research has mainly focused on climatic controls of channel incision rates, while the climatic influence on planform geometry has often been overlooked. Here we analyze nearly one million digitally mapped river junctions throughout the contiguous United States, and show that branching angles vary systematically with climatic aridity. In arid landscapes, which are thought to be dominated by surface runoff erosion, junction angles average roughly 45∘ in the driest places. Branching angles are systematically wider in humid regions, averaging roughly 72∘, which is the theoretically predicted angle for network growth in a diffusive field such as groundwater seepage. The correlation of mean junction angle with aridity is stronger than with topographic gradient, downstream concavity, or other geometric factors that have been proposed as controls of junction angles. Thus it may be possible to identify channelization processes from stream network geometry in relict landscapes, such as those on Mars.
... As shown in Table 1, 22% of the confluence angles are obtuse, 13% are normal and 65% are acute. Obtuse confluence angles have typically been associated with confluences where rapid changes in downstream channel slope and channel geometry take place (De Serres and Roy, 1990) and are believed not to be observed present in efficiently developed drainage systems unless external factors influence the flow orientation (Lublowe, 1974). However, Hackney and Carling (2011) reported that an important proportion of confluence angles (~30%) in the Mekong River are obtuse. ...
Article
Most of the past studies on river confluences dynamics are based on a limited number of experimental and field data that mainly represent the morphodynamic, hydrodynamic and sedimentary processes of alluvial river channels with limited planform activity. Moreover, these studies are concentrated mainly around the confluence region. This novel contribution focuses on the study of the planimetric configuration of confluences in tropical free meandering rivers located in the Upper Amazon catchment. Since river confluences in tropical environments represent areas where biota is concentrated, a better understanding and characterization of these features has a particular importance for the Amazonian ecosystem. Confluence of meandering rivers or meander trains comprised by the main channel (M) and the tributary (T) imposes the following general changes in the planimetric configurations of these channels: [1] modulation of the morphodynamics of the M and T channels, and [2] modulation of the morphodynamics of the downstream Main channel (MT), thus varying both the predominant arc-wavelength and amplitude, and resembling either a constructive or a destructive effect in the superposition of curvature waves. A wavelet analysis of the normalized channel curvature was performed by using the continuous Morlet Wavelet function. This analysis indicates that important transient perturbations in the curvature frequency spectrum are developed when the width-ratio between the tributary width and the main channel width, β = BT/BM, is higher than 0.45. These perturbations become more dominant when β increases.
... Zernitz [1932] identified the Allegheny Plateau in West Virginia and the southern part of the Atlantic coastal plains in Georgia and South Carolina as regions where dendritic networks are widely observed. Lubowe [1964] and Serres and Roy [1990] also identified dendritic drainages in sections of the Appalachian Plateau and the interior low plateaus in Kentucky that are underlain by sedimentary rock and horizontal strata. The parallel networks were previously classified by Zernitz [1932] and Phillips and Schumm [1987]. ...
Article
Geomorphologists have long recognized that the geometry of channel network planforms can vary significantly between regions depending on the local lithologic and tectonic conditions. This tendency has led to the classification of channel networks using terms such as dendritic, parallel, pinnate, rectangular, and trellis. Unfortunately, available classification methods are scale dependent and have little connection to any underlying quantitative theory of drainage network geometry or evolution. In this study, a new method is developed to classify drainage networks on the basis of their deviations from self-similarity. The planform geometry of dendritic networks is known to be approximately self-similar. It is our hypothesis that parallel, pinnate, rectangular, and trellis networks correspond to distinct deviations from this self-similarity. To identify such deviations, three measures of channel networks are applied to 10 networks from each classification. These measures are the incremental accumulation of drainage area along channels, the irregularity of channel courses, and the angles formed by merging channels. The results confirm and characterize the self-similarity of dendritic networks. Parallel and pinnate networks are found to exhibit anisotropic scaling. Rectangular and trellis networks are approximately self-similar although deviations from self-similarity are observed. Rectangular networks have more sinuous channels than dendritic networks across all scales, and trellis networks have a slower rate of area accumulation than dendritic networks across all scales. Such observations are used to build and test simple classification trees, which are found to perform well in classifying networks.
... As shown in Table 1, 22% of the confluence angles are obtuse, 13% are normal and 65% are acute. Obtuse confluence angles have typically been associated with confluences where rapid changes in downstream channel slope and channel geometry take place (De Serres and Roy, 1990) and are believed not to be observed present in efficiently developed drainage systems unless external factors influence the flow orientation (Lublowe, 1974). However, Hackney and Carling (2011) reported that an important proportion of confluence angles (~30%) in the Mekong River are obtuse. ...
Article
Past studies on river confluence dynamics are mostly based on a limited number of experimental and field data that mainly represent the morphodynamic, hydrodynamic, and sedimentary processes of alluvial river channels with limited planform activity and concentrated solely around the confluence region. The present contribution is novel and focuses on the study of the planimetric configuration of confluences in tropical free meandering rivers located in the upper Amazon catchment. Confluences are environmental controls that impose convective instabilities in all the associated channels, namely the main stretch channel upstream of the confluence (M), the tributary (T), and the main post-confluent channel (MT). By performing a wavelet analysis on channels' curvature, we quantify the extent of the transitional region. Our results indicate that the strength of these transitional instabilities are in some degree dependent on the confluence width ratio (β); such that for β > 0.45, marked instabilities are developed. These instabilities induce the following general changes and in the planimetric configurations of the aforementioned channels: [i] the arc-wavelength in the confluent (M and T) and post-confluence channels increase in the transitional region, and [ii] the peaks on the curvature of MT channel decrease with respect to the M channel, thus resembling a constructive effect in the superposition of the meander trains.
... (1) Junction angle. The angle at a junction is a useful parameter that can be used in flow direction and main stream inference (Serres and Roy, 1990;Paiva and Egenhofer, 2000). In general, a tributary joins into a main stream (Figure 3a), or two tributaries gather together forming a new stream (Figure 3b). ...
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Drainage networks that develop under conditions of no structural control and homogeneous lithology are generally dendritic, depending upon the shape and inclination of the surface on which they form. An experimental study was designed to investigate the effect of an increase of slope on the evolution and development of dendritic drainage patterns. As slope steepens, the pattern changes from dendritic at 1% slope, to subdendritic at 2%, to subparallel at 3%, to parallel at 5% and higher. The change from a dendritic-type pattern to a parallel-type pattern occurs at a low slope, between 2% and 3%, and primary channel junction angles decrease abruptly from about 60° to 43°. *Present address: U.S. Army Environmental Hygiene Agency, Attn: HSHB-ME-WM, Aberdeen Proving Ground, Maryland 21010-5422
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Automatic deduction of the drainage network direction from Landsat imagery is a problem in remote sensing. The problem can be formulated in the abstract as a consistent labeling problem which is given a set of units (stream segments), possible labels (flow directions), and constraints on the way adjacent stream segments must be labeled. The goal is to find a mapping from their units to the labels that satisfies the constraints. Consistent labeling problems can be solved by tree search algorithms. In this paper, the stream labeling problem is formulated as a consistent labeling problem. The extraction of stream and valley segments from the Landsat images is discussed, and constraints on segments which meet at junctions are given. The tree search algorithm, employing a method called forward checking, is given and is used to determine the flow direction of all the stream segments in a way that is globally consistent with the junction constraints.
Article
Thesis (Ph. D.)--State University of New York at Buffalo, 1981. Includes bibliographical references (leaves 314-322). Photocopy of typescript.
Quantitative Geomorphology of the San Dimas Experimental Forest, California. Department of Geology Technical Report No. 19
  • J C Maxwell
L'approche tridimensionnelle des surfaces de drainage
  • C Lemieux